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.

https://www.youtube.com/watch?v=citY6G8ePJw

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 !!!