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…

So Just this Once Justice Has Been Done

Kyle Rittenhouse goes free. Not guilty on all counts!

He shot some real dirtbags, though he didn’t know at the time just how dirtbag they were, so that can’t justify it. What justified it was the dirtbags were coming after him. He did miss one, and merely wound another (Grosskreutz, who should now be prosecuted for attacking Rittenhouse. Though maybe we owe him thanks because he blew up the persecution’s case with his testimony.)

A lot of real shitbags need to pay for this. Not just the rioters, but the persecution, the media, the political “leadership” in this country that came down against him when enough was out to acquit him almost immediately, on and on. Sure there will be defamation suits but that’s not enough. These people will probably launch gofundmes to pay their awards for them anyway; there are enough Leftist mushbrains to make that happen.

But in the meantime, we celebrate what we did get.

Loop it if you like; I will wait.

Richly deserved.

And justice, after all, is seeing that people get what they deserve, not just with criminal acts, but even in our personal lives.

Justice can be done. So…

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 $1866.10
Silver $25.42
Platinum $1091.00
Palladium $2195.00
Rhodium $15,100.00

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

Gold $1846.50
Silver $24.67
Platinum $1036.00
Palladium $2146.00
Rhodium $15,100.00

I looked earlier today and things were a bit higher, but right now it does look like gold is trying to drift downward…or is being pushed downward. I was about to say it looked solidly established in the 1850s-1860s but…nooope.

Physics — The “Standard Model”

I’m finally feeling well enough to try to take this on.

Last week I told the story of how all sorts of unexpected medium (~200 electron masses) and heavy weight particles (1800 electron masses and up) began turning up in particle physicists’ cloud chambers, leading to a ridiculous-seeming ‘zoo’ of particles that all seemed fundamental (though all except the previously-known proton are unstable).

And of Murray Gell-Mann and Zweig brought order to the confusion by postulating that there were in fact three types (called “flavors”) of quarks (and three matching types of anti-quarks) that made up all of these these particles…including the proton and neutron. A quark and anti-quark pair (usually of a different flavor) made up a meson (medium weight particle), and three quarks made up a baryon (heavy weight particle).

The three flavors are “up” (+2/3 electric charge), “down” (-1/3 electric charge) and “strange (-1/3 electric charge).

And then the idea that there was a new fundamental kind of charge, different from electric charge, called the color charge. Where the electric charge comes in positive and negative forms, the color charge has three forms, none of them quite the opposite of any of the others, but all three of them adding up to “neutral.” This reminded someone of the primary colors red, green, and blue [primary when dealing with light emitting sources, not paints, where it’s the red, blue and yellow you’re probably thinking of] and so the three charges were named red, green and blue.

It turns out that this is the real “strong force” and the “strong nuclear force” noted in the past, that holds protons and neutrons together in the nucleus is just a side effect of it. No, the real strong force holds the protons and neutrons themselves together!

Strong interactions within a proton or neutron generate a pion (a meson), which will decay almost instantly unless it runs into another proton or neutron immediately, in which case it interacts with that particle; that interaction is the “strong nuclear force.” That other proton or neutron has to be practically touching the first one for this to work at all, so that’s why the strong nuclear force had such a short range.

And these are particles a trillionth of a millimeter across, roughly, so when I say “short range” I mean “short range.”

The real strong force operating by quarks exchanging “gluons,” much like the electromagnetic force operates by charged particles exchanging photons. But it is much, much more complicated than that. A photon, once emitted, has no electric charge and no mass, so even though it carries the electromagnetic force, it’s not affected by it. It won’t be bent by electric or magnetic fields. It won’t be affected by other photons. But a gluon itself has a color charge and a mass! That means it can interact with quarks and other gluons, by exchanging yet more gluons…which can exchange yet more gluons. This was a seemingly-intractable mess that, frankly, I don’t understand the resolution to. But they did resolve it. (Richard Feynman had a lot to do with that.)

So there was this totally new and much deeper understanding of the strong force (no longer the strong “nuclear” force). The whole topic is now called “quantum chromodynamics” to match with “quantum electrodynamics” (the completely up-to-date marriage of quantum physics and Maxwell’s and Einstein’s work).

[As an aside, every experiment made to test quantum electrodynamics has been a perfect match, down to ten parts in a billion of precision. Nothing else in physics is this solid.]

Later on, physicists discovered three more quarks, the charm quark (+2/3 charge), bottom quark (-1/3 charge), and top quark (+2/3 charge) and they got grouped into three “generations: Generation 1 is the up and down quarks, and those make up protons and neutrons and thus the overwhelming majority of everything you see around you by mass (the rest of the mass is electrons; and of course you see photons; in fact you see with photons). Generation 2 is the charmed and strange quarks, while Generation 3 are the top and bottom quarks.

But what about the weak force?

The weak force, it turns out is the only force that can change a quark’s flavor, from say, down to up.

Consider a neutron, out all by its lonesome. It contains an up quark (+2/3 electric charge) and two down quarks (-1/3 each electric charge). Each of those quarks is a different color charge, but it actually doesn’t matter which one is which.

The weak force operates here by changing one of the down quarks to an up quark. That raises the charge of that quark an entire unit, from -1/3 to +2/3, which means that some particle with a negative charge unit has to be generated to make up for it (electric charge is (still) always conserved). Well, now, an electron fills the bill nicely. But if you generate an electron, you’ve created a lepton, and an anti-lepton must be generated to make up for that. (The total number of leptons can never change, but anti-leptons count as –1 lepton.) And an anti-neutrino fills that bill, since neutrinos are leptons and anti-neutrinos are therefore anti-leptons.

I’ve just described negative beta decay.

(If you get the feeling, after watching all that book-balancing going on, that physics is a lot like accounting, well, yes, yes it is! Except you’re keeping books in six different currencies at once, between conserving quark number, lepton number, electric charge, angular momentum, linear momentum and occasionally mass-energy.)

And indeed the result is a proton, and electron, and an anti-neutrino.

