Tag Archives: Einstein

Earth Around the Sun, or Not? The Earth-Centered Coordinates You Should Worry About

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.

Are they correct about this?

Continue reading

Is it Meaningful to Say that Earth Goes Round the Sun, or Not? (And Why Is This So Hard…?)

Is the statement “The Sun Orbits the Earth” false? Not according to professor Richard Muller of the University of California, Berkeley, as I discussed yesterday. Muller argues that Einstein’s theory of general relativity implies that you can view the Sun as orbiting the Earth if you like, or that both the Sun and Earth orbit Venus, or a random point in space, or anything else for that matter. Meanwhile, every science textbook in our kids’ classrooms says that “The Earth Orbits the Sun“. But for all of our discussions yesterday on this subject, we did not yet collectively come to any conclusions as to whether Muller is right or wrong. And we can’t hope to find evidence that the Earth orbits the Sun if the reverse is equally true!

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.

Continue reading

Sun Around the Earth, or Earth Around the Sun?  Did Einstein Say “It’s all the same”?

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.

Here, for example, is this statement as written in Forbes by professor Richard Muller at the University of California, Berkeley.   It opens as follows: “According to the general theory of relativity, the Sun does orbit the Earth. And the Earth orbits the Sun.”  I invite you to read the rest of it; it’s not long.

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.

Celebrating 2/22/22 (or was it 22/2/22)?

I hope you all had a good Twosday. Based on what I saw on social media, yesterday was celebrated widely in many parts of the world that use Pope Gregory’s calendar. I had two sandwiches to in honor of the date, and two scoops of ice cream.

In the United States, the joy continues today, it being now 2/23/22. Though not quite as wonderful as 2/22/22 on Tuesday, it’s still another nicely symmetric number worthy of note. In fact we get a full week of this, including 2/24/22 tomorrow, 2/25/22 on Friday, and so on, concluding on 2/29/22 … uhh, (oops) I mean, 2/28/22, because 2022 is not a Leap Year. For some reason.

In other countries, where it is 23/2/22, the celebration is over for now … because without symmetry, where’s the love? Ah, but they’re just more patient. They’ll get their chance in a month, when it’s 22/3/22, a date that will go unnoticed in the USA but not in Europe.

But what, exactly, are we getting so jazzed about? After all, what is the significance of it being the 22nd or 23rd date of the second month of a year labelled 2022? Every single bit of this is arbitrary. Somebody, long ago, decided January would be the first month, making February month number 2; but it wasn’t that long ago that March was the first month, which is why September, October, November and December (7, 8, 9, and 10) have their names. It’s arbitrary that January has 31 days instead of 30; had it been given thirty, the day we call the “22nd” would have been the “23rd” of February, and our celebration would have been one day earlier. And 2022 is arbitrary two too. Other perfectly good calendars referred to yesterday by a completely different day, month and year.

This, my friends, is exactly what General Relativity (and the rest of modern physics) tells you not to do. This is about putting all of your energies and your focus on your coordinate system — on how you represent reality, instead of on reality itself. The coordinate system is arbitrary; what matters is what actually happens, not how you describe what happens using some particular way of measuring time, or space, or anything else. To get excited about the numbers that happen to appear on your measuring stick is to put surface ahead of substance, math ahead of physics, magic ahead of science. It’s as bad as getting excited about how a word is spelled, or even what word is used to represent an object; a rose by any other name.

But we humans are not designed to think this way, it seems. We cheer when we’ve driven a thousand miles, a milestone (hah) which combines the definition of mile (arbitrary) with the fascination with the number 1,000 (which only looks like an interesting number if you count with ten fingers, rather than 12 knuckles, as the Babylonians did, or eight tentacles, as certain intelligent sea creatures might do.) We get terribly excited about numbers such as 88, or 666, which similarly depend on our having chosen to count on our ten fingers. A war was ended on 11/11 at 11:00 (and one was started on 22/2/22 — coincidence?)

Celebrating birthdays is a little better. No matter what calendar you choose, or whether it even lasts a year (as, for example, in Bali), the Sun appears to move across the sky, relative to the distant stars, in a yearly cycle. When it comes back to where it was, a year has passed. If we define your age to be the number of solar cycles you’ve experienced, then that means something, no matter what calendar you prefer. Your birthday means something too as long as we define it not by the arbitrary calendar but by the position of the Sun on the day of your birth.

Similarly, the solstices that mark the days with the shortest daylight and shortest darkness, and the equinoxes that have days and nights equal in duration, are independent of how you count hours or minutes or seconds, or even days. It doesn’t matter if your day has 24 equal hours, or if you divide your daylight into 12 and your darkness into 12, as used to be the case. It doesn’t matter what time zones you may have arbitrarily chosen. If you want to mark days, you can use the time that the Sun is highest in the sky to define “noon”, and count noons. A year is just over 365 noons, no matter what your calendar. The time from solstice to solstice is about half that. But the date we call “December 25th” does not sit on a similarly fundamental foundation; it shifts when there’s a leap year, and sometimes it’s three days after the solstice and sometimes four. Many other holidays, driven by Moon cycles rather than a Sun cycle, are even less grounded in the cosmos.

Being too focused on coordinates can cause a lot of trouble. The flat maps that try to describe our spherical Earth make all sorts of things seem to be true that aren’t. They all make the shortest path between two points impossible to guess. Some wildly exaggerate Greenland’s size and minimize the entire African continent. Most of them make it difficult to imagine what travel over the north or south pole is like, because there’s a sort of “coordinate singularity” there — a single point is spread out over a whole line at the top of the map, and similarly at the bottom, which makes places that are in fact very close together seem very far apart.

