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 $1808.90
Silver $26.19
Platinum $1105
Palladium $2903
Rhodium $18,500

This week, markets closed as of 3PM MT.

Gold $1812.20
Silver $25.74
Platinum $1105.00
Palladium $2712.00
Rhodium $20,100.00

Not much action this week, other than palladium taking a beating and rhodium staging a partial recovery.

(Update: Real gold can now be had for $125 over paper gold spot prices at places like Kitco. If you arent too fussy about branding you could get even lower (however, you’ll end up selling for less at the other end of the pipe).)

1905 – Quadruple BOOM!!!
(Part XI of a Long Series)

Introduction

Let us start off by recapping our list of mysteries and conservation laws.

1. Conservation of mass
2. Conservation of momentum
3. Conservation of energy
4. Conservation of electric charge
5. Conservation of angular momentum

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?

I’ve crossed off #5 because J. J. Thomson’s discovery of the electron answered that question.

Because of Max Planck’s work, we had something that might answer #9, depending on how real energy “quanta” were. So I’ll leave that un-crossed-out for now.

And thanks to the discovery of radioactivity we had a hint of a sort of thing that might explain #3. But that’s a lot more tenuous than even Planck’s hypothesis.

With that reminder in place, 1905 saw the publication of four very important papers.

1 – Brownian Motion.

Brownian motion is the jiggling around of bacteria or specks of pollen when looking at them in a drop of water, under a microscope.

This paper used statistical mechanics to come up with a model for how often molecules of water might just happen to “kick” a small object suspended in the water. Statistical mechanics assumes that molecules in a fluid (gas or liquid) will have an average momentum with the particles distributed around that average. Max Planck (and many others) considered it a bit suspect, but today we know it to be the underpinning of thermodynamics. Planck, as we saw in Part X, had found that statistical mechanics could provide a model that would explain the blackbody curve (the Maxwell – Boltzmann distribution). By assuming that atoms could only emit energy in discrete packets, the amount of energy depending on the frequency, he was able to match the curve.

Anyhow, this paper showed that if water consisted of molecules, actual molecules, not just a convenient construct, and statistical mechanics were true, then Browning motion was explained. It had been one of those minor mysteries up until then (one which I didn’t even put in my list, but, let’s face it, I should have).

So now we have a paper showing that Brownian motion is actually hard evidence that atoms and molecules exist, rather than just being a convenient mental “crutch” to understand chemistry. And the position of statistical mechanics is much more solid.

So the last holdouts who didn’t believe atoms were real were finally convinced as this paper made the rounds.

BOOM!!!

2 – Photoelectric Effect

In Part 8, I described how Heinrich Hertz was able to produce, and prove the existence of radio waves. However, he had died in 1894 leaving a bit of a puzzle behind, the photoelectric effect (item 8 on our list of mysteries). Sparks would jump a gap more easily, if ultraviolet light were hitting the gap. Even dim ultraviolet light would have some effect. But lower frequency/longer wavelength light would do absolutely nothing no matter how bright it was.

What turning up the ultraviolet intensity did do, however was cause more electrons to jump the gap, resulting in a bigger spark.

So the frequency had to be high to enable the spark jumping in the first place; if enabled, the intensity was proportional to how big the spark was. If not enabled, no spark, no matter what.

Recall that with a wave, the energy in the wave is in the amplitude, in other words, the intensity of the wave, not its frequency. And Maxwell had pretty much demonstrated to everyone’s satisfaction that light is a wave. Newton had thought it was a particle but between Maxwell and certain earlier investigators who got light to diffract and generate interference patterns (and even measured the frequency of some forms of light), the particle hypothesis looked to be deader than Hitlary Klinton’s conscience.

But this paper begged to differ.

If light came in little pieces, and the energy in those pieces depended on the frequency, then the photoelectric effect made sense. If a piece…call it a photon…had a high enough energy, it could knock an electron loose and it could jump the gap in Hertz’s apparatus. If a photon didn’t have the energy necessary, it wouldn’t. And neither would any number of those low-energy photons, hitting different electrons in the metal.

But even one high energy photon would knock an electron loose; a bunch of them would knock many electrons loose.

So if light consisted of photons and if the energy of a photon depended on the frequency of the light, then the photoelectric effect could be explained.

But this bit about energy depending on frequency should sound familiar (unless you blew Part X off last week).

Yes, this paper invoked E = h ν. Energy depending on frequency, times that h constant.

And so Planck’s crazy idea that just happened to “fit” with black body radiation now also explained the photoelectric effect.

But even more: Planck had concluded that the quantum principle was a limitation on the atoms that emitted the black body radiation. This paper claimed it was a limitation on the light itself.

So now, we can cross off #9. And #8 as well, as a reward for our patience with #9.

But not in 1905. Most physicists rejected this paper at first, because it strongly implied that light was a particle, not a wave. James Clerk Maxwell had pulled together his four equations, after all, and other people before him had succeeded in measuring wavelengths of light. Something that makes no sense if light is particles, not even particles whose name begins with the 17th letter of the alphabet.

Hold on, though, before we go further. Is light a particle or a wave?

The best answer to that, after a lot of tussling in the early 20th century turned out to be: “Yes.” It’s not a wiseacre answer either, it turns out that light is either/or depending on the circumstance, or if you like our host’s formulation, “AND Logic” applies here.

The greatly oversimplified statement would be that light propagates as a wave, as Maxwell showed, but when it interacts with something (generally consuming the photon) it will behave like a particle, as this paper was the first to claim.

OK, that’s counter-intuitive, you say. Why yes, yes it is. It’s a particle sometimes and a wave other times and it will develop it’s sometimes got aspects of both. But physicists a hell of a light brighter than anyone reading these words (and I do read them myself, so I am not excluding myself from this comparison) have wrestled with this for over a century, and as near as they can tell, that’s Just. The. Way. It. Is.

They might pretend to understand it in a deep sense, but the more honest ones will tell you, no they don’t, in fact, they’ll even quote an old saw that if you think you understand it, that’s proof positive you don’t (this was from Richard Feynman). But physicists can describe the behavior to a T, with excruciating precision.

Incidentally, photons themselves have no mass, and no electric charge (even though they carry the electromagnetic force, they aren’t themselves affected by it). So they don’t interact with anything, until they hit something and are absorbed. And “interacting” with something includes being detected by it, like, say, being seen by your eyes. When your eye sees a photon, it’s now gone. Any photon you don’t see, because it misses your eye, is effectively invisible to you and you can’t know it’s there unless it hits something else and affects it in a way that you can see. There will be plenty of other particles that are similar. Many forms of radiation that go right through you, for instance, are harmless–it doesn’t interact with your body. It’s when you stop radiation with your body that you have a problem. (Note, however, that if a charged particle goes through your body, it can cause all kinds of havoc as it passes by, because it affects the molecules in your body, but in turn, you will deflect the particle slightly in the process.)

In 1921 this paper won its author the Nobel Prize. By then the arguments against it had largely been resolved.

BOOM !!!! (even if it was a delayed blast).

3 – The Electrodynamics of Moving Bodies

There was (and is) a conundrum in Maxwell’s equations. If you moved a coil of wire through a stationary magnetic field, a current is induced in the wire. The problem is, if you looked at it from the point of view of the wire, the effect is due to an electrical force. But from the point of view of the magnet, the effect is due to a magnetic force.

Which kind of force it was depended on who was moving and who was stationary.

However, we had known since Galileo that as long as you’re moving without changing speed, the laws of physics look the same whether you’re moving or not. He used the example of a ship moving smoothly through water. You can play dodgeball on that ship (including all that fun velocity, momentum, mass, and force) without having any way of knowing that it’s in motion. If people outside can see the game, they’ll note different velocities (because they will add the velocity of the ship to everything), but still see everything being consistent with Newton’s laws.

All of those things I dragged you through weeks ago work the same if they’re happening in a moving frame of reference…or not. This is now referred to as Galilean relativity: The laws of nature are the same in all inertial reference frames (i.e., ones not accelerating). He put this forward clear back in 1632.

So it shouldn’t matter whether you’re in the frame of reference of the loop of wire (and see the magnet as moving) or in the frame of reference of the magnet (and see the loop as moving).

Oddly enough, the fact that Michelson and Morley had been unable to tell any difference in the speed of light through a vacuum (mystery #2) no matter what direction they measured it in, turned out to be part of the solution for this.

This paper showed that if you posit Galilean relativity and that the speed of light in a vacuum is one of those things that’s always the same no matter what inertial frame you are in, then the conundrum found in Maxwell’s Equations is resolved.

The paper mentioned the Michelson-Morley experiments in passing; later on the author would not even remember he had done so. But their experiment strongly implied the second postulate (the invariance of the speed of light in a vacuum, in any inertial reference frame, even one that’s moving at near light speed as seen by us) is actually true. And indeed we have never, ever seen this fail.

I’ll explain later some of the ramifications of this. Get ready for a bit of a wild ride.

If you measure the speed of light in a vacuum, which is denoted by the symbol c, with perfect accuracy and precision (while riding your invisible pink unicorn, which came bundled with your perfectly accurate and precise lab equipment) you will get precisely 299,792,458 meters per second.

The invariance is so well accepted that now, the meter has been defined in terms of the speed of light. You’ll occasionally read some article claiming that the speed of light is changing. Although scientists are trained to never say never, they’re so confident that c does not change that they define their units by it–if they’re wrong about this it would wreak havoc.

I’ll have more to say about this presently, but first, a minor rant.

To the popular reader in America, the speed of light is often given as 186,000 miles per second. Of course, that’s an attempt to make it more relatable to us Yanks since it’s not in kilometers, but it’s still a fail.

We don’t think in miles per second. We think in miles per hour. (Unless, of course, we’re astrodynamics or rocketry geeks–but those folks have mostly gone metric, outside of some rocket production facilities.)

The speed of light is almost precisely one billion kilometers per hour, or 671 million miles per hour.

That’s not really relatable either, but at least when you read that you know just how unrelatable that is.

Most of us have never even traveled at the speed of sound (since the SST never really took hold). That’s 767 miles per hour at standard temperature and pressure (sea level or 29.92 inches of mercury at 20 C/68 F). Under those conditions, that’s Mach 1. Light moves at Mach 874,837.

It’s going to be a while before we get moving that fast.

