Hey China!

Or rather, “Hey Chinese Communist Party and your entire array of servitors, ass-wipers, and fellators!”

You’re not even worth my time this week. When you decide to act like civilized people, maybe I’ll give you a lesson or two in how non-barbarians behave.

Hey BiteMe!
(Or, Whoever Has Their Hand Rammed Up That Putrefying Meat Puppet’s Ass)

[Language warning]

You and yours have caused a lot of injury. Literal injury with your war on people who don’t want to take an untested vaccine. When people die in an emergency room because a hospital won’t admit them because they haven’t had their clot shot, that’s a crime.

I’m going to address here the insult on top of the injury, because I am among the insulted. I still have my health but apparently you want me to live under the 8th Street Bridge (which actually isn’t on 8th Street, but whatever, that’s what the I-25 overpass over Cimarron is called), so maybe if you have your way that won’t be true for long. Dreadful time of year to become homeless.

No, you’re just trying to make me unemployed, because I won’t take your fucking shots.

Well, that threat is NOT going to work. I. Won’t. Take. Your. Fucking. Shots.

And neither will any of my coworkers who haven’t already had them…and those people who got the shots are a small minority. Most of those got the shots before we began to understand how nasty they truly are.

One of my coworkers was thinking he might have to knuckle under at least until he found another job…but don’t you even think (you do sometimes think, don’t you?) of finding that encouraging.

Don’t think that, because his resolve has hardened.

You’re LOSING.

You LOSER.

You Chinese-bought ratfucking traitor.

I would love to see you die an agonizing, humiliating death. (This isn’t a threat, because I am not threatening to cause that death. I am just announcing my intention to party if it happens.) It would be just recompense for the way you’re killing America…and millions of Americans.

Anti-Science?

So you think I’m anti-science for refusing the “vaccine”?

Uh, you do know who you’re talking about, right? The guy who writes the physics posts?

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.

(I’d like to add, I find it entirely plausible, even likely, that His Fraudulency is also His Figureheadedness. (Apparently that wasn’t a word; it got a red underline. Well it is now.) Where I differ with the hopium addicts is on the subject of who is really in charge. It ain’t anyone we like.)

Justice Must Be Done.

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

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

The Audit

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

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

But at least it finally is out.

Lawyer Appeasement Section

OK now for the fine print.

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

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

And remember Wheatie’s Rules:

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

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

Spot Prices.

Kitco Ask. Last week:

Gold $1793.00
Silver $24.40
Platinum $1047.00
Palladium $2104
Rhodium $15,250

This week, markets closed as of 3PM MT.

Gold $1785.10
Silver $23.99
Platinum $1028.00
Palladium $2087.00
Rhodium $15,250.00

Gold at least seems to have pulled out of the 1750s. The PGMs are basically going nowhere, perhaps because their demand largely rests on cars and no one can build cars right now because of the supply chain blah blah blah.

Extreme Stars

Last week, I mentioned in passing several kinds of what one might think of as “extreme” stars.

Ordinary stars are fusing hydrogen to make helium. Astronomers call them “main sequence stars” and they range from large, hot, very luminous (and hence short-lived) blue stars all the way down through small, faint, cool, dim (and hence long-lived, none have died of old age yet) red stars called “red dwarfs.”

Stars go “extreme” when they run out of hydrogen fuel. Red dwarfs, we believe, will simply turn into white dwarfs–stars that consist of the “ash” of nuclear fusion, and are no longer generating heat…rather, they radiate their residual heat, albeit at very high temperatures. Medium-sized stars like our sun will become red giant stars that fuse the helium ash of their prior main sequence lives, then after running out of helium while making carbon and oxygen, they too will become white dwarfs.

Red Giants and Supergiants

Red giant stars are pretty extreme…in physical size, at least; when the sun goes red giant it will swell up immensely. It may well swallow up the earth, and certainly will swallow up Mercury and Venus.

Red giant phases are the common denominator, for stars about 30% of sun-mass and up. (A star about ten times the mass of the sun becomes a ‘supergiant’ but that’s essentially the same thing, just much bigger. Examples are Betelegeuse and Antares.) All such stars swell up and burn helium; the more massive ones will continue past that, burning carbon, oxygen and eventually silicon; then they will start on iron.

White Dwarfs

White dwarfs are even more extreme. They’re about the size of the earth (and remember they’re the corpses of something a few tens or even hundreds of thousand times the mass of earth), so they are very dense, many tons per teaspoonful. There’s basically nothing to stop the star from collapsing once it no longer generates energy and heat from nuclear fusion, so it does precisely that: collapses. The end result is a star corpse, held “up” purely by the repulsion of the electrons in it. It does, of course grow hotter as the pressure increases during the collapse, so this corpse glows white hot. But that heat simply radiates away, never to be replaced. White dwarfs will cool off and stop radiating visible light…eventually.

Heavier stars go through all of this, but at the end, the electron repulsion won’t stop the collapse. The star is simply too massive, the self-gravitation of all that mass is just…too much.

This sort of star shows up after a core-collapse supernova, which isn’t just a Boom! or even a KaBoom!!! It’s most assuredly an earth-shattering kaboom.

Literally. If our sun were to do this, Earth would be literally blown to bits. Not just “oh all the life on the surface got wiped out,” I mean blown to bits. Fortunately our Sun isn’t nearly massive enough for this to happen…and it won’t even get to white dwarf status for another five billion years or so. (So no, you shouldn’t skip paying your bills.)

Neutron Stars (Pulsars)

In a neutron star the pressure is so great that the electrons are forced into the nuclei. They combine with the protons, and the star simply turns into a big mass of neutrons.

Neutron stars will form whenever the leftover remnant of the star is more than 1.4 times the mass of the sun. This number is known as Chandrasekhar’s limit because was calculated in 1931 by Subrahmanyan Chandrasekhar. At that time, though, he had simply calculated when the electron pressure would fail; he didn’t realize that a ball of neutrons would form if, say, the star’s mass was just above his number. (The neutron hadn’t been discovered yet.)

A neutron star is roughly ten miles across.

Compressing the star into something that small makes for a very dense object. Imagine the weight of the Great Pyramid in a teaspoon. It also does two other things: First, remember your angular momentum. As a rotating object shrinks, it rotates faster and faster. And stars do rotate.

The typical neutron star rotates a couple of thousand times per second.

Also, the star had a magnetic field. Concentrating that into a smaller star simply makes it more intense. More than likely the poles of the magnet won’t be lined up with the axis of rotation, so as the star rotates, its magnetic poles sweep across the sky like a lighthouse. A lighthouse on your washing machine’s spin cycle. (Though even that isn’t nearly fast enough.) The star ejects all sorts of particles along its magnetic axes, and over time it slows down.

These stars were first discovered via radio telescope in 1967 by Jocelyn Bell. The signals from them are so regular that at first some thought we might finally have found little green men. Eventually we figured out what was going on and they were dubbed “pulsars” (from pulsating stars).

