Another week, another deluge of BS from the White House and from the Controlled Opposition.

The Audit is over, now the spin doctoring begins. Other efforts are afoot in other states. Good. The more the merrier.

The collapse of the Covidschina continues.

No doubt much will be said about those today. (And I have missed a lot this past week.)

To my mind the audits are the last hope for a within-the-system fix to what happened last November. “Within the system” meaning the audits find fraud, the various states decertify the results, and some dang judge rules that Biden must step down and Trump must be installed.

That last step is crucial. The way our system works, “fraud” isn’t a fact until some “competent authority” (i.e., meaning “one that has jurisdiction,” not “one that won’t end up with an ice cream cone on its forehead”) rules it is so. That must happen before the system will accept that the election is vitiated by fraud. No finding of fraud means, as far as they are concerned no fraud, no fraud means nothing vitiated. We sit and fume, because the system has failed.

I’ll leave it to you to decide how likely you think it is that a judge will rule against the Left given the riots that would likely endanger his/her family.

As for the military stepping forward and doing the job instead? Well, that’s technically “outside of the system” and besides…this military, that’s being made woke as we speak?

What do we do in the likely event that fraud is found, but no judge will find it to be “fact” as far as the Federal Government is concerned? I keep hoping someone will come up with a suggestion, and so far “general strike” (H/T Scott) is the only one I’ve seen.

Justice Must Be Done.

The prior election must be acknowledged as fraudulent, and steps must be taken to prosecute the fraudsters and restore integrity to the system. (This doesn’t necessarily include deposing Joe and Hoe and putting Trump where he belongs, but it would certainly be a lot easier to fix our broken electoral system with the right people in charge.)

Nothing else matters at this point. Talking about trying again in 2022 or 2024 is pointless otherwise. Which is not to say one must never talk about this, but rather that one must account for this in ones planning; if fixing the fraud in the system is not part of the plan, you have no plan.

This will necessarily be piecemeal, state by state, which is why I am encouraged by those states working to change their laws to alleviate the fraud both via computer and via bogus voters. If enough states do that we might end up with a working majority in Congress and that would be something Trump never really had.

Lawyer Appeasement Section

OK now for the fine print.

This is the WQTH Daily Thread. You know the drill. There’s no Poltical correctness, but civility is a requirement. There are Important Guidelines,  here, with an addendum on 20191110.

We have a new board – called The U Tree – where people can take each other to the woodshed without fear of censorship or moderation.

And remember Wheatie’s Rules:

1. No food fights
2. No running with scissors.
3. If you bring snacks, bring enough for everyone.
4. Zeroth rule of gun safety: Don’t let the government get your guns.
5. Rule one of gun safety: The gun is always loaded.
5a. If you actually want the gun to be loaded, like because you’re checking out a bump in the night, then it’s empty.
6. Rule two of gun safety: Never point the gun at anything you’re not willing to destroy.
7. Rule three: Keep your finger off the trigger until ready to fire.
8. Rule the fourth: Be sure of your target and what is behind it.

(Hmm a few extras seem to have crept in.)

Spot Prices

Last week:

Gold $1751.20
Silver $22.49
Platinum $986.00
Palladium $2047.00
Rhodium $15,750.00

This week, 3 PM MT on Friday, markets closed for the weekend

Gold $1762.00
Silver $22.65
Platinum $981.00
Palladium $2000.00
Rhodium $14,050.00

Minor shifts in almost everything. Gold and silver up a bit, the PGMs down a bit. I, as always, intend to hold.

Part XX – The Little Neutral One

Let us start off by recapping our list of “as of 1894” mysteries and conservation laws, and bring things up to date including the neutron.

• Conservation of mass
• Conservation of momentum
• Conservation of energy
• Conservation of electric charge
• Conservation of angular momentum
• (ADD:) Conservation of mass-energy

The following mysteries were unanswered at the end of 1894. I’ve crossed out the ones that have been answered up to this installment.

• Why was the long axis of Mercury’s orbit precessing more than expected, by 43 arcseconds every century? Was it, indeed, a planet even closer to the sun? If so, it’d have been nice to actually see it.
• Why was Michelson unable to measure any difference in speed of light despite the fact we, being on planet Earth that is orbiting the sun, had to be moving through the medium in which it propagates?
• What makes the sun (and other stars) shine (beyond the obvious “they shine because they’re hot” answer). What keeps the sun hot, what energy is it harnessing?
• How did the solar system form? Any answer to this must account for how the planets, only a tiny fraction of the mass of the solar system, ended up with the vast majority of the angular momentum in the system.
• What is the electrical “fluid” that moves around when there is an electric current, and that somehow seems imbalanced when we perceive that an object has a charge? Were there both negative and positive fluids, or just one fluid that had a natural neutral level; below it was negative (deficit), above it was positive (excess)?
• Why are there so many different kinds of atoms? How did electrical charges relate to chemistry? How is it that 94 thousand coulombs of charge are needed to bust apart certain molecules (though it often had to be delivered at different voltages depending on the molecule)?
• Why were the atomic weights almost always a multiple of hydrogen’s? Why was it never quite a perfect multiple? Why was it sometimes nowhere near to being a multiple?
• Why does the photoelectric effect work the way it does, where it depends on the frequency of the light hitting the object, not the intensity?
• Why does black body radiation have a “hump” in its frequency graph?

As of 1930, we had a notion of the rough answer to #3, thanks to Arthur Eddington. I hinted at it last time. But details still needed to be worked out.

Number 4 was still a mystery back then, as far as I know.

Recaps and Refreshers

There are some preliminaries to get out of the way here, some of them are refreshers on what came before. Back in part 17, when I told the story of the discovery of the neutron, I brought in the concept of “spin” in regards to electrons and protons. But it’s not spinning like a top, it’s something else, still measured as angular momentum. But apparently one “rotation” doesn’t bring the particle back to where it was before, it’s somehow upside down, and another rotation is needed to get it back to where it was. (Yes, that does not make sense to us here in our macroscopic world.) It takes 720 degrees of rotation, not 360, to put the particle back the way it was. (And yes, that doesn’t make sense.)

As I said, it does get measured in units of angular momentum, and Planck’s constant, h, has the same dimensions as angular momentum. Angular momentum can be thought of in terms of whole revolutions of whatever is spinning, or in rotations through an angle of one radian (which is preferred), so Planck’s constant is often divided by 2π to give a “reduced Planck’s constant” called ℏ (pronounced “h-bar”).

It turns out that electrons and protons have a spin of 1/2ℏ. Physicists will often drop the ℏ and just say that electrons and protons have “spin 1/2”. Two electrons, side by side, might be oriented the same way, or in opposite ways, in which case one of the electrons is assigned +1/2 spin and the other one is “upside down” and has spin -1/2. Similarly for protons. And neutrons. All have +/- 1/2 spins.

Like angular momentum, spin is expected to be conserved, because it is a funky form of angular momentum.

If you have many protons (and neutrons) in a nucleus, the nucleus itself has a total spin, which is just the sum of all those half spins. The combined number of protons and neutrons is the atomic mass number, so for an atom of nitrogen-14, there are seven protons (because it’s nitrogen, and nitrogen by definition has seven protons) and seven neutrons, total 14. So the spins of seven protons and seven neutrons have to be added up. When actually measured, the total spin is 1.

It turns out there’s a rule here: If the mass number is even, the total spin is an integer. If it’s odd, the total spin has a 1/2 (or -1/2) in it. This makes sense, if you think about it. You can go through the protons and neutrons in a nucleus and group them, arbitrarily into pairs. Each pair will consist of two +1/2 spins (total 1), a +1/2 and a -1/2 spin (total 0), or two -1/2 spins (total -1). And it doesn’t matter which protons and neutrons you arbitrarily choose to pair together. The result is that all of the pairs put together will make up a whole number spin since you’re adding 1s, 0s, and -1s. So if the nucleus has an even mass number, its spin is the sum of a bunch of pairs of nucleons and will be an integer. If it has an odd mass number, there will be one proton (or neutron) left over after you make up your pairs, again no matter which pairings you use, you have one left over. It will have spin -1/2 or +1/2, so you’ll end up adding or subtracting 1/2 from the integer spin you get from the pairs. In general, a spin with a 1/2 in it is called a half-integer spin, because when you double it, you get an integer.

Before the discovery of the neutron in 1932, there was an idea that a nucleus consisted of protons–as many as the mass number–and some electrons to cancel the charges on some protons. So the nitrogen-14 nucleus would have 14 protons and 7 electrons, leaving a total charge of 7, and that total charge made it a nitrogen nucleus. On one level (considering electrical charge) this makes sense, but it turns out to make no sense at all when considering spin. That (hypothetical) nucleus would have 21 particles in it, all with half spins (remember that electrons too have a half spin), so it should have a total spin with a 1/2 in it, a half integer spin. Yet the nitrogen-14 nucleus, as I mentioned earlier, had a measured spin of 1. That was a powerful argument used as support for the existence of a hypothetical “neutron” and indeed the discovery of the neutron made the math work out; now there were an even number of particles in the nucleus so it could have an integer total spin. However, as we shall see below, this solved one problem but left another problem in place.

When the anti-electron or positron was discovered, it turned out to have the opposite spin of an electron. Even when oriented the same way as an electron, its spin was -1/2 compared to the electron’s 1/2. And this is true of anti-protons and anti-neutrons as well; in fact the difference in spin is the only obvious difference between a neutron and an anti-neutron (but it’s enough!).

In 1925, Wolfgang Pauli enunciated the “Pauli exclusion principle.” At first he applied it only to electrons, but in 1940 it was generalized to all particles with half-integer spins. In short, it states that no two such particles can occupy the same quantum state. An example of this is the lowest energy level of an atom, the “1s” orbital. An electron in that orbital is in a certain quantum state. But spin is part of the quantum state, so you can put a second electron in that orbital, so long as it’s oriented the other way and has spin -1/2. But after that, no more. You have to put a third and fourth electron in the “2s” orbital, then six subsequent electrons into the three “2p” oribtals (two each), and so on. (This is why the periodic table “rows” (or periods) all have even numbers of elements in them; if you subdivide them into blocks corresponding to the s, p, and d orbitals, those blocks also each have even numbers of elements in them.)

This is fundamentally the reason why two material objects can’t be in the same place at the same time. They’re made up of electrons, protons, and neutrons with half spins.

This principle does not apply to particles with integer spins, like photons (spin 0). Photons can pile onto the same quantum state by the billions, and it’s no problem. That’s very “non-matter” behavior, and indeed photons aren’t considered to be “matter” as we know it. They can occupy the same place at the same time, and often do. Beams of light can cross through each other without a problem.

Eventually, the name “fermion” (for Enrico Fermi) was given to all half-integer spin particles as a class, and “boson” (For Satyendra Nath Bose) to particles with integer spin.

OK, that’s enough about spin (for now).

I’ve also already told the story of how physicists had discovered the “Strong Nuclear Force,” often just called the Strong force. It’s responsible for keeping nuclei together, and when it’s just not strong enough to do the job, you get alpha decay, where the nucleus ejects an alpha particle (after 1932, known to consist of two protons and two neutrons), total four mass units. When this happens to a uranium-238 atom, it becomes a thorium-234 atom; four mass units less. And the charge has decreased by two, from 92 (uranium) to 90 (thorium).

It was beginning to look, by the way, as if the total number of nucleons (be they protons or neutrons) was something that was conserved, a new conservation law. Eventually this would be called “conservation of baryon number” (other similar particles would be discovered after 1950, they ware all called baryons). Protons and neutrons each had a baryon number of 1. The only way to wipe them completely out was to hit them with antimatter, but the antimatter was regarded as having negative baryon numbers, an anti-proton or anti-neutron had baryon number of -1. So proton-anti-proton annihilation took a +1 and -1 and turned them into zero. Nice and tidy.

Beta Decay Spells Doom?

But there was another kind of radioactive decay, beta decay.

And it was causing headaches for physicists.

As a reminder, this is when a nucleus spits out an electron. The charge of the nucleus goes up by one, but its mass number stays the same. For example, that thorium-234 atom undergoes beta decay to become protactinium-234. Same mass number, but the charge has changed from 90 (thorium) to 91 (protactinium). That process repeats to get you to uranium-234.

The old notion of the nucleus as consisting of one proton per mass number, counterbalanced partially by electrons, seemed plausible because of this. One of those electrons could be kicked out, “uncovering” a proton and increasing the charge. But as I described above, this notion of electrons in the nucleus left an issue with spin. This was solved with the discovery that the nucleus in fact contained protons and neutrons, and no electrons, but there was still a problem with beta decay.

That thorium-234 nucleus has to have an integer spin (just like the nitrogen-14 nucleus) because 234 is an even number, and the discovery of the neutron explained why. (According to wikipedia the spin happens to be 0.) The resulting protactinium-234 nucleus similarly has to have an integer spin (also happening to be zero). But in moving from thorium-234 to protactinium-234, an electron was ejected; it has a spin of 1/2. Shouldn’t the resulting nucleus have a half spin as well?

It doesn’t. So it appears that beta decay violates conservation of angular momentum.

Another issue popped up when energy was measured. With alpha decay, the masses (considered as their energy equivalents) and kinetic energy of the particles before and after the event balanced, once you added everything up, including the recoil of the nucleus like a rifle firing a bullet.

With beta decay, some of the energy disappeared. The energy of the nucleus (including its recoil) plus the kinetic energy of the electron, did not add up to what was there before. There was always some missing energy, but the amount could vary from very tiny to most of it.

This of course looked very much like a violation of mass/energy conservation.

[I’ll pause here to note that physicists typically simply speak of “energy conservation”, not “mass/energy conservation” because they consider matter to just be another form of energy; so a change in mass of a nucleus due to binding energy and so forth, is just another change of energy to them. I’m going to follow that convention from here on out.]

Yet another issue was noted when the recoil of beta decay was considered. With alpha decay, the alpha particle and nucleus recoiled in exactly opposite directions, much like a cannon firing a cannonball is shoved back in the opposite direction. The two new momenta (a relatively light alpha particle traveling quickly, versus a relatively heavy nucleus traveling in the opposite direction slowly) cancel out, leaving the total momentum unchanged.

But with beta decay, the recoil was not in the opposite direction from the velocity of the beta particle that was ejected. If the two directions aren’t opposite one another they cannot cancel completely–there’ll be some slight motion to the side left over–so there’s some “new” momentum where there had been none before.

And this looks a lot like a violation of the conservation of momentum.

So beta decay broke not just one, but THREE conservation principles!

Oh, dear.

This was hard to stomach. Sure, these conservation principles are generalizations. We see them work all the time without fail, but there’s always a smidgen of a chance that we’ll discover that they don’t really hold true. After all, we had once had conservation of mass, and conservation of energy, but then realized they weren’t true after all. But in that case, they were still true afterwards when combined into the conservation of mass/energy (or conservation of energy could be kept if mass was simply regarded as another form of energy, but that still involved “scratching” conservation of mass).

But three such violations at once was hard to believe.

At least, baryon number was safe.

And the problem persisted in 1934, when a second form of beta decay was discovered as part of the discovery of antimatter. A phosphorus-30 nucleus (one which does not exist in nature) would decay by spitting out a positron not an electron. It would end up moving to the left on the periodic table (because a proton had turned into a neutron) and become a nucleus of silicon-30, which is stable. This new mode of decay is now known as beta-plus or beta-positive decay, and it suffered from the same issues with conservation of angular momentum, energy, and momentum.

There was another violation on top of all of these but one much less troublesome. It had been suggested that the total number of electrons was fixed. Before the neutron was discovered, back when the nucleus was thought to contain protons and electrons, beta decay was just considered ejecting a pre-existing electron from a nucleus, so it wasn’t unreasonable to think that there might be some law conserving electrons. So we never saw electrons being created from nothing. But with the new understanding, beta decay consisted of a neutron turning into a proton and ejecting a brand-spanking, made-from-nothing electron. And beta positive decay transformed a neutron to a proton, creating a positron from nothing. So conservation of electrons, never very well established to begin with, seemed to have been scotched.

Wolfgang Pauli (of the Pauli exclusion principle) pondered this problem and realized there might be a way to rescue all of these conservation numbers. He wrote a very famous letter in 1930 (two years before the discovery of the neutron), in which he suggested there might be a totally new particle, one that was very light (lighter than the electron) and had no charge. As such it would be very difficult to detect.

This could solve all of these problems and save all of the conservation laws.

The spin issue could be solved by positing that the particle had the opposite spin as the electron (or positron), so that the two ejected particles together added up to zero spin, so the nucleus didn’t have to have a spin change at all in order to comply with conservation of angular momentum.

If the new particle carried away some of the energy, it would cover the “missing energy” that seemed to suggest a violation of conservation of energy.

And if beta decay resulted in three entities, not just two, then any two of them could move in directions not opposite each other, with the third particle serving to cancel the sideways momentum.

Pauli named his proposed particle the neutron. (Remember this was two years before Chadwick detected “the” neutron, and the name wasn’t taken yet.) Enrico Fermi, the next year, renamed the hypothetical particle the neutrino, This is Italian for “little neutral one,” as opposed to the big neutral one, the expected but still undiscovered neutron we know today.

And in 1933 Fermi proposed a new force, the weak nuclear force (to contrast it from the strong nuclear force). This force would cause a neutron to turn into a proton, neutrino, and electron, or alternatively a proton to turn into a neutron, neutrino and positron. In other words, it would be the force that governs beta decay–both kinds of beta decay.

In fact if we assume that there are also anti-neutrinos, we can even create a new conservation law from the ashes of the conservation of electrons. If we classify electrons and neutrinos as “leptons,” then a hypothetical “conservation of lepton number” might work better.

“Regular” beta decay, then, would turn a neutron into a proton, electron, and an anti-neutrino. Baryon number is preserved (neutron +1, proton +1, electron and anti-neutrino both 0), and the new lepton number is too; no leptons before the decay balances with the situation after the decay where there is one electron (+1 lepton) and one anti-neutrino (-1 lepton). Beta plus decay spits out a positron; to balance this anti-lepton we need a neutrino lepton.

This is very tidy. Not only are the three old conservation laws saved, a new one is created. It must have been very tempting to just assume it’s true. But it’s not enough.

We need to find the particle.

The neutron, after all had been a suggestion that would solve a lot of problems, but few were willing to take its existence on faith. Fortunately it was found, fairly quickly.

But this particle was going to be a cast-iron bitch to find. Because it didn’t have an electric charge, so it wouldn’t interact with the electromagnetic force. And it, like the electron, wouldn’t be affected by the strong force. It could only “feel” the weak nuclear force. (Just forget about gravity, it’s so weak.)

The weak force has a very, very short range. In fact, now we know its range is less than a tenth the diameter of a proton. So the only way a neutrino could interact at all is when it is directly in contact with a nucleus.