The implications of this turn out to be staggering and mind-bending, and I’ve promised to try to walk you through them below.

But because of those implications, this is a BOOM!!! too. And we get to cross Mystery #2 off the list.

Now on to the fourth paper, in some ways the biggest BOOM of all.

4 – Does the Inertia of a Body Depend Upon Its Energy Content?

The third paper seemed to raise paradoxes, so the fourth paper took them on and came up with a surprising result, and I will try to explain that too, below. Here I’ll just state it.

An object, just sitting there, doing nothing, has energy. In fact, because it’s not moving and isn’t kinetic energy, it’s called rest energy.

How much energy? A LOT of energy. A one kilogram object, in fact, contains 89.875 quadrillion joules of energy. That will run a million 100 watt light bulbs for almost 28 1/2 years.

One very big implication of this was that mass and energy were equivalent, meaning that in some cases some mass could become energy.

But that violates the first and third conservation laws I listed up above.

Or rather, it combines them into a new law, the conservation of mass-energy. However, particle physicists just tend to think of matter as a form of energy by preference (it’s more convenient than thinking of energy as a form of matter) so they will still talk about conservation of energy, while never talking about conservation of mass (they see it change far too often…as you will eventually see).

Another consequence is that even a massless particle, like a photon, has momentum. If you recall, though, momentum requires both mass and speed. Well the photon has speed and energy. Energy is equivalent to mass, so it can have momentum. Which is why light sails work in space, albeit not very quickly; the sun’s light can push–ever so slightly–on the sail, which provides a tiny amount of thrust, without the need for rocket propellant. Because the thrust is so small, you have to already be in free fall for it to do any good, but there it is (oh, a super duper powerful laser might succeed in launching a payload, but we probably couldn’t power such a thing without blacking out the entire planet). But not having to put the mass of the propellant onto the space probe means we can launch a bigger actual probe, or launch it at higher speed, or some of each. And you get continuous thrust. It’s surprising how much a continuous small thrust can do over time. This is huge from a space exploration standpoint; if we can get into orbit we can potentially get places cheaply as long as we aren’t in an absolute tearing hurry.

BOOM!!!!

And I do mean “boom” here because that kind of energy can be explosive.

As the Japanese learned on two days in summer, 1945.

Muck with America, and you just might get a physics lesson a lot more painful than any of my posts.

(Talk about physics lessons–right after I wrote that sentence a bolt in my chair broke and I got a few more lessons in physics.

All in 1905

All four of these papers came out in 1905. Some had an immediate impact, others were disregarded, because they were too outlandish.

But today they are all landmark papers, and 1905 is considered one of the biggest years in the history of science, on a par with 1666 when Newton had the key insights that resulted in the theory of universal gravitation and the spectrum and calculus.

Who wrote these papers? I never mentioned their authors, did I.

WRONG. I never mentioned their author.

One man.

This man.

That is a photo from 1904. One year before what is now called the Annus Mirabilis. He was 26 when he wrote those papers.

And in case you still don’t recognize him, here he is in 1947.

Yes, this was Albert Einstein. And he wasn’t done yet!

Oh, and the formula that tells you how much energy there is in a mass (or vice versa)?

E = mc²

The units of E are joules, which are kg m² / s². Notice on the right there is mass (kg) and a speed, squared, which is to say m/s, squared. The units match.

The units always must match!

If Albert Einstein had, after all his algebra, come up with some formula where the units didn’t match, he’d have known to start over. Or in other words, this could not have happened (but it’s too funny to pass up).

And yes, c is the speed of light. The one kilogram mass thus has, or rather, is (1kg)(299,792,458 m/s)(299,792,458 m/s) = 89,875,517,873,681,764 joules.

And this is a gigantic hint, as to where the huge amounts of radiation in radioactivity might be coming from.

Roundup

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?

Almost all of those crossoffs are Einstein’s work.

Even better, two and a half of the rest of the items will get crossed off in the future, either by Einstein, or by people using what he did in 1905.

Boom!!! Boom!!! Boom!!! and KABOOM!!!!

Special Relativity

The third and fourth of Einstein’s 1905 papers were on what we today call “Special Relativity” and some of its implications. It’s “special” relativity, because it applies only to inertial reference frames, a “General” theory of relativity would apply even to accelerating reference frames.

I’m going to be honest with you, this won’t be easy to explain, and it won’t be easy to understand, either. So let us gird our loins, and jump in.

The two postulates are 1) that the laws of physics are the same in any inertial reference frame, and 2) that the speed of light in a vacuum, c, is the same in any inertial reference frame.

The first was and is utterly uncontroversial. Galileo had used the example of a smoothly moving ship (as in sea vessel) to explain it clear back in 1632. (The only thing that had changed by 1905 was that people would used moving trains to visualize the principle. Gotta keep up with progress. Nowadays we use rocket ships or airplanes. But we’ll stick to vintage 1905 imagery for now.)

The second postulate doesn’t sound too crazy, either, right? If you’re standing on a train, moving at, say, 60 percent of the speed of light and aim a laser pointer directly ahead, and light it off, you expect it to look to you like it’s moving away at the speed of light. And the same if you fire it sideways, or backwards. Just as if you were firing a gun, or throwing a baseball. (Nor does it matter if you’re doing something distinctly less American.) You shouldn’t be able to tell the train is moving, or in which direction, just by the way the light, or bullet, or baseball (or, egad, soccer ball) behaves.

And likewise, if you’re instead standing on the railway station platform. Things should look the same there, too. You can’t tell which frame of reference is moving, because there is no “God’s Eye point of view” fixed, absolute reference frame. Any such frame can be treated as if it were fixed and the rest of the universe were moving.

Yes, that seems reasonable. But this will not: If you’re standing on the train and point the laser pointer straight ahead, and turn it on, not only will you measure its speed as c, but so will someone standing on the railroad platform!!! Now, you would expect the guy on the railroad platform to measure 0.6c + 1.0c = 1.6c for the speed of the light beam coming off the laser pointer, but he does not. He measures it as c. You cannot just add the velocities together, as you do for baseballs and bullets and trains. When I said “the speed of light in a vacuum, c, is the same in any inertial reference frame,” I meant it, thoroughly. It applies even to a beam of light starting in some other reference frame!

How can this be?

Velocity, remember, is distance over time. If the velocity stays the same no matter what, perhaps the time and distance don’t.

Time Dilation

Well, let’s think about this somewhat mathematically. Light travels a bit less than a foot in a billionth of a second (a nanosecond). So I’m going to actually define a new unit of length, a bit less than a foot, the distance light travels in a billionth of a second. I am going to call it a pod (from the Greek for “foot,” as in tripod and bipod, to say nothing of tetrapods (amphibians, reptiles, birds and mammals)). Expressed in pods, then, c is 1 pod per nanosecond ( 1 pod/ns ).

So returning to our 0.6c train, in the time it takes light to move ten pods’ distance (a hundred-millionth of a second), the train moves 6 pods’ distance.

Imagine the inside of the train car is 8 pods high, and call that distance L. Your friend is in the train, and he sets a laser pointer on the floor, pointing straight up. On the ceiling is a mirror, and the pointer also has a detector in it, waiting for the reflected beam. He sets the laser pointer to fire a very short burst instead of continuous beam.

He fires it off, the pulse goes straight up, bounces off the mirror, and comes straight back down. Total trip, 16 pods, total time 16 nanoseconds. Like in the picture below:

But what do you, standing on the railway platform, see?

You see the pulse of light traveling from the floor of the train, up at a slant to hit the mirror on the ceiling (because the train is moving, remember), then back down at the same slant to hit the detector.

Rather than turn this into a story problem and ask you to figure out how long D and 1/2 v delta t prime is, I’ll give it to you. D is 10 pods long. The train moves 60 percent as fast, so going from A to B it moves 6 pods. The light beam travels a total of 20 pods (10 each way). So our lengths are 8, 6 and 10 pods (and our times are 8, 6 and 10 nanoseconds). This is consistent with Pythagoras:

c² = a² + b²
10² = 8² + 6²

You measure the pulse’s speed as c, and measure the time it took to be 20 nanoseconds.

The same trip took 16 nanoseconds as far as the man on the train is concerned, and 20 nanoseconds as far as you are concerned.

This is not an illusion. If you could see a clock running on that train as it went past, it would show as running 20 percent slow. Time would actually be slower on the train, as seen from outside the train.

If this seems totally against your intuition–that time can literally crawl just because of how fast you’re moving, you’re not alone. You never see that in real life.

But in real life you don’t move close to light speed, either!

This is time dilation. It’s absolutely real, and has been confirmed again and again and again in experiments for the last 116 years.

And you thought time zones were bad.

Given something moving past at some speed, how much is the time dilation? Gee, I think it’s time for some algebra. I’m going to call the time running on the train t_t, the time on the platform t_p, and the speed of the train v_p (v as seen from the platform. v_t, the speed of the train seen from the train, is, of course, zero.) I’m doing this instead of what’s in the diagrams because I find it hard to keep track of what the tick mark means (and I think these diagrams are using it for the other side of things than my physics textbook did, to boot).

OK, so the time measured on the train is:

t_t = 2L/c.

Pretty simple.

For you on the platform, you need 2D, and you can get there with a right triangle and Pythagoras, solving for D (which is ct_p/2)

[ct_p/2]² = L² + [t_pv_p/2]²

So let’s do some cleanup here. First multiply everything by 4, it will get the two-squareds out of the denominators.

[ct_p]² = 4L² + [t_pv_p]²

Then divide by c² and just write out all the squareds in full:

t_p² = 4L²/c² + [t_pv_p/c]²
t_p² = 4L²/c² + t_p²v_p²/c²

Now bring the t_p²v_p²/c² on the right over to the left.

t_p² – t_p²v_p²/c² = 4L²/c²

Factor out the t_p²:

t_p²[ 1 – v_p²/c²] = 4L²/c²

Divide both sides by what’s in the square brackets.

t_p² = 4L²/c² ( 1/[ 1 – v_p²/c²] )

Now take the square root of both sides.

t_p = 2L/c ( 1/sqrt[ 1 – v_p²/c²] )

But, going way back, the guy on the train measured the total time as t_t = 2L/c, so:

t_p = t_t ( 1/sqrt[ 1 – v_p²/c²] )

That whole thing inside the parentheses shows up again and again, so it’s often written as gamma (γ).

t_p = γt_t

Let’s check this against our original specific example, of the train moving at 60 percent of c.

v_p/c is 0.6. Square this, and get 0.36. Subtract from one, get 0.64. Take the square root, get 0.8. Divide that into one, get 1.25–that’s γ. And indeed the time on the platform, 20 ns, is 1.25 times the time measured on the train, 16 ns. Cool!