Logically, there should be particles that mediate this force too, and indeed predictions were made in 1968. This had come about because, fresh off the success of quantum electrodynamics, physicists had turned to trying to “crack” the weak force, and Sheldon Glashow (1932 and still alive), Stephen Weinberg (1933-July 23 2021), and Abdus Salam (1926-1996) put forward a prediction that not only related the weak force to electromagnetism, but suggested three new particles. The first two were the W⁺ and W^– “bosons” (bosons are particles with integer spin, force carrying particles are all bosons), named W for the weak force, and they have + and – 1 unit of electric charge, respectively. The third particle is the Z boson, which has no charge at all (and Z for Zero).

These particles were found in 1973.

Beta Decay, the Modern Understanding

So what really happens in a beta decay? One of the down quarks in a neutron emits a W- boson. That alone turns the down quark to an up quark, and that quark’s involvement is over. About 10^-25 seconds later (enough time for the W particle to move about 3 percent of the width of the neutron it’s inside), the W particle breaks down into the electron (which carries off all the charge) and antineutrino. That avoids having three things happen at once.

Below is a Feynman Diagram of the interaction. Starting at the lower left, the neutron, consisting of one up and two down quarks is moving (in space) slightly to the right, but is climbing along the time axis. Then one of the down quarks spits out the W^– particles, and the neutron turns into a proton, which recoils…exactly like a rifle firing a bullet. Exit shiny new proton, stage upper left. The W boson moves off then becomes an anti-neutrino (with that Greek “nu” ν that looks like a v to us for a symbol, the bar over it denotes it’s an antiparticle, as does the arrow pointing backwards in time), and an electron.

Feynman diagrams are actually enormously powerful visualization tools (and helped solve the mess with gluon-gluon interactions) and I really should have found some excuse to introduce them sooner. Actually, I’m being charitable: I feel like an idiot for not using them sooner.

I just dropped a tiny spoiler (soon to be resolved) in that diagram; notice the antineutrino is subscripted with an e, ν_e.

Muon Decay

Another place where the weak force comes into play is the decays of muons and tauons. Recall that these are basically bigger “cousins” of the electron, and indeed these particles decay, ultimately, into electrons. These are all leptons.

Let’s look at the muon decay, in another Feynman diagram.

Here the muon (μ^–), in many ways just a bloated electron, enters at stage lower left, decides it’s bored with being a muon, and decides to become a neutrino (with zero charge). So it upchucks a W^– to get rid of the charge. [Sorry about the imagery, but recent events in my life suggested it to me.] Everything is kosher to the guys with the green eyeshades, because there’s one lepton going in and one going out (neutrinos are leptons). But that W^– lives only about ten times as long as a politician’s promise not to violate your rights, and breaks down into an antineutrino and an electron. The electron bears the charge of the W^– particle, the anti-neutrino balances the lepton number of the electron.

So what’s the deal here? That neutrino that the muon turned into has a cute little μ subscript (ν_μ) and the antineutrino from the W^– breakdown has an e subscript (ν_e, though unfortunately I can’t draw the bar over it in this text editor).

As it turns out the charged leptons come in three generations, electron, muon, and tauon…and so do the neutrinos!

As if the dang neutrino isn’t a slippery enough little bugger, now there’s three kinds of them?

In fact there seem to be three generations of everything: leptons, quarks, and subdividing, three generations of neutrinos, “electron-ish” leptons, -1/3 quarks and +2/3 quarks.

The Sun is Safe, and You Still Have To Do Your Taxes (Dammit).

And this helped to solve a mystery that was beginning to bother people. Really bother them.

Nuclear fusion should generate neutrinos. We can check this because there is a big fusion reactor less than a hundred million miles away: the Sun. Based on the energy output of the sun, and the amount of energy each fusion reaction generates (measured in a laboratory), we can know how many reactions are taking place each second; we can use simple geometry to figure out how many neutrinos should pass through detectors here on Earth. And we can do further calculations to figure out the tiny number of neutrinos that should actually react with the detector and therefore be detected rather than just cruising on through to go on, probably, forever.

The problem was, we only detected a third as many neutrinos as we thought. Either we just didn’t understand something…or the Sun was shutting down for some reason. Which would be bad. We’d only find out ten thousand years or so after it happened, because it takes that long for the heat and light generated by the fusion to work its way out (the neutrinos zip out instantly since all the matter of the sun is nothing to them). When, suddenly, no more light and heat…we’re up shit creek.

It turns out that neutrinos can change generation. This suggestion was made clear back in 1957 by Bruno Pontecorvo (1913-1993) and eventually was confirmed by experiments done at neutrino detectors. It takes some time for neutrinos to do this, which is why the effect was visible in solar neutrinos (which are 8 minutes, 20 seconds old) but not in neutrinos generated by nuclear reactors here on earth (which are less than a millionth of a second old). One implication of this is that neutrinos do have a mass, albeit one we still can’t measure (much, much less than an electron, which is the lightest thing we know of that isn’t zero mass). The details are still being worked out.

The last bit of fallout from the work done in 1968 was the Higgs boson. It turns out to be the particle representing a field that gives particles mass. So electrons, muons, tauons and quarks interact with it (as do the W, Z, and gluon), but photons do not. [At least one theory of neutrino mass claims it gets its mass from something other than the Higgs field.]

That particle was finally found in 2012 at the Large Hadron Collider. And if you’ve wondered why on earth it’s the Large Hadron Collider, recall that a hadron is any particle made of quarks including both mesons and baryons.

[And yes, it must be told. Richard Dawkins (yes, that Richard Dawkins) mentioned the LHC in a book he wrote before the Higgs was finally discovered, and he got the proofs back from the publisher. And sure enough someone had flubbed and in print was “Large Hardon Collider.” He has quite a good sense of humor, actually, and he begged the publisher to leave the misprint in, but they removed it. (There is, or at least was, on his website a troll named “Rawhard Dickins” that he tolerated.) It was only a couple of years later that “the typo we’ve all been waiting for” finally appeared on a website.]

The Standard Model…Ta Da!!

So that completes what is actually named “the standard model” of particle physics. It pretty much sums up everything we’ve every seen in a collider.

