We’re more than a week into a discussion of Professor Richard Muller’s claim that“According to the general theory of relativity, the Sun does orbit the Earth. And the Earth orbits the Sun. And they both orbit together around a place in between. And both the Sun and the Earth are orbiting the Moon.” Though many readers have made interesting and compelling attempts to prove the Earth orbits the Sun, none have yet been able to say why Muller is wrong.
A number of readers suggested, in one way or another, that we go far from the Sun and Earth and use the fact that out there, far from any complications, Newtonian physics should be good. From there, we can look back at the Sun and Earth, and see what’s going on in an unbiased way. Although Muller would say that you could still claim the Sun orbits the Earth by using “geocentric” coordinates centered on the Earth, these readers argued that such coordinates would not make sense in this distant, Newtonian region.
It’s far from a perfect image. [Note added: if you need an introduction to what images like this actually represent (they aren’t photographs of black holes, which are, after all, black…), start with this.]
EHT’s blurry time-averaged image of the ring of material surrounding the black hole at the center of our galaxy
It’s blurred out in space by imperfections in the telescopic array that is the “Event Horizon Telescope” (EHT) and by dust between us and our galaxy’s center. It’s blurred out in time by the fact that the glowing material around the black hole changes appreciably by the hour, while the EHT’s effective exposure time is a day. There are bright spots in the image that may just be artifacts of exactly where the telescopes are located that are combined together to make up the EHT. The details of the reconstructed image depend on exactly what assumptions are made.
At best, it shows us just a thick ring of radio waves emitted over a day by an ever-changing thick disk of matter around a black hole.
But it’s our galaxy’s black hole. And it’s just the first image. There will be many more to come, sharper and more detailed. Movies will follow. A decade or two from now, what we have been shown today will look quaint.
We already knew the mass of this black hole from other measurements, so there was a prediction for the size of the ring to within twenty percent or so. The prediction was verified today, a basic test of Einstein’s gravity equations. Moreover, EHT’s results now provide some indications that the black hole spins (as expected). And (by pure luck) its spin axis points, very roughly, toward Earth (much like M87’s black hole, whose image was provided by EHT in 2019.)
We can explore these and other details in coming days, and there’s much more to learn in the coming years. But for now, let’s appreciate the picture for what it is. It is an achievement that history will always remember.
In 2019, the first image of the surroundings of a black hole was produced, to great fanfare, by the astronomers at the Event Horizon Telescope (EHT). The black hole in question was the enormous one at the center of the galaxy M87.
The “image” of the surroundings of a black hole in galaxy M87. What does it actually show? It is most likely an image (in radio waves) of an “accretion disk” of material around the black hole, its radio emissions somewhat distorted by the warped geometry around the black hole.
At the time, there was also hope that the EHT would produce an image of the region around the black hole at the center of our own galaxy, the Milky Way. That black hole is thousands of times smaller, but also thousands of times closer, than the one in M87, and so appears about the same size on the sky (just as the Moon and Sun appear the same size, despite the Sun being much further away.)
However, the measurements of the Milky Way’s black hole proved somewhat more challenging, precisely because it is smaller. EHT takes about a day to gather the information needed for an image. M87’s black hole is so large that it takes days and weeks for it to change substantially — even light takes many days to cross from one side of the accretion disk to the other — so EHT’s image is like a short-exposure photo and the image of M87 is relatively clear. But the Milky Way’s galaxy’s black hole can change on the times scale of minutes and hours, so EHT is making a long-exposure image, somewhat like taking a 1-second exposure of a tree on a windy day. Things get blurred out, and it can be difficult to determine the true shape of what was captured in the image.
Apparently, the EHT scientists have now met these challenges, at least in part. We will learn new things about our own galaxy’s black hole on Thursday morning; links to the press conferences are here.
In preparation for Thursday, you might find my non-expert’s guide to a black hole “silhouette” useful. This was written just before the 2019 announcement, when we didn’t yet know what EHT’s first image would show. The title is a double-entendre, because I myself wasn’t entirely expert yet when I wrote it. The vast majority of it, however, is correct, so I still recommend it if you want to be prepared for Thursday’s presentation.
The only thing that’s not correct in the guide (and the offending sections are clearly marked as such) are the statements about the “photon ring”. It took me until my third follow-up post, two months later, to get it straight; that post is accurate, but it is long and very detailed. Most readers probably won’t want to go into that much detail, so what I’ll do here is summarize the correct parts of what I wrote in the weeks following the announcement, repeating a few of the figures that I made at the time, and then tell you about a couple of new things that have been learned since then about M87’s black hole. Hopefully you’ll find this both interesting on its own and useful for Thursday.
Today I’m continuing the reader-requested explanation of the “triplet model,” (a classic and simple variation on the Standard Model of particle physics, in which the W boson mass can be raised slightly relative to Standard Model predictions without affecting other current experiments.) The math required is pre-university level, just algebra this time.
The third webpage, showing how to combine knowledge from the first page and second page of the series into a more complete cartoon of the triplet model, is ready. It illustrates, in rough form, how a small modification of the Higgs mechanism of the Standard Model can shift a “W” particle’s mass upward.
Future pages will seek to explain why the triplet model resembles this cartoon closely, and also to explore the implications for the Higgs boson.
When we’re trying to figure out whether a confusing statement is really true or not, we have to speak precisely. Up to this stage, I haven’t been careful enough, and in this post, I’m going to try to improve upon that. There are a few small but significant points of clarification to make first. Then we’ll look in detail at what it means to “change coordinates” in such a way that would put the Sun in orbit around the Earth, instead of the other way round.
We’re all taught in school that the Earth goes round the Sun. But if you look around on the internet, you will find websites that say something quite different. There you will find the argument that Einstein’s great insights imply otherwise — that in fact the statements “The Earth goes round the Sun” and “The Sun goes round the Earth” are equally true, or equally false, or equally meaningless.
What’s his point? In Einstein’s theory of gravity (“general relativity”), time and three-dimensional space combine together to form a four-dimensional shape, called “space-time”, which is complex and curved. And in general relativity, you can choose whatever coordinates you want on this space-time.
So you are perfectly free to choose a set of coordinates, according to this point of view, in which the Earth is at the center of the solar system. In these coordinates, the Earth does not move, and the Sun goes round the Earth. The heliocentric picture of the planets and the Sun merely represents the simplest choice of coordinates; but there’s nothing wrong with choosing something else, as you like.
This is very much like saying that to use latitude and longitude on the Earth is just a choice. I could use whatever coordinates I want. The equator is special in the latitude-longitude system, since it lies at latitude=0; the poles are special too, at latitude +90 degrees and -90 degrees. But I could just as well choose a coordinate system in which the equator and poles don’t look special at all.
And so, after Einstein, the whole Copernican question — “is the solar system geocentric or heliocentric?” — is a complete red herring… much ado about nothing. As Muller argues in his article, “the revolution of Copernicus was actually a revolution in finding a simpler way to depict the motion, not a more correct way.“
Well? Is this true? If not, why not? Comments are open.