Let’s examine γ some more:

γ = 1/sqrt[ 1 – v_p²/c²]

When v is very, very low, like, say walking speed which is about one billionth of c, then v/c is a small, small fraction, and if you square it, it gets even smaller, it’s now a quintillionth. Subtract from one, and you still get, basically, one, as close as you can measure it, just a bit under. Take the square root and you get even closer to 1, and when you divide that into one, you get a number just a teensy bit over one. So both times are so close to being the same, you can’t tell the difference. And this is what you see in everyday life.

Now set vp to 86.6 percent of the speed of light. Dividing by C of course you get .866; square it and you get .75, subtract from one and get .25, take the square root of that, get 1/2, divide into 1 to get 2. Two hours, two years, pass on the platform for every hour or year on the train.

Note that you have to get to over 86 percent of the speed of light just to make γ equal to 2. After that, though, it takes off. At 99 percent of light speed, γ is 7. At 99.9 percent of light speed, γ is 22.3. Which means the entire Barack Obola administration, which was about 22.3 years long [wasn’t it?], could have gone by in one year.

The number explodes the closer you get to light speed. When actually at light speed, the part inside the square root sign becomes zero, and you are dividing 1 by zero. Technically you’re not supposed to say “that’s infinity”, but that’s basically what it is.

γ is always one or more. Sometimes a lot more.

OK, if you’ve thought about this a bit, you’ve probably come up with an objection to this.

If I see the train traveling at 0.6c and its clocks are running slow, how about what the people on the train see when they look at the big clock on the station tower, as they move past it? From their point of view, the station is moving at 0.6c (albeit backwards); shouldn’t they see its clock run slow, too?

Yes, they do.

Doesn’t that seem contradictory, though? How can you have two clocks, and each one is slower than the other?

I don’t have a good intuitive explanation of this one, and the one I found on wikipedia is kind of weak, too (they drew an analogy to two people far apart both looking small to each other). The fancy explanation is, you can’t really get into a contradiction until you bring the two clocks close to each other, stationary with respect to each other, and check total elapsed time. But doing that means you have to decelerate one (or both) of the clocks, and once you’ve done that you’re not dealing with inertial rest frames any more. The frame that accelerated is now a different case from the one that didn’t, they’re not symmetric any more and one clock can indeed mark off less total time than the other without it being a contradiction.

I’m sure you’ve heard about the “twins paradox” too. One twin gets on a starship, takes a long journey at close to the speed of light, comes back, and he ends up being younger than the other twin, who stayed behind. The same objection seemingly applies. From the point of view of the traveling twin, the guy who stayed behind traveled away from him and came back, why isn’t he the younger one, or better yet, why are they not the same age at the end?

The reason why is because the traveling twin accelerated, decelerated at his destination, accelerated to come back, and decelerated to arrive back here on Earth. He was not in an inertial frame, but the stay-behind twin was.

That sounds pretty arbitrary and lazy, but the more detailed answer involves going back to our train and railway platform, and demonstrating that two events in two different locations that seem simultaneous to someone at the platform will not seem simultaneous to someone on the train…and vice versa. I’ll talk about that in a moment, but first there’s something else to get out of the way.

Length Contraction

Imagine a passenger on that train…the one moving at 0.6c. He’s going to a destination six trillion pods away. Light covers a billion pods a second, so light would cover this distance in six thousand seconds (less than two hours). The train, though is moving at .6c and conveniently will take exactly ten thousand seconds to make the trip. But the clock on the train is running slower, it’s running at 80 percent of the speed of the clock at the station. The people on the train will perceive that 8000 seconds have gone by when they reach their destination. But the train measures the rest of the world’s velocity as .6c backwards. Multiplying the time by the velocity, they will think the trip was only 4.8 trillion pods (4/5ths) as far.

This is length contraction.

This too is symmetrical. The people on the train see the world shortened in the direction of travel. But the people on the ground see the train shortened in the direction of travel, too. Remember, from the standpoint of the train, the clock on the platform is running slowly as the train goes by, so it must take less time for those people on the platform to see the train go by, than it would otherwise. So they see the train 20 percent shorter than it would be, were it standing right next to the platform at rest.

In fact if l_t is the length of the train, as seen on the train, and l_p is the length of the train as seen from the platform:

l_p = l_t/γ

This time you divide by gamma. And again, this effect is totally immeasurable and imperceptible at day-to-day speeds, but it’s as real as Joe’s pedophilia at close to light speed. Again, it has been measured, time and time again.

Simultaneity

Now it’s kind of hard to get a handle on “simultaneous.” How can you tell that two events happening fairly far away (but in different directions) are simultaneous? If there is a flash of light to the north, and another to the south, how can you decide they’re simultaneous, when you know it took some amount of time for the light from the two events to reach you?

Well, the simple case is if you’re halfway between the two events. The light from both should arrive at the same time if they’re simultaneous, because in both cases they had to travel the same distance. Similarly, if you know the distances to the events, you can simply correct for light speed delay even if they’re not equidistant from you, figure out when the events happened by subtracting the delay from when you saw it happen, and compare.

OK, let’s go back to the railway station.

You set up a pair of sensors. When the train reaches the sensor, it will flash green. When it passes the sensor (i.e., the sensor sees that there is no train right there any more) it will flash red.

Now you set the sensors as far apart as the length of the train, on the edge of the platform (after figuring in its contraction).

You stand precisely in between the sensors.

When the train reaches the first sensor, it flashes green. When it reaches the second sensor, that sensor flashes green, but the train is just finishing passing the first sensor, so it flashes red at the same time. You see the red flash and the green flash simultaneously, and you know you’re standing exactly midway between them, so you conclude that you got the two sensors at the right distance because the train started passing one at the same instant it finished passing the other.

What about someone standing in the middle of the train? He is moving toward the second beacon as it flashes green, and away from the first beacon as it flashes red. He will therefore see the green flash before the red flash. At the time you see them both flash, he is already down the track, and therefore must have seen the green flash already! Since he knows he was midway between the beacons (from his viewpoint one was at the front of the train, the other at the back), and he knows the speed of light is a constant, he concludes that the two flashes were not simultaneous, the green flash from the front of the train came first.

This is actually consistent with the length contraction of the station that he sees. He sees that the sensors are too close together because of the length contraction, thus the front of the train reached the second sensor before the back of the train reached the (too close) first sensor. Thus the first sensor fires its red flash after the second sensor fires its green flash. And that is precisely what he saw happen.

If you are thinking that this is an artifact of the fact that the train is moving and the platform is stationary, think again. From the standpoint of the train, the train is stationary and the platform is moving. From the standpoint of a third party, they might both be moving while that third party is at rest.

None of these reference frames is any better or “truer” than the others. That’s what the Galilean equivalence means. You can’t even tell which one is moving by measuring how fast light moves in the stationary aether…as Michelson and Morley demonstrated (to their puzzlement at the time)…because there is no stationary aether.

Imagine that there is a clock right next to each sensor, and that the train passed them at midnight, precisely. The guy on the train will see the second clock the same time he sees the green flash, and it will say midnight. Later on he will see the red flash from the first sensor, and see that the clock there reads midnight. From his standpoint the clock that passed him first (going backwards) at sensor one, is lagging behind the clock that is “chasing” it (clock and sensor #2). And the formula for just how far off they are is:

t₂ – t₁ = L v /c²

Here L is the length of the train, as seen on the train. In other words, the length of the train when you don’t see it as moving, because if you see it moving, its length will contract. The answer is how far the second (chasing) clock is ahead of the first (leading) clock in the train’s reference frame, when the two clocks are synchronized in their own (platform) reference frame.

If the train is 60 pods long, those two clocks will seem to be off by: 60 x 0.6pod/ns divided by 1 pod²/nsec² = 36 nanoseconds, which given how fast things are moving and how short our time scale is, is very significant. The train requires 100 ns to move its length, and the apparent discrepancy in the clocks is over a third that much.

The Twins Paradox

Now we can go back to the “twins paradox.” Let’s say the ship is going to Sirius, which close to 8 light years away (we’ll ignore the difference for purposes of illustration). A light year is the distance light travels in a year, so light would take eight years to make the trip. From d = vt, we can write a light year as ct with t in years (1), and c in meters per year instead of per second. And let’s figure the ship is going to travel at .8c. The ship will therefore take ten years to get there, as seen from earth. It will then immediately turn around and come back at the same speed. Total time, as seen from earth, 20 years.

Billy is going on the expedition. Bob is staying home.

Bob analyzes the trip. He sees the ship traveling 8 light years at .8c and concludes the one way trip will take ten years. Two ways, 20 years.

Let’s look at Billy’s perspective. Calculating γ at 1 2/3s, he can divide by that (since he’s going to be the one on the train, by the math) and see that the distance to Sirius will contract by 40 percent (he will multiply it by .6). So once he’s on that ship, traveling at .8c, Sirius will be 8 x .6 = 4.8 light years, and traveling at .8c, it will take him six years, one way, 12 years round trip.

From Billy’s point of view, however, it’s Bob that’s doing the traveling, so he should be younger than Billy when they meet again. In fact, while Billy ages 6 years, Bob should be aging 6 x .6 = 3.6 years, or in total, Billy ages 12 years, Bob ages 7.2 years. Not 20! So Billy is scratching his head, wondering how that “twenty years” of aging that Bob will do, possibly can be.

It’s resolved this way. Imagine a clock on earth, and a clock at Sirius, that were synchronized with each other. A person midway between them, at rest with respect to both of them, sees them both reading four years ago (he is four light years from each clock, so their signals are delayed by four years when they reach him).

While Billy is traveling to Sirius, it’s going to look like two clocks moving past him at .8c, separated by 8 light years. It will look like the one at Sirius is chasing the one at earth. Go back to our formula:

t₂ – t₁ = L v /c²

L is 8 light years, v is equal to 0.8 c, so the Sirius clock looks to Billy (after correcting for all light-speed delay) as if it were 6.4 years ahead of the clock on Earth. (You have to convert everything back to meters and seconds and use 299,792,458 meters/second for that to work out. I just did it, that’s the right answer.)