This video is audio of a few pulsars, first ones rotating slowly enough we perceive the individual pulses. But at higher frequencies we simply hear a tone of the matching frequency.

https://www.youtube.com/watch?v=j_3sHeUNn1k

But even this is not as extreme as it gets.

Black Holes

If the star’s core remnant (after large parts of it get blown away) is sufficiently massive, even the neutrons are crushed.

As far as we know, there’s nothing to stop complete collapse at this point. And by complete, I mean collapse until the star has zero diameter. And I do mean zero. Which also means an infinite density.

An infinite density doesn’t seem physically possible–nature abhors infinities–but if there’s anything to prevent it, it’s beyond the ken of present day physics.

Or perhaps it’s not an issue at all.

Yes, I am talking about black holes.

Why is it called a black hole?

As you might imagine, these extreme stars (even the relatively un-extreme white dwarf) have very high surface gravities. After all that’s part-and-parcel of crushing matter down to such small sizes.

The sun’s surface gravity is about 28 times that of earth. That’s 28 g. An object that weighs one pound on earth would weigh 28 pounds on the sun.

A white dwarf might have the same mass as the sun but be far more compact, that means the radius is smaller and the strength of the force of gravity goes up as the radius goes down. In fact, half the radius is four times the strength. So a white dwarf might have a surface gravity of 100,000 g.

A neutron star typically has a surface gravity of 100 billion g.

Each of these implies a surface escape velocity. The earth’s escape velocity is about 11 km/second, the sun’s escape velocity is 617 kilometers per second. That white dwarf will come in at about 3000 kilometers per second. A neutron star will come in at 100,000 kilometers per second.

That’s about a third of the speed of light.

Well, that should bring up the question: Can something exist where the surface gravity is so high that the escape velocity is the speed of light? Or higher?

If so it’d be impossible to escape that object. You can’t launch a rocket that fast, because any object with mass can’t even reach the speed of light–let alone exceed it.

This idea isn’t particularly new. John Michel, in 1784, wondered if there might be stars so massive their light couldn’t escape them. He called them dark stars. He imagined an object the same density as the sun, but perhaps 500 times the diameter.

Of course he didn’t understand that an object so massive would simply crush itself down to a denser, smaller object, even going past the neutron star limit. He had no idea what neutrons were; no one did.

The critique his idea faced wasn’t on that basis. A couple of decades after his suggestion, light became understood as a wave with no mass, and by Newtonian theory the force of gravity requires an object with mass, acting on another object with mass. The two masses are multiplied together (then multiplied and divided by other things) to compute the force

If one of the two objects has no mass, the force is zero. According to the Newtonian understanding of gravity, therefore, light should be totally unaffected by gravity, and it would still escape the so-called “dark star” which wouldn’t, therefore, be dark at all.

But then the idea became worth taking seriously again after 1915, when Albert Einstein’s theory of general relativity was put forth. And even more so after general relativity was bolstered by Arthur Eddington’s measurements of apparent star positions during a solar eclipse.

Gravity now was understood not as a force between two masses, which had to be proportional to their product, but rather as distortions in spacetime caused by any mass.

So a high-mass star bends spacetime. And any object travelling freely, without any acceleration being applied to it, would try to follow those bends. Even an object with no mass at all, because the object’s mass plays no role in determining its path. It’s not experiencing a force at all.

This is not to say there isn’t a force involved when standing, say, on a planet. The Newtonian understanding is that an object is being pulled toward another object by a force, and (if it’s an apple and a planet) the surface of the planet is acted upon by the force on the apple, giving the sensation that the apple has weight. The Einsteinian understanding is that the apple is trying to travel a straight line in space time, because that’s what all things do, but the surface of the planet is pushing the apple off the path, applying a force to it, and thereby presenting the sensation of weight.

Once the idea of a dark star became reasonable again, the theory guys got back to work.

The Tolman-Oppenheimer-Volkoff limit, about 2.17 solar masses (though it’s a lot harder to nail down this value, so don’t hold me to it), is the upper limit of neutron star mass. Past that, the neutrons can’t hold the star “up” and it just keeps collapsing.

There’s nothing known that can prevent it from collapsing down to an infinitely dense mathematical point. Which is a physical absurdity. But of course, we don’t know everything, and as I hinted at above, it might not even be an issue.

What would one of these objects look like?

It would emit absolutely no light. Or anything else. (It might emit Hawking radiation, which I’ll hopefully remember to explain a bit later.)

Regardless of the actual size of the object, there is a certain radius from the center, above which the escape velocity is below the speed of light, and below which, the escape velocity is above the speed of light.

Because of that anything below that radius, is invisible to us, it’s gone from the universe, never to return. This level is called the event horizon, or sometimes the Schwarzschild surface, after the man who first did this particular computation, characterizing a non-rotating black hole. And the radius of that surface is called the Schwarzschild radius.

And its blackness led to the name “black hole,” which was coined by a student of John Wheeler’s in 1967. Wheeler decided it was perfect and used it himself and it caught on.

The only way we can tell anything is there is from the object’s gravitation. The black hole has two other properties: if the stuff inside the event horizon has a net electrical charge, so will the black hole, and also, the black hole might rotate, which could change the shape of the event horizon.

A black hole formed from a collapsing star will certainly be rotating, even faster than the pulsars do because the radius is that much smaller.

If we can’t see one of these things, how will we ever detect one?

I dropped a couple of hints above, but there’s also another way, and that’s to detect the matter falling into a black hole before it crosses the event horizon.

Consider a binary star system. The two stars are formed at the same time, but the more massive of the pair ultimately goes supernova and ends up being a black hole. The black hole and what’s left of the other star after the big kaboom will continue orbiting each other. If the distance between the two is small enough, then an interesting thing occurs. Ordinary stars constantly lose some mass through their “solar wind” and coronal mass ejections. In this case, some of that mass will hit the black hole, or come very close to it. It can be gravitationally captured by the black hole, resulting in a spinning disc of gas.

Gas, in orbit, will eventually collapse into the black hole. This wouldn’t necessarily be true of a single discrete object, but the gas consists of individual atoms that bump into each other, and some of those particles lose velocity as a result. Over time, the gas spirals inward, at faster and faster speeds: its temperature can reach millions of degrees, and it will emit X-rays due to its black body radiation.

We can see those X rays.

The very first black hole to be seen is known as Cygnus X-1, because it was the first X-ray source discovered in the constellation Cygnus (which contains the northern cross–at this time of year it’s in the western sky immediately after sunset). This source was discovered in 1964, and by the mid 1970s it was accepted as being a black hole, with a companion star losing mass through the “accretion disc.”

The amount of energy lost by matter in the accretion disc is about a third of the energy of the mass of that material from E=mc². If we could actually “tame” a black hole and feed anything, even garbage into it, then harness the radiation output from the accretion disc, it’d be a fantastic source of energy.