Remember that a nucleus is about 1/10,000 the width of an atom, so even with solid matter like lead, only 1/10,000 x 1/10,000 x 1/10,000 or one trillionth of the space is actually nuclei. So a neutrino, travelling through a block of solid lead at pretty basically the speed of light, is only in contact with a nucleus one trillionth of the time. So, only a trillionth of the time could it interact with a proton or neutron. So for some reaction that has a half life of (say) 1/10,000th of a second, the neutrino would have to spend 100,000,000 seconds travelling through the lead before it had a fifty percent chance of interacting one of the lead nuclei. That works out to be about three years. In those three years about half of the neutrines will have traveled three light years, or basically 18 trillion miles, and come out the other side, intact.

It’s a common trope that neutrinos will pass through light years of solid lead (if you could arrange for that to be set up) without interacting, and this is basically why. They need to spend a fairly long time (1/10,000 of a second is an eternity inside a nucleus) near very small things and they’re buzzing along at the speed of light. More realistically, the vast majority of neutrinos would simply drill right through the earth without affecting it. In fact, sixty five billion neutrinos pass through every square centimeter of the arth every second, and no one notices. More to the point, that many neutrinos also pass through every square centimeter of you every second, and you don’t notice, because they pass through, and don’t get stopped by your body.

The first detection was actually of antineutrinos generated in a nuclear reactor by the huge number of beta decays occuring in the reactor core.

When a an antineutrino does condescend to react with a proton, the proton becomes a neutron and a positron is spat out; it’s basically anti-neutrino induced beta decay, except that this decay absorbs an antineutrino instead of creating a neutrino (the books balance either way). And this was how neutrinos were eventually detected…in 1956.

Clyde Cowan, Frederick Reines, Francis B. Harrison, Herald W. Kruse and Austin D. McGuire did this by parking their apparatus–which largely consisted of large tanks of water–near a nuclear reactor, which generates a lot of antineutrinos, then waited for the tiny fraction of them that would interact with their detector. The reaction, as noted turned a proton into a neutron and spits out a positron; the positron finds an electron and mutually annihilates it, generating two gamma rays. If the nucleus hit is one of the hydrogen atoms in a water molecule, it turns from a single proton to a single neutron, which will wander off until it hits a nucleus and is absorbed–in this case cadmium was used since it absorbs neutrons readily. When this happens the neutron also generates a gamma ray. By watching for both of these events, two gamma rays from the electron-positron annihilation followed shortly after by a different-strength gamma ray from the neutron absorption, the experimenters could see that the signal matched the profile of the reaction and conclude a neutrino had hit a proton.

Even though ten trillion neutrinos passed through every square centimeter of the detector every second, only about three neutrino events per hour were detected. And just to prove that it was neutrinos from the reactor, they shut the reactor off and continued monitoring the detectors, and noticed a drop in the number of events.

But the actual detection of neutrinos (well, actually, antineutrinos) is getting ahead of our story.

Next time we’ll tackle Mystery Number 3.

Obligatory PSAs and Reminders

China is Lower than Whale Shit

To conclude: My standard Public Service Announcement. We don’t want to forget this!!!

Remember Hong Kong!!!

中国是个混蛋 !!!
Zhōngguò shì gè hùndàn !!!
China is asshoe !!!

China is in the White House

Since Wednesday, January 20 at Noon EST, the bought-and-paid for Joseph Biden has been in the White House. It’s as good as having China in the Oval Office.

Joe Biden is Asshoe

China is in the White House, because Joe Biden is in the White House, and Joe Biden is identically equal to China. China is Asshoe. Therefore, Joe Biden is Asshoe.

But of course the much more important thing to realize:

Joe Biden Didn’t Win

乔*拜登没赢 !!!
Qiáo Bài dēng méi yíng !!!
Joe Biden didn’t win !!!

His Fraudulency

Joe Biteme, properly styled His Fraudulency, continues to infest the White House, we haven’t heard much from the person who should have been declared the victor, and hopium is still being dispensed even as our military appears to have joined the political establishment in knuckling under to the fraud.

One can hope that all is not as it seems.

I’d love to feast on that crow.

Justice Must Be Done.

The prior election must be acknowledged as fraudulent, and steps must be taken to prosecute the fraudsters and restore integrity to the system.

Nothing else matters at this point. Talking about trying again in 2022 or 2024 is hopeless otherwise. Which is not to say one must never talk about this, but rather that one must account for this in ones planning; if fixing the fraud is not part of the plan, you have no plan.

The Audit

On that note, reading comments on the Friday thread, there seems to be mixed opinions on whether the audit was good news, bad news, and if good news, exactly what could be done with it.

I suspect a lot of discussion will be going on today, as we digest what we’ve seen and read.

But at least it finally is out.

Lawyer Appeasement Section

OK now for the fine print.

This is the WQTH Daily Thread. You know the drill. There’s no Poltical correctness, but civility is a requirement. There are Important Guidelines,  here, with an addendum on 20191110.

We have a new board – called The U Tree – where people can take each other to the woodshed without fear of censorship or moderation.

And remember Wheatie’s Rules:

1. No food fights
2. No running with scissors.
3. If you bring snacks, bring enough for everyone.
4. Zeroth rule of gun safety: Don’t let the government get your guns.
5. Rule one of gun safety: The gun is always loaded.
5a. If you actually want the gun to be loaded, like because you’re checking out a bump in the night, then it’s empty.
6. Rule two of gun safety: Never point the gun at anything you’re not willing to destroy.
7. Rule three: Keep your finger off the trigger until ready to fire.
8. Rule the fourth: Be sure of your target and what is behind it.

(Hmm a few extras seem to have crept in.)

Spot Prices.

Kitco Ask. Last week:

Gold $1754.80
Silver $22.46
Platinum $944
Palladium $2100
Rhodium $13,900

This week, markets closed as of 3PM MT.

Gold $1751.20
Silver $22.49
Platinum $986.00
Palladium $2047.00
Rhodium $15,750.00

All prices are down from a few weeks ago, however this week some are up a bit and some are down a bit. Perhaps we’re bottoming out? Or just reversing for a bit before continuing the trend? Who knows? I was in a local coin shop and people were buying silver, taking advantage of the relatively low prices.

Physics?

I fought a futile battle to write something coherent.

About halfway through, I realized it needed rework, and probably should be split into two posts. So perhaps next week…

I didn’t even have time to write an anti-ChiComChimpanzee rant.

Obligatory PSAs and Reminders

China is Lower than Whale Shit

Remember Hong Kong!!!

中国是个混蛋 !!!
Zhōngguò shì gè hùndàn !!!
China is asshoe !!!

China is in the White House

Since Wednesday, January 20 at Noon EST, the bought-and-paid for His Fraudulency Joseph Biden has been in the White House. It’s as good as having China in the Oval Office.

Joe Biden is Asshoe

China is in the White House, because Joe Biden is in the White House, and Joe Biden is identically equal to China. China is Asshoe. Therefore, Joe Biden is Asshoe.

But of course the much more important thing to realize:

Joe Biden Didn’t Win

乔*拜登没赢 !!!
Qiáo Bài dēng méi yíng !!!
Joe Biden didn’t win !!!

Okay you knuckledragging ChiComs trying to take us down…here’s a history lesson for you.

For millennia, you had to suffer from this:

Yep. Steppe Nomads. They laid waste to your country, burned, raped and pillaged (but not in that order–they’re smarter than you are) for century after century.

You know who figured out how to take them on and win? The Russians.

Not you, the Russians. And it took them less than two centuries. And Oh By The Way they were among the most backward cultures in Europe at the time.

You couldn’t invent an alphabet, you couldn’t take care of barbarians on horseback, and you think you can take this board down?

HAHAHAHAHAHAHA!!!! We’re laughing at you, you knuckledragging dehumanized communists…worshipers of a mass-murderer who killed sixty million people!

I mean, you still think Communism is a good idea even after having lived through it!

By my reckoning that makes you orders of magnitude more stupid than AOC, and that takes serious effort.

His Fraudulency

Joe Biteme, properly styled His Fraudulency, continues to infest the White House, and hopium is still being dispensed even as our military appears to have joined the political establishment in knuckling under to the fraud.

All realistic hope lies in the audits, and perhaps the Lindell lawsuit (that will depend on how honestly the system responds to the suit).

One can hope that all is not as it seems.

I’d love to feast on that crow.

Justice Must Be Done.

The prior election must be acknowledged as fraudulent, and steps must be taken to prosecute the fraudsters and restore integrity to the system.

Nothing else matters at this point. Talking about trying again in 2022 or 2024 is hopeless otherwise. Which is not to say one must never talk about this, but rather that one must account for this in ones planning; if fixing the fraud is not part of the plan, you have no plan.

Lawyer Appeasement Section

OK now for the fine print.

This is the WQTH Daily Thread. You know the drill. There’s no Poltical correctness, but civility is a requirement. There are Important Guidelines,  here, with an addendum on 20191110.

We have a new board – called The U Tree – where people can take each other to the woodshed without fear of censorship or moderation.

And remember Wheatie’s Rules:

1. No food fights
2. No running with scissors.
3. If you bring snacks, bring enough for everyone.
4. Zeroth rule of gun safety: Don’t let the government get your guns.
5. Rule one of gun safety: The gun is always loaded.
5a. If you actually want the gun to be loaded, like because you’re checking out a bump in the night, then it’s empty.
6. Rule two of gun safety: Never point the gun at anything you’re not willing to destroy.
7. Rule three: Keep your finger off the trigger until ready to fire.
8. Rule the fourth: Be sure of your target and what is behind it.

(Hmm a few extras seem to have crept in.)

(Paper) Spot Prices

Last week:

Gold $1787.80
Silver $23.78
Platinum $962.00
Palladium $2220.00
Rhodium $16000.00

This week, 3PM Mountain Time, markets have closed for the weekend.

Gold $1754.80
Silver $22.46
Platinum $944
Palladium $2100
Rhodium $13,900

Remember when rhodium was pushing $30K an ounce? And palladium was on the verge of $3000? Maybe I should have sold my palladium back then! I’ve now “lost” over 900 dollars per ounce. On the other hand I paid much less than $1000 an ounce for it, decades ago. I’m still way ahead. [Full disclosure, my luck with platinum hasn’t been as good.]

But my purpose with precious metals is to buy and hold them. I’m not going to freak out if gold drops 30 cents. There are large commodity traders who make their living buying and selling on the short term–those are mostly the paper gold people–and they have to worry about that sort of thing. A wrong move at the wrong time could cost them everything. But I don’t worry. If you believe precious metals are worth having, this is an increasingly good time to buy…not sell and punch out.

Which is why I am not forecasting DOOM for precious metals right now. And if you’re still building your stock up, you’re presented with an opportunity that might make up for whatever you “lost” buying a few weeks ago. (It’s not a true loss until you sell and “realize” it. And that doesn’t mean “realize” like “I realized voting for Biden was a mistake” but the much older original meaning: real-ize…to make real.)

XIX Antimatter

In 1928 British physicist Paul Dirac (1902-1984 [Wow, he was still alive when I was in college!]) noted that Schroedinger’s equation did not account for relativistic effects. If the charged particle was traveling at close to the speed of light, Schroedinger’s Equation wouldn’t work.

Hoping that a properly written equation would explain a few puzzling things about energy levels, and hence spectral lines, Dirac eventually derived:

Which is now known as Dirac’s Equation.

One thing to note is that β and α are actually fourth order tensors (I think), not just simple scalar numbers. And furthermore there are three α’s, α₁ α₂ and α₃, each multiplied by a corresponding p_n. (That’s what that large capital sigma is telling you to do.)

I once saw another form of this equation, a very different looking form:

∫∫∫ [∣Ψ₁∣²+∣Ψ₂∣²+∣Ψ₃∣²+∣Ψ₄∣²] dx dy dz = 1

(The three symbols at the left should be larger, but apparently you can’t change the font size of only part of a paragraph.) You’re squaring the wave function Ψ along four different directions, then doing “triple integration” to the result…and getting 1.

The four squares have to add up to something, and that something, triple integrated, will be one.

But for every solution to this, there is an equal-but-opposite solution. If ∣Ψ₁∣² equals a certain value, then so does ∣−Ψ₁∣², in exactly the same way that 3 and −3 both square to equal 9. And so the whole mess will have the same total, 1, as it did before.

The implication is that something the exact opposite of an already-known particle, one that behaves as described by this equation, could also exist.

In 1930, Paul Dirac predicted antimatter on the basis of this fact.

According to this concept, for every type of particle, there is an opposite particle. For an electron, there would be an anti-electron. It would the opposite charge (positive instead of negative) but that’s not the only thing that would be opposite; it’s just the most obvious thing. One thing that is the same is the mass.

There would also be an anti-proton, of negative charge, and an anti-neutron…well, of no charge, but still an anti-neutron, somehow on a quantum level the opposite of a neutron despite there being no electric charge to serve as a “marker.”

This doesn’t seem to apply to particles that carry a force; a photon is its own anti-particle, as are other force carrying particles totally unknown in the 1920s.

One could imagine an anti-hydrogen atom consisting of an antiproton being orbited by an antielectron. You’d not be able to tell it was anti-hydrogen from the outside, though; the mass would be the same as hydrogen’s, and the anti-electron would jump to different energy levels by absorbing or emitting regular photons.

But, as it turns out, if an electron meets an anti-electron, both are instantly and completely converted to energy in the form of gamma rays, following E=mc². A single electron’s mass is equivalent to 511 thousand electron volts (511 keV), so a bit more than one million electron volts is released when both of the electron/anti-electron pair annihilate. If a proton (or neutron) meets an anti-proton (or antineutron), then there is a big burst of energy but at least some of the debris is other sorts of particles (particles not yet known in 1930), which will themselves decay to other things, releasing a lot of energy. The total energy of two protons is about two billion electron volts.

On the face of it this was a pretty outrageous prediction, one which was largely ignored.

But then, like a thunderbolt hurled by Zeus, the evidence came out of the sky.

Cosmic Rays

Back in 1909 Theodor Wulf had developed a device called an electrometer. It consisted of a hermetically sealed container, with a vertical conducting rod piercing the barrier. On the inside of the container, there was a swinging needle, attached to the rod. If the rod picked up an electric charge then so would the needle, and the needle and the rod would repel each other. The needle’s angle was an indication of the strength of the charge; it could even be put against a curved scale and read like the needle in any old analog voltmeter.

Wulf claimed that an electrometer at the top of the Eiffel Tower picked up more of a charge than one at its base. There were issues with his data, so it wasn’t taken quite as seriously as it should have been, nonetheless others were inspired to investigate.

In 1911 Domenico Pacini took electrometers over lakes and seas, and also three meters below the surface. He concluded, based on the lower readings underwater, that the radiation that was causing the charges wasn’t coming from the Earth.

In 1912 Victor Hess carried four improved electrometers to 5300 meters in a balloon, and they picked up four times as much charge as ones left at ground level. Could this be coming from the Sun? Probably not, because he repeated the experiment during a near-total eclipse, and that made no difference even though the moon would have been blocking most radiation from the sun at that time. This was confirmed by other researchers, and Victor Hess won the 1936 Nobel Prize for Physics as a result (yes, twenty four years later).

The rays were coming from space–deep space. Robert Millikan (who earlier had measured the charge of an electron) dubbed them “cosmic rays.”

These turned out to be very energetic protons, for the most part, smashing into something in the upper atmosphere and creating a cascade of secondary and tertiary particles. It’s nature’s particle accelerator.

Physicists continued to investigate cosmic rays, often by taking a “cloud chamber” aloft. This was a device with gas supersaturated, so that any charged particle passing through leaves a contrail. If the chamber is placed within a magnetic field, then any charged particles would be bent. And experiments in the late 1920s and 1930 started revealing curved traces.

On August 2, 1932, Carl Anderson caught an anti-electron in the act, a curve like a beta particle (electron) but in the opposite direction.

The outrageous prediction had proved true, only two years later.

The new particle was named the positron. And it is indeed antimatter.

If you’ve ever had a PET scan, PET stands for Positron Emission Tomography. And that means you got subjected to positron radiation. You survived your encounter with antimatter.

Antimatter/Matter annihilation is the only known means of completely converting mass into energy. A half a kilogram (a bit over a pound) of antimatter, dropped on the floor, would annihilate itself and half a kilogram of matter and produce a 21 megaton blast. (That is about a thousand times as much as hit either Nagasaki or Hiroshima). (One megaton is 4.184 petajoules or 4,184,000,000,000,000 joules.)

It’s Real

Antimatter is essentially a mirror image of matter. As far as we can tell, the universe could just as easily have been made of antimatter instead of matter…but of course the anti-scientists in such an anti-universe wouldn’t call that stuff antimatter, they’d call our matter “antimatter.”

One of the ongoing mysteries of physics is why our universe isn’t half-and-half matter and antimatter. That’s not an 1894 mystery, that’s a 2021 mystery.

Another loose end, is that based on theory, antimatter ought to behave exactly like matter in a gravitational field. In other words, it should fall, and at the same rate. (Which is fine until it impacts, then KABOOM!!!!! doesn’t begin to cover it.) But this really should be confirmed; the problem is it’s hard to make antimatter, then slow it down (since it generally comes out of particle accelerators), then keep it from touching anything [or kaboom!] long enough to see if it will fall when the magnetic containment is released. This would have to be done in a vacuum, of course, lest the antimatter simply collide with an air molecule and annihilate.

I mentioned anti-scientists above; this should not be confused with the likes of Fauci, the Climate Research Unit, etc.

Also, apparently the most that can happen combining antipasta and pasta is indigestion or weight gain (it creates mass!).

And of course, Joe Biden didn’t win.

Obligatory PSAs and Reminders

China is Lower than Whale Shit

Remember Hong Kong!!!

中国是个混蛋 !!!
Zhōngguò shì gè hùndàn !!!
China is asshoe !!!

China is in the White House

Since Wednesday, January 20 at Noon EST, the bought-and-paid for His Fraudulency Joseph Biden has been in the White House. It’s as good as having China in the Oval Office.

Joe Biden is Asshoe

China is in the White House, because Joe Biden is in the White House, and Joe Biden is identically equal to China. China is Asshoe. Therefore, Joe Biden is Asshoe.

But of course the much more important thing to realize:

Joe Biden Didn’t Win

乔*拜登没赢 !!!
Qiáo Bài dēng méi yíng !!!
Joe Biden didn’t win !!!

SPECIAL SECTION: Message For Our “Friends” In The Middle Kingdom

You knuckle-dragging barbarians are still trying to muck with this site, so I’ll just repeat what I said last time.

Up your shit-kicking barbarian asses. Yes, barbarian! It took a bunch of sailors in Western Asia to invent a real alphabet instead of badly drawn cartoons to write with. So much for your “civilization.”

Yeah, the WORLD noticed you had to borrow the Latin alphabet to make Pinyin. Like with every other idea you had to steal from us “Foreign Devils” since you rammed your heads up your asses five centuries ago, you sure managed to bastardize it badly in the process.

Have you stopped eating bats yet? Are you shit-kickers still sleeping with farm animals?

Or maybe even just had the slightest inkling of treating lives as something you don’t just casually dispose of?

中国是个混蛋 !!!
Zhōngguò shì gè hùndàn !!!
China is asshoe !!!