Here’s a graphic. This one includes the anti-particles in columns 4-6. (Most such diagrams do not; it’s assumed you know they’re there.)

[Sorry, Zoe, I don’t know a quick way to describe this one, and listing what’s in each cell in a 8×4 grid would be tedious.]

One thing sometimes included in the diagram, but not this diagram, is the “graviton,” the force carrying particle for the gravitational force. But, we really can’t even hazard much of a guess as to what such a particle would be like, because we’d need a quantum theory of gravity.

We don’t have one. Personally I’m not even sure there can be one, but really, I am WAY beyond my pay grade here.

There are a couple of other details that still need to be worked out (neutrino mass would result in a tweak to the theory, not its breakage), but again, it seems like everything we’ve ever seen in a particle collider or a lab of any type fits into this, with the nagging exception of gravity–we just have to figure out how to bolt that onto the schema.

So is physics done?

Nope.

Not even close.

Because we have excellent reason to believe that this diagram only categorizes one sixth of the matter in the universe.

Wait, since this explains everything we do see…that would mean we only see one sixth of the matter in the universe!

And if we can’t see it, how do we even know it exists?

What’s up with that?

Back to the astronomers…

Fuck Joe Biden

No expansion on this thought necessary.

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 !!!

RINOs an Endangered Species?
If Only!

According to Wikipoo, et. al., the Northern White Rhinoceros (Ceratotherium simum cottoni) is a critically endangered species. Apparently two females live on a wildlife preserve in Sudan, and no males are known to be alive. So basically, this species is dead as soon as the females die of old age. Presently they are watched over by armed guards 24/7.

Biologists have been trying to cross them with the other subspecies, Southern White Rhinoceroses (Rhinoceri?) without success; and some genetic analyses suggest that perhaps they aren’t two subspecies at all, but two distinct species, which would make the whole project a lot more difficult.

I should hope if the American RINO (Parasitus rectum pseudoconservativum) is ever this endangered, there will be heroic efforts not to save the species, but rather to push the remainder off a cliff. Onto punji sticks. With feces smeared on them. Failing that a good bath in red fuming nitric acid will do.

But I’m not done ranting about RINOs.

The RINOs (if they are capable of any introspection whatsoever) probably wonder why they constantly have to deal with “populist” eruptions like the Trump-led MAGA movement. That would be because the so-called populists stand for absolutely nothing except for going along to get along. That allows the Left to drive the culture and politics.

Given the results of Tuesday’s elections, the Left will now push harder, and the RINOs will now turn even squishier than they were before.

I well remember 1989-1990 in my state when the RINO establishment started preaching the message that a conservative simply couldn’t win in Colorado. Never mind the fact that Reagan had won the state TWICE (in 1984 bringing in a veto-proof state house and senate with him) and GHWB had won after (falsely!) assuring everyone that a vote for him was a vote for Reagan’s third term.

This is how the RINOs function. They push, push, push the line that only a “moderate” can get elected. Stomp them when they pull that shit. Tell everyone in ear shot that that’s exactly what the Left wants you to think, and oh-by-the-way-Mister-RINO if you’re in this party selling the same message as the Left…well, whythefuckexactly are you in this party, you piece of rancid weasel shit?

Election Cheating

Republicans won…in Virginia, and maybe in New Jersey, and in a lot of local races nationwide (including school boards–very critical in the long term).

If we can’t possibly win without an honest system, and we know the system has not been fixed…uh, what’s up? Seems like a bit of a contradiction.

So I will modify my stance somewhat, in the light of new information: Apparently the automated cheating that’s rather subtle could be overcome. And indeed it was overcome in 2020 as well.

That’s when the Left/Establishment went to good old fashioned blatant ballot-box stuffing, putting up cardboard to block the view into election centers and running ballot after ballot through the machines. To say nothing of the six figure dumps of votes entirely for China Joe and Skanky Hoe.

This time, for whatever reason, they didn’t go that far.

Perhaps it’s just so they can claim “See, Republicans can win elections, so we’re not cheating and Trump was just a Loser.” In which case, I’ll go back to my original stance and say that we cannot win until the election process is fixed. But then I’ll go on to add: unless they decide for tactical reasons to let us win a couple.

So for now, I’ll stick with:

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

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

Gold $1819.00
Silver $24.25
Platinum $1042.00
Palladium $2117.00
Rhodium $15,500.00

Everything is UP. Gold has busted $1800. Silver has busted $24. I suspect they’re going to continue upward, for now.

The Distance Ladder

A couple of go-backs

A couple of things I failed to mention last time.

Schwarzschild (the name is German for “black shield,” ironically enough) did his theoretical work in 1915, immediately after Einstein published the theory of general relativity. His solution to the Einstein field equations of general relativity was the first one, in fact. Astrophysicists are still careful to distinguish “Schwarzschild black holes” from rotating black holes. Schwarzschild was killed in action on the Eastern Front in World War I.

There probably is no such thing as an actual non-rotating black hole. Such would have to be formed from a non-rotating massive star (or a nebula with absolutely no rotation, in the case of the supermassive black holes). Remember that even the tiniest rotation will be magnified, and magnified a lot, as the object shrinks down from light years (or tens of trillions of kilometers) across, to star-sized (hundreds of thousands of kilometers) to just a few kilometers in radius, just as the figure skater spins much faster when she pulls her arms in.

Black holes are generally safe…as long as you’re far enough away. If the sun were magically to be replaced by an equal-mass black hole, the Earth would continue in its orbit and not be sucked in. It’s only when you get to within about 3 Schwarzschild radii that you can’t have a stable orbit. (And the Schwarzschild radius is the radius at which the escape velocity is equal to the speed of light.) For the sun the Schwarzschild radius is 2,950 meters (not kilometers, meters). Earth could be made into a black hole too–if you could manage to compress it until its radius is 8.87 millimeters.