For reasons that (as I understand it) are still unclear, there are often two jets of energy coming out from near the event horizon perpendicular to the accretion disk, too. Below is an artist’s conception:

There was, however, another surprise in store for astronomers. When they began using radio telescopes in the 1950s, they identified a number of point-like radio sources, and by analyzing their spectra they were able to tell that these objects were very, very, very distant (I’ll discuss that some more next time). They were named “Quasi Stellar radio sources” which got shortened to “quasar.” For many years these were a mystery. It turned out that these things were belting out truly enormous amounts of energy, far more so entire galaxies. And we had every reason to believe they were small.

We now believe we understand these objects.

It turns out that every galaxy has, at its center, a supermassive black hole, one with anywhere from ten thousand to billions of times the mass of the sun. The one at the center of the galaxy M-87 is particularly enormous, about 6.5 billion solar masses, and we’ve been able to image its accretion disc with radio telescopes; below is a false color image based on that data:

With M-87’s central black hole we can even see one of the jets being shot out of the thing. Below is a picture of the core of M-87 taken by the Hubble Space Telescope; the blue is a false color rendering of one of the jets.

Quasars are far away, which means we are seeing the light that left them a long time ago, many billions of years. It seems that young galaxies go through a phase where vast quantities of matter is falling into their central black holes, and that accounts for the astounding amount of energy blasting out of these things.

What about our galaxy, the Milky Way? Though we can’t see, with visible light, the center of our galaxy–there’s too much dust and gas in the line of sight–we can see the stars near the center with infrared light.

And after watching them for about ten or fifteen years, it became clear they were orbiting something invisible. They were orbiting close enough that that put an upper constraint on that object’s size, and their orbital speed showed the mass of the object: four million times the mass of the sun. This object is known as Sagittarius A* (pronounced “A-star”) because it too is a radio source; it’s constantly sucking in small amounts of debris and gas.

One of these central stars has been rather imaginitively named S2 and its motion over the past couple of years is practically iconic to astronomers:

Here is plot of S2’s position over time:

And a plot of the orbits of dozens of stars shows them in orbit about something. Here are a few prominent ones including S2.

[If you remember that objects orbiting much more massive ones do so in ellipses, with the primary object at one of the foci of the ellipse, you might object to what you’re seeing in this last diagram. The black dot represents the black hole, and it’s clearly not at the focus of many of those ellipses. (The foci of an ellipse are both on the center-line, drawn along the long axis of the ellipse, called the major axis; in the case of S2 that centerline is to the right of the black dot.) This difficulty is overcome, though, when we realize we’re not looking at those ellipses face on. We’re looking at them at some sort of oblique angle. What you see when you look at an ellipse at an oblique angle is always a different ellipse with different (apparent) foci. Think of looking at the outline of a circular manhole cover from, say 30 feet away and five or six feet above the roadway; that outline appears elliptical. If the manhole cover itself were elliptical, you’d see some different ellipse, depending on its orientation from your point of view it might appear skinnier (more eccentric) or rounder (less eccentric) than the actual ellipse is.]

The conclusion that the dark object at the center of this mess has the mass of four million suns came from determining, based on the speed of the objects at different points on the ellipses, the actual orientation of their orbits (if an object moves most quickly at a certain point on the ellipse, you know that, whatever the ellipse looks like to us, that point is actually the point nearest the primary), and from this the actual lengths of the axes of these ellipses, and hence going from there to the mass of the primary. (The period of the orbit depends on the mass of the primary and the major axis, only–though astronomers’ formulae actually work with half the length of the major axis, called the “semi-major axis.”)

It should be a source of amazement that we can collect this data from so far away (approximately 30,000 light years or 180 quadrillion miles) and infer there is a nearly invisible object there, at the very center of our galaxy, and figure out its mass.

But in telling you this, I’ve actually gotten ahead of myself.

We really need to go back to the 1920s again. And explain galaxies and those staggering distances to the quasars.

But before I conclude, there’s a lot I did not say here. I didn’t discuss wormholes and using black holes to get into hyperspace, and all of that. Largely because all of that is very, very speculative and even if true, would probably destroy any spaceship that tried it.

As you get close to a black hole you feel very high tidal stresses. If you’re going in foot first, your feet feel considerably more gravity than your head, because they’re closer to the source of the gravity. (This effect exists even here, but is unnoticeable because the difference in force between your feet and your head is small.) This results in a net force that tries to stretch you out; if it’s strong enough it will stretch you out, it will be stronger than the bonds between the molecules that make you up. And the closer you get the stronger this tidal stress gets.

People who study black holes actually, and I am not making this up, call it “spaghettification.” Any solid object gets stretched into something looking like spaghetti.

If it were you, you’d feel this happen very quickly.

If someone were well outside the black hole watching, though, he’d never see the process end. Remember that under general relativity, lower objects’s clocks run slower than higher objects’ clocks do. And you can’t get any lower than the event horizon of a black hole. The observer far away will see you come to a standstill as your clock gets slower and slower, never quite reaching the time at which you cross the event horizon.

This might be the answer to the objection that an infinitely dense mass at a point is physically absurd. The collapse of the black hole itself might not ever complete because the clock runs slower and slower. This is actually speculation too; the math is extremely difficult and as far as I know no one has managed to solve the problem yet.

Well, that’s my rather over-simplified and under-coherent account of black holes. If you want a much more complete treatment, I suggest you go to the Wikipoo article on black holes.

Obligatory PSAs and Reminders

China is Lower than Whale Shit

Remember Hong Kong!!!

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

China is in the White House

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

Joe Biden is Asshoe

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

But of course the much more important thing to realize:

Joe Biden Didn’t Win

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

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

For millennia, you had to suffer from this:

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

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

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

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

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

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

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

His Fraudulency

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

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

One can hope that all is not as it seems.

I’d love to feast on that crow.

Justice Must Be Done.

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

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

Political Science In Summation

It’s really just a matter of people who can’t be happy unless they control others…versus those who want to be left alone. The oldest conflict within mankind. Government is necessary, but government attracts the assholes (a highly technical term for the control freaks).

(A comment I wrote last week that garnered some praise.)

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 $1768.40
Silver $23.40
Platinum $1059.00
Palladium $2162.00
Rhodium $15,150.00

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

Gold $1793.00
Silver $24.40
Platinum $1047.00
Palladium $2104
Rhodium $15,250

Nice moves upward for gold and silver, but the platinum group metals are considerably mixed.

XXII Powering Stars

One of the things that was puzzling physicists and astronomers in the late 1800s and even into the early 1900s is how stars could continue to belt out such phenomenal amounts of energy every second, year in, year out for millions and even billions of years.

Our sun, for instance, has been pumping out 3.828 x 10²⁶ watts, continuously, for billions of years. To be sure the current conclusion is that this number is actually increasing slowly so that in the past, say a billion years ago, it might have been ten percent less.

To put that into some sort of context, the best estimate we can make is that the entire human race uses 15 terawatts, that’s 1.5 x 10¹³ watts. The sun belts out ten trillion times as much power as we consume.