So Billy arrives at Sirius, and stops. He’s now in the frame of reference of the Sirius clock, which, remember, was, while he was moving, 6.4 years fast. The clock did not just run backwards, so it still reads what it read before. But that means the clock back on earth must have advanced 6.4 years while Billy was slowing down to a stop, because in this reference frame, the two clocks are synchronized. So Billy thought Bob had aged 3.6 years during the trip; now he has to add 6.4 years to that to get…10 years. So Bob ages ten years during half of the trip.

It might also help to have the two twins send each other messages once a year (as they perceive it). Each twin can then monitor the aging of the other by simply counting signals. They don’t even need to correct for light speed delay, because they will receive all of the signals sent by the time they are re-united at the end of the round trip; some will be later than others but all will get there before the end of the trip. As it turns out, when they are moving further apart, each will get a signal from the other once every three years. When they are heading towards each other, the signals arrive every four months (a third of a year).

Looking at it from Traveler Billy’s point of view, during the six years he spends traveling to Sirius, he gets two signals. When he turns around and heads back to earth, he starts getting three signals a year for six years, total eighteen, grand total 20. The last signal from Bob reaches Billy in earth orbit just as the journey ends. Bob aged twenty years.

From Stay at Home Bob’s point of view, while Billy is travelling out for ten years, he gets three signals, the last arriving at year nine. But then he continues to get signals after ten years, from Billy as he was traveling outwards, because the last signal was sent from Sirius, eight light years away, ten years after the trip started. So Bob gets six signals over the course of eighteen years. Then the signals from Bob as he’s coming back arrive, 3 per year, for two years, for a total of six more signals, including the last one from earth orbit that arrives just as Bob arrives. total, twelve signals; Bob aged 12 years.

There are aspects of this I could not cover, including the Doppler shift, which is how one gets the 3 per year, one every three year numbers I just used.

I also didn’t have time to explain how E = mc² comes from all of this (Einstein’s fourth paper, the big kaboom!!! both literally and figuratively).

But I am running out of time and I have to produce the diagram for simultaneity still (no good one to be had online). But it’s now done and it’s 12:26. Just need to fix the precious metal prices!

Obligatory PSAs and Reminders

China is Lower than Whale Shit

Remember Hong Kong!!!

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

China is in the White House

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

Joe Biden is Asshoe

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

But of course the much more important thing to realize:

Joe Biden Didn’t Win

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

His Fraudulency

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

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

One can hope that all is not as it seems.

I’d love to feast on that crow.

Physics?

It looks like the next couple of months aren’t going to be as busy I had thought so I can do some physics posts. See below.

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 $1788.30
Silver $26.53
Platinum $1094.00
Palladium $2874.00
Rhodium $19,400.00

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

Gold $1808.90
Silver $26.19
Platinum $1105
Palladium $2903
Rhodium $18,500

UPDATE: Apparently paper prices are getting closer to reality. I was quoted $125 over spot for an American Gold Eagle (the modern day one ounce bullion piece).

Gold is slowly climbing again, Silver down a touch, Platinum and Palladium up a bit, Rhodium is down. In fact at the beginning of the day today it was at $17,500 but jumped a grand sometime before close.

Max Planck: Physics Starts Getting Weird

Introduction

This is going to start to tie together a few dangling threads out there, notably Hertz’s discovery of the photoelectric effect (how even dim, weak ultraviolet light would help the spark jump the gap but glaringly bright visible light would not), and the puzzle of why black body radiation had a “hump” in its frequency distribution (instead of just going to infinity with higher frequency/lower wavelength).

To recap, we knew of the existence of X rays, ultraviolet, infrared and radio, in addition to “ordinary” visible light.

Also, to avoid getting bogged down in Spockian numbers specified to nine decimal places, I’m going to round a lot of things off.

Max Planck

Planck was born in 1858 in Kiel, Holstein (now the German state of Schleswig-Holstein, it’s the area immediately adjacent to modern-day Denmark).

He was raised as a geek, and ended up teaching at the Humboldt University in Berlin. In 1894 he decided to take up the black body radiation problem. Why did it behave the way it did?

To recap, black body radiation is the glow given off by hot objects (in the idealized case that the hot object is perfectly black). As shown in the figure below, if you plot the wavelength of the light versus intensity you get a hump that’s steep on the high frequency side (left side of the diagram), and less steep on the low frequency side. The peak of the curve tends towards blue (leftward) the higher the temperature, and the height of the curve increases very rapidly as the temperature increases.

The best physicists could do as of 1894 (when Planck put his shoulder to the wheel) is design a theory (the Rayleigh-Jeans law) that predicted the distribution should look like the black line in the figure. It’s not a bad match at the low frequencies (longer wavelengths, at the far right) but is totally, ridiculously wrong at higher frequencies/lower wavelengths; the prediction was basically that the higher the frequency the more should be radiated at that frequency. Since you can’t get a sunburn (caused by ultraviolet) off of a wood fire–because the wood fire is not super hot and emits no UV–we know that’s not actually what’s going on here.

An alternate law, Wien’s Law, was proposed by Wilhelm Wien in 1896 (after Planck began his work). It worked well at high frequencies and was wrong at low frequencies. It was a much better fit, but not perfect; it was a bit too low. Alas this diagram is “backwards” (compared to 10-1) with high wavelengths on the left.

Wien’s Law looks pretty close, but it’s not right-on, so there was still a problem here.

Max Planck’s goal was to solve the problem, to come up with a formula that gave results consistent with what was actually measured. And since the line that’s “true” in figure 10-3 is labeled “Planck” you can probably guess that he ultimately succeeded.

But not without some trials and tribulations. He tried to imagine the atoms in the glowing object as little oscillators, because that way he could apply entropy to an ideal oscillator. He came up with a proposed law (the Wien-Planck law) in 1899…that, alas, turned out not to match measurements either.

In October of the next year, 1900, he did succeed in writing a law that described experimental results well. This derivation avoided any sort of statistical mechanics, which Planck had an aversion to.

Statistical mechanics was a fairly new thing at the time, it studied large assemblies of microscopic units in a statistical manner; in fact modern thermodynamics relies heavily on it. But in 1900 it was still considered suspect by many, including Max Planck. It had philosophical and physical implications that were distasteful to many.

But Planck, having got a law that looked good on paper…couldn’t for the life of him explain why it worked–and without some explanation of that, it was interesting that his law could match what was seen, but not enlightening. Over the course of the next few months, he did finally, in desperation, decide to accept statistical mechanics as a tool, incorporating Boltzmann’s statistical interpretation of the second law of thermodynamics.

This is like a dedicated Marxist coming to the dawning realization that capitalism works and Marxism cannot. That is how desperate Planck was to try new things to figure this out. It was, as he said, “an act of despair … I was ready to sacrifice any of my previous convictions about physics.”

His derivation started with an assumption that seemed totally whacky, and had no obvious basis in reality, but it was: Energy could only be emitted in multiples of a certain base amount. That amount was:

E = h ν

(As a reminder ν is the lower case Greek letter “nu” and stands for the frequency of the light being emitted.)

This meant that there wasn’t just a minimum amount of energy, but that any amount of energy had to be an integer multiple of this amount. It’s sort of like money…you don’t see fractions of a cent. Any amount can be expressed as a whole number of cents, but never is there a fraction of a cent (not withstanding nominal US gasoline prices that end in 9/10 of a cent without fail).

This minimum amount was termed a “quanta.”

But note that it depends on the frequency. So at, say, 600 THz (yellow light) the minimum quanta would be one size, but at 300 THz (infrared), it would be half as much. It’s rather like exchanging your dollars for euros and now the minimum amount you can work with is the Euro cent rather than our cent.

The minimum “quanta” of energy not only depended on the frequency it would be radiated at, but also on this new number, h, which is a constant, now known as Planck’s constant, and it’s one of the most important numbers in physics:

h = 6.62607015×10⁻³⁴ J s

It’s going to turn up again, and again, and again from here on out.

The units are joule seconds, not joules per second (which is power measured in watts). When you multiply this by a frequency (which is cycles per second) the seconds cancel out and leave you with energy in joules.

In fact, it’s really joules per cycle or per hertz, i.e., one cycle of the wave of the light, but the cycle is expressed as one over seconds (1/s) so when you divide by that, you’re multiplying by seconds.

(As usual when a scientist brings a new constant into things, Planck didn’t actually know the value of h; he just realized that there had to be a value to this number. Today, of course, we know it precisely, because the latest iteration of the metric system actually defines a number of physical constants, including h, to have specific values, and the size of the units involved is set by that action. Thus we have the meter…which is defined to be the distance traveled by light (in a vacuum) in 1/299792458 of a second. Planck’s constant is set to the number above, and from that, we get a definition of the kilogram [because a joule second is a kg m²/s; we have a defined second and a defined meter, so that gives us a defined kilogram]. Before 2019, however, the kilogram was still defined as the mass of a certain metal cylinder kept in a vault in France…a definition which was starting to cause problems, because exact copies made decades ago were no longer the same mass, making one wonder if any of those cylinders was not changing.)

Even with typical visible light, yellow light in particular, having a frequency of about 600 THz, or 6×10¹⁴ Hz, you can see that doing the multiplication is going to leave you with a very small number, basically about 4×10^-19 joules. Given that a joule is very roughly the energy it takes to lift an apple a meter, this is a very small amount of energy. And as mentioned, the size of the “quanta” depends on the frequency; twice the frequency, twice as much energy in a quanta.

He wasn’t the only one who was skeptical nor was he the most skeptical, Lorentz, Rayleigh and Jeans tried setting h to zero in their work, i.e., meaning that there was no minimum energy unit. That was too conservative even for Planck, who compared Jeans’s inflexibility to Hegel’s: “I am unable to understand Jeans’ stubbornness – he is an example of a theoretician as should never be existing, the same as Hegel was for philosophy. So much the worse for the facts if they don’t fit.”

But, at the time (1900) Planck did regard this as a mere formalism with no real basis in reality, much as there were, at that time, still holdouts in chemistry who thought atoms didn’t really exist, but were convenient conceptual tools. The quantum concept was convenient but didn’t represent something that really existed.