Measuring Distances

Astronomers can easily measure the direction of a star. This was being done with surprisingly high precision even before the invention of the telescope. As seen from earth, the sky forms a “celestial sphere” and every star’s position on that sphere can be measured and plotted in star charts. The celestial sphere appears to rotate on an axis (really it’s the earth that rotates on that axis, in the opposite direction), so that defines north and south “poles” on the celestial sphere; and halfway between them is the celestial equator. So you can get something like “latitude” on the celestial sphere, only it’s called “declination” or “Dec.” Longitude is trickier because there’s no objective zero point, but can be handled too. The sun, of course, moves along the celestial sphere following the “zodiac” which is a circle tilted at a 23.5 degree angle to the celestial equator (and again, it’s not the sun that’s really moving, it’s the earth orbiting the sun making the sun appear to move). The place where the zodiac crosses the celestial equator, when the sun is moving from the southern celestial hemisphere into the northern celestial hemisphere, is called “the first point of Aries” and is also the zero “longitude” point by convention. When you see a statement like “Spring will start at 4:46 PM on March 21″ that’s really the time the sun will (appear to) cross through the first point of Aries”. But here’s a wrinkle with regard to celestial longitude: It’s measured not in degrees but in hours. 24 hours makes up the full circle, then those are divided into minutes and seconds just like degrees are. And it’s called “Right Ascension” or “R.A.,” not longitude.

If you remember last week I posted a rather colorful plot of the orbits of some stars at the center of the Milky Way around the supermassive black hole there, plotted on a grid. The grid is marked off in seconds of arc (i.e., the kind of second that is 1/3600th of a degree, not the kind of second that is 1/3600th of an hour of right ascension), with respect to the declination and right ascension of that black hole. That is what those scales mean.

In any case it’s easy to measure this sort of thing; one of the two most manifestly obvious things about a star is what direction it’s in. (The other is how bright it is.)

But that alone will not tell us where the star is. In three dimensional space, you need three coordinates. In a Cartesian (square/cubic) grid, you need x, y, and z. In this case, you’re dealing with spherical coordinates, and you still need three of them (that’s why it’s “three dimensional” space): Right ascension, declination, and distance.

And unlike right ascension and declination, distance to a star is a cast-iron bitch to measure accurately.

I’ve told, here and especially elsewhere, the story of how we first determined the distance from Earth to the Sun (and hence all of the other distances within the solar system, since we already knew the ratios of the distances to each other). This was in the 1760s and it required observations of Venus transiting the Sun (i.e., crossing directly between Earth and the Sun so as to appear as a black dot crossing the fact of the sun, rather than crossing north/”above” or south/”below” the sun as it laps us in its orbit). This distance is called an “Astronomical Unit” (AU), and is currently defined to be 149,597,870,700 meters (in other words if we ever measure it in the future and it turns out the actual distance isn’t quite this, we’ll keep this number for the astronomical unit anyway). (And [Oh By The Way] knowing the average distance from the earth to the sun to the nearest 100 meters is, in and of itself, quite a triumph of measurement.)

With extremely painstaking measurements, best done on photographic plates, it became possible to measure distances to some stars once we knew this. It took until the mid 1800s. What happens is, as the earth revolves around the sun, its position changes by roughly 300 million kilometers, and that will cause nearer stars to appear to shift back and forth in relation to farther stars, just like you can shift your head back and forth and, say, a nearby light pole in a parking lot will appear to move back and forth with respect to the mountains in the background. (Folks in Kansas and especially Florida and Louisiana will have to adjust that example a bit.) This is known as parallax.

If you know how far you are moving your head, and can measure how many degrees along the horizon the pole appears to shift, it’s straightforward trigonometry to determine the distance to the light pole.

Even with the earth moving back-and-forth 300 million kilometers, the parallax of even the nearest star is less than one second of arc. (But note, this is quoted, for historical reasons, with respect to half of the earth’s orbital diameter, i.e., its orbital radius, which is to say, versus a 1 AU baseline, not a 2 AU baseline.) An arcsecond is about the width of a quarter at eighteen thousand feet (over three miles).

It’s possible to compute how far away something has to be to have a (half) parallax of one arc second as seen from a body orbiting with a radius of 1AU. Again, straightforward trigonometry. And, to the nearest meter (it has to be rounded because the formula has pi in it), it’s 30,856,775,814,913,673 meters. Or about 31 quadrillion meters or 31 trillion kilometers. This is called a “parsec” (short for “parallax-second”), and it’s roughly equal to 206,000 AU. (If you consider that Neptune’s orbit is roughly 30 AUs in radius, you can see how truly vast this distance is even compared to our solar system, which is measured in billions of miles. And this is closer than the nearest star.)

Astronomers–and I mean people who do astronomy for a living–think in and use parsecs. You’ve heard of light years, I am sure. That’s the distance light travels in a year. A parsec is actually about 3.26 light years, or alternatively, it takes 3.26 years for light to travel one parsec.

Astronomers talking to the public basically have to multiply everything by 3.26 so they can express it in light years. Why work in parsecs, then? Well, when they measure a parallax, they just have to divide it into 1 arc second to get the distance in parsecs. A 0.5 second parallax, means a two parsec distance, and so on.

The first successful parallax-based distance measurement was of the star Vega (visible low in the west shortly after sunset this time of year; it’s part of the Summer Triangle asterism); its parallax is almost exactly 1/8th of an arc second, so its distance was roughly 8 parsecs.

This was conceptually easy, but parallaxes were so small that by 1900 only 60 stars had had their distances measured. The process sped up in the early 20th century, to be sure…but since even with a small telescope hundreds of thousands of stars are visible, we weren’t going to finish off the list any time soon. Plus, of course, the fact that most of these stars are so distant they couldn’t be measured by the instruments of the time–they were in fact used as the backdrop for the nearer stars to move against. (Even today, with satellites doing the work, we really can’t get past about 1600 light years with this method.)

Clearly, if we were going to measure lots of stellar distances, we’d need another method.

But now for a wrenching change of subject.

The Shape of the Universe

William Herschel (1738-1822) is best known as the discoverer of the planet George. At least, that’s what he wanted to name it, after the King of England, George III.

(I’ll pause now and give you all a chance to quit vomiting at the prospect of naming a planet after that particular asshole.)