That power goes out in all directions from the sun, and only a tiny fraction of it hits the earth. By my calculations, the earth catches about 1/2 of one billionth of all of that energy, because that’s the fraction of the possible directions for light shining from the sun, that is covered by the disc of the earth as seen from the sun. (I may very well have dropped a decimal somewhere.) If that number is right, the Earth absorbs solar energy at a rate of 176,000 terawatts.

Where does this energy come from?

In the 1800s the only imaginable energy sources were combustion (like burning coal), the sun getting hotter as it shrank, and objects striking the sun. These were all unsatisfactory answers. A sun-sized pile of coal (never mind the oxygen needed to burn it) would have run out in a couple of thousand years [not long enough even to account for history since Caesar, much less all of recorded history]. The other two sources would last less than a million years at most (and there’s simply not enough junk in the solar system to hit the sun and supply the energy that way, or we ourselves would be getting bombarded by it).

We had every reason back then to believe the Earth is tens of millions of years old, though many argued it had to be much older. They were correct. We now have every reason to believe it’s roughly 4.5 billion years old. (Anyone disagreeing today is either simply ignorant of the evidence in favor of this statement and the massive preponderance of evidence in favor of earth being billions of years old (without putting a precise number on it), or is (in rare cases) quite aware of the evidence and is lying.)

So we need a way to power the Sun–and other stars–that can keep them going for billions of years.

And indeed Arthur Eddington–he is the astronomer who measured the deflection of starlight by the sun in 1919, which was strong evidence in favor of Einstein’s theory of General Relativity, which in turn had been published in 1915–well, Arthur Eddington suggested in 1920 that perhaps it was nuclear energy that powered the stars.

Nuclear energy had not been known in the 1800s, but it was now apparent that nuclear energy could supply roughly a million times as much energy as coal, per unit mass.

Fission of uranium would be plentiful, if only the sun were made of uranium, but honestly the biggest yield would come from the fusion of hydrogen into helium. If only the sun were made of hydrogen.

We know today that it is roughly 3/4 hydrogen, but that was not clear in 1920. We had spectroscopic evidence that the Sun contained certain ingredients (most of the elements are in the Sun at some concentration or another) but it wasn’t clear how much of anything there was. The proportions were a mystery. In fact the consensus at the time was that the Sun was pretty much made up of the same sorts of things, in the same proportion, as Earth. There was some reason to believe this, but we didn’t have all the facts.

Enter Cecilia Payne (later Ceclia Payne-Gaposhkin) (1900-1979).

Classifying Stars

But first, let’s go back a bit further to Annie Jump Cannon (1863-1941).

Annie Jump Cannon, along with Edward Pickering, was responsible for the current scheme by which stars are classified. She did most of the grunt work, he got most of the credit (though that is changing). This current scheme is known as the Harvard classification because, well, they were working at Harvard (pronounced HAH-vahd).

How do you classify stars? The same way you classify anything else: on the basis of what you can perceive about the objects. And with stars, that’s very confined. You have the star’s direction in the sky, its brightness, and its color. With telescopes, and some very specialized accessories, you can get the star’s spectrum, which is actually very useful since it can tell us what the star is made of, how fast it’s moving radially (towards or away from us–but this won’t include any sideways motion as seen from Earth), and even how fast it’s rotating in absolute terms. Today we can even use those spectra to detect planets orbiting those stars.

We truly didn’t have a science of astrophysics until we got a good close look at those spectra.

All of those things I mentioned as being able to be determined from spectra depend on absorption lines. These had first been noticed by Joseph von Fraunhofer (1787-1826) in the Sun’s spectrum (and so they are called “Fraunhofer lines”). They are dark bands visible in star spectra.

Later on in the 1800s it was realized that these lines were actually characteristic of different elements in the Sun. Different atoms would either absorb or emit certain wavelengths of light under differing circumstances. For instance if you heat a sample in a Bunsen burner flame, the atoms in the sample will emit only certain frequencies of light, creating an emission spectrum; under other circumstances those atoms will absorb those same frequencies from “white” light, leaving dark bands in the spectrum.

It turns out the Fraunhofer lines were due to the Sun’s atmosphere absorbing some of the light emitted by the photosphere (which is the part of the sun we actually see if we are so foolish as to look directly at it).

And indeed helium was detected in the sun’s atmosphere by this means decades before it was discovered on earth. The name “helium” comes from Helios, the Greek god of the Sun who rode his very bright chariot across the sky every day.

When we turned telescopes to look at (other) stars, they too exhibited absorption lines, but they didn’t all exhibit the same absorption lines.

And those differences gave way to a variety of classification systems.

Annie Jump Cannon looked at hundreds of thousands of spectra and could classify them on sight, according to systems then in use, and eventually according to the system she refined in 1901-1912.

One thing that had been noticed, certainly by her and probably by others before her, was that there was a strong correlation between the color of a star, and which spectral lines were prominent.

And we already knew from studying blackbody radiation that the color of a star was determined by its temperature. Blue stars are hot, at least ten thousand Kelvins. White stars are hotter than our sun, which is a yellow-white and therefore has a temperature of 5,772K–or rather the other way around.

(And this is why you can’t buy a light bulb any more without selecting its “color temperature,” you’re picking the color of the light according to the temperature it simulates. A true tungsten light bulb filament actually did get as hot as its color temperature, and the light it emitted tended to be quite yellowish in color. And of course this is a “thing” in photography since the camera cannot adjust what it sees, but our eyes can, based on ambient color temperature.)

Annie Jump Cannon divided stars into classes with letter names (holdovers from older systems) O, B, A, F, G, K, M. Type O stars were the bluest (and hottest) of stars, down through G (like our sun) to M (reddish color).

Why these particular colors? A “white” star has the peak of its black body emission curve in the middle of the visible part of the spectrum, so the curve is about the same height at both the purple and red ends of the spectrum. It’s fairly uniform across that range, and we perceive that mixture as “white.” A cooler star has its peak somewhere below the red end of the spectrum so what we see contains more red light than yellow or blue light–so we see orange or red. And blue stars are so hot most of their radiation is ultraviolet; the visible light part has much more blue than red in it.

Cannon actually subdivided each of those letters into ten sub-types, numbered from 0-9 with zero being the hottest. Since these plots always put the hot end of the spectrum at the left (which is counterintuitive, but the habit formed, and once formed, stuck, and we are stuck with it today), you’d see a progression from O0 to O9, then B0 through B9, and so on.

Another useful thing to consider is how bright the star is, intrinsically. Not just how bright it looked, but how much light did it actually emit, compared to our sun? But in order to know that, we have to know two things: how bright it appeared to be here on Earth, and how far away it was. The first was easy, the second very hard, and in fact impossible to determine much of the time because the star was too far away for our measuring methods to work.

Nevertheless, when plotting luminosity against temperature, we saw some clear trends, and not entirely what was expected.

Most stars ran along a diagonal line that got named the “Main Sequence.” Other stars were of similar colors but much, much brighter intrinsically. And a few were obviously very hot, but also very dim. In particular, Sirius B was one of the latter (I described it in my second post on stars).