That’s what he thought at the time. Today, we look upon Planck’s use of this concept as the birth of quantum mechanics–which, if it were wrong, would mean that semiconductors don’t work and you are not reading this on a computer screen.

One last wrinkle here; as I mentioned, the constant is “per cycle” which is regarded as analogous to going all the way around a circle. That’s 2π radians. But many formulas (like for angular momentum and rotation rate, when expressed in terms of angles) operate in radians, so there’s a version of Planck’s constant that accounts for this and is expressed in a “per radian” sense instead of a “per cycle” sense. It’s written ħ (a crossed h, called “h bar” in speaking), and is h/2π. This symbol is seen, if anything, even more often than h in modern physics.

But anyway, back to 1900.

Planck was banging on the door to modern physics, unwilling as yet to open it.

Soon, very soon, others would kick the damn thing down.

Obligatory PSAs and Reminders

China is Lower than Whale Shit

Remember Hong Kong!!!

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

China is in the White House

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

Joe Biden is Asshoe

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

But of course the much more important thing to realize:

Joe Biden Didn’t Win

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

Justice Must Be Done.

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

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

Mid-Independence Day

Yesterday was the Second, and tomorrow is the Fourth, of July.

Although the Declaration of Independence proudly proclaims “In Congress, July 4th, 1776,” the actual resolution of independence, the Lee Resolution ( https://en.wikipedia.org/wiki/Lee_Resolution ) was passed on July 2nd.

July 4th was when the text of the masterfully-written-and-butchered document was approved. It includes the Lee Resolution in its own text, in the last paragraph:

We, therefore, the Representatives of the united States of America, in General Congress, Assembled, appealing to the Supreme Judge of the world for the rectitude of our intentions, do, in the Name, and by Authority of the good People of these Colonies, solemnly publish and declare, That these united Colonies are, and of Right ought to be Free and Independent States; that they are Absolved from all Allegiance to the British Crown, and that all political connection between them and the State of Great Britain, is and ought to be totally dissolved; and that as Free and Independent States, they have full Power to levy War, conclude Peace, contract Alliances, establish Commerce, and to do all other Acts and Things which Independent States may of right do. And for the support of this Declaration, with a firm reliance on the protection of divine Providence, we mutually pledge to each other our Lives, our Fortunes and our sacred Honor.

Declaration of Independence of the United States, last paragraph; Lee Resolution in bold.

So in a sense Friday was the real Independence Day, and today is just the average of the real one, and the commonly celebrated one on Sunday.

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 $1782.30
Silver $26.20
Platinum $1114.00
Palladium $2724.00
Rhodium $19,200.00

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

Gold $1788.30
Silver $26.53
Platinum $1094.00
Palladium $2874.00
Rhodium $19,400.00

Obligatory PSAs and Reminders

China is Lower than Whale Shit

Remember Hong Kong!!!

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

China is in the White House

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

Joe Biden is Asshoe

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

But of course the much more important thing to realize:

Joe Biden Didn’t Win

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

His Fraudulency

Joe Biteme, properly styled His Fraudulency, continues to infest the White House, 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 $1893
Silver $27.91
Platinum $1172
Palladium $2890
Rhodium $21,000

This week, markets closed as of 3PM MT.

Gold $1877.40
Silver $28.02
Platinum $1153.00
Palladium $2854.00
Rhodium $22,000.00

Gold was actually just below $1900 at open. The others have changed even less on a percentage basis. Since rhodium didn’t just jump right back up to nearly $30K, I’m thinking this price might not be a short term “spike” (but downward).

(Be advised that if you want to go buy some gold, you will have to pay at least $200 over these spot prices. They represent “paper” gold, not “physical” gold, a lump you can hold in your hand. Incidentally, if you do have a lump of some size, doesn’t it give you a nice warm feeling to heft it?)

The Atom
(Part VII of a Long Series)

Introduction

The general outline of this story is to start off by putting you “in touch” with the state of physics at the beginning of 1895. Physicists were feeling pretty confident that they understood most everything. Sure there were a few loose ends, but they were just loose ends.

1895 marks the year when people began tugging at the loose ends and things unraveled a bit. In the next three years, three major discoveries made it plain there was still a lot to learn at the fundamental level.

Once I’m there I will concentrate on a very, very small object…that ties in with stars, arguably the biggest objects there are (galaxies are basically collections of stars). And we would never have seen this but for those discoveries in the 1890s.

It’s such a long story I decided to break it down into pieces, and this is the seventh of those pieces. (Though to be sure this series seems to have taken on a life of its own.)

And here is the caveat: I will be explaining, at first, what the scientific consensus was in 1895. So much of what I have to say is out of date, and I know it…but going past it would be a spoiler. So I’d appreciate not being “corrected” in the comments when I say things like “mass is conserved.” I know that that isn’t considered true any more, but the point is in 1895 we didn’t know that. I will get there in due time. (On the other hand, if I do misrepresent the state of understanding as it was in 1895, I do want to know it.)

Also, to avoid getting bogged down in Spockian numbers specified to nine decimal places, I’m going to round a lot of things off. I used 9.8 kg m/s² in Part for a number that’s actually closer to 9.80665, for instance, similarly for the number 32. In fact, I’ll be rounding off a lot today.

NOTE: A YUUUGE debt is owed here to “Discovery of the Elements,” 2nd edition, by James L. Marshall.

Why Talk About Atoms?

This post is going to seem like it actually is about chemistry, and in many ways it is.

However, physics and chemistry are right next door to each other. Physics is the most fundamental of the sciences, the others build on it, with chemistry being the one directly “on top” of the physics foundation. Thus it’s the major branch of science most directly connected to physics. And you’ll see some of that here. (Of course, where we divide sciences into major branches is largely arbitrary. For example, if there were a major branch for electricity and magnetism, it’d be tied even closer to physics than chemistry is, but in fact, E&M is considered a branch of physics rather than a major science in its own right.)

Phlogiston

Our story begins with Georg Ernest Stahl, in the 1600s. Before he came on the scene, what we now think of as chemistry was still under the sway of the alchemists, many of whom were trying to turn lead (and other base metals) into gold.

They had a basic theory of chemistry, to wit that the world was made of exactly four basic substances, earth, water, air, and fire (and in some cases they believed the heavens were made out of “aether”, something not encountered “down here”). Everything we see around us, they maintained, was some sort of mixture of these basic elements. So to change lead into gold, all one needed to do was change the mixture, removing some things and adding others.

Of course, that never came to anything, but during all their efforts they amassed a huge amount of knowledge about what would happen if you mixed certain things together and treated them in certain ways.

For example you could mix potash and sulphur, and create liver of sulphur. But you could also create liver of sulphur by heating vitriolated tartar together with charcoal.

(I use the older names here so that you can see how totally arbitrary this must have seemed to the people who used those names.)

So what we had by the 1600s was a vast collection of information like this, with no real way to connect the pieces and understand what was really going on.

And this is where Georg Ernest Stahl comes in.

He was the first to put forward a theory that seemed to tie this disparate trivia together. The theory could also be used to make predictions about what would happen with previoiusly untried processes. This would help tremendously if the theory were right, but would also, if the theory were wrong, allow it to be discredited because it had made a specific prediction that hadn’t come to pass.

(A lot of things people believe are “unfalsifiable.” That means there’s no way, even in principle to disprove it even if it’s wrong. Most real “conspiracy theories” are like this, actually; if any evidence is turned up against the theory, the advocates will dismiss it as falsified as part of the cover up. If your hypothesis can explain away anything this way, and you can disregard evidence against your hypothesis, you can’t be convinced it’s wrong, and the theory itself is worthless since it can be neither proved or disproved, and can make no meaningful predictions, either–any outcome can be made to fit the theory, so any outcome is possible if the theory is true.)

So here it is: Stahl noted some similarities between combustion (burning things), calcining (rust, corrosion), and respiration (both plant and animal “breathing”). He concluded that at a very basic level three of these four were the same thing–he excepted plant respiration, but claimed that it was fundamentally animal respiration in reverse.

His proposed explanation for all of these processes? That wood, when it burns, and metal when it rusts, and animals when they breathe, all give off a substance called phlogiston. Thus, the calx of some metal, say iron rust was a purer substance than the metal, because the metal had given up phlogiston to turn into the rust. Similarly, when you burned a log you could even hear it hiss as the plogiston was released.

The ancients had believed that fire, once released, went up into the heavens; Stalh believed that plogiston combined with the atmosphere, to form phlogisticated air.

Plants would simply recapture the phlogiston from the air, turning the air into dephlogisticated air, and incorporate it into their tissues, forming a sort of closed cycle, ready to be burned again, or eaten by an animal that would breathe and release the phlogiston into the atmosphere once again.

OK, there were a couple of simple objections to this. Wood, when burned would lose weight, but metals, when rusting, gained weight. But it was readily noted that burning wood released a lot of smoke, which surely weighed something, and it was presumed there was a weight gain there, too (which in fact is the case). It was proposed, therefore, that phlogiston had negative weight. This was a concrete prediction of the theory, that phlogiston, if isolated, would have what amounted to antigravity, or as they called it back then, levity.

Chemists made a bunch of progress in the 1770s towards proving this theory and bringing some order to chemistry, much like Newton had done with mechanics a century earlier.

Unfortunately things fell apart under the weight of too much evidence. Too much special pleading had to occur to explain away anomalies.

Phlogisticated air was produced by Daniel Rutherford in 1772. He would burn a candle in a closed container, let a mouse asphyxiate (which took about 15 minutes) in a closed container, and also could get metal to calcine in a closed container. The resultant gas from one of these processes (say the burning candle) could be tested in another (the mouse) and fail to support the new process as well, which gave him a warm fuzzy that all three gases were actually the same thing; air loaded to capacity with phlogiston.

Dephlogisticated air was prepareed by Scheele and Priestly separately but almost simultaneously in 1774. Scheele heated calx of mercury and collected the gas that came out; that gas would support combustion and respiration quite nicely so clearly it was air with no phlogiston in it at all.

Phlogiston was isolated by Henry Cavendish. This is the same Henry Cavendish who determined the value of the gravitational constant G over in physics land, as described in Part I of this series.

Cavendish added Mars (iron) to oil of vitriol to produce a gas which he collected in a bladder. The bladder actually floated in the air, which meant that he likely had phlogiston (which was supposed to have negative weight, after all), and the gas was also very combustible; logical for something released during burning. This new gas was “inflammable air” and had also been identified as being phlogiston.