And here’s my response to barbarian “asshoes” like you:

OK, with that rant out of my system…

20 Years Since 9/11

I’ve got only three minutes left, so I am going to have to jump to my conclusion.

Over three thousand people died 20 years ago today, they must not be forgotten. There are memorials at three sites; I’ve been to the one in Pennsylvania. Plenty of people were there, including a large group of very patriotic, Q-following bikers.

The deed was done by very evil men, almost certainly Islamic jihadis, but…aided and abetted by whom? Do we really know that yet? Were they acting only with other jihadis’ support, or was someone behind the scenes, pulling the strings? If the latter (and I have no real opinion of this, though I do have one on the physical cause of the buildings’ collapse–let’s leave that aside), then they STILL need to be punished.

After all, justice must be done.

Justice Must Be Done

The prior election must be acknowledged as fraudulent, and steps must be taken to prosecute the fraudsters and restore integrity to the system.

Nothing else matters at this point. Talking about trying again in 2022 or 2024 is hopeless otherwise. Which is not to say one must never talk about this, but rather that one must account for this in ones planning; if fixing the fraud is not part of the plan, you have no plan.

The Audit

The Audit is definitely heating up. Let’s see if the Opposition manages to squelch it and its consequences. I’ll be honest; I expect it to be ignored by anyone capable of ordering Biden/Harris to step down.

Nevertheless, anything that can be done to make Biden look less legitimate is a worthy thing!

Lawyer Appeasement Section

OK now for the fine print.

This is the WQTH Daily Thread. You know the drill. There’s no Poltical correctness, but civility is a requirement. There are Important Guidelines,  here, with an addendum on 20191110.

We have a new board – called The U Tree – where people can take each other to the woodshed without fear of censorship or moderation.

And remember Wheatie’s Rules:

1. No food fights
2. No running with scissors.
3. If you bring snacks, bring enough for everyone.
4. Zeroth rule of gun safety: Don’t let the government get your guns.
5. Rule one of gun safety: The gun is always loaded.
5a. If you actually want the gun to be loaded, like because you’re checking out a bump in the night, then it’s empty.
6. Rule two of gun safety: Never point the gun at anything you’re not willing to destroy.
7. Rule three: Keep your finger off the trigger until ready to fire.
8. Rule the fourth: Be sure of your target and what is behind it.

(Hmm a few extras seem to have crept in.)

Spot (i.e., paper) Prices

Last week:

Gold $1828.60
Silver $24.77
Platinum $1032.00
Palladium $2506.00
Rhodium $17,750.00

This week, 3PM Mountain Time, markets have closed for the weekend.

Gold $1787.80
Silver $23.78
Platinum $962.00
Palladium $2220.00
Rhodium $16000.00

Wow, they’ve ALL taken a thumping! Is this a buying opportunity or are we watching a bubble burst? Well I’m not one of those kinds of prognosticator.

To be honest, I don’t buy this stuff for the short term. I buy it for the long term, and pretty much everything I hold in precious metals (except for the small amount of platinum I have) is higher than I paid for it.

That will probably be true for anyone buying today, twenty years from now. Assuming western civilization is still running twenty years from now.

Part XVIII – Quantum Weirdness Explained by Richard Feynman

A couple of weeks ago I embedded a video of a lecture by Richard Feynman on just how weird quantum mechanics is.

Here’s a (slightly different) version of the same video. (This one has a short introductory shot of the campus of Cornell U, and a title graphic.)

the Messenger Lectures, PROBABILITY & UNCERTAINTY–the quantum mechanical view of nature

This week’s physics article is going to be me paralleling what is said in this video. I may sometimes duplicate Dr. Feynman’s wording, but mostly I will not. Why am I doing this? Because this is the best explanation I’ve ever seen for just how whacky quantum mechanics is. And I know many don’t have the patience to watch a video…I’m one of those people, 99% of the time.

My summary/regurgitation/mangling of what’s in the video starts in the next paragraph. Things that are purely my own comments rather than me paraphrasing or summarizing Feynman are [in brackets].

When we first began using scientific observation, it largely started with intuition, but that is actually based on our experiences with every day objects. These largely suggest “reasonable” explanations for things. As we continued pursuing scientific knowledge, we observed more phenomena and created generalizations we call ‘laws.’ But we also are seeing a situation where the laws become more and more ‘unreasonable,’ more and more intuitively far from obvious.

With twenty-twenty hindsight, there was no reason this shouldn’t be the case. Our everyday lives involve large numbers of particles (even a dust mote has billions of billions of atoms in it), objects moving slowly (compared to how fast they could be moving), or other very special conditions. Our direct view of the world is actually very limited; all we can see is a narrow set of cases. But with refined and careful measurements using instruments that extend our sensory “reach” we get a more complete picture and we start seeing unexpected things. We see things that are far from what we would guess. We see things that are far from what we could have imagined. Our imagination is stretched, not to create or follow fiction, but just to understand what is actually there.

[Feynman gave the example of special relativity and its conclusion that simultaneity–which we intuitively think is an absolute in that if I see two events as simultaneous, so will you–depends on the observer’s situation.]

It’’s this kind of unexpected thing that is our topic.

Let’’s start with light. At first it was seen to behave as a rain of particles, corpuscles, like rain, like bullets from a gun. Then with further research that turned out to be wrong. Instead light behaved like a wave, water waves for instance. This seemed absolutely solid, thanks to various experiments that could only work for waves, and Maxwell’s equations. Then at the beginning of the 20th century after more research, it looked once again like light was made up of particles, for example with the photoelectric effect, and the particles are now called ‘photons.’ Electrons were first believed to be particles, but further experimentation with electron diffraction shows that they behave like waves. There was a lot of confusion until 1925-26 when the correct quantum mechanical equations were written. [Much of this was covered in prior installments.]

Unfortunately there just isn’t a word for what photons and electrons really are. Particle doesn’t fit, wave doesn’t fit. You can’t use either of these because you give the wrong impression. They behave a third way, a way like nothing you’ve ever seen before.

[My flip joke about this is when someone asks if light (or electrons) is a particle or a wave, I reply, “yes.”]

Well there is one thing that makes the situation simpler than it otherwise could be. Electrons and photons behave the same, that is they’re both screwy, but in exactly the same way. (After all they could have turned out to have been screwy in different ways.)

The newspapers say there was a time when only twelve people understood relativity. [Feynman] doesn’t believe there was ever such a time. There was a time when ONE person understood it, but once he published, a number of people were able to understand it, at least sort of.

But, [Feynman says] no one understands quantum mechanics. [Good then I have plenty of company.]

So we are going to describe the behavior of electrons and photons by a mixture of contrast and analogy. Pure analogy would break down, of course, since they’re not like anything in our normal experience.

Bullets

So we’re going to compare and contrast particles, for which we will use bullets [no PC woke stuff then!], and waves, for which we’ll use water waves. We’re going to describe an experiment run on bullets, then water waves, then electrons or photons. This one experiment will encapsulate everything weird about quantum mechanics. Any other weird thing about quantum mechanics, you can say “you remember the experiment with the two holes? It’s the same thing.”

For bullets, our experimental apparatus is as shown below. This is a view from above. On your left there’s a source (machine gun) firing through a hole in armor plate. The gun is a bit wobbly, so the bullets don’t all follow the same trajectory. To your right from this, is another piece of armor plate, with two holes in it, a bit to the left or right as seen from the source, but from your point a bit above and below the center line, symmetrically situated–number these 1 and 2 since they’ll be talked about a lot. This plate is a ways to your right from the first plate, but just to fit it on the blackboard I’ll draw them close together [and so will I, below]. Also, this is really three dimensions. The plates extend into and out of your monitor, and to repeat you’re looking down on the thing from above, with the plates edge on. Finally at your far right is a line of bullet detectors (a backstop with sand), so we can see where the bullets went.

[Note: I did not have time to draw the diagrams. So unfortunately, I’m going to use a generic diagram I found on line, and modified, quickly! It’s going to have its shortcomings.]

There are a couple of key differences between this scenario and actual reality. First, these bullets can ricochet off the edges of the holes, so that will tend to spread their impact points out a bit. But if they hit a barrier head on and don’t go through the holes, they stop, rather than ricocheting. They’re also indestructible (not liable to break in half on impact).

So we run the experiment and the first thing we notice is something obvious but we need to take note of it. Bullets are lumps, all the same size (one bullet each). The bullets have distinct locations where they hit the sand at the backstop. Also, we never get two bullets impacting at the same time. If the machine gun is firing slowly you hear “plink, plink plink” rather than “plink, plink, plinkety plink.” These are all aspects of a characteristic that Feynman labels “comes in lumps.”

So say you let the machine gun fire for an hour, then you go from top to bottom on the diagram, (or left to right as seen from the machine gun) along the backstop and plot how many bullets you find in the sand.

You end up with a double-humped distribution (imagine a Bactrian camel). And you can say that this double hump is proportional to the probability that the next bullet will hit at that location. At the tops of the humps it is most likely. Let’s call that distribution N₁₂ because it results from both holes being open. You can run this experiment for even longer and come up with good average figures, even if it’s 2 1/2 bullets hitting a particular spot per hour. (Just like you hear about the average family having 2.4 kids. But no family has .4 kids in it; children come in lumps. Some families have more, some have less.) [Feynman actually brought that up, not me.] You can also run the experiment again but this time covering one or the other hole, in which case you get two different single-hump distributions, N₁ and N₂. And then you’ll notice a key fact; if you add N₁ and N₂, you get N₁₂. It works this way because there is, as Feynman says, “no interference” between the two holes.

Water Waves

Okay, we’re done with bullets. Now place this exact layout in a pool or lake. Instead of armor plate, we’re talking breakwaters or jetties or lines of barges. And instead of a machine gun, there’s some big massive object being moved up and down in a regular fashion to make waves, which then pass through the slit in the left hand barrier, then through the two slits in the middle barrier, to reach measuring devices at the third barrier (instead of a sand trap, though if the barrier is the beach, there might still be sand involved). The measuring devices measure the amplitude (height) of the wave that arrives at that point, which is proportional to the energy carried by the waves.

When you do this, whatever arrives at the detectors can have any size at all. It doesn’t come in lumps. [The waves can be a meter high, a centimeter, a micron…] What’s measured is the intensity, not a count of lumps.

The result is a curve like this. [Note, Feynman actually drew the wrong curve in the lecture at about 21 minutes. He later noticed that he had drawn the wrong curve (at about 21:30). “Which is the exact opposite of this curve..” and he did a quick fix.]

The reason for this rather complicated curve is that when the source wave hits the two openings in the middle barrier, it reaches them at the same time, and those two openings themselves act like sources, and waves ripple outwards from them. The two sets of waves will add together. Along the center line the peak of the wave from opening 1 arrives at the same time as the peak from opening 2, so the waves add together to make something twice as tall, or twice the energy. A bit off the center line, the trough from wave 1 will hit the spot at the same time as the peak from wave 2, or vice versa, resulting in canceling out. A measurement here will see no wave height at all and an energy of zero. Even further off the center line, a peak from one opening will arrive at the same time as the following peak from the other opening, and they will add to each other rather than canceling out. (However one of those waves will have traveled farther and will be weaker, so this peak will not be as high as the one on the center line.)

The waves interfere with each other. This is used in science in a funny way because sometimes the interference from a wave strengthens the other wave (“constructive interference”) and sometimes it cancels (“destructive interference”); in ordinary language interference always works against someone, never with them.

The interference creates the complex pattern shown, I₁₂ (I for intensity). If you close one hole or the other, you get a smooth curve, just like you did with the bullets. In fact the patterns are basically identical, N₁ looks like I₁, and N₂ looks like I₂. But these two patterns, I₁ and I₂ do not add up to make I₁₂.

This distribution is known as an interference pattern.

So we see several key differences between particles and waves: lumpiness/non-lumpiness, discrete/continuous values, non-simultaneous/simultaneous arrival times, and the lack/presence of interference.

Electrons

OK now for electrons (metal plates). Or photons (for which the barriers are made out of black paper). But I’m only going to discuss electrons. [But remember, they’re both screwy in the same way.]

What we receive at the detector are lumps. Click, click, click, all the same size, like small bullets. If the source of electrons is made weaker, you hear the clicks further apart, but each individual click remains the same size, just like slowing down the machine gun for the bullets. And no two electrons arrive at the same time, because they aren’t emitted at the same time, again like the machine gun firing one bullet at a time. The key here is that the electrons come to one place, one at a time.

So we can now play the same game we did with the bullets, let the emitter rip for a while and then look at the distribution and equate it to a probability curve, with high areas corresponding to a greater probability of receiving the next electron fired.

We should expect to see the double humped N₁₂ curve, right? That’s how our lumpy bullets behave.

But (@27:20)…we get a probability curve looking like the multiple humped I₁₂ intensity curve, the interference pattern.

THAT is weird. These things are lumpy, and behave just like lumps…except for how they are distributed, where the distribution shows wave interference. But what would a wave have to do with particles? Or vice versa?

[Yes, it makes no sense. But it does work this way, we’ve never seen it not work this way. And this is why light was confusing around the turn of the 20th century. When experimenting with its distribution it appeared like a wave. But when we did things with the photoelectric effect that would actually depend on the lumps, we got lumpy behavior.]

[Ok, it’s mad. Stark raving mad, But this is the way things work.]

Some Additional Subtleties

There are some subtleties.

One might state as “obvious” that an electron–which is a “lump”–has to have gone through hole #1 or hole #2. Call that “Proposition A”

That of course would imply that the total number of electrons that reach the detector is the sum of those which go through hole #1, and those which go through hole #2. But you can’t sum the two one-hole distributions to get the interference pattern, so Proposition A would appear to be false; the electrons must be splitting up, somehow.

This is science, we test it even though it seems like ironclad logic.

So we set up lights over each hole to watch the electrons.

Lo and behold, you will see a flash in one hole, or the other hole, and these match the times of hits on the detector, so Proposition A appears to be true after all!

And it is true. But you can’t add the distributions together to get the interference pattern!

Well, I haven’t told you the whole story. Because when you set people to watching the holes and reporting, for each hit on the detector, which hole the electron went through…the distribution on the detector switches from being the interference pattern to the double hump pattern! So now that you know what I₁ and I₂ are…I₁₂ is equal to their sum!

So, obviously, the light is doing something to the electrons. This is not surprising, after all, light has enough energy to shove electrons around (hence emission and absorption lines in spectra), so we decide to turn the intensity of the light down enough to have less of an effect.

But light, too, is “lumpy.” Turning down the light reduces the number of lumps or photons. If you reduce the light enough, electrons might get through the hole without running into a photon at all, in which case the guy monitoring the holes will say he didn’t see the electron at all.

Guess what? If you plot the electrons that didn’t get seen, and ignore the rest, you get the multiple hump distribution. If you look only at the ones that were seen, you get the double hump distribution. If you look at them all, you get some sort of weighted sum of the two, depending on what fraction of electrons were or were not seen.

Other methods can be arranged to determine which hole an electron goes through, and they all lead to the same result. If you make the sensor too gentle to muck with the electron…you end up not seeing the electron. There is no way to detect an electron without disturbing it and wrecking the interference pattern.

[Feynman summarizes the way scientists describe the situation:] If you set up an apparatus to monitor the holes, then you can say that it goes through one hole or the other (and Proposition A is true). If you don’t have such an apparatus, then you cannot say that it goes through one hole or the other, because when you’re not looking, electrons don’t behave as if they do go through one hole or the other.

No one can give you a deeper explanation of this than [Feynman] has given you. They might come up with more examples, but this is the basic conundrum of quantum mechanics.

Another subtlety. We use probability in daily life for things like, say, the throw of a dice. We shouldn’t have to do this. We should be able to calculate how the die will land, given its orientation, speed, the nature of the surface it will land on, and so forth. Straight mechanics, even if very, very complicated. But since we don’t know the initial conditions well enough, the die toss appears to be a random event, we can’t predict what it’s going to do. But again that’s because we don’t know the initial conditions and haven’t the skill to do the computation fast enough.

With these electrons, one might think if they behave as though they have a probability of doing something, we could somehow write laws that would tell us where the electron will be. But this turns out not to be the case. True randomness–the randomness we don’t actually see in our macroscopic world–is built into it. We can’t know the state of the electron and be able to compute what it will do; if we could, we’d lose the interference pattern. “Nature herself doesn’t know which way the electron is going to go.”

Feynman’s Concluding Rant

[nearly verbatim]

[Feynman puts on a pompous voice and quotes a philosopher as saying “It is necessary for the very existence of science that the same conditions always produce the same result.”] Well, they don’t. And yet the science goes on. [So much for that philosopher.]

What is necessary for the very existence of science and so forth and what the characteristics of nature are not to be determined by pompous preconditions, they are determined always by the material with which we work, by Nature herself. We look and we see what we find and we cannot say ahead of time what it’s going to look like. The most “reasonable” possibilities turn out often not to be the situation.

What [actually] is necessary for the very existence of science is just the ability to experiment, the honesty in reporting results (the results must be reported without somebody [instead] saying what they’d like the results to have been), and finally an important thing is the intelligence to interpret the results. [Take THAT, Climate Research Unit!]

But an important thing about this intelligence is that it should not be sure ahead of time about what must be. Now it can be prejudiced and say “that’s very unlikely, I don’t like that.” Prejudice is different than absolute certainty, I don’t mean absolute prejudice, just bias, not complete prejudice. Even if you’re strongly biased, the experiments will pile up until you cannot ignore them any longer.

In fact the only thing needed is that minds exist that do not demand that nature must satisfy some preconceived conditions, like those of our philosopher.

[Oh, and we need to fix elections, too. And we need bacon.]

Obligatory PSAs and Reminders

China is Lower than Whale Shit

Remember Hong Kong!!!

中国是个混蛋 !!!
Zhōngguò shì gè hùndàn !!!
China is asshoe !!!

China is in the White House

Since Wednesday, January 20 at Noon EST, the bought-and-paid for His Fraudulency Joseph Biden has been in the White House. It’s as good as having China in the Oval Office.

Joe Biden is Asshoe

China is in the White House, because Joe Biden is in the White House, and Joe Biden is identically equal to China. China is Asshoe. Therefore, Joe Biden is Asshoe.

But of course the much more important thing to realize:

Joe Biden Didn’t Win

乔*拜登没赢 !!!
Qiáo Bài dēng méi yíng !!!
Joe Biden didn’t win !!!

The Marines, Sailors, and Soldiers Who Died in Afghanistan

Unless otherwise mentioned, these people are Marines.

All died in Afghanistan, serving us, their lives expended stupidly by His Fraudulency.

That does not take away from the debt we owe them, in fact it increases it. We owe it to them to remove His Fraudulency and his cohorts from power.

Justin Allen, 23

Brett Linley, 29

Matthew Weikert, 29

Justus Bartett, 27

Dave Santos, 21

Jesse Reed, 26

Matthew Johnson, 21

Zachary Fisher, 24

Brandon King, 23

Christopher Goeke, 23

Sheldon Tate, 27

Max Soviak (USN)

Rylee McCollum, Wyoming

David Lee Espinoza, 20,  Texas

Sgt. Nicole Gee

SSGT Ryan Knauss (USA)

Normal Introduction

Another week, another deluge of BS from the White House and from the Controlled Opposition.