Once we had absolute luminosities in hand, something became apparent. You would expect a hotter star to be brighter, just as white hot coals in your fireplace are brighter than redder coals. And we could indeed calculate how bright they should be compared to cooler stars from the Stefan-Boltzmann equation. (An object twice as hot as another object emits sixteen times the energy as that other one does.)

When we looked at the luminosity of hotter stars, though, they were even brighter than they should have been. But there was a very simple answer to that. They were brighter than one would expect, because they were physically larger than the dimmer stars, just as a coal twice the size as another coal will emit twice as much light as the other, even at the same temperature.

So combine the two: Imagine a white hot coal twice the size of a red hot coal, and the white hot coal is now 32 times brighter than the red coal; more than can be accounted for just by its temperature or by its size.

Eventually we were even able to figure out the mass of these stars (especially when they were parts of binary star systems–we could determine the mass by watching how fast the stars orbited each other), and all of this was confirmed.

And all this largely from the data that Annie Jump Cannon meticulously collected, analyzed and cataloged.

Cecilia Payne Fills the Gas Tank

OK, now we are ready for Cecilia Payne-Gaposhkin.

She was at Harvard (yes, HAHvuhd again) in 1924, working on her doctoral thesis–she would go on to become the first female given a doctorate in astronomy by HAHvuhd…though it was actually Radcliffe, the associated womens’ college.

She took up an issue, that being what stars are made of.

That should have been pretty easy, right? We had their spectra with all of those wonderful absorption lines, after all. O stars had lots of helium in then. A stars had lots of iron and magnesium and silicon in them. And so on, down to M stars that had spectra of molecules in them like TiO₂. That was how we divided them into their classes, after all!

But it turns out that many of these absorption lines weren’t from (say) ordinary iron or ordinary helium. They were from ionized iron, iron that had lost a couple of electrons. What difference does that make? The absorption lines (or emission lines under other circumstances) are caused by electrons absorbing (emitting) that precise wavelength of light in order to jump to a higher (lower) orbit.

When an atom is ionized, it has lost some electrons, and it hangs on to the remaining electrons more strongly, so it takes more energy for them to jump to higher orbits. This changes the absorption spectrum of that atom.

One way to knock those electrons off in the first place is to heat the atoms; that makes them move faster and when they slam into each other it could be hard enough to knock some electrons away. Thus the amount of ionized substances depends on their temperature.

This had first been realized by the Indian physicist Megnad Saha, but Cecilia Payne (she married Gaposhkin in 1934, so she was still Cecilia Payne in 1924) was the first to try to apply it to stars.

The prevailing theory at the time was that our Sun was made up of pretty much the same things as the Earth. All that calcium in the spectrum seemed to fit (there is a lot of calcium in the Earth’s rocks), as do other spectral lines from unionized (i.e., not ionized, rather than not a member of the UAW or Teamsters) elements. Meanwhile the hydrogen lines are very weak, especially compared to bigger stars.

Payne corrected for all those temperature effects, and came to the realization that the Sun…and other stars as well…were mostly hydrogen and helium. In fact the Sun is 74.9 percent hydrogen, 23.8 percent helium, and only 1.8 percent everything else.

This is so striking that astrophysicists today call everything that isn’t hydrogen and helium “metals” as a short hand. Since most of the elements in the periodic table are metals, that’s not a bad bit of scientific slang.

When Payne submitted her dissertation for review, it was criticized severely. She (unfortunately) backed down and wrote a paragraph into it dismissing her own data as spurious.

By 1929 her main critic, Henry Norris Russel, came to the same conclusion by a different method. He had the integrity to mention in his paper that Payne had got there first, but he still often gets the credit for discovering the stars are mostly hydrogen.

Mostly hydrogen.

So maybe (getting back, at last, to where we started) stars really did get their energy from fusing hydrogen. They certainly had the raw ingredient for it. The sun has the mass of 333,000 Earths, and three quarters of that is hydrogen. That is an absolute shitload of the stuff.

We knew from the binding energy curve how much energy is released (how much mass is converted to energy) per hydrogen atom, when four of them are brought together to form helium. We know the power output of the sun. Given those numbers it’s simple arithmetic to figure out how much the sun would have to “burn” and that amount is 620 million metric tons per second (a metric ton is a thousand kilograms, which on earth weighs roughly 2200 lbs).

4.26 million metric tons of this mass is converted to energy. That is a LOT of energy. And this happens every second. When you plug that into E=mc², you get that number I quoted above, 3.838×10²⁶ joules, and since that’s every second, that’s the number of Watts as well.

Divide that 620 million metric tons into the mass of the sun, and it’s clear that there’s enough fuel in the Sun to last billions of years–and indeed it has; we are about midway through that phase of the Sun’s life.

Tunneling Through Hurdles

But I am getting ahead of myself.

There was an additional hurdle the hydrogen fusion suggestion (not even really a hypothesis even now) had to clear before it could be taken seriously. And it was a difficulty Arthur Eddington had recognized clear back in 1920.

In order to fuse hydrogen into helium, you have to bring two protons together close enough that the strong nuclear force (which is so short range the protons have to be almost touching each other for it to take effect) overwhelms the electrical repulsion of the protons…which, if you’ll remember is a strong enough that we people could feel it (even out of those dinky little protons).

This can be done by making the protons move fast enough right toward each other. The repulsion causes them to slow down, stop, and reverse course…but if they’re moving so fast that they don’t stop until they get close enough, then they’ve climbed over the so-called “Coulomb barrier” (named after Coulomb, who first discovered the law of electrostatic forces) and can stick to each other.

How to make protons move fast? Heat them up. Temperature, after all, is simply a measure of the average kinetic energy of the atoms in a substance. Hotter temperatures mean higher speed of the atoms, particularly in a gas or superheated plasma.

At the kinds of temperatures we’re talking about, the electrons are stripped off the atoms, completely. You have bare protons zipping around in a swarm of loose electrons. (This is called a plasma, and it’s a fourth state of matter: solid, liquid, gas, plasma.)

The problem was, the interior of the Sun was believed to be at 17 million K, and even that temperature simply isn’t high enough.

But there actually is a way, and it’s supplied by quantum mechanics. Because of the Heisenberg uncertainty principle, the speed and position of particles isn’t precisely set at any given time, and if the speed isn’t set, the kinetic energy isn’t either. A particle with not enough energy (one would think) to jump over a potential “barrier” therefore gets to do so sometimes anyway. It’s much more likely if the particle is close to having enough, than if it is not.

This bit of quantum strangeness is called “quantum tunneling” and allows a particle which has no business jumping over a barrier to do so anyway, and physicists likened it to “tunneling” through the wall.

At the temperatures inside the sun, the probability of this happening is small, but not so small it never happens (as you see in the more familiar world where you fail to tunnel through blank walls unless you’re in a Road Runner cartoon).

If it were hotter inside the sun, the energy levels would be higher and the probability of tunneling through the barrier would be higher. But even as it is, it’s high enough that a tiny fraction of the protons do manage to “tunnel” through the barrier, and fusion can then happen.