A coordinate singularity of a more subtle type prevented scientists (Einstein among them) from realizing for decades that black holes, which were once called “frozen stars,” have an interior, and that you could potentially fall in. The coordinates originally in use made it seem as though time would stop for someone reaching the edge of the star. Bad coordinates can obscure reality.

Physics, and science more generally, pushes us to focus on what really happens — on events whose existence does not depend on how we describe them. It’s a lesson that we humans don’t easily learn. While it’s fine to find a little harmless and silly joy at non-events such as 22/2/22 or 2/22/22, that’s as far as it should go: anything that depends on your particular and arbitrary choice of coordinate system cannot have any fundamental meaning. It’s a lesson from Einstein himself, advising us on what not two do.

Science Festival About to Start in Cambridge, MA

It’s a busy time here in Cambridge, Massachusetts, as the US’s oldest urban Science Festival opens tomorrow for its 2015 edition.  It has been 100 years since Einstein wrote his equations for gravity, known as his Theory of General Relativity, and so this year a significant part of the festival involves Celebrating Einstein.  The festival kicks off tomorrow with a panel discussion of Einstein and his legacy near Harvard University — and I hope some of you can go!   Here are more details:


First Parish in Cambridge, 1446 Massachusetts Avenue, Harvard Square, Cambridge
Friday, April 17; 7:30pm-9:30pm

Officially kicking off the Cambridge Science Festival, four influential physicists will sit down to discuss how Einstein’s work shaped the world we live in today and where his influence will continue to push the frontiers of science in the future!

Our esteemed panelists include:
Lisa Randall | Professor of Physics, Harvard University
Priyamvada Natarajan | Professor of Astronomy & Physics, Yale University
Clifford Will | Professor of Physics, University of Florida
Peter Galison | Professor of History of Science, Harvard University
David Kaiser | Professor of the History of Science, MIT

Cost: $10 per person, $5 per student, Tickets available now at https://speakingofeinstein.eventbrite.com

Did BICEP2 Detect Gravitational Waves Directly or Indirectly?

A few weeks ago there was (justified) hullabaloo following the release of results from the BICEP2 experiment, which (if correct as an experiment, and if correctly interpreted) may indicate the detection of gravitational waves that were generated at an extremely early stage in the universe (or at least in its current phase)… during a (still hypothetical but increasingly plausible) stage known as cosmic inflation.  (Here’s my description of the history of the early universe as we currently understand it, and my cautionary tale on which parts of the history are well understood (and why) and which parts are not.)

During that wild day or two following the announcement, a number of scientists stated that this was “the first direct observation of gravitational waves”.  Others, including me, emphasized that this was an “indirect observation of gravitational waves.”  I’m sure many readers noticed this discrepancy.  Who was right?

No one was wrong, not on this point anyway.  It was a matter of perspective. Since I think some readers would be interested to understand this point, here’s the story, and you can make your own judgment. Continue reading

Did The Universe Really Begin With a Singularity?

Did the universe begin with a singularity?  A point in space and/or a moment in time where everything in the universe was crushed together, infinitely hot and infinitely densely packed?

Doesn’t the Big Bang Theory say so?

Well, let me ask you a question. Did you begin with a singularity?

Let’s see. Some decades ago, you were smaller. And then before that, you were even smaller. At some point you could fit inside your mother’s body, and if we follow time backwards, you were even much smaller than that.

If we follow your growth curve back, it would be very natural — if we didn’t know anything about biology, cells, and human reproduction — to assume that initially you were infinitesimally small… that you were created from a single point!

But that would be wrong. The mistake is obvious — it doesn’t make sense to assume that the period of rapid growth that you went through as a tiny embryo was the simple continuation of a process that extends on and on into the past, back until you were infinitely small.  Instead, there was a point where something changed… the growth began not from a point but from a single object of definite size: a fertilized egg.

The notion that the Universe started with a Big Bang, and that this Big Bang started from a singularity — a point in space and/or a moment in time where the universe was infinitely hot and dense — is not that different, really, from assuming humans begin their lives as infinitely small eggs. It’s about over-extrapolating into the past. Continue reading

If It Holds Up, What Might BICEP2’s Discovery Mean?

Well, yesterday was quite a day, and I’m still sifting through the consequences.

First things first.  As with all major claims of discovery, considerable caution is advised until the BICEP2 measurement has been verified by some other experiment.   Moreover, even if the measurement is correct, one should not assume that the interpretation in terms of gravitational waves and inflation is correct; this requires more study and further confirmation.

The media is assuming BICEP2’s measurement is correct, and that the interpretation in terms of inflation is correct, but leading scientists are not so quick to rush to judgment, and are thinking things through carefully.  Scientists are cautious not just because they’re trained to be thoughtful and careful but also because they’ve seen many claims of discovery withdrawn or discredited; discoveries are made when humans go where no one has previously gone, with technology that no one has previously used — and surprises, mistakes, and misinterpretations happen often.

But in this post, I’m going to assume assume assume that BICEP2’s results are correct, or essentially correct, and are being correctly interpreted.  Let’s assume that [here’s a primer on yesterday’s result that defines these terms]

  • they really have detected “B-mode polarization” in the “CMB” [Cosmic Microwave Background, the photons (particles of light) that are the ancient, cool glow leftover from the Hot Big Bang]
  • that this B-mode polarization really is a sign of gravitational waves generated during a brief but dramatic period of cosmic inflation that immediately preceded the Hot Big Bang,

Then — IF BICEP2’s results were basically right and were being correctly interpreted concerning inflation — what would be the implications?

Well… Wow…  They’d really be quite amazing. Continue reading