The Audit continues.

The collapse of the Covidschina continues.

No doubt much will be said about those today. (And I have missed a lot this past week.)

To my mind the audits are the last hope for a within-the-system fix to what happened last November. “Within the system” meaning the audits find fraud, the various states decertify the results, and some dang judge rules that Biden must step down and Trump must be installed.

That last step is crucial. The way our system works, “fraud” isn’t a fact until some “competent authority” (i.e., meaning “one that has jurisdiction,” not “one that won’t end up with an ice cream cone on its forehead”) rules it is so. That must happen before the system will accept that the election is vitiated by fraud. No finding of fraud means, as far as they are concerned no fraud, no fraud means nothing vitiated. We sit and fume, because the system has failed.

I’ll leave it to you to decide how likely you think it is that a judge will rule against the Left given the riots that would likely endanger his/her family.

As for the military stepping forward and doing the job instead? Well, that’s technically “outside of the system” and besides…this military, that’s being made woke as we speak?

What do we do in the likely event that fraud is found, but no judge will find it to be “fact” as far as the Federal Government is concerned? I keep hoping someone will come up with a suggestion, and so far “general strike” (H/T Scott) is the only one I’ve seen.

Justice Must Be Done.

The prior election must be acknowledged as fraudulent, and steps must be taken to prosecute the fraudsters and restore integrity to the system. (This doesn’t necessarily include deposing Joe and Hoe and putting Trump where he belongs, but it would certainly be a lot easier to fix our broken electoral system with the right people in charge.)

Nothing else matters at this point. Talking about trying again in 2022 or 2024 is pointless otherwise. Which is not to say one must never talk about this, but rather that one must account for this in ones planning; if fixing the fraud in the system is not part of the plan, you have no plan.

This will necessarily be piecemeal, state by state, which is why I am encouraged by those states working to change their laws to alleviate the fraud both via computer and via bogus voters. If enough states do that we might end up with a working majority in Congress and that would be something Trump never really had.

Lawyer Appeasement Section

OK now for the fine print.

This is the WQTH Daily Thread. You know the drill. There’s no Poltical correctness, but civility is a requirement. There are Important Guidelines,  here, with an addendum on 20191110.

We have a new board – called The U Tree – where people can take each other to the woodshed without fear of censorship or moderation.

And remember Wheatie’s Rules:

1. No food fights
2. No running with scissors.
3. If you bring snacks, bring enough for everyone.
4. Zeroth rule of gun safety: Don’t let the government get your guns.
5. Rule one of gun safety: The gun is always loaded.
5a. If you actually want the gun to be loaded, like because you’re checking out a bump in the night, then it’s empty.
6. Rule two of gun safety: Never point the gun at anything you’re not willing to destroy.
7. Rule three: Keep your finger off the trigger until ready to fire.
8. Rule the fourth: Be sure of your target and what is behind it.

(Hmm a few extras seem to have crept in.)

Spot Prices

Last week:

Gold 1781.50
Silver 23.13
Platinum 1000
Palladium 2354
Rhodium 17,100

This week, 3 PM MT on Friday, markets closed for the weekend

Gold $1817.80
Silver $24.08
Platinum $1016.00
Palladium $2498.00
Rhodium $18,400.00

Everything was much lower this week (except for rhodium and palladium which had been creeping upward), but suddenly on Friday, gold jumped 24 bucks, silver 44 cents, platinum $33, palladium $22, and rhodium $100 (that’s a very small move for rhodium, by the way; it usually moves a lot more in whatever direction it is going). So now it’s a net improvement for the week.

Part XVI – De Broglie, Schrödinger, and Heisenberg

Very flaky connection. Who knows whether I’ll be able to finish this.

I can’t figure out a coherent history of the 1920s; apparently a lot of stuff was happening simultaneously. So I will treat three different threads as though they were independent. They weren’t.

De Broglie

(Which is pronounced “Deh Broil-ee” or at least was by my physics professor–the four alternatives given for pronunciation in Wikipoo are different from this), put 2 and 2 together.

We had already established that light, even though a wave of energy, has particle behavior (that was largely Einstein in 1905). And we also knew, thanks to Max Planck (1905), that the particles (“photons”) had energy proportional to their frequency.

But we also knew that matter is basically equivalent to energy, that thanks to Einstein as well in 1905.

Since light was energy and could behave as both a particle and a wave, could matter, which was equivalent to energy, also behave as both a particle (which you’d expect from matter) and a wave (which you would not expect)?

De Broglie said, in essence, “yes,” in his doctoral thesis in 1924.

Here is the Planck-Einstein relation:

E = h ν

…which relates the energy of the photon to its frequency ν (Greek letter nu) and Planck’s constant, h.

And light turned out to have momentum (p), too, based on the energy E or wavelength λ:

p = E / c = h / λ

You can simply rearrange this last to get:

λ =h / p

And of course p is mass times velocity, mv.

The implication is that any chunk of matter is a wave, at least while it is in motion. However, if you consider the very tiny size of Planck’s constant, 6.6 x 10^-34, and realize it is being divided by, say 100 (a 100 kg object moving at one meter per second, for instance) for any sort of object you will deal with in your daily life, the wavelength (6.6 x 10^-36 meters) is very, very small, much, much smaller than an atomic nucleus (roughly 10^-15 m). Immeasurably small. The wavelength is about the same size, in relation to that nucleus, as the nucleus is in relation to the Earth.

But for something very, very light, like, say, an electron…you might get a reasonable wavelength. If de Broglie isn’t just talking out his ass.

An electron’s mass is about 9.1 x 10^-31 kg. So assume (for the sake of example) one is travelling roughly at one hundredth the speed of light ( 3 x 10⁶ m/s, and plug that into λ =h / p and you get:

λ = 6.6×10^-34 / ( 3 x 10⁶ * 9.1 x 10^-31 ) = 242 x 10^-12 meters

Now the diameter of a hydrogen atom is about 62 x 10^-12 meters. Its circumference is therefore roughly 195 x 10^-12 meters…which is pretty doggone close to this wavelength actually, considering I just made a guess as to how fast an electron might be moving.

Standing Waves (Not Really a Digression)

If you have ever plucked a guitar (or violin) string, you’ll have noticed it moves in a certain fashion, the top left in the diagram below:

It turns out that the other modes shown in the diagram also exist to a certain extent. You can also have standing waves (of sound) in an organ pipe or any other wind instrument.

Now back to the electron. If it is a wave, and it’s orbiting around a nucleus, the wave has to mesh cleanly with itself after one orbit around the nucleus. Look at the top right string, which is a full wavelength. So if that string was actually arranged around a circle, instead of a straight line, at any given point it would look like a smooth wave; because the end of the wave would be consistent with the beginning of the wave where it joins, it’d be a smooth wave travelling in a circle. But if the electron were to have a different wavelength, it couldn’t be in that orbit, because the wave wouldn’t be smooth–there’d be a “break” in it somewhere along the circumference.

That’s only the beginning of the argument, but it will eventually turn out that de Broglie’s hypothesis, that an electron is a wave as well as a particle, ends up explaining why electrons can only assume certain orbits in an atom. We knew, thanks to Bohr and the spectroscopists, that it did do so, but didn’t know why it followed the rule. Remember that the quantum theory was just an arbitrary-seeming restriction on various processes that seemed to work out. Now we had some hint as to why the restriction exists. It was the only way for electrons to form standing waves.

Of course it’s all very well for him to propose a hypothesis that seems whacky but seems to match the facts. But it’d be nice to do an experiment that proves that electrons can behave as waves, and Clinton Davisson and Lester Germer did so at Western Electric (later Bell Labs) in 1927, sending a beam of electrons through a sample of nickel and seeing a diffraction pattern form.

A diffraction pattern is a property of waves.

De Broglie won the 1929 Nobel Prize for Physics.

Erwin Schrödinger

But this tidy little solution was way oversimplified.

An electron is not a one-dimensional string, tied down at two points, but left free to vibrate. It instead is a wave free to move in three dimensions, but caught in a potential well, attracted to a nucleus, the more strongly the closer it got.

It’s possible to write the equations of those strings’ waves, and doing so gets you a nasty mess full of trigonometry. (Nasty, that is, to the mathematically dis-inclined.)

It’s also possible to write a three dimensional equation, using complex variables, to describe the waves an electron can make when bound to a nucleus by the electrical force.

It’s even possible to write yet a different equation, which the first equation must satisfy in order to work. That may have made your head spin just a bit, so let me back off and explain something about higher mathematics.

Arithmetic and algebra deal with functions, you plug a number in and out comes another number, that is termed “a function of” the first number. f(x) = x² is one example; plug 3 in and out comes 9.

Calculus, and even higher forms of math, actually works on functions, not on numbers; giving you another function (which you can then plug a number into).

For example, if you want to know how fast f(x) = x² changes as you change x, you can do something called “taking the derivative” to the first function, and you get another function, f'(x) = 2x. You can then plug your number into that equation, and know that not only is x² = 9 when x is 3, but you know how fast x² is increasing at that point: it’s increasing at a rate of 6 for every 1 increase in x.

In 1925 Schrödinger postulated, then in 1926 published an equation, which involves a lot of calculus, into which you plug your proposed equation for an electron wave. If it balances out, you have the equation for a wave an electron might assume. There are many possibilities for what the electron is actually doing (depending on its energy, for instance), and yours might just be the one it’s following.

[Linguistic aside: Schrödinger is sometimes spelled Schroedinger, where oe is an acceptable substitute for ö. Sometimes it’s rendered “Schrodinger” which is technically incorrect. To form the sound the Germans mean when they write ö, prepare to say “eh” as in bet but round the lips (like you do when saying “oooh”) when you say it. To some people it sounds a bit like “er” and I’ve even see “teach yourself” books that said that was how to do it. Cuppa Covfefe will no doubt amplify or correct me. Meanwhile, the same physics prof who taught me how to butcher de Broglie pronounced it “shraydinger” which would make sense…if his name was Schrädinger/Schraedinger.]

So here it is. I had to work with a simplified version of this back in college, and I do not remember how to do it; in fact certain aspects of the notation don’t make sense to me at all, so I’ve forgotten much.

Note that i, the square root of minus one, (the unit “imaginary” number) appears at the left hand side of the thing. Ψ is the actual electron wave equation, if it meets the condition shown, it’s a possible equation for an electron.

Remember that this is being done in three dimensions, and that the value of the wave function Ψ is itself a complex number, i.e., the sum of a real number and an imaginary number, a+bi. (Yes, we did a lot with complex numbers…in fact electrical engineering would be damned near impossible without them.)

In college, I had to work with a problem called “particle in a box” where the particle had free reign of a small region of space (in one dimension); at the edges of the region the potential went up to infinity, meaning the particle couldn’t go past those points. The answer was a standing wave, just like the ones in the diagram above.

When solved in three dimensions, for electrons orbiting a nucleus, you get these possibilities:

Schrödinger is most famous for his cat. Well, actually, it wasn’t his actual cat (I don’t know if he even owned any, or served as staff for any), but it was a facetious thought experiment he proposed to ridicule a certain interpretation of quantum mechanics. But that was in 1935, far in the future, but it does touch on quantum uncertainty, which brings us to…

Werner Heisenberg

In 1927, Werner Heisenberg put forward the uncertainty principle. It states that even in principle it is impossible to know a particle’s position and momentum perfectly. You could know one of them very accurately, but then you’d know the other one quite imperfectly. You can multiply the two uncertainties together, and the product will be greater than h/4π, or ℏ/2. Even if your measuring apparatus is very accurate the uncertainty cannot be less than ℏ/2.

This introduced some spookiness into quantum mechanics.

Up until now, everything physics had produced was fundamentally deterministic. If you knew the state of a system at a certain time, you could, in principle (though it would take a YUGE computer a YUGE amount of time) figure out what state it would be in at some time in the future…or what state it had been at some time in the past. it would be like playing a movie forward and backward.

Along comes Heisenberg, and says you cannot know the state of a system at a certain time. If you know where the constituents are, you don’t know how fast they are moving. If you know how fast they are moving, you don’t know where they are.

And it turns out, even the particles themselves don’t “know.”

The electron wave, it turns out, actually describes the probability of the electron particle being at various places. According to one interpretation (the one that is dominant today) called the “Copenhagen Interpretation”, the electron can be anywhere that wave function says, but at some point it will interact with something, and then it will assume a definite position. (Please note, not the same as “assum[ing] the position.”)

This is seriously weird stuff. And I’m going to leave it to a competent physicist to talk about some of the ramifications. Richard Feynman was once voted (by currently practicing physicists) as the 7th greatest physicist of all time. And his lectures are famous…they used to be for sale at dead tree bookstores (e.g., Borders), and I’m sure they’re available in printed form on the web. (I’d look but it’s already nine minutes before 10 PM my time.) This video is almost an hour long, but good.

It was this sort of thing that brought about Einstein’s quote that God does not play dice with the universe, and also led Schrödinger to propose the cat experiment, which purported to show that the Copenhagen interpretation of quantum mechanics led to a situation where a cat was neither dead nor alive but both but neither until you opened the box and looked.

But we do not need to open the box to know that Saturday is bacon day around here.

And that Joe Biden didn’t win.

[I must apologize for this article; I doubt it made anything clear at all. However, there’s an old saw about how anyone who thinks they understand quantum mechanics just shows his ignorance. I don’t know that there is actually any way at all to make this stuff clear; it’s utterly counter to anyone’s intuition to the point where intelligent/geeky people just flatly refuse to accept it, despite the fact that it has been experimentally verified again, and again, and again….]

Obligatory PSAs and Reminders

China is Lower than Whale Shit

To conclude: My standard Public Service Announcement. We don’t want to forget this!!!

Remember Hong Kong!!!

中国是个混蛋 !!!
Zhōngguò shì gè hùndàn !!!
China is asshoe !!!

China is in the White House

Since Wednesday, January 20 at Noon EST, the bought-and-paid for Joseph Biden has been in the White House. It’s as good as having China in the Oval Office.

Joe Biden is Asshoe

China is in the White House, because Joe Biden is in the White House, and Joe Biden is identically equal to China. China is Asshoe. Therefore, Joe Biden is Asshoe.

But of course the much more important thing to realize:

Joe Biden Didn’t Win

乔*拜登没赢 !!!
Qiáo Bài dēng méi yíng !!!
Joe Biden didn’t win !!!

His Fraudulency

Joe Biteme, properly styled His Fraudulency, continues to infest the White House, we haven’t heard much from the person who should have been declared the victor, and hopium is still being dispensed even as our military appears to have joined the political establishment in knuckling under to the fraud.

One can hope that all is not as it seems.

I’d love to feast on that crow.

Justice Must Be Done.

The prior election must be acknowledged as fraudulent, and steps must be taken to prosecute the fraudsters and restore integrity to the system.

Nothing else matters at this point. Talking about trying again in 2022 or 2024 is hopeless otherwise. Which is not to say one must never talk about this, but rather that one must account for this in ones planning; if fixing the fraud is not part of the plan, you have no plan.

Lawyer Appeasement Section

OK now for the fine print.

This is the WQTH Daily Thread. You know the drill. There’s no Poltical correctness, but civility is a requirement. There are Important Guidelines,  here, with an addendum on 20191110.

We have a new board – called The U Tree – where people can take each other to the woodshed without fear of censorship or moderation.

And remember Wheatie’s Rules:

1. No food fights
2. No running with scissors.
3. If you bring snacks, bring enough for everyone.
4. Zeroth rule of gun safety: Don’t let the government get your guns.
5. Rule one of gun safety: The gun is always loaded.
5a. If you actually want the gun to be loaded, like because you’re checking out a bump in the night, then it’s empty.
6. Rule two of gun safety: Never point the gun at anything you’re not willing to destroy.
7. Rule three: Keep your finger off the trigger until ready to fire.
8. Rule the fourth: Be sure of your target and what is behind it.

(Hmm a few extras seem to have crept in.)

Spot Prices.

Kitco Ask. Last week:

Gold $1780.60
Silver $23.83
Platinum $1034
Palladium $2736
Rhodium $20,200

This week, markets closed as of 3PM MT.

Gold 1781.50
Silver 23.13
Platinum 1000
Palladium 2354
Rhodium 17,100

Gold has actually moved around a bit, but the end result was a tiny gain over the week. Silver has dropped significantly (about 3 percent by eyeball). Platinum was well under a thousand yesterday, and has recovered…some. Palladium is down over ten percent. And Rhodium is getting its ass kicked; it dropped 1900 dollars on Friday alone.

From Special to General

Introduction

Let us start off by recapping our list of “as of 1894” mysteries and conservation laws, and bring things up to date including the Bohr atom and the work done on justifying the periodic table (much of which happened well beyond 1913). Otherwise, we’re at about 1913 now.

Let’s recap/update those lists.

1. Conservation of mass
2. Conservation of momentum
3. Conservation of energy
4. Conservation of electric charge
5. Conservation of angular momentum
6. (ADD:) Conservation of mass-energy

The following mysteries were unanswered at the end of 1894.

1. Why was the long axis of Mercury’s orbit precessing more than expected, by 43 arcseconds every century? Was it, indeed, a planet even closer to the sun? If so, it’d have been nice to actually see it.
2. Why was Michelson unable to measure any difference in speed of light despite the fact we, being on planet Earth that is orbiting the sun, had to be moving through the medium in which it propagates?
3. What makes the sun (and other stars) shine (beyond the obvious “they shine because they’re hot” answer). What keeps the sun hot, what energy is it harnessing?
4. How did the solar system form? Any answer to this must account for how the planets, only a tiny fraction of the mass of the solar system, ended up with the vast majority of the angular momentum in the system.
5. What is the electrical “fluid” that moves around when there is an electric current, and that somehow seems imbalanced when we perceive that an object has a charge? Were there both negative and positive fluids, or just one fluid that had a natural neutral level; below it was negative (deficit), above it was positive (excess)?
6. Why are there so many different kinds of atoms? How did electrical charges relate to chemistry? How is it that 94 thousand coulombs of charge are needed to bust apart certain molecules (though it often had to be delivered at different voltages depending on the molecule)?
7. Why were the atomic weights almost always a multiple of hydrogen’s? Why was it never quite a perfect multiple? Why was it sometimes nowhere near to being a multiple?
8. Why does the photoelectric effect work the way it does, where it depends on the frequency of the light hitting the object, not the intensity?
9. Why does black body radiation have a “hump” in its frequency graph?

In just 20 years we had come a long way. Out of nine mysteries, only three were completely left open, and another was mostly solved. And even mystery number 3 had tantalizing hints.

More Developments in Special Relativity

A few weeks ago–actually the last time I used this particular eagle–I described the four Big Papers Einstein published in 1905. Two of them had to do with what today we call “Special Relativity.”

What made it “special”? Did it ride the short bus to school?

What made it special was that it only applied to a very specific case, the case where the frames of reference are not accelerating. Constant speed, even high speed, isn’t an issue, but if there’s any sort of acceleration, it’s a different ball game.