But there is yet another hurdle, if you will pardon the expression.

When those two protons do glom onto each other, the resulting “diproton” is so unstable it simply falls apart right away.

But every once in a while, at the exact moment the diproton forms, one of the protons undergoes positive beta decay and becomes a neutron. In the process it releases a positron (anti-electron) and a neutrino. The positron finds an electron (they’re everywhere and literally anywhere in a plasma), they mutually annihilate and release a gamma ray–pure energy.

(The neutrino is a matter neutrino, not an antimatter antineutrino, because it counterbalances the antimatter positron, unlike in nuclear reactors here on earth where an antineutrino is created to counterbalance the electron produced by “regular” beta decay.)

A proton and a neutron will stick together. In fact this is hydrogen-2 or deuterium. Or rather, it’s a deuterium nucleus, known as a deuteron. (And yes, the joke is that the study of deuterons is known as deuteronomy.)

This beta decay at exactly the right time is a very rare event. And this is a good thing! Consider all those protons slam-dancing at 17 million degrees K for billions of years. If this event wasn’t rare, they’d be used up quickly rather than the supply lasting for billions of years. It’s not as if hydrogen is in a fuel tank until the sun is ready to burn it. No, it’s sitting on the fire, and has been sitting on the fire all along. It’s just that it’s burning very, very slowly.

The average survival time of a lone proton in the center of the sun is nine billion years. Yet it collides with a lot of protons at the temperature and pressure at the core of the Sun.

This was all outlined by Hans Bethe in 1939, at a Nobel lecture he gave.

The next step is for the deuteron to glom onto another proton. This takes, on average, about a second. The result is a helium-3 nucleus, two protons and one neutron.

After an average time of 400 years, two helium-3 nuclei will collide, and the result will be one helium-4 nucleus, and two freed-up protons, ready for another nine billion years on average of bachelorhood.

Six protons in, two protons out, plus one helium nucleus, plus gamma rays, plus two neutrinos. And a lot of energy. This is called the proton-proton chain.

Bethe also outlined another process, which involves four protons being added to carbon nuclei successively, with a couple of beta decays along the way, until an oxygen nucleus is created, which then spits out an alpha particle and reverts back to being the original carbon nucleus. This method is called the carbon-nitrogen-oxygen chain, or CNO chain, and it nets a helium-4 nucleus after consuming four protons.

It turns out that in stars more massive than the sun, this is the dominant mode. The temperatures are high enough to support it more readily than the proton-proton chain.

I’m now going to jump ahead to the modern understanding rather than going through the detailed history of how it was hashed out.

We know, now, that intergalactic gas consists of about three quarters hydrogen and one quarter helium. This gas is hot enough to radiate in X rays, but we can analyze the spectra.

There is only a trace of lithium in this gas, maybe a tiny bit of beryllium, and absolutely nothing else.

This is gas that was never part of a star. This is the original composition of the universe. [At least, as far as ordinary matter goes…but THAT is a future story.]

All of the “metals” we see today have to have come from somewhere. And indeed stars made them.

Because fusing hydrogen to helium isn’t the only way stars can make energy.

The Life of A Star

So let’s walk through this.

A cloud of (mostly) hydrogen gas…a very big cloud, trillions of miles across…contracts under its own gravity. As it contracts, it heats up (just like any other gas). But that’s no problem, gravity continues to crunch the cloud down.

The only thing that will stop the contraction is an equal but opposite pressure coming from the inside of the cloud. The pressure from the cloud depends on its size, a smaller cloud has less mass, less gravitation, and less pressure, so it will take less of this hypothetical internal pressure to get it to stop contracting.

I called it a hypothetical internal pressure, but it’s actually real. As the pressure and temperature at the center of the cloud go up, the hydrogen gas loses its electrons, the protons start slamming into each other, and at a temperature somewhat lower than at the center of the sun, some nuclear fusion begins to occur. If it’s a small cloud, that releases enough energy to heat the core up enough to stop the contraction. A bigger cloud will continue to contract, raising the temperature higher, to the point where more fusion happens, and then finally a balance is struck.

This balance is when the star becomes a well behaved, ordinary star, and it is now a “main sequence” star.

The main sequence is where all the hydrogen-burning stars go.

When I say “more fusion happens” I mean that more fusion happens for each ton of the star’s mass. In other words, it burns its fuel faster.

The bigger the star, the faster it burns its fuel, not just in absolute terms but in proportion to its mass. Bigger stars thus live much shorter lives than smaller ones.

It happens they are also a lot rarer than small stars.

One star in ten million is an O type star. These are 15 – 90 times as massive as the sun, but they are anywhere from 30,000 to a million times as luminous. If a star 90 times the size of the sun burns its fuel a million times as fast…well, you can see that it’s going to run out about 10000 times faster. Indeed they live only a few million years. Almost every O type star that has ever existed is long gone.

On the other end of the scale are the M type stars. About 75 percent of all stars are M type main sequence stars (at least, judging from the stars near the Sun). They are anywhere from 8% to 57% the mass of the sun, but even the biggest ones emit 7% of the light of the Sun. (The smallest emits 0.03% the light of the sun.) They’re cool and consequently reddish; they’re called “red dwarfs”.

(Red dwarfs may be 75 percent of all stars, but if you step outside at night and look up, you won’t see any red dwarfs. They’re simply too faint to be seen by the naked eye. The nearest star to us (other than the Sun, of course) is a red dwarf and cannot be seen without a telescope. This is not to say that you won’t see red stars…but those will be red giants. Which I’ll get to below.)

Red dwarf stars are long lived. It is estimated that one 16% the mass of the sun will last 2.5 trillion years. That’s an estimate, of course, because no one has seen one die. The universe isn’t even 1/100 th that age yet. Every red dwarf that has ever formed is still with us. (Even a “big” red dwarf 57% the mass of the sun should last at least 30 billion years, also older than the universe.)

OK, this is well and good. We have a pretty thorough description here of how hydrogen is made into helium. But not only is it still bottled up in a star…it’s also still not metals.

Remember that the material of the universe originally contained no metals, except maybe a smidge of lithium and beryllium. Yet we have these elements today…if not, you wouldn’t be reading this and I’d never have written it, because we would not exist.

Where did the metals come from? If they come from stars, how do they get out of the stars?

Well we need to follow this story further. (Kids, stop asking “are we there yet?” after every paragraph.)

What happens when a star runs out of hydrogen fuel?

It depends on the star. Those tiny red dwarfs, less than 25% the mass of the sun, are simply done. They shrink until the only thing holding them up is the mutual repulsion of the electrons. At this point they weigh maybe a million tons per cubic meter. They’re very hot, but that’s residual heat that slowly radiates away–no new energy is being created. Because they’re hot–hotter than they were as living stars, they are now known as white dwarfs, and are approximately the size of the Earth. Sirius B is a notable example of a white dwarf (I talked about it in one of my “stars” articles).

But wait.

Didn’t I say that no M stars had died yet? If so how do we have white dwarfs?