So this looked very good for Stahl’s theory! Equations consistent with it could be written and phlogiston had indeed turned out to have negative weight.

We could even demonstrate that sulphur was oil of vitriol mixed with phlogiston, by use of those first two reactions I mentioned at the very beginning of this story.

By looking at all of this, it was clear that metals were compounds, and so was sulphur. The calxes and oil of vitriol were most likely pure substances, elements, irreducible to anything more simple.

Along comes Anoine Lavoisier. He made a fairly obvious prediction. Reacting phlogiston/inflammable air with dephlogisticated air should produce phlogisticated air.

It was already known that inflammable air was quite combustible, so Lavoisier built a very sturdy chamber for the reaction, one that would withstand the stress of the kaboom! and retain the product.

So then he did it, using a spark to touch off the reaction, and on examining the result he did not find phlogisticated air. Instead, he found the element water. And nothing else!

Think about that. There were other reactions that produced elements. But they always also produced something else. Starting with zinc and de-phlogisticated air, you could get the zinc calx element, but phlogisticated air would also be produced. In other words, if you start with a non element and turn it into an element, part of the original compound has to go somewhere else.

(zinc calx + phlogiston) + dephlogisticated air ->
zinc calx + phlogisticated air.

You can’t start with those sorts of beginning ingredient and end up with only an element afterwars. Whatever you broke away from the element has to have gone somewhere, in this case into the air to phlogisticate it.

So what’s going on here? How do you combine things and only get an element?

Fortunately, Lavoisier was a genius, and he did figure it out. By overturning every assumption that had been made.

He figured that water was a compound, a compound of inflammable air and dephlogisticated air. Up until this point water was presumed to be an element.

And that there was no such thing as phlogiston, and everything understood up to then was backwards.

If you understand modern chemistry at all, everything I’ve described up until now should seem inverted, like phlogiston is filling the role of oxygen, but in reverse–it is leaving things as they burn or rust, instead of combining with them.

But now, thanks to Lavoisier, try the new words “oxygen” for “dephlogisticated air” and “hydrogen” for “phlogiston” and “nitrogen” for “phlogisticated air.” These, Lavoisier realized are all elements; and air was a mixture of nitrogen and oxygen.

The metals weren’t compounds of something plus a “calx,” rather the calx was a compound of the metal and oxygen. And oil of vitriol was a compound of sulphur, not the other way around. (In fact today, oil of vitriol is called “sulphuric acid,” suitable for imbibing by your favorite Deep Stater.)

After several years of effort, Lavoisier was able to correctly identify 31 substances as elements, two still bear the names he gave to them (hydrogen and oxygen). Seven of these elements had not been isolated yet, but he figured they were part of a known compound; those are chlorine, fluorine, boron, calcium, magnesium, barium, and silicon.

Oddly he didn’t realize that potash and soda were similar; he thought they were compounds of ammonium. And he thought that heat and light were elements. (This was corrected by Count Rumford, who married Lavoisier’s widow.)

All in all, mistakes aside, this is a staggering amount of insight.

But he went further. In collaboration with three other chemists, he devised the naming system we use today. “Sodium chloride” is named according to this system; it indicates a compound of the two elements, sodium and chlorine. Gone was “flowers of zinc” to be replaced by “zinc oxide.” “Liver of sulphur” was now “potassium sulfide.” “Corrosive icy oil of tin” is now “stannic chloride.” And on and on, the new names reflecting the actual elemental composition. Most of the old names are now forgotten, but every once in a while you still hear them.

And now that elements were correctly identified, a lot of real progress could be made, because the whole mental map of what was going on was no longer upside-down and inside-out.

This is why Lavoisier is called “the Father of Chemistry.”

He was also a tax collector for Louis XVI. This made him well versed in accounting, which showed in his meticulous measuring of the masses of everything in reactions, to make sure the books balanced. He had demonstrated that mass was conserved in all chemical reactions.

Unfortunately his day job put his head into the guillotine in 1792 during the French Revolution. As Comte de Joseph-Louis Lagrange put it, “It required but a moment to cut off his head and perhaps a hundred years will not suffice to produce another like it.”

It took a long time for Lavoisier’s new chemistry to be accepted in Germany (the homeland of Stahl) and the United Kingdom was resistant as well. Politics had some influence on science back then too. But in England, it didn’t take too long. Because John Dalton would soon be hard at work, and so would Humphry Davy. These two parts happen almost simultaneously.

John Dalton

John Dalton made measurements of the masses of all reactants in many different reactions and came to the realization that elements reacted in certain fixed proportions by mass. (He managed this in spite of not being nearly as proficient at measurement as Lavoisier had been.) For example one unit of hydrogen appeared to react with 5.66 units of oxygen to form water. On the basis of this, he speculated that elements consisted of small minimum units, which he named atoms from Greek atomos, “can’t be cut.” This revived a speculation than had been dormant for over two thousand years, since Democritus who lived roughly around 400 BCE. He began publishing his work in 1806.

Dalton determined, very roughly, a lot of these ratios, and the ratios became what today are called “relative atomic masses.” The are the masses of atoms, relative to some (back then) unknown reference value. (In casual speech they are “atomic weights” and sometimes “atomic masses” though the latter can be confused with the actual mass of an atom in kilograms. Both “relative atomic mass” and “atomic weight” are officially sanctioned terms, though “atomic weight” seems to be falling out of favor. After all weight is actually a misnomer.)

Dalton carefully refined his table of atomic weights, but even his last effort is barely recognizable today. He had finally measured the oxygen:hydrogen ratio as 7, which was still not right, even given some of the bad assumptions he was making.

A lot of very basic (to us today) concepts were missing from this endeavour. It wasn’t clear that hydrogen and oxygen are never present as single atoms, but rather they’d form a compound with themselves, two hydrogen (or oxygen) atoms pairing off as a molecule of H₂ or O₂. Compounded atoms got the name “molecule.” This was true of nitrogen as well.

(On the subject of these diatomic elements, my high school chemistry teacher used to say that those elements whose names end in G, E, N or I, N, E were the “fags of the chemical world” because they’d form molecules with themselves. H₂, O₂, N₂, F₂, Cl₂, Br₂, I₂ [for hydrogen, oxygen, nitrogen, fluorine, chlorine, bromine, and iodine, respectively]. I can guarantee you no high school teacher says that today. In any case, hydrogen has one bond, and shares it with the other hydrogen atom, oxygen has two bonds, and so is double bonded to the other oxygen atom in the molecule, nitrogen has three and triple-bonds. The “-ine” elements are all one bond each and are called, collectively, halogens.)

Also missing was the concept of valence; Dalton didn’t realize that it was possible for one atom to combine with more than one other atom, or even two or three times to the same other atom, and that different elements followed different rules in regards to this. Thus he never understood that water was H₂O, not just HO. That caused him to understate oxygen’s atomic weight by a factor of two. He should have got oxygen = 8 on the basis of this misunderstanding, but he never quite got there.

All this emphasis I place on what he did not understand might lead you to think I am dumping on Dalton. No, absolutely not! Even with the things he didn’t know, he had made a huge conceptual leap, which (not incidentally) was needed before we could learn more. Ironically, the things he got right eventually made it possible for us to see his mistakes.

Amadeo Avogadro

Dalton’s misunderstanding of valence was corrected in part due to Amadeo Avogadro, who noted that when working with gases, their volume appeared to match these ratios. For instance a certain volume of hydrogen weighed two grams, matching its molecular weight; the same volume of oxygen would weigh 32 grams, matching O₂‘s molecular weight. And when reacting, some volume of oxygen would combine with twice that volume of hydrogen to form water, in accordance with the H₂O molecular formula for water, and not leave anything left over. Avogadro showed that at a given temperature and pressure, a certain volume of gas would contain the same number of molecules, regardless of which gas it was. Hydrogen, oxygen, Eric Swalwell’s most recent meal, it was all the same number of molecules per liter.

Today we know that 22.4 liters of gas at standard temperature (25 C) and pressure (1 atmosphere) will weigh, in grams, its molecular weight. That much H₂ weighs two grams, that much oxygen, O₂, weighs 32g.

Chemists found this useful, and defined a new concept, the “gram molecular weight.” Which got abbreviated “mole” and got the symbol mol. It’s now an official “base unit” of the modern International (Metric) System, alongside the second, the meter, the kilogram, and the ampere. (There are only two others, and you are about to meet one of those as well.) It’s basically the number of molecules it takes so that the numerical weight of the sample, in grams, is the same as its atomic weight. This is the same number for all pure substances, compounds or elements. We just didn’t know, then, what that number was, but that didn’t mean chemists couldn’t weigh out thirteen moles of copper sulfate when they wanted to.

Even though we didn’t know what the number was, or (equivalently) had no idea how much atoms and molecules actually weighed in grams or kilograms, Avogadro gets the credit for inventing the concept, and that number (now very well known today) is called Avogadro’s number in his honor and is symbolized by N_A.

A good set of values for atomic weight became absolutely vital for chemistry. The unsung heroes of chemistry during the 1800s were those who put in years of exacting effort refining atomic weights. Their work wasn’t glamorous, and never would have won them Nobel prizes (if those had existed back then), but chemists knew these guys were doing something Very Important. The biggest “name” here was Jons Jakob Berzelius (who also discovered selenium and cerium oxide), who produced exceedingly good figures by 1826. And in fact people continue to refine the atomic weights, taking into account all sorts of factors we had no notion of until the 20th century.

It became apparent very quickly that atomic weights weren’t quite neat integers. It’s easy enough to quote that hydrogen’s atomic weight is one and oxygen’s is 16, but in fact both numbers are very, very slightly off from those integers, and this was not an artifact of inaccurate measurement. Rather, it’s the way things really are. This must have been maddening for chemists (Why be just a little way off from clean integer ratios? Why not a lot more off from them? It’s like mother nature was shooting at a target and just barely missed the bullseye. Why?)

A pause for an example of using moles.

Chemists making a compound could decide how many moles of it they wanted, for example, say, ten moles. Let’s say our goal is to start with hydrogen and oxygen and to produce ten moles of water. You start out with this idea of the equation for the reaction. It’s really a sort of shorthand recipe.