This name was not accepted by most astronomers, so instead they named it after every asshole: Uranus. And of course, that probably leads to even more bad jokes than naming it “George” would have. Astronomers school themselves to say “YER in us” instead of “your Anus” when they name that planet, but even that sounds too much like “urinous” (full or redolent of urine). Perhaps they should have gone with “OO rahn us,” probably closer to how the Greeks pronounced that name (father of the Titans) in any case. (And no, I didn’t mean to usurp Wheatie’s word of the day, but if you can find a good use for “urinous” with respect to current events–shouldn’t be that challenging–go right on ahead.)

Anyhow, Herschel did a lot of other things, perhaps the most important of which was discovery of infrared light. But for our purposes today, he was also the first to suggest that the stars, if their three-dimensional positions could be plotted, would form a disc with a central bulge, sort of like some renderings of flying saucers; and that the Sun would not be at the center of this shape.

How did he conclude this? If you get away from city lights (and that was easy to do in his day; nothing was as brightly lit back then as it is now), you will see a faintly glowing cloudy band stretching across the night sky. In fact, this cloudy band runs clear around the celestial sphere, including through the part we cannot see from the United States because it’s too far south. It’s most prominent where it runs through the constellation Sagittarius, but it also runs through Cassiopeia (the “W” in the northern sky) and the northern cross (part of Cygnus), in fact it runs along the long member of the cross. (This part of it should be readily visible shortly after dark…again, if you get the heck away from city lights.)

The ancient Greeks, of course, had spotted this band, and had named it γαλαξίας κύκλος (galaxias kyklos) or “milky circle” since the pale faint color suggested milk to them; they even had conjured up a myth that it was actual milk from the breast of Hera, queen of the gods. The Romans called it via lactea which translates directly to “Milky Way.”

When Galileo turned his telescope on the Milky Way, it turned out to be hundreds of thousands, if not millions, of stars that were individually too faint to be seen by the unaided eye, but together turned into this “milky way” stretching across the sky.

What Herschel had done was to catalogue thousands of stars and other deep sky objects, like nebulae, and to note that more of them were in the general direction of Sagittarius than any other direction, and of course most were in the plane of the Milky Way than other directions (such as 90 degrees away from it, where almost no stars are). And exactly opposite of Sagittarius, the Milky Way was thinnest.

That’s what we’d see if all the stars were spread out evenly in a fairly flat disc, and we were inside the disk but off center. We’d see the most stars looking through the center, lots of stars looking any other direction through the disc (the least when looking away from the center, because the distance to the edge of the disc is shortest in this direction) and much less looking perpendicularly to the disc.

The Milky Way is not just brighter in the direction of Sagittarius, but broader, which is why Herschel believed (correctly) there was a central bulge in that direction.

Note that Herschel was working before we could measure the distance to stars (and well before spectroscopy and stellar classification), so he was going entirely off their brightness, assuming that dimmer stars were further away. However, he was still essentially right about the shape of this conglomeration of stars.

It was believed that everything–the entire universe–was within this structure. That included not just stars, but also nebulae, in essence either dark, opaque clouds of gas and dust, or in some cases such clouds brightly lit by nearby stars.

One fairly obvious and prominent nebula is in the sword of Orion; it looks a bit fuzzy to the unaided eye (instead of being a crisp point of light like other things “up there”) but in binoculars it is obviously a glowing cloud of gas lit by stars embedded within it.

In fact, this is a place where stars and planetary systems are forming–right now. This is abundantly clear from observations, including from Hubble Space Telescope images.

Other nebulae had distinctly spiral shapes, like, for instance, this one:

And this is pretty much where things sat, clear into the early part of the 20th century. The universe was believed to consist of the Milky Way, surrounded by empty space.

But there were proponents of a different idea, that these spiral nebulae were actually separate galaxies. On April 26, 1920, in fact, there was a debate held at the Smithsonian’s Museum of Natural History; today it is known as the “Great Debate.” Harlow Shapley argued the spiral nebulae were on the outskirts of this galaxy, while Heber Curtis argued that they were in fact, distinct galaxies and therefore very far away, outside of this galaxy.

Note that this was just over a century ago. The issue wouldn’t be settled until 1924.

We have only known about other galaxies definitively for less than a century. Think about that.

How could the people who thought that “spiral nebulae” were in fact separate galaxies outside our own actually prove it? Or alternatively, be made to shut up? Well, the most straightforward way to do that would be to show that they were far, far away–or not.

Which brings me back to pointing out that in astronomy, measuring distances is a cast-iron bitch.

Even with today’s satellite technology, we can barely get parallaxes over 1% of the distance across this galaxy; certainly in 1920 using stone knives and bearskins we’d never be able to prove something was outside the galaxy with parallaxes.

A Standard Candle

But we already had a solution to this.

We go to HAH-vuhd, 1908-1912, and yet another woman, Henrietta Swan Leavitt (1868-1921).

I point out the fact that she was, indeed, a “she” because in those days it was very unusual for women to be involved with the “hard” sciences. How, then, did so many of them end up clustered at Harvard?

As it happens the astronomer Edward Charles Pickering (1848-1919) had developed a method of taking the spectra of multiple stars all at once by putting a prism in front of a photographic plate. He had,over decades, assembled a team of women to go through the data for 220,000 stars. This was primarily because they were cheap labor, but also because even back then women were appreciated for work that required attention to detail. [For instance, the US Mint preferred women for work as adjusters, who’d file excess precious metal off of unstruck planchets.] Annie Jump Cannon, whom we’ve met previously, emerged as their natural leader. The group became known as “Pickering’s Computers” (this was well before the invention of the electricity powered computer) and are now known as the Harvard Computers. They didn’t have doctorates (not by any means) but their contributions to astronomy today are well-regarded.

There were so many photographic plates involved–and back then these were sheets of glass coated with emulsion–that Pickering’s research was said to weigh 120 tons.

Cecilia Payne-Gaposhkin (whom I discussed previously; she discovered the stars were mostly made of hydrogen) was not one of the computers; she actually was a graduate student who worked closely with them.

Henrietta Swan Leavitt, on the other hand, was one of the computers and she established the first “standard candle.”