Because bigger stars also become white dwarfs. They take a more indirect route, but get there faster.

Stars bigger than 25 percent the mass of the sun follow a different path when they run out of hydrogen. They also begin to contract once again, but the temperatures in their interiors climb a lot higher.

They climb high enough, to 100 million K, that helium begins to fuse, three nuclei at a time, into carbon. (This is called the triple alpha process, because the three helium nuclei are three alpha particles.)

This happens at much higher temperatures. Under all of this heat the star expands. It gets downright bloated.

When the sun hits this phase it will probably bloat enough to swallow the earth.

That huge surface is actually rather cool for a star, it’s a hundred million miles (or more, for bigger stars) away from the raging inferno where carbon is being made.

The star is a giant, but it is red, hence the name “red giant.” It puts out a LOT more light than a red dwarf, in fact it puts out much more light than it did before. That pushes it up out of the “main sequence” and into the territory of the “giant” stars, to the top and right of that Hertzsprung-Russel diagram. These are giants in size, not mass…they’re no more massive than main sequence stars.

Helium converting to carbon produces less energy, kilogram for kilogram, than does hydrogen fusing to helium. Yet the giant star doing so must produce more energy to produce all that heat that makes it bloat.

In other words, all that helium “ash” from the hydrogen fusion, is going to itself be burned much faster than the hydrogen was. The star will get hot enough to do so, because it seeks balance.

Red giant phases don’t last very long compared to the time the star spent on the main sequence, happily burning their birthright of hydrogen.

If the star is the size of the sun, this is the end of the line. During this phase the star is a bit unstable, and may blow off some of its outer layers, producing a “planetary nebula” (called that because they used to be mistaken for planets in telescopes), and so a star like this might return some of the carbon it produced to space. But then the star dies, and it shrinks into a white dwarf. This white dwarf will contain carbon in it–a lot of carbon, but it does no good; it’s stuck in the white dwarf.

Of course, now when stars are formed from gas that already has metal in it, they return some of that too, but that’s not where that stuff came from. So where did it come from?

Big Stars are Metal Factories–complete with a shipping department.

Kids, we’re not there yet.

Stars considerably larger than the Sun, when they run out of helium in their cores, start to fuse the carbon. Again, this is at even higher temperatures. And again, this is a diminishing return. Less energy from the fusion, with a higher temperature having to be maintained, means this phase is short.

Also, around the core there is still some helium, and even the layers immediately outside the core are hot enough to fuse helium to helium, making more carbon, or helium to carbon making oxygen.

The star turns into a giant onion, each layer going inwards making bigger and bigger nuclei, and this (at last) is where all the good stuff forms, all the elements up to iron, in point of fact the elements that make up us.

Cooked in the centers of massive stars.

The only thing we need to close the loop, now, is to explain how all that stuff gets out of the stars. That would explain where all the metals that already exist in the Sun came from. Somehow, those metals were made in long-dead massive stars, then ended up in the cloud that contracted to form the Sun.

So here it is. The massive star eventually has a core of silicon, and there’s not enough other stuff in the core (though there is in layers surrounding the core) to keep going. The star heats up again, and commences to fuse the silicon into iron.

There are vast amounts of silicon in there, many times the weight of the earth.

The star rips through it in a day. Yes, a day.

It now has a core made of iron.

And now it cannot make energy any more. Because fusing iron consumes energy.

So the core collapses.

There’s a bit of a rebound effect. I say a bit. That rebound is actually one of the biggest explosions there is, a “core collapse supernova.”

The explosion is so bright, it outshines the other 100 billion (or so) stars in that galaxy, for a few weeks.

The last time one of these happened in our galaxy where we could see it was in the 1600s, just before the invention of the telescope, and the supernova was visible during the daytime.

Supermassive stars live fast and die hard. Bruce Willis has nothing on them.

That big explosion flings vast quantities of all the stuff the star has been brewing out into space, later to coalesce into new stars…and planets. And in the case of some star that blew itself to bits over four and a half billion years ago, the stuff eventually made us.

In the process, a lot of neutrons are created, and glom onto existing atoms, making heavier atoms, and until recently, it was believed that even gold, lead, and uranium were primarily produced this way. What an image: all the gold in your jewelry was once hurtling through space at a tenth the speed of light, blasted out of the guts of a star bigger than the sun.

What a pretty story. So pretty a lot of people like to say “we are made of star stuff.”

It is a fact that we owe our very existence to the death of big stars. Our bodies are made of atoms flung from their funeral pyres.

The Neutrinos Prove It

What’s the evidence?

There’s a lot of evidence, in fact, including the composition of nebulae (gas clouds), and especially the nebulae that have been blown out of supernovae. Stellar compositions are the evidence that started the whole thing, but shouldn’t be forgotten. A lot of “little things” all consistent with this framework.

But I want to focus on neutrinos.

In fact, this is why I undertook this whole damn series.

I wanted to talk about neutrinos. And connect them to stars…remember I talked about stars in the two science posts before this series. I was going to tie the smallest known particle of matter to the biggest discrete objects out there: stars (galaxies and galaxy clusters are bigger, but they don’t strike us as being objects but rather groups of objects).

But they are so ghostly, so non-reactive, that I would need to really justify their existence and tell the story of how they were discovered. And that entailed yet more background. I was going to just explain how they solved some problems with conservation laws…but then that meant I needed to explain those.

I thought maybe I’d write four parts. Then the doggone thing took on a life of its own. It ended up being twenty parts before I got to neutrinos. And another two before I connected them to stars.

So here I finally am.

One of the most important pieces of evidence that stars are, indeed, fusing hydrogen into helium, and so on as appropriate, is the neutrinos.

Those two protons coming together to make a deuteron, release a positron and a neutrino in the accompanying beta decay. This means that IF nuclear fusion powers stars, then ordinary stars are sources of neutrinos, and that most definitely includes our sun.

But also, a supernova, a dying star, gigantic numbers of neutrinos all at once in the fury of nuclear reactions going on all at once in the explosion–the reactions that give us all those heavy elements, elements heavier than iron.

There was a supernova of this kind 168,000 years ago in the Large Magellanic Cloud. The light reached us in 1987. A star known as Sanduleak -69 202 had just died.

It is estimated that this supernova released 10⁵⁸ neutrinos. All at once.

I’ve thrown some big numbers at you over the course of this series, but that number is staggering. I’m not going to pretend to imagine how much that is.

Divide it by a trillion…it’s still 10⁴⁶. Still a staggeringly huge number beyond our experience. And a hundred billion billion times as much as that ridiculously huge number I used for the power output of the sun.

If you had been a billion miles from that star when it blew up, here’s what you would have seen. The neutrinos hitting almost instantly–they were made in the core at the moment of the explosion but just zipped right on through everything. Then the light, actually delayed by all that matter being blasted out. Then the matter would have reached you as a blast wave to end all blast waves.