General relativity doesn’t have this restriction. Special relativity turns out to be a special case of general relativity.

1915 was the year Einstein first put forward general relativity, which means that historically speaking, with the last article taking us up to that about then dealing with subatomic physics, this is the right time to take up general relativity.

But there had been some developments in special relativity in the meantime. Einstein hadn’t really thought about relativity from a geometric point of view, but many others, including his former math professor Hermann Minkowski, did. They pointed out that if you simply consider time as being a fourth dimension, a lot of things fell into place.

This does make some sense. After all, if you and I agree to meet at the corner of Pikes Peak and Cascade on the 14th floor of the Holly Sugar Building (which isn’t called that any more), we’ve specified a meeting place in three dimensions…latitude, longitude (the streets run north/south east/west in that part of town), and elevation (14th floor). Or coordinates…a triplet of them…can be used to define any location in space once you’ve defined the coordinate system (and it doesn’t even have to be a cubical grid either; cylindrical or spherical coordinates can work). You need three coordinates, though, because space is three dimensional. You can get by with two if you implicitly specify the third (in this case, surface level could be assumed; that’s probably a good idea when dealing with ships).

But if you and I arrange a meeting place in this manner, we’re committing a Bidenesque screwup: Because we also need to specify a time. So really, you need four coordinates, three space coordinates x, y, and z, and a time coordinate, t.

When you specify all four, you’ve defined what physicists call an event. And you’re doing it in terms of spacetime.

And so, it turns out that special relativity fits well with the concept of spacetime and works in four dimensions. This was pointed out by Minkowski.

But there was a difference! And it becomes most manifest when considering interval. The interval is the distance between two events.

If you are using a “Cartesian” (cubic grid) coordinate system, the difference between two points in space is an extension of Pythagoras. In two dimensions, on a Cartesian grid, the distance between two points is simply the difference between their x-coordinates, squared, plus the difference between their y coordinates, squared, then take the square root of all that.

distance (2 dimensions) = sqrt( ( x₁-x₂ )² + (y₁-y₂)²)

It’s precisely equivalent to a²+b²=c². (And note, it doesn’t make any difference whether you subtract point 1 from point 2, or vice versa. Sure, you will get opposite signs depending on the order, but those get wiped out when you square the differences.)

To move up to three dimensions, you can square the two dimensional distance again, then square the difference in the third coordinate. But when you do that, it’s algebraically equivalent to just squaring all three differences, adding them together, then taking the square root:

distance (3 dimensions) = sqrt( ( x₁-x₂ )² + (y₁-y₂)² + (z₁-z₂)²)

So it stands to reason that for four dimensions you’d square the time difference as well, like this, right?

distance (spacetime) = sqrt( ( x₁-x₂ )² + (y₁-y₂)² + (z₁-z₂)² + (t₁-t₂)²) (wrong, don’t do this)

Well, it might stand to reason, but it’s wrong.

First there’s one issue to clear out of the way: time is measured in seconds and distance is measured in meters; by simply taking a difference in time and jumbling it in with three differences in meters, you are mixing apples and roadcones.

It turns out that with spacetime, a distance of d = ct is equivalent to a duration of t. In other words a one second time difference is equivalent to a distance of 299,792,458 meters. So when doing this computation, if you divide your space distances by the speed of light, you get units of seconds, and now the four “pieces” of the equation all match units. You’ll have to multiply the result by c again to get back to meters.

So let’s imagine two events at the same x and y, but with z differing by 299,792.458 meters, and t differing by one second. Dividing all of the space coordinates by c, you get the x and y differences = 0, the z difference being 1 second, and of course the t difference is 1 second.

Incidentally a difference is often denoted by Δ, the Greek letter delta, so we can say Δx=0, Δy=0, Δz=1, and Δt=1. It’s a lot more convenient, and amongst techie types “delta” is often slang for “change” or “difference.” (“What’s the delta in the cost of gas switching from the orange guy with the mean tweets to His Fraudulency?” for instance.)

So square everything and get 0, 0, 1, 1, add them together to get 2, take the square root, and the interval is 1.414 seconds, or about 424 million meters, right?

Well, no. The BIG difference is that with space time you subtract the space components from the time component!

Here is the correct formula:

distance (spacetime) = sqrt( (t₁-t₂)² – ( x₁-x₂ )² – (y₁-y₂)² – (z₁-z₂)² )

Note that the time difference is first and all the space differences are subtracted from it.

So in this case the interval is zero seconds; the two ones cancel.

(Equivalently, you could multiply the time by c and work entirely in meters, rather than seconds…but that would have made the arithmetic ugly.)

Now there’s only one thing that can get from that first event, to that second event. The one thing that can move 299,792,458 meters in one second, and that, of course, is light in a vacuum.

But the light, in doing so, covers no interval. Which means that the light beam perceives no distance traveled and no time elapsed! But if you remember the time and distance dilation formulas from the last time we talked about special relativity, that’s what we would expect. At light speed, both effects cause the elapsed time and traveled distance (from the point of view of the light beam) to reach zero.

So what we have here is a geometric model of special relativity.

OK, let’s play another game here. Let’s make the space distance twice as much as it was before, while leaving the time distance 1. You end up with Δx=0, Δy=0, Δz=2, Δt=1.

Plugging that in, we get sqrt( 1² – 0² – 0² – 2² ) = sqrt( 1 – 4 ) = sqrt( -3 ).

Now you can’t take the square root of -3 and get a meaningful distance (or time) out of it. What the spacetime model is telling you is you cannot get from one event to the other. If you could, it would be by traveling faster than the speed of light. So the spacetime model has built into it a rationale for not being able to exceed the speed of light in a vacuum.

Einstein didn’t use this in 1905, but he adopted it shortly thereafter. (I wonder if Minkowski ever told his former student how proud he was of him.)

Minkowski invented the spacetime diagram, where the vertical axis is time, and the horizontal axis is space. Objects traveling on this diagram cannot do so at a slant of less than 45 degrees (that implies traveling faster than c), light itself moves at a 45 degree slant on the diagrams.

An interesting consequence of spacetime is that everything moves at exactly the same speed through it. You, sitting in your chair reading this are traveling through time purely, at one second every second. Move fast enough, and your motion becomes predominantly through space and you are moving slower through time. The second motion is called spacelike because most of the motion is through space, and time slows down signficantly, the first motion is called timelike not because it’d be snarky to refer to it as “sitting on your ass” but because most of the motion is along the time axis.

More Einsteinian Thought Experiments

Spacetime, it turns out, is the easiest way of dealing with general relativity. Not that it’s easy.

I actually wasn’t that far off when I talked about special relativity riding the short bus. The math involved with it is an absolute breeze compared with the math in general relativity. It’s a major event when someone is able to solve the general relativity equation for a certain specific scenario. In fact, I will be honest with you: I don’t understand the math. I never got exposed to tensors; I just have a vague idea that they’re sort of like matrices (which are a power tool in mathematics I do know something about), but not quite.

So with that, I can’t comprehend the real situation then try to explain it to you. I have to rely on the same science-for-senators handwaving that you’ve probably already seen. As such, I’ve been half-dreading writing this post.

But, it does start with Einstein’s doing thought experiments, so at least that part should be comprehensible if I am doing my job right. [Only later will you see the wild leap I can’t justify.]

The supposition this time is that if you were in a locked chamber, no way to see in or out, and were feeling earth-normal gravity, you’d be unable to distinguish it from being in a room that is being accelerated ‘upward’ at g, the acceleration due to gravity. The rules of physics would be the same; any experiment you could carry out would have the same result.

That doesn’t seem too unreasonable. If you drop your four hundred ounce gold brick on your foot in either scenario, it will hurt just as much, just as quickly.

But this does lead to differences with the conventional understanding when you deal with light.

The conventional understanding is that light has no mass, so gravity should not act on it. A beam off your laser pointer should travel in a straight line no matter how strong the gravity is.

On the other hand, if you’re in a room that’s under acceleration, it feels like gravity, there’s an obvious up and a down. But you should be able to tell the difference between an accelerating room and one experiencing gravity, because if you fire your laser pointer horizontally, and the room is accelerating, you should see the beam bend. That is because the beam of light is moving vertically at the same speed you are, but once it has left the laser pointer, it doesn’t speed up in the vertical direction, but you and the room do, so you see the beam drop.

So if the room is feeling gravity, the beam shouldn’t bend because the force of gravity on a massless object should be zero, but if the room is being accelerated, the beam should bend, because the room is moving faster than it was before, by the time the beam hits the wall.

But if Einstein is right and there really is no way to tell the difference, then either both beams need to move in a straight line, or both beams need to bend. In the second case, light is affected by gravity even though it has no mass.

You need really strong gravity to see this, though. Or a long distance. Because light crosses any normal everyday distance in microseconds or even nanoseconds, and if it’s going to “drop” due to gravity, well, gravity only gets to act on it for a few billionths of a second. Plug that in to d=1/2at² and it’s almost nothing.

OK, but there is a concrete prediction. A light beam going by a massive object, should bend a bit. This is testable with great difficulty.

Here’s another: If light is affected by gravity, light traveling upward has to lose energy, just like a thrown baseball loses kinetic energy (trading it for potential energy) and slowing down. But light cannot lose energy by slowing down, its speed in any particular medium is a constant.

It can lose energy another way, however. Remember E = hv? (Where ν is the frequency?)

So the light, climbing in a gravity field, should decrease in frequency. That’s the only way it can lose energy. Similarly, light going “downhill” should increase in frequency to gain energy.

There’s an alternative way of looking at this though. Imagine that light beam in the accelerating room, firing upward from the floor. By the time the beam reaches the ceiling, the ceiling has sped up, so there’s a doppler shift in the wavelength, towards the red. Since you can’t tell this case from a room feeling “real” gravity, in that room the light has to redshift too.

This is gravitational red shift. Visible light becomes redder as it moves uphill. Again, this effect is tiny on Earth, but it’s measurable today (I don’t think it was measurable using 1915 equipment).

Hiding inside that effect is another.

Imagine someone on the surface of earth, shining a light straight up. He blinks, and then a second later he blinks again. In the meantime, about 600 trillion wavelengths of the light are emitted.

Someone, up in space, will see the same sequence of events. Blink, 600 trillion wavelengths, then a blink. But the light is red shifted when he sees it. 600 trillion wavelengths takes more than a second to pass by him, because the frequency has dropped.

Therefore he sees it take more than a second between the two blinks. From his point of view, time is running slower down on earth than it is for him in space.

This is gravitational time dilation.

So these are concrete, comprehensible predictions to see whether an accelerating reference frame, where effects happen due to inertia, is truly the same as one with gravity (effects due to mass).

But when Einstein followed the math…it got interesting. And I’m going to have to state it without trying to justify it. Sorry. Complicated business!

Gravity, it turns out, isn’t a “force” like electromagnetism is. It turns out that any object not being accelerated by a real force (like a rocket motor), travels a straight line in space time, the shortest distance between two events. If you think it’s curving because, for instance it’s a space probe doing a “flyby” of Jupiter, it’s because spacetime is curved.

OK, now this takes time to wrap one’s brain around, and if you fail at it you’re in very good company. How does space itself actually bend? Objects bend in space, space itself, can’t bend, there’s nothing to bend.

Nevertheless it does. Not just in Einstein’s thought experiments, but in reality.

Einstein used his new concepts to compute the orbit of Mercury.

Remember there had been a long-standing mystery about Mercury. It orbits the sun in a markedly elliptical orbit, and under Newtonian two-body gravity, the long (or “major”) axis of the ellipse should never change direction. But in fact it does change direction. Some of this can be shown to be due to the other planets’ pulling on Mercury constantly. But not all. After subtracting all of that out, the major axis still shifts by 43 arc seconds every century. That’s an angle about three quarters the width of a quarter set out at a hundred yards, and it takes a century (about 400 revolutions of Mercury about the sun) for it to make that shift.

People had theorized that an undiscovered planet closer to the Sun than Mercury could be perturbing Mercury’s orbit, but it would be frustratingly difficult to see such a planet so close to the Sun.

But when Einstein did the computation with his modified law of gravity, he found that an object orbiting that close to a very massive object like the sun…would see a shift of exactly this amount!

The net effect of Einstein’s new law of gravity is that near very massive objects, gravity’s effect is slightly greater than an inverse square law. Which means that at perihelion (closest approach) gravity is a bit stronger than Newton would expect. However, Kepler’s second law still applies (a line from the sun to the planet sweeping out equal areas in equal times) because it depends on the conservation of angular momentum. So this manifests itself as the elliptical orbit behaving like something out of a Spirograph set.

OK, so Einstein had made one prediction he could test himself. But to be really solid science, predicting new phenomena (rather than just being a possible explanation of a known phenomenon) would be good.

Testing General Relativity

The light bending, doppler effect, and time dilation effects were something that had not been seen before, had not been predicted by any other theory, and if seen would be otherwise unexpected; i.e., a successful prediction by this theory…three successful predictions, actually.

As it turned out, the light bending was the easiest. For this you can use a large massive body that’s between you and stuff of known position, if the position of those background objects appears shifted near the body, you have gravity (from the massive body) bending the light coming to you from the background objects.

This is a job for the Sun. As seen from earth, it moves against the background (it’s really the Earth moving), which is a known pattern of stars. We’ve got plenty of star maps taken when the sun is nowhere along the line of sight (in fact when the sun is behind the mapper, because he’s doing this at night and the sun is below his feet somewhere). So we just need to see if the stars seem shifted (away from the sun as it turns out) when the sun is on the line of sight to the stars.

Did I mention earlier the sun is bright? This makes it impossible to see stars that are almost behind it.

Except during a solar eclipse, when the moon neatly covers the sun!

There was a solar eclipse in 1919. Astronomer Arthur Eddington took photographs, not of the corona (as people usually do during eclipses) but of the stars near the Sun. The elegant mathematical reasoning of Albert Einstein was put to the test. (If you don’t find it elegant, it’s because you haven’t seen and understood the math; I haven’t understood it myself, so I’m taking other peoples’ word for it that its elegant.)

It was hard to measure accurately enough to truly nail it down, but the stars’ apparent position had indeed shifted and the measured effect was consistent with General Relativity.

This was big news. I mean, really big news. It made the newspapers read by regular people. This was when Einstein became famous outside of scientific circles.

Today, we can see entire galaxies bending the light of galaxies behind them. In fact, there’s a spectacular instance of two almost-perfectly-lined up galaxies causing the background galaxy to look like a ring, known as an Einstein Ring:

The gravitational redshift took longer. For this, the ideal situation is a bright, massive, small object (small is better because the gravity is more intense, and a white dwarf, which is a sun-sized star that has run out of nuclear fuel and collapsed down to the size of the earth, is ideal. It still shines brightly because it will take millions or even billions of years to cool off, but it has a very strong gravitational field. As early as 1925, someone attempted to measure the gravitational redshift off of the star Sirius B (see my article on Sirius A and B: https://www.theqtree.com/2020/01/01/another-sirius-tale-of-two-stars/), but other scientists pointed out there was too much glare from Sirius A (which is, after all the brightest star in the nighttime sky). Finally in 1954 Popper got a good measurement off of 40 Eridani B and confirmed this prediction. It’s also possible now to measure the shift in frequency of gamma rays going up several stories here on Earth.

The gravitational time dilation can be measured by two different atomic clocks at different elevations. Eventually, the lower one will fall behind the upper one.

Most famously, the GPS constellation of satellites demonstrates both special relativity time dilation, and general relativity time dilation.

The GPS system works by having each satellite sending out time signals. Their position at any time can be computed by your GPS receiver, so it’s just a matter of comparing the signals from at least four (but even more is better), noticing the differences of the times in the signals, turning that into different distances from the satellites, then doing a lot of geometry to triangulate, and figure out where the receiver must be.

Extremely accurate time sources on the satellites are an absolute necessity. If one is off by ten nanoseconds, your position will be off by ten feet (light travels roughly a foot per nanosecond).

The satellites are moving quickly, which means a clock on that satellite will seem, from down here on earth, to be ticking more slowly due to special relativity time dilation. (Not much more slowly, but enough to be measurable with modern atomic clocks.) They are also higher so due to gravitational time dilation, our clocks should run more slowly than the GPS satellite ones. The two effects are in opposite directions, so they will tend to cancel each other out. The gravitational effect is the larger of the two, so from our standpoint the GPS clocks look like they’re running faster than they would to someone actually on one of the satellites. In fact, it will run 38 microseconds per day faster than you’d expect without either time dilation effect. That would be enough to throw position calculations off by several miles…after one day.

This effect is real, it does happen. What the GPS engineers do is slow the satellites’ clocks down to compensate. That way in orbit when they speed up (as seen by us), we see the clocks ticking off normal seconds, and so if you drive your car into the Mississippi river when trying to get to Pikes Peak, it’s not the fault of GPS.

GPS wasn’t designed for the purpose of testing general relativity, but there are a couple of rather more detailed predictions involving a phenomenon called “frame dragging” (which I am not even going to try to explain, because I want to publish this this week, not sometime in October) that have been confirmed by satellites deliberately launched to test general relativity.

General relativity has met every test thrown at it. It’s real. Spacetime bends. And objects move along the shortest possible path through spacetime.

As famously put by John Archibald Wheeler (1911-2008, a veteran of the Manhattan Project) in 2000, “Spacetime tells matter how to move; matter tells spacetime how to curve.”

I debated whether to put a “rubber sheet” diagram in this post. They’re very problematic. Yes, you can see how an object might follow a curved path on the rubber sheet, which is supposed to be how gravity works, but the rubber sheet is itself bent by gravity pulling on an object. If you can’t ignore that, you’re going to be hung up on the fact that (demoed) “gravity” is caused by (real) gravity. I decided, ultimately, not to do it even though I could write disclaimer after disclaimer that it’s a visualization tool only, not an explanatory one. (And I believe I hear Wolf breathing a sigh of relief.)

But one doesn’t need a rubber sheet diagram to know that Joe Biden didn’t win.

And, in case you didn’t notice…we can cross mystery number one off the list. Thanks, Herr Doktor Einstein!

Obligatory PSAs and Reminders

China is Lower than Whale Shit

Remember Hong Kong!!!

中国是个混蛋 !!!
Zhōngguò shì gè hùndàn !!!
China is asshoe !!!

China is in the White House

Since Wednesday, January 20 at Noon EST, the bought-and-paid for His Fraudulency Joseph Biden has been in the White House. It’s as good as having China in the Oval Office.

Joe Biden is Asshoe

China is in the White House, because Joe Biden is in the White House, and Joe Biden is identically equal to China. China is Asshoe. Therefore, Joe Biden is Asshoe.

But of course the much more important thing to realize:

Joe Biden Didn’t Win

乔*拜登没赢 !!!
Qiáo Bài dēng méi yíng !!!
Joe Biden didn’t win !!!

His Fraudulency

Joe Biteme, properly styled His Fraudulency, continues to infest the White House, and hopium is still being dispensed even as our military appears to have joined the political establishment in knuckling under to the fraud.

