*tl;dr:* Executive summary: It is not fundamentally true that the Earth goes around the Sun; it is just easier to calculate things that way.

We like to say that the critical event that started the scientific revolution is the discovery that the Earth goes around the Sun, and not the other way around. This was incredibly important; the hypothesis by Copernicus led to the immensely important data-taking by Tycho Brahe and the quantitative, theoretical explanation of it by Kepler. Galileo's discovery of moons of Jupiter bolstered the case in important ways, and Newton's quantitative description of it all in terms of the inverse-square law solidified it all into an edifice of great importance, that is just as important and valuable today as it was then. It is also a great example of how a scientific discovery requires both observational and theoretical backing to become confidently adopted by the community.

In the 20th Century, Einstein brought us General Relativity, with the eponymous generality granting us immense coordinate freedom. That is, there are (infinitely) many ways we can make decisions about what is stationary and what is moving, and what we choose as reference points. In some choices, calculations are harder. In other choices, calculations are easier. In yet others, certain symmetries become more obvious or more valuable for making predictions. That is, GR delivers to us lots of choices about how to think about what's moving and how.

So the crazy insane thing is this: *In GR, there is no answer to the question* of whether the Earth goes around the Sun or whether the Sun goes around the Earth. There is literally no observational answer to the question, and no theoretical answer. All observations can be incorporated to an analysis from either perspective. The question of which goes around which is *not a question you can ask in the theory*.

That said, it really is far, far easier to do calculations in the Copernican frame. Indeed, absolutely all calculations of Solar System dynamics are done in this frame with post-Newtonian code. The way I see it (with modern eyes) is that Copernicus's hypothesis was based on *parsimony* or *simplicity* and was adopted for that reason. Brahe and Kepler confirmed that the data are consistent with Copernicus's simple model (though with the eccentricities added). After Brahe and Kepler it was still *possible* to understand the observations in an Earth-centered (or even stranger) coordinate system, but was *far, far easier* to do calculations in the heliocentric frame.

Even today, now that GR is our model of gravity, we still calculate the Solar System with Newtonian codes (with adjustments to approximate GR corrections). And even today, now that we have this amazingly accurate model of the Solar System, we still often calculate the positions of celestial bodies by looking at paths on the celestial sphere, as did Ptolemy. How we calculate something is incredibly context-dependent, and doesn't always respect our most fundamental ideas. And the *truth* of Copernicus's hypothesis really just represents the *pragmatism* of the present-day mathematical tools. All these thoughts bolster my rejection of *scientific realism* and play into questions of social construction and so on. It also bolsters my view that Ockham's Razor should be thought of as a statement about calculation, not *truth*.

Sure the Earth goes around the Sun! But let's remember that this is a statement about calculation and pragmatism, not *the fact of the matter*.

I think I disagree.

ReplyDeleteThere is a real asymmetry between the valid GR frame in which the Earth is at rest and one where it moves: it's not just the Sun that goes around the Earth, but the *entire Universe*. The Universe has a preferred frame—that of the CMB.

But even focusing on the Earth-centric vs. Solar System barycenter frames, I think that there is a *reason* calculations are easier in the center-of-mass frame that goes beyond accidents of how we do the math. The math reflects the physics, and I think it's fundamental to the physics that the COM frame is special (COM is a conserved quantity, after all, and by Noether's theorem that reflects fundamental symmetries of the universe.)

But with respect to the frame where the Sun is truly at rest vs. the Earth is at rest, I agree: both are equally good/poor frames for describing the physics.

Also, I don't think the *rotating* frame in which the Earth's surface is at rest is a valid, inertial GR frame? It's been a while since I did GR, so I'm a bit fuzzy on that one, but surely we can say that the original geocentric models with a *non-rotating* Earth are truly invalid?

ReplyDeleteIn answer to both: There is a preferred rest-frame, for the SS, for the Milky Way, and for the Hubble Volume, both in terms of rotation and in terms of velocity and acceleration. And these are very real! But I don't think they truly break the coordinate freedom symmetry of GR, any more than they break the relative-velocity symmetry of SR. Despite the existence of a CMB rest frame, there still is no preferred rest frame for SR calculations, and no object that can be said to be "truly" at rest.

ReplyDeleteps. I am answering in the context of GR and SR. Of course these are no-doubt approximations to a more true theory, in which Lorentz invariance might be (very weakly) broken and establish a truly true reference frame and coordinate system. That isn't ruled out at present, and is consistent with all your points.

ReplyDeleteObservation of stellar parallaxes of stars and the aberration of light are strong evidences that the Earth is moving around the Sun. I don't think a geocentric frame of reference can explain that. In fact, historically stellar parallax has been a contentious point of debate between geocentrists and heliocentrists. Since nobody can observe parallaxes until the early 19th century, heliocentrists never gained serious ground for millenia. Before then, we need Kepler and Newton to get heliocentrism really going by giving it a robust theoretical foundation.

ReplyDelete@Anonymous: I agree that it is simpler to compute things in the heliocentric frame! But I don't think in GR the fact that parallax happens makes it true that the Earth goes around the Sun. But we could define that to be the definition of heliocentrism.

ReplyDeleteps. In conversations with Geoff Ryan (NYU), I realized that the correct question for this blog is: Can the question "does the Earth go around the Sun?" be turned into a question about coordinate-free objects in GR. If it can, then the Earth goes around the Sun! If it can't, then this isn't a question that has an answer in GR.

ReplyDelete