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 !!!

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 !!!