All realistic hope lies in the audits, and perhaps the Lindell lawsuit (that will depend on how honestly the system responds to the suit).

One can hope that all is not as it seems.

I’d love to feast on that crow.

The Lindell Reports

It sounds worse that most of us imagined. And we have good evidence (if placed before a judge who understands probability, combinatorics, and statistics (three closely-connected branches of mathematics).

The question is, now that we have this, what’s next?

Can we get more states to do forensic audits? It will be tougher in states where the auditors themselves ended up in their positions of authority through cheating!

Even if not, it’s good to go into whatever comes next with the certitude that we were and are right about…

Joe Biden Didn’t Win. And neither did Hoe, and neither did half the craptastic Dems out there. RINOs might have won the general because at that point voters had a choice between a definite Dem and a maybe-not-as-bad “Republican.” But how many got in due to a corrupted primary?

We have to do our best to force this to stick and force “them” to pay attention to it!

Justice Must Be Done.

The prior election must be acknowledged as fraudulent, and steps must be taken to prosecute the fraudsters and restore integrity to the system.

Nothing else matters at this point. Talking about trying again in 2022 or 2024 is hopeless otherwise. Which is not to say one must never talk about this, but rather that one must account for this in ones planning; if fixing the fraud is not part of the plan, you have no plan.

Lawyer Appeasement Section

OK now for the fine print.

This is the WQTH Daily Thread. You know the drill. There’s no Poltical correctness, but civility is a requirement. There are Important Guidelines,  here, with an addendum on 20191110.

We have a new board – called The U Tree – where people can take each other to the woodshed without fear of censorship or moderation.

And remember Wheatie’s Rules:

1. No food fights
2. No running with scissors.
3. If you bring snacks, bring enough for everyone.
4. Zeroth rule of gun safety: Don’t let the government get your guns.
5. Rule one of gun safety: The gun is always loaded.
5a. If you actually want the gun to be loaded, like because you’re checking out a bump in the night, then it’s empty.
6. Rule two of gun safety: Never point the gun at anything you’re not willing to destroy.
7. Rule three: Keep your finger off the trigger until ready to fire.
8. Rule the fourth: Be sure of your target and what is behind it.

(Hmm a few extras seem to have crept in.)

(Paper) Spot Prices

Last week:

Gold $1763.90
Silver $24.48
Platinum $985.00
Palladium $2712.00
Rhodium $21,150.00

This week, 3PM Mountain Time, markets have closed for the weekend.

Gold $1780.60
Silver $23.83
Platinum $1034
Palladium $2736
Rhodium $20,200

This might be a good time to buy silver. On the other hand it could drop even m0re.

Electrons Get Quanta

If you’ll recall, last time I mentioned that in 1911 van den Broek suggested that an atom’s place in the periodic table depended on the positive charge of the nucleus; when that charge was expressed as a positive-signed multiple of e, you had a simple integer number which is that atom’s atomic number. I then said it was merely an idea for about two years, and then I left you hanging.

I’m going to pick up that thread, but I’m going to do it my way: I’m going to back up a bit and follow another thread to that same place.

As of 1900, chemists were pretty sure they were missing eight elements on the periodic table. Because they didn’t know how many lanthanides (“rare earths”) actually existed (some guesses ran as high as 25) and simply had no idea what was going on there, they didn’t know how many they were missing. (We now know that lanthanum through lutetium is fifteen elements inclusive; chemists back then knew twelve in that range, and suspected there were more.)

Remember in 1900 they didn’t know about atomic number. They did have the periodic table, and it had holes in it that were clearly missing elements, but the lanthanides didn’t seem to fit into that scheme at all so they were a big question mark.

In 1901, europium–a lanthanide whose atomic weight was between samarium and gadolinium–was discovered, and then in 1902-03 actinium was discovered during investigations of the radioactive decay chains. (From the radioactive decay series, astatine, francium and protactinium were not known yet as of 1911, but the first two were “known” holes in the table, below iodine and cesium, and protactinium was probably suspected–it’s hard to tell because back then chemists didn’t realize the actinides were like the lanthanides. My extensive discussion last week was based largely on current knowledge.)

1906 saw the discovery of lutetium, at the time the heaviest of the rare earths.

So in 1911, van den Broek came up with the concept of the atomic number. And the periodic table was pretty “tidy” right up through barium, but after barium were the lanthanides. So I believe they were able to assign every element up to barium atomic numbers, with barium at Z=56. There was a gap at Z=43. Then with an unknown number of lanthanides, it would be impossible to assign an actual number to the first known element after the lanthanides, tantalum, but we knew what group tantalum was in, so we could basically restart counting from there, identifying more holes. Two spaces to the right, under that hole for Z=43, was another hole. Then a hole under iodine and a hole under cesium, as previously mentioned.

Protactinium was discovered in 1913, so we may not have realized it at the time but everything from radium (directly below barium) on up was known.

In 1913 the picture became a lot clearer. Henry Moseley (a student of Rutherford’s), in 1913 was doing x-ray spectroscopy on a variety of elements and measuring the wavelengths. He noticed a fairly simple mathematical relationship between the atomic number (where known) and at least one of the x-ray wavelengths. From this he formulated Moseley’s law. (I’d quote the law here, but although the formula is simple, explaining what the symbols meant would be a royal pain.)

So now the guesswork was gone. Moseley could zap even a rare earth metal with his x ray device, and calculate its atomic number. Lanthanum was 57. Lutetium was Z=71. We had, without realizing it, already nearly completed the list in between: Cerium (58), praseodymium (59), neodymium (60), samarium (62), europium (63), gadolinium (64), terbium (65), dysprosium (66), holmium (67), erbium (68), thulium (69), ytterbium (70), and lutetium (71). Only #61 was missing. {Yes I am enough of a geek to known those by heart.)

So now that numbers could be assigned to every element and not just the first 56, we knew we were missing #43 (right below manganese), #61 (a rare earth), #72, #75 (below #43), #85 and #87. Uranium came in at #92 and was the last element.

Moseley’s law was consistent with the Bohr model of the atom, which was put forward that year (just two years after the Rutherford model).

And the Bohr model is our main topic today, but I will finish Moseley’s story first. Sadly, it won’t take long.

It sure looked like Moseley was destined for bigger and better things, and he had certainly earned himself a Nobel Prize for putting the atomic number on a solid footing. But World War I broke out the next year and Moseley volunteered. He was sent to Gallipoli in modern day Turkey and was killed on August 10, 1915. The Nobel Prize committee gave no award for physics in 1916. We can only speculate, but it seems as if they intended to give that award to Moseley but as they do not give posthumous awards, had to change their plans.

The Bohr model of the atom is actually considered a modification of the prior Rutherford model, which was unsatisfactory for a number of reasons. So it’s technically the “Bohr-Rutherford” model, but most just call it the Bohr model, after the Danish physicist Neils Bohr (1885-1962).

Why was the Rutherford model unsatisfactory? Chief among the issues was that if it were accurate, no atom would last more than about ten billionths of a second. Since I am writing this, and you will soon be reading this, and you and I are both made up of atoms that haven’t collapsed yet, there’s clearly a disconnect.

The Rutherford model supposed that the negatively charged, light electrons orbited the much more massive and very tiny positively charged nucleus. It didn’t discuss orbital periods of the electrons, or anything like that, so it wasn’t very specific. But that wasn’t the big issue.

The problem is that any electric charge that is being accelerated will emit electromagnetic energy. And electrons in orbit about a nucleus are constantly being accelerated. Remember that an object in motion will continue moving at that speed and direction unless acted on by an outside force (this goes back to part 1). An outside force, of course, will cause an acceleration. Since the electrons are following a curved path, they are being accelerated.

Calculations at the time based on Maxwell’s equations showed that it would take about ten billionths of a second for an orbiting electron to radiate away all of its kinetic energy, causing it to spiral in and plow into the nucleus.

How to solve this problem?

Well, there was a sketchy tool in the physicist’s tool kit that essentially functioned by forbidding certain values of energy, or momentum. If this tool could be applied here, then an electron in an orbit would be unable to drop downward, unless it took a big step downward all at once. And there’d be a minimum orbital energy it could not drop below.

That tool was quantum theory. It’s not the same quantum theory that we have today. As I hinted, it basically functioned as an overlay on classical physics, forbidding certain values of some parameters. It had been used by Max Planck to explain the black body spectrum in 1900, and it had been invoked by Albert Einstein to explain the photoelectric effect in 1905 (for which he eventually won the Nobel prize–for this, not for relativity!).

Energy came in fixed quanta, and these quanta’s sizes were always related somehow to Planck’s constant, which is:

h = 6.62607015×10⁻³⁴ J⋅Hz⁻¹

Or equivalently (since a hertz is a “per second”):

h = 6.62607015×10⁻³⁴ J⋅s

This turns out to have the same dimensions as angular momentum. A joule is a kg⋅m²/s², or as a dimension rather than units, m⋅d²/t². Multiply that by time to match Planck’s constant and it’s m⋅d²/t. Angular momentum is speed, times mass, times the distance from the central point around which angular momentum is being measured, or (d/t⋅m⋅d) which is also m⋅d²/t.

However h is defined in terms of full revolutions, and angular momentum operates in radians, so we really need h/2π, a number that turns up so often, it has it’s own symbol, ħ, pronounced “H-bar” and often known as the “reduced Planck constant.” It’s equal to 1.054571817…×10⁻³⁴ J⋅s. Or, since we are talking about atoms here, the preferred units are in terms of electron volts, so the reduced Planck constant is 6.582119569…×10⁻¹⁶ eV⋅s

So if the angular momentum of electrons in an atom were restricted to multiples of ħ, it could keep the main descriptive feature of the Rutherford model (electrons orbiting about the nucleus) while solving the problem of having them spiral into the nucleus, radiating energy all the while. The lowest possible orbit would be the one where the angular momentum was equal to ħ, the next one up (higher energy), 2ħ, and so on.

Well, it’s a fine idea, but does it actually make things look the way they really are?

Let’s work with hydrogen. One electron, one proton. No other electrons to cause complications because they repel the first electron.

Assuming a circular orbit (so that the requisite cross product becomes equal to multiplying distance by velocity), the angular momentum of the electron is going to equal its mass, times its velocity in orbit, times its distance from the nucleus:

m_evr = nħ

The n is the integer multiplier and is now known as the principal quantum number.

Well, we know one of these, the mass. But we can actually express the velocity needed to maintain a circular orbit, in terms of distance and the attractive force between the proton and the electron (which we know), so that gets us down to one unknown. And we can eventually work our way down to figuring that when n is 1, the orbital radius is 0.0529 nanometers (billionths of a meter) for a hydrogen atom (one electron orbiting one proton).

OK, so by analogy with orbital mechanics, the lowest energy orbit is indeed this n = 1 orbit. What could make the electron move out of that orbit?

The hydrogen atom could actually hit another hydrogen atom, transferring kinetic energy to the electron, enough that it could jump to n=2. Thus a hot hydrogen gas, where the kinetic energy of the atoms is higher, could result in electrons being “jumped up” to higher orbits. So, basically, heat can do it.

Or the electron could absorb a photon with enough energy to make the jump.

And if in a higher orbit, how could an electron drop? It could do so by emitting a photon. But it would be a photon that contains precisely the energy difference between the two orbits! .

Remember that E = h ν for light (that last letter being Greek “nu” not a “vee”). So if we know the energy difference, we should be able to figure out the frequency, ν of the photon, then get to its wavelength in nanometers. For wavelengths between 400 and 770 nanometers, the photon will be visible to our eyes and will have a certain exact color.

The lowest orbit has the minimum energy. Just like with astrodynamic orbits, the energy is set to zero at a distance of infinity, and becomes more and more negative the closer the orbit gets to the nucleus, so the energy of the minimum orbit (n=1) is -13.6 eV. The second orbit (n=2) is at -3.4 eV, the third (n=3) is -1.51 eV, and so on, approaching but never equaling zero. So an electron in the third orbit can shed a photon and drop all the way down from -1.51 eV to -13.6 eV, a difference of 12.1 eV. This corresponds to a wavelength of 102.57 nm. That’s an ultraviolet wavelength.

But how about dropping from n=3 to n=2? That difference is about 1.9 eV. And that corresponds to a wavelength of 656.3 nm, which is visible light.

That number no doubt leaped out at someone. And when they computed the numbers for jumping from n=4 to n=2, then n=5 to n=2, and so on, those numbers looked familiar, too.

They were the wavelengths of light in the hydrogen emission spectrum. This is known as the Balmer series, all the lines you get from dropping from some higher n down to 2.

The series of lines corresponding to dropping down to n=1 is called the Lyman series, and as previously indicated, they’re all ultraviolet.

So now we have an explanation of the hydrogen emission spectrum.

Maybe there was something “real” behind this quantum buggery!

The Bohr atom model stopped here. It explained hydrogen very well, but it couldn’t, by itself, cope with more than one electron. However its underlying principles do hold for other cases.

What Moseley had done was identify, via his X ray work, the transition down to n=1, which in heavier atoms is in the x-ray band. This gets progressively more energetic as the charge in the nucleus increases, such that one can actually tell what the nuclear charge is from the x ray wavelength. So this, too, validated the Bohr model in principle, at least insofar as the Bohr model assumes quantum effects are in play.

I’m going to carry this story through (in a grossly oversimplified way) to the present day, except I won’t delve too deeply into the quantum mechanical aspects of it–quantum theory turns out to be seriously weird but this wouldn’t begin to become apparent until about 1925. So far (as of the 1910s), this bowdlerized version where it just arbitrarily restricts what can happen in an otherwise classical physics realm was working pretty well (this is now called “old quantum theory”).

The n=1, n=2, n=3 and so on principal quantum numbers were named electron shells. It became apparent as time went on, though, that each of these shells contained subshells, according to a simple rule: The 1st shell consisted of one subshell, the second shell had two subshells, and so on. The subshells got labeled s, p, d, and f. This arose from quantum mechanical considerations.

Each subshell can only hold a certain number of electrons. An s subshell could hold 2 electrons, a p subshell 6 electrons, a d subshell 10 electrons, and an f subshell 14 electrons. We’ve never dealt with a fifth subshell, but it would probably be labeled g, with 18 electrons. Each goes up four electrons. This, too, arose from quantum mechanical considerations.

The subshells are in turn divided into orbitals holding 2 electrons each, but I won’t tread there. (And again, quantum mechanical considerations).

So, the following subshells exist: 1s, 2s, 2p, 3s, 3p, 3d, 4s, 4p, 4d, 4f, and so on.

Electrons are added to the lowest energy shell that isn’t already full. That’s whether you’re creating an ion by adding extra electrons, or just trying to get a large atom up to its normal complement.

Let’s take oxygen as an example. It has eight protons in its nucleus, it will want eight electrons in its shells.

So the first two electrons go into the 1s subshell. Then the 2s subshell gets the next two electrons. Finally, the four remaining electrons go into the 2p subshell, which could accept another two electrons if they were available.

Now let us consider iron, Z=26. The first eight electrons go like oxygen’s. The next two fill up the remainder of the 2p subshell, after which we move on to the 3s subshell, which takes two more electrons (12 so far). 3p takes up another six electrons (18 so far). You might expect that now we will move to the 3d subshell…but that turns out to be wrong. The 3d subshell’s energy is actually slightly higher than the 4s subshell, so we will fill the 4s before the 3d. Electrons 19 and 20 go into the 4s subshell, then the last six electrons do go into the 3d subshell. If we were to continue, the next subshell to fill would be the 4p subshell.

So we’re seeing at the end a sequence where we fill a 2 electron s subshell, a 10 electron d one, then a six electron p one. If we were to carry on to lead (Z=82), we’d encounter our first f subshell, 4f, right after the 6s subshell but before the 5d subshell; lead takes us into the 6p subshell.

The numbers 2, 6, 10, and 14 might be tickling your brain trying to be noticed. If not, perhaps their successive sums will: 2, 8 (2+6), 18 (2+6+10) and 32 (2+6+10+14).

These are the lengths of the rows on the periodic table. In fact, if you look at the table, the left hand side is a “tower” two elements wide–corresponding to the s subshell. The left side is a block six elements wide–corresponding to the p subshell. The central skinny part is ten elements wide, and corresponds to the d subshell. Looking at the two rows that are “footnoted” below the main body of the table, those are usually depicted as 15 units wide, but they are supposed to tuck into a square in the third column, so one of those 15 squares really belongs to the d block. The other 14 are the f subshell. (By the way, chemists argue over whether the first or last of the fifteen is the one in the d-block; they seem to have recently decided to go with the last one of the fifteen.)

So the very shape of the periodic table reflects the shells and subshells, which in turn derive from quantum principles.

The periodic table is on a firm footing now. Atomic number is on a secure footing, We now even understand those elements whose atomic weights aren’t close to integers. We just don’t know why they aren’t exact integers yet.

Obligatory PSAs and Reminders

China is Lower than Whale Shit

Remember Hong Kong!!!

中国是个混蛋 !!!
Zhōngguò shì gè hùndàn !!!
China is asshoe !!!

China is in the White House

Since Wednesday, January 20 at Noon EST, the bought-and-paid for His Fraudulency Joseph Biden has been in the White House. It’s as good as having China in the Oval Office.

Joe Biden is Asshoe

China is in the White House, because Joe Biden is in the White House, and Joe Biden is identically equal to China. China is Asshoe. Therefore, Joe Biden is Asshoe.

But of course the much more important thing to realize:

Joe Biden Didn’t Win

乔*拜登没赢 !!!
Qiáo Bài dēng méi yíng !!!
Joe Biden didn’t win !!!

Justice Must Be Done.

The prior election must be acknowledged as fraudulent, and steps must be taken to prosecute the fraudsters and restore integrity to the system.

Nothing else matters at this point. Talking about trying again in 2022 or 2024 is hopeless otherwise. Which is not to say one must never talk about this, but rather that one must account for this in ones planning; if fixing the fraud is not part of the plan, you have no plan.

The Audit

The Audit is definitely heating up. Let’s see if the Opposition manages to squelch it and its consequences. I’ll be honest; I expect it to be ignored by anyone capable of ordering Biden/Harris to step down.

Nevertheless, anything that can be done to make Biden look less legitimate is a worthy thing!

Lawyer Appeasement Section

OK now for the fine print.

This is the WQTH Daily Thread. You know the drill. There’s no Poltical correctness, but civility is a requirement. There are Important Guidelines,  here, with an addendum on 20191110.

We have a new board – called The U Tree – where people can take each other to the woodshed without fear of censorship or moderation.

And remember Wheatie’s Rules:

1. No food fights
2. No running with scissors.
3. If you bring snacks, bring enough for everyone.
4. Zeroth rule of gun safety: Don’t let the government get your guns.
5. Rule one of gun safety: The gun is always loaded.
5a. If you actually want the gun to be loaded, like because you’re checking out a bump in the night, then it’s empty.
6. Rule two of gun safety: Never point the gun at anything you’re not willing to destroy.
7. Rule three: Keep your finger off the trigger until ready to fire.
8. Rule the fourth: Be sure of your target and what is behind it.