Except that you wouldn’t have seen the light or the matter, because you’d have been killed instantly by the neutrinos. There were so many of them that even at their ridiculously low likelihood of interacting with you rather than passing right on through, enough of them would have interacted with you to kill you instantly from the radiation.

It’s estimated that the light from the explosion–which, remember, outshines billions of stars–is one percent of the energy contained from the actual material blast. And that is one percent of the energy carried off by the neutrinos.

The light, bright enough to be seen from earth that far away (one of the first people to see the supernova was an astronomer at a major observatory in the Andes, outside taking a smoke break; he noticed that the Large Magellanic Cloud had a “new” star in it), was a sideshow.

So why are the neutrinos from the sun and exploding blue supergiants such a big deal?

Because we can detect neutrinos. And therefore, if we don’t see these neutrinos, something is wrong with our theory.

Large tanks of water, deep underground in mines so that nothing can get to them other than neutrinos, can be surrounded by flash detectors, which will register a hit every now and again. We can even tell, from the direction of motion of the products of the reaction, what direction the neutrinos came from. (And it’s a neutrino detector–we don’t have to wait for daytime or nighttime, it runs 24/7, and it doesn’t matter whether the sun or the supernova is “up” or not.

Twenty five neutrinos (a big signal for neutrinos) were detected from the supernova.

More importantly, these tanks have been detecting neutrinos from the Sun for years. That is a sure sign that nuclear fusion is happening there. And, they are of precisely the energy one would expect from the creation of deuterium from regular hydrogen.

There was just one hitch, with regard to the Sun’s neutrinos. We can calculate, from the power output of the sun, how many fusion reactions must be happening each second inside the sun, because we know how much energy each individual reaction releases. (It’s a geek’s story problem.) That gives us the number of neutrinos. We can figure out how many of them must be going through the detectors. And we know how likely it is that any given neutrino will be stopped inside the detector, letting us detect it. In other words, we know how many neutrinos should be detected coming from the sun, on average, during a given time period.

The number we detected was 1/3rd as much as it should be.

Ah, well, you solve one mystery (what makes the sun and other stars shine?) and you get presented with another mystery (where are the neutrinos?).

This is science moving forward.

And now, I think, I’m going to continue this series, even though it has reached the original planned conclusion.

I’m going to step from the neutrino, to something very, very big….much bigger than stars.

And then I’ll tell the story of that missing third…but that’s going to take a few installments.

Bonus Stuff

You put out more energy than the sun…sort of

The core of the Sun is at 17 million K, but what is its energy density?

How much energy is being generated in each cubic meter? The very high temperature has no bearing on this; some particular cubic meter of the sun stays at 17 million K because its surroundings are at that temperature. Heat leaks out of the core only where it meets the higher layers of the Sun. In fact it takes tens of thousands of years for a photon in the sun’s core to make it to the surface.

Energy density is how much energy is generated per…kilogram or cubic meter depending. Gasoline has a higher energy density than car batteries (even the ones for electric cars), for instance.

The energy density of the core of the sun turns out to be…wait for it…about 276.5 watts per cubic meter.

That is not a typo. Yes, we think of the core of the sun as a raging inferno, because there’s a lot of energy trapped in there. But as to how much new energy it generates every second, it’s actually quite sparse.

YOU produce 100-150 Watts just sitting on your butt reading this (more if you’re scratching your head really hard), because you have to keep your body temperature above room temperature. And your volume is a LOT less than a cubic meter. In other words, you generate more energy than a same-sized piece of the Sun’s core.

In fact a cubic meter of compost generates about the same amount of power as a cubic meter of sun’s core. (It just can’t do it for billions of years, so no, the sun isn’t a big compost heap.)

The reason the sun puts out so much power is that the core of the Sun is huge, roughly 200,000 miles across. That is a lot of cubic meters!!

So where did the gold come from?

I alluded to the belief that gold primarily came out of supernovas being an “until recently” sort of thing. So what’s the current theory? Core collapse supernovas leave behind either (for stars a couple of times more massive than the sun) a neutron star) or (very massive stars) a black hole.

What is a neutron star? It’s almost the ultimate collapse. It is what happens when even electron-to-electron repulsion can’t stop a star from collapsing, and the star doesn’t stop collapsing at white dwarf levels. Much of the star in a supernova gets blown away, but the remainder is usually much more massive than the sun. That remnant collapses. The electrons are forced into the nuclei, and combine with the protons to make neutrons. The entire remnant becomes one big ball of neutrons, with maybe a surface layer of white dwarf-style matter. The entire mass of the thing ends up in a ball perhaps ten miles across, weighing billions of tons per teaspoon.

When two of these neutron stars happen to collide–perhaps because two massive stars both went supernova and the neutron stars eventually lost all of their orbital energy to gravitational waves and then collided with each other–a lot of neutron debris splashes out there, decays and becomes heavy atoms, like gold. Entire earth-masses of gold are produced in this way and scattered across the cosmos. Now that we have observed neutron star collisions, we realize that most of the really heavy elements out there came from neutron star collisions, not from supernovae.

Obligatory PSAs and Reminders

China is Lower than Whale Shit

Remember Hong Kong!!!

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

China is in the White House

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

Joe Biden is Asshoe

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

But of course the much more important thing to realize:

Joe Biden Didn’t Win

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

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

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

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

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

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

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

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

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

OK, with that rant out of my system…

Justice Must Be Done

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

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

The Audit

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

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

Lawyer Appeasement Section

OK now for the fine print.

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

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

And remember Wheatie’s Rules:

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

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

Spot (i.e., paper) Prices

Last week:

Gold $1758.00
Silver $22.75
Platinum $1031.00
Palladium $2167.00
Rhodium $14,850.00

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

Gold $1768.40
Silver $23.40
Platinum $1059.00
Palladium $2162.00
Rhodium $15,150.00

A bit of a break out upward earlier this week, things looked good early Thursday for gold. But it took a major hit Friday. Palladium dropped 65 bucks on Friday.

Sorry No Physics Today

Too much going on in my life right now. I might get to it next week. I might not.

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 !!!

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

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

The collapse of the Covidschina continues.

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

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

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

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

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

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

Justice Must Be Done.

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

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

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

Lawyer Appeasement Section

OK now for the fine print.

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

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

And remember Wheatie’s Rules:

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

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

Spot Prices

Last week:

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

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

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

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

Part XX – The Little Neutral One

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

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

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

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

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

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

Recaps and Refreshers

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Beta Decay Spells Doom?

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

And it was causing headaches for physicists.

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

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

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

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

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

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

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

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

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

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

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

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

Oh, dear.

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

But three such violations at once was hard to believe.

At least, baryon number was safe.

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

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

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

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

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

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

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

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

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

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

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

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

We need to find the particle.

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

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

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

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

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

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

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

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

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

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

Next time we’ll tackle Mystery Number 3.

Obligatory PSAs and Reminders

China is Lower than Whale Shit

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

Remember Hong Kong!!!

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

China is in the White House

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

Joe Biden is Asshoe

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

But of course the much more important thing to realize:

Joe Biden Didn’t Win

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