Clear back in September of 1784, Edward Pigott noticed that the star Eta Aquilae was variable; it would regularly dim, then brighten suddenly, then dim again. It would do so with the same period; every pulsation took the same amount of time, known as the period. (We now know that stars like this actually pulsate in size, like a yo-yo dieter only much more rapidly.) Just a few months later a different astronomer noticed the same for Delta Cephei. The periods range from a few days to a few months.[A digression about these names. There are thousands of stars in the sky visible to the naked eye; countless more visible with a telescope. They can’t all be given unique names (though hundreds have been, everything from Betelgeuse [famous] to Zubenelschamali [not so famous]). So in 1603, just before the invention of the telescope, Johann Bayer came up with a system of labeling the brightest star in a constellation as “alpha” (such as Alpha Orionis–Betelgeuse). Beta would go to the second brightest star and so on. This would be followed by the Latin genitive of the constellation name. So Betelgeuse was “Alpha of Orion,” strictly translated. This is called the Bayer designation, and has been extended since then. Continuing to look at Orion, alpha through kappa, the brightest ten stars: Eight of them have “real” names, one (theta) is actually the Orion nebula, and eta is (as far as Wikipoo knows) nameless. The three belt stars are among the named stars, the four stars of the not-quite-a-rectangle also all have names. Returning to Cepheids, Delta Cephei was designated the fourth brightest star in Cepheus by Bayer.]

There turned out to be an entire class of these variable stars and they became known as Cepheid variables in honor of Delta Cephei. Several dozen had been discovered by the end of the 19th century. Today we know that they are typically stars four to twenty times as massive as the sun, and therefore very bright, up to 100,000 times as bright–but this was not apparent before Henrietta Swan Leavitt studied them.

In 1908 Henrietta Swan Leavitt began measuring the apparent brightness and periods of numerous Cepheids in the Small and Large Magellanic Clouds. Apparently there are thousands of Cepheids in these clouds, though they appear quite faint compared to the ones previously discovered.

The SMC and LMC are patches of milkiness that are quite apparent to the naked eye, provided you are far enough south; they are deep in the southern celestial hemisphere, and the further south an object is, the further south you have to be for it to be above the horizon. The Large and Small Magellanic Clouds were noted by Antonio Pigafetta, who was with Ferdinand Magellan on his voyage (yes, that Magellan, famous for being the first to circumnavigate the Earth in the early 1500s). Of course many had noticed them before, anyone from Australian aborigines to Arabic astronomers and some other early European explorers, but for some reason this guy was able to tell the European scientific community about them and have it “stick.”

Leavitt noticed that the Cepheids in the Magellanic Clouds had an interesting correlation: the brighter they appeared, the longer their periods.

It was logical to suppose that Cepheids in one of the clouds are all at about the same distance from us. Which would mean the brighter ones really were intrinsically brighter than their dimmer cousins. And if the brighter ones had the longer periods…well then!

So what we had was a “standard candle” (Leavitt coined the term), in other words something of known intrinsic brightness. If you could measure the period of a Cepheid, and it had a long period, you knew it was the same intrinsic brightness as one with the same period in the Large Magellanic Cloud. If it looked dimmer, then it was actually further away. If it looked brighter, it was closer. So you could tell the (relative) distance of a Cepheid by measuring its period.

Leavitt published in 1912.

All we needed now was to measure the distance to one Cepheid variable by some other means and we’d know the distance to all of them. Eijnar Hertzsprung (as in “Hertzsprung Russell Diagram”, 1873-1967) measured the distance to several Cepheids by parallax in 1913.

We had our standard candle and were off to the races now.

In 1924, Edwin Hubble (after whom the space telescope is named, 1889-1953) working at the Mt. Wilson observatory in southern California, was able to detect very faint Cepheids in many of the “spiral nebulae,” measure their periods, determine that they were well outside the bounds of “the” “one and only” galaxy, and could therefore establish, once and for all, that the spiral nebulae they were in were actually separate galaxies.

The universe had just gotten bigger. A lot bigger. Some of the galaxies Hubble was able to measure were sixty or so million light years away; which is to say six hundred million trillion kilometers away (which is to say six hundred quintillion kilometers). That’s a lot more than the 100,000 light year diameter of this galaxy, which hitherto had been thought to be the entire universe.

A bunch of those galaxies about fifty or sixty million light years away are in the constellation Virgo, and that group is now known as the “Virgo cluster.”

And there were many, many dimmer “spiral nebulae” in which no Cepheids could be detected at all–presumably because those nebulae were so far away the Cepheids in them were too faint to see. So how big, precisely, is this universe of ours? Certainly at least hundreds of millions of light years!

At the other end of the scale, and most famously, there is a “spiral nebula” in Andromeda. You can see it with your own unaided eye, far away from city lights. (I personally find it hard to see; I have to look away from it slightly to see it. But it certainly shows up in binoculars!) It’s now called the Andromeda Galaxy, thanks to Hubble. It’s about 2 million light years away. The LMC and SMC are much closer, they’re now considered satellite smaller galaxies in orbit about our own galaxy. There are a few other very close galaxies, such as M-33; together with the Andromeda and Milky Way galaxies they make up the imaginatively-named “Local Group.” Twenty quadrillion kilometers may not seem terribly “local” to you, but for galaxies, that’s Standing Room Only and get your elbow out of my eye!

That telescope on Mt. Wilson? It was a monster in its day, with a 100 inch mirror. It still exists today; you can see it on tours during the daytime. It is not, however, used by professional astronomers any more as it’s simply not powerful enough. However, for several thousand dollars a night, you can rent the telescope–though as far as I know that opportunity is only extended to astronomy clubs.

But in terms of its historical impact on our view of the universe, it is probably second only to Galileo’s telescopes. Hubble himself is considered a Giant of astronomy; those astronomy clubs can actually use the same telescope he used.

But Hubble was not done in 1924. If anything, what he went on to do after this was even more important.

Redshifts

Vesto Melvin Slipher (1875-1969), had, back in the 1910s, looked at “spiral neblulae” through a spectroscope and had been able to measure their velocity towards or away from us (the “radial” velocity) by noting the Doppler shift of the spectral lines.