(Hmm a few extras seem to have crept in.)

Spot (i.e., paper) Prices

Last week:

Gold $1815.20
Silver $25.56
Platinum $1053.00
Palladium $2747.00
Rhodium $19,500.00

This week, 3PM Mountain Time, markets have closed for the weekend.

Gold $1763.90
Silver $24.48
Platinum $985.00
Palladium $2712.00
Rhodium $21,150.00

Gold was up in the 1810s all week up to Friday morning, but tanked HARD on that day, down $41.20. Everything took a beating, honestly, except rhodium which went up.

Part XIII – Rutherford On A Roll

We left off, circa 1903, having discovered radioactivity and the electron, and making quite a bit of progress with them.

To try to recap (and there are a few things in this so-called “recap” that I should have mentioned earlier, but didn’t), an electron is a negatively charged particle about 1/1830th the mass of a hydrogen atom, which up to then had been the lightest thing known to exist. They could be knocked off of atoms in a Crookes tube and they would then form what was called a cathode ray (yes, the same “cathode ray” in those big tubes in those old boxy TVs). It is possible to strip one electron off a hydrogen atom, at which point the remaining piece of the hydrogen atom (called an ion) had a positive charge that balanced the electron’s negative charge. The atom as a whole was neutral, charge 0; the individual pieces also added up to 0. Even though there was plenty of mass left in the ion, easily enough for hundreds more electrons, no one could get a second electron to come out of a hydrogen atom.

Thomson, the discoverer of the electron, suggested that atoms were fairly solid spheres of positive electrical charge with little electron inclusions that could be knocked out to ionize the atom; this was called the plum pudding model of the atom.

Radioactivity had been discovered in 1896. Uranium and thorium, it turns out, are radioactive. Radioactivity turned out to consist of three types of rays, alpha, beta, and gamma.

Alpha rays turned out to be identical to doubly-ionized helium, i.e., helium from which two electrons had been stripped (and there was no sign of being able to strip away a third electron from helium). Helium itself had been discovered on Earth back in 1895, trapped in a uranium ore; its atomic mass was four times that of hydrogen. Clearly the helium had begun as alpha particles, then combined with electrons in the ore to become helium gas. The charge of an alpha particle is 2e.

Beta rays turned out to be high-speed electrons. Their charge, of course, is –e.

Gamma rays turned out to be electromagnetic radiation, extremely strong electromagnetic radiation, like X-rays on steroids. Gamma rays, like all photons, have no electrical charge at all.

Alpha rays could be stopped by a sheet of paper. Beta rays could penetrate many sheets of paper, but would be stopped by a thin sheet of metal. Gamma rays required a lot of shielding to stop.

Uranium (atomic weight ~238) and thorium (atomic weight ~232), which had just been discovered to be radioactive, were the heaviest known elements, roughly 238 and 232 times as massive, atom for atom, as hydrogen. The Curies discovered that uranium ore was four times as radioactive as the ores it contained; they were able to isolate two new elements, radium (atomic weight 226) and polonium (atomic weight 210), by processing tons of the ore pitchblende.

It was also clear that a pure block of refined uranium would grow more radioactive over time, eventually reaching a level significantly higher than before, but not nearly as high as the ores.

In radioactive decay, the total amount of energy released, relative to the mass, turned out to be staggeringly huge, thousands if not millions of times more than what was released by burning chemicals. In 1904 Ernest Rutherford (who had named the three types of radiation, and who is the star of today’s story) suggested that radioactivity could provide enough energy to power the sun for the many millions of years necessary for Darwinian evolution to take place. (Previously known sources of energy were woefully inadequate; it was one of the 1895 mysteries I listed.)

At the time atomic weight was considered to be a defining characteristic of an element. This would cause some confusion for a few years.

Some stuff I should have covered previously, but didn’t:

The electric charge of an electron is about -1.602 x 10^-19 coulombs. This is a negative number (because Benjamin Franklin arbitrarily picked one kind of charge to be positive and the other negative, and when the electron was discovered, it happened to be the one he tagged as negative), so, perhaps a bit counterintuitively, physicists define the minimum charge e to be +1.602 x 10^-19 coulombs, i.e., -1 times the charge of an electron. Physicists, in fact, find it far more convenient to use e as the unit of electric charge when talking about atoms, that way they don’t have to sling 10^-19s everywhere.

And they do something similar for energy. Just like a falling weight generates kinetic energy (a mass being attracted to another mass by gravity, speeds up that mass), an electron responding to one volt of electrical potential generates a certain amount of energy, which is defined to be an “electron volt.” This is abbreviated eV (which spell checkers will try to “fix” the capitalization of). This ends up being 1.602 x 10^-19 joules. (Notice it’s the same factor, 1.602 x 10^-19. This is a consequence of the way the joule, coulomb, and volt are defined.) Energy at the atomic level, particularly when dealing with chemical energy, tends to be a convenient, human-relatable number of electron volts.

And a reminder: An atomic mass unit was defined, in 1898, as 1/16th the mass of an oxygen molecule. This was very close to the mass of a hydrogen atom, but because oxygen reacted with more things, it was easier to use it as a yardstick. [This definition has since been modified, for reasons I’ll explain below.] It was equal to 1.6604675209 x 10^-27 kilograms. (This is slightly different from today’s value.) It was abbreviated “amu.” Atomic weights were expressed in amu’s, so oxygen’s atomic weight was 16.0000, and hydrogen’s was almost exactly 1.0: In 1949, under this definition, it was measured at 1.008 amu. (At least, according to a 1951-52 CRC handbook–well, it’s a book that fits King Kong’s hand–that I happen to own.)

OK, so that, I believe, catches us up.

A Plethora of Radioactive Elements?

Scientists continued to investigate radioactivity. They would find more and more elements, distinguished by their atomic masses, in both uranium and thorium ores.

Even as early as 1900-1903 Rutherford was involved in this effort. Looking at thorium “emanations” with his student Frederick Soddy, they discovered thorium x and a gas, thoron. At first they thought these were special forms of thorium, but then they realized these were not thorium. By 1903 they had concluded that these emanations were the result of thorium changing into another element. This was a very bold conclusion, since chemists up to now had believed elements were immutable, that such things were alchemist balogna. (And under normal circumstances this was true…but radioactivity was something fundamentally new, and certainly nothing like what the alchemists had thought of.)

So perhaps these new elements could fill in the large gap between bismuth and thorium in the periodic table? Well, they could, but it turned out that in fact, there were way too many of them. Realistically between lead and uranium there was room for nine elements, and we already had five of them: bismuth, polonium, radium, radon (which was basically the thoron gas) and thorium. But just in uranium ore there seemed to be about thirty of them (based on my count looking at a chart in Wikipoo–perhaps they had found fewer than that before they figured out what was actually going on). Thorium ores brought in another ten or so.

But it was very, very difficult to separate out these putative elements. For instance Soddy in 1910 showed that mesothorium, atomic weight 228, radium, atomic weight 226, and thorium X, atomic weight 224, were impossible to separate chemically, as if they were the same element. But how could that be so when the atomic weights were different? Trying to place these elements in the table led Soddy and Kazimierz Fajans to independently come up with the notion of radioactive displacement in 1913. Basically, this stated that an alpha decay reduced an atom’s mass by about four amu (the mass of the alpha particle), and also moved it two places to the left on the periodic table. (If such a thing were to happen to (say) nickel, it would become iron, which is two spots to the left of nickel. But it won’t.) A beta decay left the mass almost unchanged (the mass of the electron that gets kicked out is relatively insignificant), but moved the element one place to the right. (If an atom of palladium were to undergo a beta decay, it would become silver. This has happened under very special circumstances, ones that won’t affect the palladium bullion I hope you own.) Gamma decay had no such effect; apparently it was just a way to get rid of energy.

For this work Rutherford won the 1908 Nobel Prize for Physics.

But he hadn’t even got started yet.

The Isotope

Now if one used the radioactive displacement principle, it appeared that two or more different “elements” could occupy the same place on the periodic table. The three I named above all fit in the same square, directly under barium. Because they occupied the same place, they were termed isotopes, from Greek for “the same place.”

So you had “elements” of different mass that otherwise behaved identically. At this point chemists decided that the mass wasn’t as important as the behavior, and swallowed the concept of two different atomic weights representing the same element, rather than insisting they must be different elements solely because of different atomic weights. Atomic weight wasn’t necessarily a crucial characteristic of an element, particularly when it came to ones extracted from radioactive ones.

In 1912, meanwhile, J. J. Thomson, who had discovered the electron in 1897 (with some help from Rutherford, it turns out) wasn’t done yet, had ionized neon (which was the tenth element listed on the periodic table at the time) in a Crookes tube and magnetically and electrically deflected its ions, the same way that he had deflected electrons in 1897, to determine the ions’ charge to mass ratio. He was quite surprised to see these ions, which should have weighed in at about 21.18 amus, went to two different locations! Some were deflecting more than others, because they were lighter than those others.

Assuming that they were singly ionized, with one electron removed (it takes a lot more energy to take the second electron off than it did the first), one group of ions had an atomic weight of almost exactly 20, the other had an atomic weight of almost exactly 22. The atomic weight of neon had been measured as 20.179, which made it one of those cases where the atomic weight was not almost a whole number, but now it looked like that was actually an average value. Most neon had atomic weight of almost exactly 20, but some came in at about 22, and the weighted (ahem) average was 20.179.

So now, even perfectly ordinary stable elements had isotopes, and this time no one thought these must be two different elements because the weights are different. In modern terms neon consists of a mix of neon-20 and neon-22.

I have mentioned in the past that many elements had “atomic weights” or “atomic masses” that were almost a perfect multiple of hydrogen’s. These mostly turn out to be elements with exactly one isotope in nature, or perhaps more than one isotope but one of them is much, much more common than the other(s).

Hydrogen, it turns out, has two isotopes found in nature, hydrogen-1 and hydrogen-2. Hydrogen-1 is overwhelmingly common, hydrogen-2 is rare, a bit more than one atom in ten thousand hydrogen atoms is hydrogen-2.

For various reasons, the isotopes of hydrogen actually ended up with “real” names–not true for any other element! Hydrogen-1 is called protium and hydrogen-2 is called deuterium.

The actual atomic mass of hydrogen is a bit higher than the atomic weight of pure protium expressed in kilograms, because the tiny amount of deuterium pulls the average up.

If, in an alternate universe, the atomic mass unit had been defined differently so that hydrogen–mixed hydrogen–got an atomic mass of 1 unit, this would actually have been slightly higher than the atomic mass of pure protium, because the occasional deuterium atom pulls the average up.

But in the real world, the atomic mass unit was defined to be 1/16th the atomic weight of oxygen. So oxygen was 16.0000 by definition. Hydrogen ended up being a hair more than 1.008. Could the excess be due to the deuterium? Not so fast. Oxygen, it turned out in 1919, consists of three isotopes. Oxygen-16 is overwhelmingly more common than oxygen-17 and oxygen-18. But even if you set pure oxygen-16’s atomic weight to 16.00 by definition, and then look at the atomic weight of pure protium, pure protium doesn’t come in at precisely 1.000. There’s still this slight tendency to be off just a bit from integers. At the time no one knew why, but they knew about it well enough to talk about a mass defect. But at least now, we understood the elements that were way off from being whole integer atomic weights–they were mixtures of isotopes. So this is a partial answer to one of our mysteries.

Physicists often discussed different isotopes of the same element. Chemists rarely did back then. Physicists used the whole number to label them, rather than the exact number. This whole number was termed the “mass number” and had the symbol A (from German Atomgewicht). I’ve been using these mass numbers a lot so far, and will continue to do so.

So we have three things with similar-sounding names. There’s the atomic mass unit (amu), almost (but not quite) equal to the mass of a hydrogen atom. There’s an atomic weight, measured in atomic mass units, which represents the mass of the atom. But there is also a mass number, which is a rounded version of the atomic weight, for a specific isotope. Hydrogen’s atomic weight is 1.0008, but the mass number of its most common isotope was just simply 1. When doing ordinary chemistry weighing out reactants the atomic weight is used to compute the number of moles of each reactant. When talking about isotopes, the mass number is used, without fail.

(Looking ahead a little: In the 1920s physicists began using a physical atomic mass unit, that really was based on oxygen-16 rather than mixed oxygen. To distinguish it from the other one, the prior one was called the chemical atomic mass unit–which the chemists kept on using. And then it turned out that oxygen obtained from water had a slightly different isotope mixture and hence real atomic weight, than oxygen extracted from the air. So the chemists’ unit was based on a foundation of quicksand. But even using the physical amu, the atomic weight of a pure isotope was still never a clean, perfect integer, except for oxygen-16.

(But now we had two slightly different units with very similar names. In 1961 they compromised, and created the “unified atomic mass unit” (symbol u, also called the dalton, symbol Da) that was 1/12th of the mass of a carbon-12 atom. This was closer to the chemists’ standard than to the physicists’.

(No matter what standard was chosen, however, the only isotope that had a perfect integer mass was the reference isotope. All others were off, just a bit.

(But that was all in the future. Let’s return to our story, back to 1912.)

The Nucleus

Backing up just a couple of years from there, there had been another very important discovery in 1909 by Ernest Rutherford. He was collaborating with Hans Geiger (who is definitely a counter) and Ernest Marsden.

They used a beam of alpha rays (which, as a reminder, are heavy and positively charged) to bombard a very thin layer of gold foil. They were pretty much expecting those alpha particles to plow through the “plum pudding” atoms. Instead, though most indeed cruised right through the gold atoms as if nothing were there, a very few of them bounced away at sharp angles, repelled by an intense and concentrated positive charge. Some even bounced back towards the beam source! Rutherford said, in a very famous quote: “It was quite the most incredible event that has ever happened to me in my life. It was almost as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you.”

In 1911 Rutherford argued that those alpha particles were bouncing off an atomic nucleus. This meant that an atom consisted almost entirely of empty space. All of that positive charge (and almost all of the mass of the atom) was in a tiny, tiny, very dense body about 1/10,000th the width of the atom; the rest of the space was the domain of the electrons, which orbited the nucleus much like planets orbit the sun, except in this case the attractive force wasn’t gravity, but the attraction between the positively charged nucleus and the negatively charged electrons. This was a new model of the atom, called the “Rutherford Model.” Rutherford is credited with discovering the atomic nucleus.

And in fact that number understates things; according to modern measurements entire atoms can be anywhere from 26,000 to 60,000 times as wide as their nuclei. Which works to to be anywhere from 17.6 – 216 trillion times the volume.

Atomic Number

Later that year, Antonius van den Broek proposed that the sequential location of each element in the periodic table was equal to its nuclear charge, this charge (in units of e) was the atom’s atomic number. This fit well for hydrogen, which could only have one electron stripped off, leaving a +1e charged nucleus behind. And for helium, which could be ionized twice leaving a +2e charged nucleus behind. They were the first and second elements listed in the table. However, we couldn’t strip every atom down to a bare nucleus to see its charge; the heavier the atom the harder it was to do that.

This was a new concept. Chemists had talked about the atomic weight of an atom, never its number. You could list the elements in the order they appeared in the periodic table, of course (accounting for the very few unfilled “holes” in the grid), but the place on the list wasn’t considered terribly significant. But now it appeared as if charges came in discrete quantities, and given that one could only remove one electron from a hydrogen atom, and two from the atom with the next higher weight, the implication was that this nucleus had a specific charge, an integer multiple of the charge of an electron (but with the opposite sign). So hydrogen’s atomic number was 1, helium’s was 2. Lithium’s was 3. And so on, through carbon (6), oxygen (8), aluminum (13), iron (26), zinc (30), rhodium (45), silver (47), tin (50), platinum (78), gold (79), lead (82), thorium (90), and uranium (92), to give some examples. (However the exact numbers for anything above the upper fifties really weren’t certain at this point.)

This was only a suggestion…until about two years later. I will pick that story up next time, because it actually ties in more with electrons, and this week I want to concentrate on the nucleus. Suffice it for now to say that van den Broek was absolutely right. I’m going to reference the concept of atomic number, abbreviated Z (from German Zahl, ‘number’), from here forward.

The Proton

So, let’s continue Rutherford’s story. In 1917 he ran some more experiments. He fired alpha beams into air (which is mostly nitrogen), and detected hydrogen ions. After refining his experiment, he realized that the alpha particles were reacting with the nitrogen. When he reported his results in 1919, he claimed that the alpha particle had simply knocked a hydrogen nucleus out of a nitrogen nucleus, reducing the nitrogen nucleus’ charge (and atomic number) and weight by one and thereby turning it into carbon. Nitrogen-14 was seemingly becoming carbon-13, a rare (but stable) isotope of carbon, which is mostly carbon-12.

But by then we had cloud chambers and could see some forms of radioactivity and ions leaving trails through the chamber. In 1925, Rutherford examined some cloud chamber tracks of this reaction, and he realized he was totally wrong about what was happening. The alpha particle wasn’t bouncing off the nitrogen nucleus after knocking one proton out of it. No, it was disappearing. What was in fact happening was the nitrogen nucleus, 7 positive charges, total mass 14, was absorbing the alpha particle.

I mentioned, up above, the principle of radioactive displacement. An atom, spitting out an alpha particle moves two places to the left on the periodic table. That means its atomic number decreases by two. The atomic mass drops by four.

Absorbing an alpha particle has exactly the opposite effect. The atomic number increases by two, and the atomic mass increases by four. So the nitrogen-14 was becoming fluorine-18.

Immediately upon becoming fluorine-18, the nucleus then shed a proton, which was the hydrogen ion that Rutherford saw. This turned it into oxygen-17, stable but uncommon (most oxygen being oxygen-16).

But in the meantime, people had decided that that hydrogen nucleus was a basic particle, and it was named the proton. It’s regarded as having been discovered in 1919, since that was the first time it was seen to exist having come from some source other than hydrogen gas. or in 1920 when someone suggested it might be an elementary particle. Rutherford, as the discoverer, got to name it.

William Prout, clear back in 1815, had suggested that the other elements might be built up, somehow, from hydrogen, and now it looked like he was at least partly right. Hydrogen indeed consisted of a single proton, mass 1, and an electron, and other elements apparently had 2, 3, 4 or more protons, all the way up to uranium with 92 of them–each with a matching electron. You couldn’t just bundle hydrogen atoms together to get other kinds of atoms, but conceivably, if you separated the electrons and protons, then combined the protons, and put the electrons back in place, you could get larger atoms.

In fact, Rutherford had suggested both the name “proton” and the name “prouton” for this particle, the latter to honor Prout. (The English would have pronounced “prouton” as if it rhymed with “grout on”, and the French would have made it rhyme with “crouton” so we dodged a bullet of linguistic confusion there.)

The proton’s mass is 1.007 amus (using the modern AMU scale). Again, maddeningly close to a whole number. But because of this, the proton looked like the underpinning for atomic number but it couldn’t be the underpinning of atomic mass. That’s because, to take an example, oxygen’s nucleus has eight protons in it, but a mass of sixteen, twice as much as the protons. Uranium is even more out of whack. It has 92 protons, but its most common isotope has a mass of 238, leaving 146 mass units unaccounted for! Why? We didn’t know, yet.