H₂ + O₂ -> H₂O

Ten moles of H₂O is going to contain ten moles of oxygen atoms, and twenty moles of hydrogen atoms, because there are two hydrogen atoms in every one water molecule.

But before you rush off and put 30 moles of gas into a container, there’s one thing to remember. The oxygen going into the reaction is not oxygen atoms, it’s oxygen molecules. And each of those contains two oxygen atoms. So you need five moles, not ten, of O₂. And by the same token you need ten moles, not twenty, of H₂.

So really, to include the quantities, we should write the equation like this:

10H₂ + 5O₂ -> 10H₂O

But let’s sanity check it. Let’s see if mass is conserved.

Hydrogen’s atomic weight is one. Molecular hydrogen therefore has a molecular weight of 2. So ten moles of this is 20 grams of hydrogen.

Oxygen’s atomic weight is sixteen. Molecular oxygen therefore has a molecular weight of 32. So five moles of this is 160 grams of oxygen.

The total weight of all the ingrediens is 180 grams.

Over on the right hand side, the result is ten moles of water. Water, of course, has a molecular weight of eighteen (one + one + sixteen), and ten moles of it is therefore 180 grams.

The equation seems to balance.

Of course that equation only looks like it does because our goal was ten moles of water. To be generally useful it has to be reduced by dividing through by the lowest common factor. In this case that’s 5, so:

2H₂ + O₂ -> 2H₂O

(One of the things taught in chemistry class is how to balance these equations, like we just did here. In some cases it can get very complicated.)

Any future chemist can scale this up or down, just like working with a recipe that doesn’t make enough (or makes too much) food for your needs.

Let me again emphasize that at this point we didn’t know the mass of any atoms and molecules, and therefore we didn’t know how many were in a mole. But it didn’t matter, we knew the ratios of those masses and could just use moles to keep those ratios consistent.

One last note about atomic weight before we move on.

Because oxygen reacts with a lot of things, and because (unless you are dealing with a gas) you pretty much have to be able to react with something to measure its atomic weight it was convenient to set oxygen’s atomic weight to exactly sixteen, and measure everything in terms of that. So hydrogen’s atomic weight was 1.008 (that’s the best number as of 1949). Much later on we ended up modifying this convention just a tiny bit.

More on Gases…and Heat

As mentioned, a mole of any gas will occupy 22.4 liters at standard temperature and pressure. What happens if you alter one of these parameters?

If you halve the volume, yet keep the temperature constant, you will double the pressure exerted by the gas.

On the other hand, if you double the temperature, either the volume will double and the pressure stays the same or vice versa.

…wait. FULL STOP.

What does it mean to double the temperature? If it’s 20° Celsius, is 40° Celsius twice as hot? Really? Well, 20° C is 68 F, and 40° C is 104 F. But 104 isn’t two times 68.

So it’s only twice as hot if you’re using a Celsius thermometer.

Well, that sure seems stupid, doesn’t it?

We don’t have this problem when doubling mass or halving a length or quadrupling an electric current or waiting for the end of the Biden administration, even if it seems six times longer than it is.

That’s because we can tell what zero mass (or length, or current) is. It’s pretty obvious; if you have none of something, its mass is 0 kg. So doubling the 5 in “5 kg” gives you “10 kg” and by golly, that really is twice as much.

The problem with temperature is that 0° F or 0° C isn’t really “no temperature” or “no heat” in any meaningful sense. What we need to do is to first realize that there’s actually a true zero point to temperature, then figure what it is. Then, it becomes possible to measure with respect to it.

We’re looking to determine absolute zero.

And it turns out we’re already on the right path. We don’t know what half or double the temperature is, but we can figure it out by cooling, or heating the gas until its pressure halves or doubles. And once we know that (just making up numbers) that 559° F is double the temperature of 50° F, we can backtrack and figure out what the real zero point is.

Chemists/physicists did something very much like this. They had to be careful not to let the gas liquefy (all bets are off if that happens), but it turns out that when they plotted the lines, an “ideal” gas would hit zero volume and pressure at -273.15° C, or about -459° F. This is absolute zero.

(I lied. I didn’t just make those numbers up. 50° F is 509° Fahrenheit degrees above absolute zero, so 509 + 50° F = 559° F is twice as hot.)

And chemists and physicists both use a temperature scale that starts at this point, with degree sizes the same as for Celsius (9/5 of a degree Fahrenheit). This is called the kelvin, after Lord Kelvin, an important figure in the history of thermodynamics. In fact it’s not even called “degrees kelvin,” it’s just “kelvins.” This is the sixth of the basic metric units.

300 K works out to 80.33° F, just to help you get a feel for it. And scientists consistently work in kelvins, everything from chemists having to figure out when a material will melt or boil, or how hot something must get before it will react, to astronomers telling you the temperature of Pluto, or Sirius.

As the 1800s wore on, it turned out that, deep down, the temperature of an object was directly related to the average kinetic energy of the molecules inside it. The total energy of the heat in the object is of course the sum of all the molecules’ kinetic energy, or in essence the total kinetic energy inside the object. But now we knew what heat was…it’s actually a manifestation of kinetic energy. And this is why when friction occurs objects heat up; the energy of motion is being transferred to the individual molecules. The object as a whole slows down, but the molecules start moving around with respect to each other (picking up the momentum the object loses, remember momentum is conserved) and the object heats up.

Humphry Davy

We now turn to the other thing that was going on starting in the 1800s (this time I don’t mean the century but rather the “zero years” of that first decade). I mentioned this in passing in part IV.

Sir Humphry Davy (1778-1829) exploited the voltaic pile (battery) to bust apart molecules that had been impervious to other methods (a typical method was to try to bring oxygen in to grab one constituent of a molecule, since oxygen is very good at “cutting in”).

The basic procedure was to prepare a solution of whatever it was you wanted to break apart, stick two electrodes into the solution, connect them to a battery, and wait for the electricity to do the work. One part of the molecule would collect around the positive electrode and the other part around the negative electrode.

Apparently, moving an electric charge around could induce at least some molecules to break apart.

Convinced that potash contained an undiscovered element (in spite of Lavoisier not thinking so), Davy made up a solution of it in water, hooked up the electrodes, and got hydrogen and oxygen. Whoops. He was busting up the water. But he needed a liquid for this to work. So he tried molten potash, and that worked like gangbusters. There were flames at the negative electrode. Taking a closer look, there were globules of silvery metal forming there, which would immediately burst into flame, just from contact with the air.

Davy was able to capture some of these globules before they self-torched and tried putting them in water. They’d race around the surface of the water and burst into lavender light. It turned out that the water was being broken apart into hydrogen and hydroxide (OH) and the hydroxide was reacting with the metal, to form KOH (potash lye). The hydrogen, on the other hand, was hot enough to spontaneously combust to form water vapor. Whatever this new stuff was, water would burn it!

According to witnesses, Davy danced around the laboratory with joy. He had just discovered potassium.

He tried soda (no, not coca cola). It took more voltage (electrical potential, the push) but he isolated sodium in short order. Sodium, of course is now famous for pyrotechnics when put into water. (It’s very, very dangerous, by the way, to simply throw a piece of sodium into a lake–a jet of hot, fresh soda lye (NaOH) might just shoot out the way the sodium came, land on you and blind you. However, I can promise Barry Obola that he is so anointed that he will come to no harm whatsoever if he does this. Trust me, Barry.)

Davy also nabbed magnesium, calcium, strontium and barium, elements that Lavoisier had identified as being there without them having been isolated. With the exception of magnesium, these would all spontaneously react with air and moisture energetically. Magnesium, the one metal that didn’t, was barely a successful find; it turned out a more successful method of isolating it was to react one of its compounds with pure sodium, so as it happens Davy was a key part of that effort anyway.

Davy had even more trouble with lithium; only small, wretchedly contaminated samples resulted from his efforts, and indeed it wasn’t until 1855 that good samples of lithium were isolated.

Michael Faraday (again)

All this was in 1807-1808, but Davy wasn’t done contributing to this story.

In 1813 he hired Michael Faraday. Yes, that Michael Faraday. The Michael Faraday, who alongside Newton and Maxwell, had his picture hung in Albert Einstein’s office. The Michael Faraday from last week that you were supposed to thank the next time you flipped a light switch (did you?).

Given that Faraday never had formal education, and learned all his science on the job, Davy did the world a tremendous favor giving him a chance. (So thank him, too, the next time you flip a light switch.)

As if unifying electricity and magnetism and laying the groundwork for modern civilization weren’t enough, Faraday also investigated electrolysis, following in Davy’s footsteps. In fact, he invented the words “anode,” “cathode,” “ion” and “electrode.”

Faraday is responsible for the discovery that in order to break a single bond, like say that between sodium and chlorine in salt, with electrolysis, a certain amount of electrical charge has to be supplied. And this number was the same per bond, per mol. This is, in fact, Faraday’s Constant.

To break one mole of single bond, it required 96,485.3 colombs. (Remember, once again, how humongous an electric charge one coulomb is.)

If it was a double bond, it would take twice as much charge.

This alone should be enough to convince anyone that there is a lot of electrical charge in simple, ordinary materials. We never noticed because it’s almost always perfectly balanced. When it falls out of balance, your sheets stick to each other coming out of the drier, your cat gets covered in packing peanuts, balloons pull your hair into a mess, and so on. On the plus side, if you can get the electrical fluid to move (without causing a huge imbalance) you can get it to work; a lot of work.

You could even think of this number as a mole of electric charge, since it operated to break one mol of single bonds (or half a mol of double bonds).

Chemistry, it was becoming quite apparent, is actually an electrical thing. Remember when I said, last time, that electricity is responsible for every physical phenomenon you see around you, except for gravity? That included things like why it’s hard to break rocks (electrical forces keep the rock bonded to itself), why water takes as much heat as it does to boil, anything having to do with light, and on and on. It includes things set on fire. It includes the question of why you and I aren’t just loose piles of disorganized atoms.