Almost all of them were moving away from us, as indicated by a shift towards longer wavelengths (lower frequencies). This is the famous “red shift” because the lines in the visible spectrum were shifted towards red, the longer wavelengths of visible light. Very few were shifted towards violet (which, for some reason is called a blue shift, not a violet shift). This was peculiar; after all a bunch of objects “out there” should have a pretty random assortment of radial velocities…yet almost all of these spirals were moving away from us, and rather rapidly, too.

For example, M-87 in the Virgo Cluster (this is the one with the really big black hole at its center–but Slipher had no idea about that) is moving away from us at 1284 kilometers per second. Which is pretty doggone fast.

Hubble took this data, combined it with his distance measurements, and made a plot.

And got the surprise of his life.

It turns out that the farther away a galaxy is, the faster it is receding, The main exceptions turned out to be within the Local Group; some of those galaxies actually are headed towards us (like Andromeda, which will collide with this galaxy in about five billion years).

M-87 is 16.4 megaparsecs (million parsecs) away from us which puts it at about 53.5 million light years off.

What is it about the Milky Way galaxy that is repelling almost all of the other galaxies?

Nothing, actually. It turns out that a hypothetical observer in any galaxy will see all of the other galaxies rushing away from him, the further away, the faster.

Hubble was able to determine that for every megaparsec of distance, a galaxy is going to be moving 500 kilometers per second. As it turns out, there were significant problems with using Cepheid variables–it turns out there are two distinct classes of them that behave differently. I’ve ignored that fact up til now. But now, this recession rate is known to be 74 km/second…for each megaparsec of distance. This is known as the Hubble parameter, now. And the fact that further galaxies recede faster is now known as Hubble’s Law.

Bang!

But, run the movie backwards! What happens? Since galaxies twice as far away move twice as fast, if you run the movie backwards, all galaxies come together simultaneously at some point. Which means (if you halt the reverse at this point and start looking at it in forward motion) everything was in one place, then there was a big explosion (or something like that) and all of the pieces got blown away from from the other pieces at some point in the distant past, eventually leading to what we see today.

Time for Einstein and Company to step in.

One thing that was instantly apparent to Albert Einstein when he formulated General Relativity was that it could be applied to the universe as a whole. Einstein believed (as most did in 1915) that the universe was essentially static and unchanging on a large scale. What we see now was pretty much what had been there…back forever.

However, both General Relativity and Newtonian gravity said that if the universe consisted of a bunch of stationary objects, they’d simply attract each other and start to move closer to each other, in exactly the same way that a stationary apple a meter above the floor will, without support, fall.

So Einstein, believing that this wasn’t what was happening (he really didn’t have evidence of that; this was before Hubble), put a fudge factor into his equation, a cosmological constant repulsion that counteracted what would otherwise be the natural inclination of the universe to contract.

Hubble’s discovery was an attitude adjuster for Einstein. The universe was not static and unchanging, it had not always existed. It had instead had a beginning, and from that beginning everything rushed apart. Clearly, ever since then, the galaxies had been slowing down due to their mutual attraction, but also, clearly, they hadn’t come to a halt. With the residual motion evident even today, there was no need for the cosmological constant fudge factor in his equations.

Einstein later considered it the biggest mistake of his life and he was probably right because he didn’t vote for Joe Biden.

[I say that, but perhaps a check of the voter rolls for Princeton, NJ is in order.]

In 1922, Alexander Alexandrovich Friedmann (1888-1925) worked with Einstein’s General Relativity equation, and derived a relationship between the average density of the universe (in kilograms per cubic meter, for instance–and by the way this number is very, very small!), its current expansion velocity, and its acceleration; this equation could be used to determine the future state of the universe (or any past state). You could essentially get the Hubble parameter out of it with the right inputs; and the equation can be rearranged to use the Hubble parameter as one of its coefficients.

The equation makes it clear that the Hubble parameter is not a constant, it can change. And indeed it’s expected to start out at a high value when everything was bunched together, then drop as things slow down over time as galaxies attract each other–exactly the way an apple thrown up into the air slows down and stops.

Another part of the equation is an expression for how fast the Hubble parameter is changing with time.

The big unknown, actually, is the average density of the universe. There is a certain value of it, which will cause the universe to expand forever, but as the time goes to infinity the speeds drop to zero…as if everything were currently moving exactly at escape velocity. This is the critical density, and the actual density could conceivably be one billionth (or a centillionth) of that value, or a billion times as much.

Determining the ratio of the actual density to the critical density has occupied a large part of the efforts of cosmologists over the last century. I had originally written a bunch more on that here…but this article has gotten long enough, and I don’t want to get too historically askew. Suffice it to say that early estimates were less than 1, but more than 0.01, meaning that there didn’t appear to be enough matter in the universe to cause its expansion to slow down and have it recollapse. But these numbers are suspiciously close to 1 when you consider the range of conceivable values is literally infinite.

It appeared at the time as though it was one third of the value, which is close enough to 1 (compared to all of the other possible ratios) to make scientists suspect it really is 1 and we’re just not measuring it right.

But this is general relativity we are dealing with here, not Newtonian mechanics, so the Friedman equation is actually an equation about how much space time is warped. That makes it more than just an equation about escape velocity. And so there are some things about it that are distinctly counter-intuitive.

First off, the galaxies that rushed away from the original point location are not moving through space. Instead, space itself is expanding. Originally, space itself was small; as it expanded all the matter in the universe stretched out with it, and eventually coalesced to form galaxies. (If the galaxies started moving in some different direction after the Big Bang, because they were near some giant cluster and are attracted to it, that’s actual motion. (And today we believe the Milky Way is moving towards the Virgo cluster.)

One consequence of space expanding is that the red shifts that we see are actually due, not to a Doppler effect but rather, to the fact that while the photon was travelling from the distant galaxy to our eyes the space stretched, which stretched the photon into a longer wavelength. One rather odd consequence of this is that a photon, once emitted, will lose energy as it travels through intergalactic space because its frequency is dropping.

Second, space-time across the expanse of the universe has a shape. And it turns out that a value of density lower than the critical density would imply that space has negative curvature, and a value that is higher would imply that space has positive curvature.