In 1920, Rutherford voiced a suggestion. He thought that the excess mass consisted of a number of protons and electron pairs, bound to each other to make a net neutral bundle. So an oxygen-16 nucleus actually contained sixteen protons, but eight of them were bundled with, and masked by, electrons. The net positive charge is eight, and that’s critical because it requires eight orbiting electrons to balance out, and those eight orbiting electrons are responsible for oxygen’s chemical properties. So the chemical nature of an atom ultimately depended on the number of protons not in these bundles.

This actually made quite a bit of sense. Remember beta decay? This is where a nucleus can spit out an electron. The electron has a single negative charge. In order to make up for that loss, the nucleus has to gain a positive charge; it’s as if a new proton were appearing. But if Rutherford’s idea were correct, rather than a proton and an electron being magically created, one of these bound pairs was breaking apart, freeing the electron and unmasking the hidden proton.

Another thing arguing in Rutherford’s favor was the fact that whatever-it-is that was left over in the nucleus had a mass that was nearly that of a whole number of protons; it would make sense for the missing ingredient to be that number of “masked” protons.

Physicists would spend the 1920s thinking that the nucleus consisted of a number of protons equal to the mass number A, plus a bunch of nuclear electrons, which left a net number of “unmasked” protons equal to Z. With some mysterious “mass defect” making the total mass slightly off.

But there were some theoretical difficulties with this…which I will take up in a future installment.

Who Cares About Isotopes?

Until late in the last century, chemists almost never concerned themselves with differing isotopes. That’s because oxygen-16’s chemical behavior is nearly indistinguishable from oxygen-17’s. Because the oxygen-17 is a bit heavier, it’s perhaps a tiny bit slower to react than oxygen-16, but not much. If you were to liquefy oxygen-16 and oxygen-17, then measure their boiling points, the oxygen-17 would require a slightly higher temperature to boil, because it would take just a little bit more energy to kick those heavier oxygen-17 atoms into vapor. Melting and boiling points are in fact the biggest difference a chemist might see…if he had separated samples to work with in the first place. And chemical means of separation were simply untenable; they were too much alike.

Water made with oxygen-17 and oxygen-18 evaporates a bit less readily than water with oxygen-16, so rainwater tends to be slightly richer in oxygen-16 than seawater (and this is part of the reason we had to stop defining the atomic mass unit as 1/16th of mixed oxygen–the mix could differ depending on where you got the oxygen from).

The chemical differences between protium (hydrogen-1) and deuterium (hydrogen-2) are actually significant, due to the fact that proportionally, the difference is greater than for any other pair of isotopes. Water made out of deuterium (“heavy water”) instead of protium actually melts at 4C, rather than 0C. I’ve seen a video of a heavy water ice cube sunk to the bottom of a glass of cold (regular) water. It’s not going to melt as long as that water is properly chilled. Note that I said the bottom of a glass of cold water. It doesn’t float because it’s heavier than regular ice and heavier even than regular water. (Now, if it were in a glass of heavy water, it would float.)

And of course, heavy water, because of its significantly different chemical behavior, is toxic when pure.

Other than that, for “traditional” chemistry, isotopes just didn’t matter.

Today things are a bit different. Mass spectrometers–which are the descendant of Crookes tubes, designed to ionize, accelerate, and deflect atoms and molecules to see how much they deflect and thus figure out the masses–are relatively cheap, and they can read out absolute numbers of “hits” at each possible mass. So one can run a sample of water through one of these and get a very precise notion of the isotopic composition. Now, you can tell whether a sample of water was rain water or ground water. Or you can analyze a sample of metal and be able to tell where it was mined, because it turns out each mine has a slightly different isotopic mix of the metal. Or one can prove that CO₂ was added to champagne artificially, because the CO₂ used has no carbon-14 in it (whereas the carbon dioxide in fermentation does).

Incidentally, if you’ve ever had TSA swab your luggage then stuff the swab into a machine which tells them you aren’t carrying explosives–that device is a mass spectrometer.

That’s today. But back in 1910, chemists didn’t give a rip about isotopes. Physicists studying radioactivity, on the other hand, knew that “which isotope is this?” could make all the difference in the world. And that’s even more true today too, now that we can artificially make all sorts of radioactive isotopes that don’t exist in nature. We now have to concern ourselves with radioactive hydrogen-3 (“tritium”), cesium-137, iodine-131 and strontium-90…and these were elements that were never radioactive in the days of the Model T and the Wright Flyer.

In 1910 we were just starting down this road. Remember, Rutherford had made fluorine-18 and oxygen-17 artificially.

Decay Chains

Keep this in mind as we go back now to uranium (atomic number Z=92) and thorium (Z=90). Remember that whole process of figuring out the pieces of an atom started in part because of the discovery of radioactivity, a property of these two elements in particular.

At the time of today’s story, had become quite clear that when there was radioactivity, one kind of atom was changing into another, this is called “decay.”

Uranium and thorium decay very slowly, or I should say, uranium-235, uranium-238, and thorium-232 decay very slowly (as I said, the isotope matters). It’s a statistical process. When you are looking at one uranium-235 atom, it could decay a second from now…or it could wait a billion years. There’s no way to know when it will happen, but it’s almost a stable nucleus; it’s very, very unlikely to blow in the next second. And if that atom is still around in a billion years, someone watching it then is just as unlikely to see it go kablooey in the next second as you are today.

I’m going to get on a soap box here, for just a minute. Let’s say you watch someone flip a coin 20 times and it comes up tails each time. Do you think, “wow, it’s overdue to come up heads, I’ll bet it comes up heads next time?” If so, you have a “naive” view of probability. The more sophisticated view is that, since the tosses are independent events they aren’t affected by each other. The chance is 50/50 of heads next time, no matter how many times in a row it has come up tails just now. But then, there is the cynic’s view. He doesn’t believe the odds are fifty/fifty either. But he doesn’t figure it’s overdue to come up heads; he figures the coin probably is crooked; perhaps tails on both sides! And he might have a point there. The smart bet, if you’re not allowed to examine the coin, is probably to bet on “tails.” But, if the coin really is fair, the 50/50 view is correct.

Similarly, for the chances of an unstable nucleus going kablooey in the next second, or minute. A billion years from now, provided your unstable nucleus hasn’t gone kablooey in the meantime and it’s still around, it’s just as likely to not go kablooey in the next second, as it is to not go kablooey in the next second today.

At an individual atom level, radioactivity isn’t predictable. But, if you take a large number of atoms of one of these three isotopes (or of any unstable isotope for that matter), you can make some predictions.

You can say, for instance, that any large sample of uranium-235 will be half gone in about 700 million years. Half of the atoms (no way to predict beforehand which specific ones) will have decayed to something else. Does that mean that the other half will decay in another 700 million years? Absolutely not. If you start with a pound sample of uranium-235, after 700 million years, you now have a half-pound sample of uranium-235, now mixed in with a bunch of impurities to be sure, but a half pound sample nonetheless, and half of that sample will decay in the next 700 million years.

700 million years is the half life of uranium-235. Similarly, uranium-238 has a 4.5 billion year half life, and thorium-232 comes in at 14 billion years.

You get one guess as to who discovered the concept of a half life in 1907. I’ll give you a tiny hint: He did it using one of the short-lived isotopes in the thorium decay chain, one that was deposited by decaying radon gas.

Thorium-232’s half life is about three times that of uranium-238. As you can imagine, given a godzillion uranium-238 atoms, and a godzillion thorium-232 atoms, you’ll see three times as many decays in a day from the uranium as from the thorium. But it also scales by quantity; two godzillion thorium-232 atoms will produce twice as many decays in a day as one godzillion will. And three godzillion thorium-232 atoms will produce as many decays in a day as one godzillion uranium-238 atoms. Keep this in mind–the ratio of the half lives is same as the ratio of quantity, for the same number of decays to occur from samples of two different isotopes.

[A “godzillion” is a highly technical word someone made up once for a really large number. He used it to describe the national debt when it was a lot smaller than it is now. However, even today’s national debt pales next to the number of atoms in a mole (which would be 600 sextillion or so). I decided to adapt the term rather than just say “zillions” or “jillions.”]

When an atom of (say) thorium spits out an alpha particle, it actually changes to another element and another isotope; it is decaying. If the new isotope is also unstable, it too will decay, again and again until the result is a stable nucleus. Eventually the starting thorium-232 nucleus will have become a lead-208 nucleus.

OK, with thorium being Z=90 and lead being Z=82, we can do a little bit of accounting-style sleuthing. The difference between these two masses–the change in A–is 24. That’s the equivalent of six alpha particles. In fact, since the only mode of decay that changes an atomic weight is alpha decay, we expect exactly six alpha decays to occur during this process.

But going from thorium to lead would involve changing Z by eight, which is something you’d get from four alpha decays at two apiece. Six alpha decays, absolutely required by the mass change, give you a reduction of Z by 12, and so it looks like you’d end not with lead-208 but rather platinum-208 (which if it even exists, surely isn’t stable).

Beta decays come to the rescue. They move you one element to the right, without changing the mass. So if you figure that the total number of alpha decays is six, reducing Z by 12, but then throw four beta decays into the mix, increasing Z by four, it balances; the net reduction of Z is 8. The total set of reactions boils down to:

Thorium-232 (Z=90, A=232) – 6 alphas (Z=12, A=24) – 4 betas (Z=-4, A=0) = Lead-208 (Z=82, A=208).

(Remember when subtracting the four betas, you are subtracting a negative number, which means to add the opposite positive number.)

If you look at the detailed sequence of events, this is exactly what happens. Thorium-232 decays by alpha particle to radium 228 (Z=88, A=228 one alpha decay so far). Radium-228 then undergoes a beta decay to get actinium-228 (Z=89, A=228, alpha, one beta so far). Actinium-228 undergoes another beta decay to get thorium-228 (Z=90, A=228; one alpha, two betas so far).

Let’s pause here to look at the half lives. The original thorium-232 has a fourteen billion year half life. That means that (on a percentage basis) very, very little of it decays in (say) one day. The radium-228 has a 5.7 year half life. The actinium-228 has a 6.1 hour half life. The thorium-228 has a … wait for it! … 1.9 year half life. (It’s thorium, but it’s not thorium-232 and that makes all the difference in the world when it comes to half lives.)

If you started with a pure thorium-232 sample and waited about ten years, a certain amount of radium-228 has accumulated. As it accumulates, you can detect more and more decays of it (because there is more and more of it over time. But it won’t accumulate forever: It turns out that after a few years of building up, there’s now enough of it that it’s decaying about as fast as it’s being created. So you should be able to see based on our discussion above that, given thorium-232’s half life is three billion times as long as radium-228’s, when there is one radium-228 atom for every three billion thorium-232 atoms, then they’ll both produce the same number of decays. But the radium-228 doesn’t go away, because it’s being replenished by the thorium-232 decays. Since the amount isn’t changing over time the radium-228 is in equilibrium with the thorium-232. (The thorium-232 is slowly going away, of course, as it does so it will produce slightly less radium-228 during a given time, so the radium-228 will decline at the same percentage rate. But people don’t live long enough to see this happen, not with a 14 billion year half life!) Equilibrium is reached in something like 1 1/2 or two half lives of the daughter isotope.

Similarly for the actinium-228–because it has a much shorter half life than radium-228, it reaches equilibrium with the radium-228 almost instantly. And so on down the chain. Once everything is at equilibrium, there is one decay of each daughter isotope, for each decay of a thorium-232 atom. This is why a “pure” sample of thorium actually grows more radioactive right after it’s made.

So back to that chain. It continues. Thorium-228 alpha decays to radium-224 (Z=88, A=224, two alphas, two betas so far). Radium-224 alpha decays to radon-220 (Z=86, A=220, three alphas, two betas so far). Radon-220 alpha decays to polonium-216 (Z=84, A=216, four alphas, two betas so far). Polonium-216 alpha decays to lead-212 (Z=82, A=212, now five alphas and two betas so far).

Lead-212 is lead, and lead dug out of the ground is stable, but lead-212 is not stable. It’s an unstable isotope, a very unstable one in fact. Its half life is 10.6 minutes.

The next step is a beta decay, lead-212 becomes bismuth-212 (Z=93, A=212, five alphas, three betas). We now have just one alpha and one beta decay left to get to lead-208. But now, the path splits. We can either do the alpha decay first then the beta decay (thallium-208 (Z=81), then lead-208) or the other way round (polonium-212 (Z=84), then lead-208).

All of these decays from thorium-228 onwards have half lives of days or less, one even has a half life of less than a millionth of a second. So once the thorium-228 reaches equilibrium with its great-grandparent thorium-232, the rest of the chain ends up in equilibrium in just a few days.

The diagram below summarizes this whole process. And it uses a notation I haven’t used yet. So far when I’ve named an isotope, I’ve done it as [element name]-[mass number]. But you can also use a superscript before the element symbol like this: ²³²Th. Superscripting is a bit of a pain in the ass in the WordPus editor (and besides you might not know all the symbols), so I didn’t do it this way. It can even be taken a step further (and is, in the diagram below). You can put the atomic number Z as a subscript before the symbol, like this: ₉₀Th. (Or you can do both. And I do mean you can do both. I can’t. If I try, I get something like this: ²³²₉₀Th. I can’t get the super and subscripts one over the other.)

Technically the atomic number is superfluous, thorium is by definition atomic number Z=90. But it’s helpful for all the non-geeks out there who don’t have the numbers memorized.

(Even chemists don’t usually know all of the atomic numbers, nor do they know all of the symbols; I watched one give a lecture on this very sort of thing, and when he showed the symbol Pa, he called it “palladium” (it’s actually protactinium, atomic number Z=91; palladium’s symbol is Pd and its atomic number is Z=46 and its price is almost three thousand dollars an ounce. The symbol was right, his verbal reading was wrong). Chemists will know the common elements like sulfur (16, S), plus ones they themselves are personally working with…unless they’re complete geeks, in which case they’ve memorized them all. By the way, if you ever run into someone claiming to be an organic chemist and they don’t know that carbon’s atomic number is Z=6, he’s a faker. Actually, he’s a lying sack of bearded dragon shit. Run, do not walk, away, from this person, and do not believe him if he tells you that the sky is blue; don’t even believe him if he says that Joe Biden lost.)

One last thing to note about the thorium decay series. Every single isotope on it has a mass number A that divides by four. The starting number divides by four, and any time the mass number changes, it changes by four, so it will always be divisible by four.

The other two decay series have uranium in them. Uranium has two long-lived isotopes, and they are each at the beginning of their own decay chains. You can walk through them if you so desire, but I’m just going to put up the diagrams. The first is the “Uranium decay series” starting with uranium-238:

Every one of these isotopes’ mass numbers, when divided by four, leaves a remainder of 2. Therefore, none of these isotopes appears in the thorium decay series, and none of these appear there either. Never the twain shall meet.

Note that one of the intermediates is uranium-234 with 245,000 year half life. If you (personally) start out with pure uranium-238, you won’t live long enough to see it come into equilibrium with its daughter isotopes, because uranium-234 decays too slowly. Over about the next half million years, ²³⁴U will build up in the sample and then be in equilibrium. Everything downstream from it is much faster. You will see, rather quickly, the intermediate thorium and protactinium 234 isotopes reach equilibrium, though.

The uranium-235 series is actually called the “actinium decay series” to avoid confusion with the other uranium decay series. It includes the longest-lived actinium isotope, actinium-227.

All of these isotope mass numbers, when divided by four, leave a remainder of 3. They therefore won’t appear in either of the first two series, or vice versa.

There ought to be a fourth series, one where all the mass numbers leave a remainder of one when divided by four. Right?

Well, there was. A long time ago. The problem is no isotope in that series (which we can reconstruct today since we can make artificial isotopes) has more than a 2,140,000 year half life. That’s much shorter than the uranium and thorium isotopes in the other series. That isotope is neptunium-237 (Z=93). One of its daughters is uranium-233, with a half life of 159,200 years. Everything else in that series is shorter, much shorter.

If there was any neptunium-237 on earth when it first formed, ten half lives (21.4 million years) would have reduced it to 1/1024th of its original amount. Another ten half lives would have reduced it to less than a thousandth of a thousandth, or less than a millionth of the original amount. A total of eighty half lives would be enough to reduce an entire mole of neptunium to less than one atom on average, an undetectably small concentration, especially since the neptunium probably started out as a minor constituent of whatever rock it was in, to begin with. (Realistically, fifty half lives is probably enough to escape detection by modern equipment.) Seventy half lives is about 170 million years.

There was either never any neptunium-237 when the earth formed, or the earth is at least 170 million years old. In fact, there are a lot of isotopes with even longer half lives (like plutonium-244, half life roughly 80 million years) that do not exist in nature, and the same logic applies: either that isotope was never around, or the earth is hundreds of millions of years old, or even older–plutonium-244’s absence implies billions of years.

Returning to the “neptunium decay series,” because it has no sufficiently long lived isotope, it is extinct. When we started making isotopes artificially, we eventually found neptunium-237, and uranium-233, and all the others, and could then figure out what the neptunium decay series looked like. But back in the 1910s, this was all well in the future.

[Actually, oddball nuclear reactions sometimes create a trace of these isotopes in uranium ore, but that’s an almost immeasurable trace, and clearly not remnants of an original stock.]

The second to last product of the neptunium decay series is bismuth-209. It was long thought to be a stable isotope, but fairly recently it was discovered to have a half life of 19 quintillion years-almost a million years for every dollar of our national debt. It is so weakly radioactive that it might as well be stable, and its radioactivity is consequently almost impossible to measure. When it bestirs itself to do so, it decays to thallium-205, which is unfortunately quite stable. I say unfortunately, because thallium is extremely toxic. There is actually plenty of thallium-205 out there already, but it has to almost all be original or primordial stock, because hardly any bismuth-209 has decayed in a mere few billions of years.

Summing it up

Radioactivity was discovered in 1896. At that time, the words electron and proton didn’t exist. Atoms were indivisible things. Twenty years later, we knew that last bit was wrong, and we were well on our way to knowing the real nature of matter. In large part thanks to Ernest Rutherford.

OK. Next time, we take one step out, back into the realm of the electrons.

Obligatory PSAs and Reminders

China is Lower than Whale Shit

Remember Hong Kong!!!

中国是个混蛋 !!!
Zhōngguò shì gè hùndàn !!!
China is asshoe !!!

China is in the White House

Since Wednesday, January 20 at Noon EST, the bought-and-paid for His Fraudulency Joseph Biden has been in the White House. It’s as good as having China in the Oval Office.

Joe Biden is Asshoe

China is in the White House, because Joe Biden is in the White House, and Joe Biden is identically equal to China. China is Asshoe. Therefore, Joe Biden is Asshoe.

But of course the much more important thing to realize:

Joe Biden Didn’t Win

乔*拜登没赢 !!!
Qiáo Bài dēng méi yíng !!!
Joe Biden didn’t win !!!