Dmitri Ivanovich Mendeleyev

(A quick linguistic note. Mendeleyev’s name is properly spelt: Дмитрий Иванович Менделеев, but I suspect most of my readers can’t read Cyrillic, so it’s necessary to transliterate his name into the Latin alphabet. Usually when this is done, the “y” is not included, but I think it’s better to use the y, because it is most definitely pronounced when English speakers pronounce his name (and for that matter is implicit in the second of the pair of еs in the original Russian). Those in the know know it’s “men-del-A-yev” rather than “men-del EVE” (it’s probably a way of hazing noob chemistry students who don’t know the trick and blunder) but the most-common transliteration doesn’t reflect this. Since the transliteration is supposed to be helpful, I decided to use the more-helpful, less-common alternative here.)

I started this article by pointing out that chemistry was a collection of unsorted trivia until Lavoisier, who finally got us on the right track to figuring out what substances were compounds, and which ones were elements, the basic building blocks of everything you can drop on your foot.

But Lavoisier knew of thirty one elements. By 1869 there were sixty three of them (including one mistake, didymium, that was really two elements that today we call praseodymium and neodymium).

This is an awful lot of different basic building blocks, isn’t it?

There seemed no rhyme or reason to it. Most of their masses were almost, but maddeningly not quite, integers, but even ignoring the tiny fractions, the numbers were chaotic. In order, hydrogen 1, lithium 7, beryllium 9.4, boron 11, carbon 12, nitrogen 14, oxygen 16, fluorine 19, sodium 23, magnesium 24 for the first ten.

What went into the holes? Was there something with an atomic weight of almost-but-not-quite 2, 3, 4, 5 or 6? What was up with beryllium?

Some chemists had begun to notice that some elements seemed chemically similar, for example, fluorine, chlorine and bromine, or copper, silver and gold, or chromium, molybdenum and tungsten. There seemed to be a lot of “triads” of elements like this.

But it was Dmitri Mendeleyev (1834-1907) who was the first to perceive the entire pattern…and to put a lot of confidence into it.

He sorted the elements according how they combined with oxygen. The first group (hydrogen, lithium, sodium, combined 2-1, two atoms of the element to one of oxygen. Each of these took up one of oxygen’s two bonds. You can write a generic formula, R₂O for this. And to make the pattern clear, figure that an average atom of the first group combined with one half of an oxygen atom.

The second group was one-for-one. Beryllium, magnesium, calcium all took up both of oxygen’s bonds, generic formula RO.

Then there was a two-to-three group, boron, aluminum, etc, where two atoms of the element, with three bonds apiece, would combine with three atoms of oxygen, for a generic formula R₂O₃, or each atom combining with one and a half oxygen atoms.

This could be carried through until you got to elements that would combine with four full oxygen atoms (RO₄), giving a total of eight possibilities, with elements sorted into eight groups.

Mendeleyev could sort these groups each by increasing atomic weight, then set these groups next to each other as columns in a grid. When he did that, he could read across, from group 1 to group 8, increasing atomic weights in the top row. Then the next row started in group 1 with a higher atomic weight and repeated the process. It was a periodic trend, every eighth element landed in the same group.

There were a few irregularities. For instance group eight, the one-to-four group, would either be empty on a given row, or hold three neighboring elements (iron-cobalt-nickel, ruthenium-rhodium-palladium, osmium-iridium-platinum), which was a bit of an irregularity, but it was a regular irregularity as every other row had one of these triples in column 8; the empty cells and the cells with three elements alternated.

That was far less interesting than some of the other irregularities in the sequence. For instance calcium belonged with beryllium and magnesium above it (and strontium and barium below it) in the one-to-one column, column 2. But the next element after that was titanium, which was a two-to-one which did not belong in the next three-to-two column which had boron and aluminum. Rather, it belonged better in column 4. So maybe this was all a waste of time?

Or maaaaybe the cell skipped over was a hitherto unknown element! So leave that spot open, and put titanium under carbon and silicon, the one to two column, where it belongs. (Titanium dioxide is a thing.)

There were two more holes between zinc and arsenic. And others, but Mendeleyev chose to focus on these three.

Mendeleyev predicted three new elements to fill these holes. The first one he predicted an atomic weight of 44, an oxide R₂O₃ weighing about 3.5 grams per cubic centimeter. He made other predictions for the other two elements.

All three of these elements were found in the next 20 years, they are scandium, gallium, and germanium respectively. And they matched up with Mendeleev’s predictions pretty damn well. Not exactly, but far too close to be random chance.

Mendeleyev was definitely onto something. Previously, elements had popped up at random, with no rhyme or reason, totally unpredictably. A bright chemist might have a hunch that some mineral (say) had something new in it, and might even be able to prove it without isolating the element, but one could never tell when such a thing would turn up, or what the new element would be like, until isolated.

But now Mendeleyev could tell you, before anyone else had so much of an inkling as to the existence of an element, what it would be like!

Because of this, it didn’t take long for chemists to accept this pattern. It’s now called the periodic table of the elements. It has gone through several changes (the most important going from 8 columns to 18, or actually, 32) but it traces right back to Mendeleyev. It became so deeply ingrained, that chemists were even willing to disregard atomic weights if they were out of the periodic table sequence. In particular, 1889 a chemist named Brauner measured the atomic weight of tellurium very carefully and got a higher value than before, 127.6. This was a group 6 element, in the column headed by oxygen. Its next door neighbor in group 7 was iodine, and iodine had an atomic weight of 127. So now all of the sudden, tellurium had a higher weight than the next element in the sequence.

Does this mean that iodine and tellurium should swap places? Nope. Leave them where they are. There must be some reason for the oddity, but matching group membership was more important than arranging things in order by atomic weight. (Mendeleyev’s attitude was a bit different. He apparnetly figured the new number for tellurium must be mistaken; he wasn’t willing to part with the assumption that the atomic weights had to increase as you read across the rows, but he clearly did think the periodic sequence was more important; given a “contradiction” he went with the periodic table, not the atomic weight data.)

But even as the periodic table was being accepted as an organizing principle, it looked like it was starting to unravel. In the early 1800s chemists started discovering “rare earth elements” with atomic weights between 138 and 175. (No other elements were in this big gap.) They found more and more of these elements…and they were similar to each other, enough so that they were hard to separate, and the similarities were in fact why newer elements were able to hide within older ones. It’s like they were all trying to cram into the square below scandium and yttrium! (Mendeleyev knew of four in 1871, there would ultimately turn out to be fifteen of them.)

As more and more of these elements were discovered, Mendeleyev simply didn’t know what to do with them and just gave up trying to fit them in–leaving it for a future genius to solve. Other chemists tried to organize them and failed to do anything convincing with them. Since they didn’t follow the rules, there wasn’t even any way to know for certain how many of them there were!

So it was frustrating. There was only partial order to the elements, but then, where there was order, it was very, very useful. Call it a win, overall, even if it wasn’t a rout.

Sir William Ramsay

In fact, there wasn’t even any assurance that there wasn’t a totally unseen column in the table.

Wheatie asked me the question, once, as to whether there could be undiscovered elements between the ones we know about. Without pulling in a spoiler, the answer is basically “not no, but hell no!”

That’s the answer today, because of discoveries made in the 1910s. Back then, that was not the answer by a long shot; there were known holes in the table such as Mendeleyev’s three predictions. And who the heck knew how many of those damn rare earths there were, not to mention more holes like the one at atomic weight about-a-hundred.

Well, back up to 1785. Cavendish…remember him? G? Flammable air (i.e., phlogiston hydrogen)?

In a totally different experiment, Cavendish had reacted phlogisticated air (nitrogen) and dephlogisticated air (oxygen) with a spark, repeatedly, making niter. But some of the nitrogen just wouldn’t react. Since his source for these gases was the atmosphere, he was able to determine that this residue accounted for 1/120th of the atmosphere. (He was a very careful, meticulous and precise measurer, which is how he was able to determine G, a difficult thing to measure even today.)

And there that matter stood, basically forgotten, for almost a hundred years. Until 1882 when Lord Raleigh at Cambridge University’s Cavendish Laboratory (the irony!) was working with hydrogen, oxygen and nitrogen, trying to determine their densities and hence (thanks to Avogadro’s law) their atomic weights. He got good solid values for hydrogen and oxygen, but for nitrogen, he couldn’t get consistent results. If the nitrogen came from ammonia, his result was 1/2 of a percent lower than if the nitrogen came from the atmosphere. Raleigh was probably banging his head on the wall in frustration. He wrote to Nature, the preeminent scientific journal, asking if anyone else had any idea what was going on, just like today we might post on a chemistry forum online. He got a bunch of suggestions, including that the leftover gas might be N₃, a hypothetical, less reactive form of nitrogen, just as oxygen could form O₃ (ozone) instead of its usual O₂.

Sir William Ramsay took another approach. He took some air, passed it over hot copper to remove the oxygen, hot magnesium to get rid of the nitrogen, soda lime to get rid of the carbon dioxide, and phosphorus pentoxide to get rid of the water vapor.

What he had left was about 1/80th of what he started with. At first he and others thought that this was indeed N₃. But Sir William Crooks was able to prove that whatever this was, it wasn’t any kind of nitrogen.

In 1894, Ramsay realized the truth. This was a new element, one that didn’t react to oxygen at all. For that matter, it didn’t react with anything else either, including itself. This was argon, and it’s in every breath you take. An utterly non-reactive gas.

In addition to group 1, where every atom reacted with half an oxygen atom, through group 8, where every atom reacted with four oxygen atoms, in steps of half an oxygen atom, there was something one step to the left. Atoms that would react with no oxygen atoms.

This explained what Cavendish had seen.

There was a whole new column in the periodic table, call it Group 0.

Ramsay continued working into 1895 looking for other members of this column, unaware that he’d been partially scooped.

But 1895 is our line. We’re not quite yet ready to step across it.

Conclusion

There’s no new conservation law this time, rather a reinforcement of the conservation of mass and the conservation of energy, but we have plenty of mysteries.

Why are there so many different kinds of atoms? It’s nice that they form a pattern, but it’s not a perfect pattern, and those damnable rare earths really bork it in one place. Why is there a pattern, and why is it not perfect?

What is the relationship between atoms and electricity? We still don’t know what the electric fluid is. We have one tantalizing clue, that a bazillion coulombs (okay, 96,485.3 colombs, but that’s a lot) of charge seems able to bust up one mole of a single bonded molecule.

Remember, as far as we knew, an atom was an indivisible thing. Yet they seemed to be swapping electrical charges (or something) when forming compounds, with electrolysis somehow undoing that to break compounds apart.

All of which just pointed to a need to keep investigating atoms.

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 !!!