Now what the heck does that mean? How can space be curved? Well, we already know it can be warped and that’s what gravity actually is. But this deserves some elaboration.

You were taught in geometry class that the sum of the three interior angles of a triangle is always 180 degrees. That’s a fundamental property of flat space.

But really, this is only true if the triangle is drawn on a flat plane.

If you were to travel from the equator directly to the north pole, make a right-angle (90 degree) left turn, then head back to the equator (traveling south), then, on reaching the equator, make another right-angle left turn (now traveling east), you’d end up back where you started, eventually. You could then turn left 90 degrees and be facing north, like you were in the beginning.

You’ve drawn three straight lines, and are back where you started; that’s a triangle. But every interior angle is 90 degrees so the total of the three is 270 degrees.

This “breaks” that 180 degree rule I just reminded you of, but the earth is not flat, it’s (roughly) spherical. It exhibits positive curvature.

Now imagine a surface like a saddle or a Pringles chip, extended to infinity. (The bell of a tuba also works.) Drawing a triangle on that kind of surface gives you a sum of interior angles less than 180 degrees.

If the universe has too high a density, its expansion will eventually cease (at a time short of infinity) and it will collapse back in on itself again. This would render space-time the four dimensional equivalent of a sphere.

If it’s below the critical density, then even at infinity there’s velocity left to the expansion, and space time is shaped somewhat like that saddle.

If it’s exactly at the critical density, then space time is, on the whole, flat.

How can we tell? Try measuring the interior angles of a really big triangle. Preferably one billions of light years in size. (And believe it or not, today’s scientists think they’ve actually done something like that, and they believe the universe to be flat. But I am WAY ahead of the story here.)

If this makes your head hurt, you’re not alone, believe me.

Anyhow, to return to our narrative, a lot of astronomers did not want to accept that the universe didn’t have a definite beginning. Fred Hoyle, famously, refused to accept it, and died in 2002 still refusing to believe it.

It’s not that he didn’t believe that the galaxies were rushing away from each other, but rather, he imagined that as galaxies grew further apart, new matter in the form of hydrogen atoms was being spontaneously created, which would then coalesce to form new galaxies. This would result in the universe of the distant past, or the distant future, looking about the same as it does today, rather than the galaxies being closer together, or further apart, respectively. This is known as the steady state theory, and from what I can see, virtually no scientist accepts it today. Certainly, we’ve never detected any sign of hydrogen spontaneously being created throughout space, as it would have to be if Steady State were true.

Hoyle, trying to characterize the theory he disagreed with so vehemently, came up with the moniker “Big Bang.” He claims he wasn’t trying to be derisive, but many took it as such. The proponents proudly adopted the term to describe that instant–roughly 11 to 13 billion years ago–when everything in the universe was jammed close together.

(It’s not as if people haven’t, at other times, proudly adopted what was supposed to be a derisive label. Right, oh fellow Deplorables?)

The Big Bang theory was simultaneously worked out by Georges Lemaitre (1894-1966), who was not only an astronomer, but also a Catholic priest. He certainly had no problem with the universe having a beginning! In fact Hubble’s Law is often called the Hubble-Lemaitre’s Law.

There was one minor issue though.

Running the tape backwards, the Big Bang appeared to be ten or eleven billion years old. This was based on extrapolating the current expansion rate backwards, and accounting for how the expansion rate was undoubtedly faster in the past. Yet we also had good reason to believe that globular clusters–groupings of thousands to millions of stars that mostly exist above and below the plane of this galaxy–are at least 13 billion years old. Clearly it’s absurd that globular clusters could be older than the universe that they are part of, so this was a nagging issue for quite some time.

The Next Rung Of The Ladder

With Hubble-Lemaitre’s Law established, we had a new way to measure distance. If we couldn’t see Cepheid variables in some galaxy because it was too far away from us, we could instead measure its red shift, turn a mathematical crank, and get a distance out, one likely to be over a hundred million light years.

In fact, when quasars were first discovered, their red shifts were measured and they were instantly some of the most distant objects ever detected. Some were even billions of light years away. But there is a complication here. The farther away a galaxy is, the further back in time we are looking. If we look at M-87, we are seeing it as it was 53 million years ago, because the light has traveled 53 million light years to get to us, and for the light to be getting to us now, it has to have left M-87 53 million years ago.

Similarly for more distant galaxies. As our telescopes became more and more sensitive, we were looking at galaxies further and further into the past. Quasars, it turns out, all happened well in the past, and now we know they are a “young galaxy” thing as the black holes at the galactic centers devour interstellar gas. In older galaxies, that interstellar gas is as gone as last Thanksgiving’s dinner.

But, if the universe has been slowing down its expansion rate, 53 million years ago, or a billion years ago, the Hubble parameter must have been higher. If we compute a distance to a galaxy using a constant Hubble parameter, we’re introducing an error.

Of course this relies on what is ultimately an assumption: That the Hubble parameter is indeed decreasing. It’s an assumption that seems to make sense, because after all everything in the universe is being attracted to everything else. On the other hand, if you’re a galaxy surrounded by other galaxies, their pulls should all cancel out, and that same is true of all of those other galaxies too–they’re all surrounded by other galaxies.

So scientists wanted to check that assumption–and the data gathered would help nail down the average density of the universe a bit better.

So we needed some other way to measure the distance to a galaxy, and compare it to the distance inferred from its red shift. If the first distance was further, that would imply that the Hubble parameter used to be bigger than it is today (as expected) and we could even, if we did this with enough galaxies with different red shifts, be able to plot how much the Hubble parameter was at any given time in the past.

But to do that, we needed another “Standard Candle,” one a lot brighter than Cepheid variables.

And we eventually found one.

But here, I think, is where I need to pause.

I’m going to shift gears next time. But not really. Because as you investigate the very earliest stages of the universe (I am talking about, say, 1 second after the Big Bang) you find yourself needing to know about particle physics.

So switching from talking about the entire universe, to talking about stuff much smaller than atoms, isn’t as jarring as it might seem at first.

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 !!!

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.

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 !!!