# Reality Conditions

## Thursday, February 09, 2006

### Does the Earth "really" go around the Sun?

At Pharyngula PZ has pointed to some lunatic geocentrist society and their challenge for anyone to "prove" that the Earth moves. As it is almost inevitable, this has launched a discussion over whether it is correct to state as an absolute fact that the Earth moves around the Sun, or whether motion is purely relative and the only difference between the Sun-centered and the Earth-centered model is pragmatical -calculating and making predictions is easier if one puts the Sun at the center. Popular understanding of the theory of relativity seems to include the second position, but the actual truth is a bit more subtle than that. I copy below the two comments I made in succession there explaining the issue as I see it, and hope to see comments by people more expert than I am approving them or correcting them.

I had once this discussion with a fellow physics student. It lasted about 5 hours, getting more and more intricate all the time. The issue of whether "all motion is really relative" in General Relativity is a lot more trickier than most popularizations make it seem.

My present position is this one: All coodinate systems are equivalent in the sense that one could describe all facts equally well adopting any of them, and the laws of Nature are the same in all of them (this is at the core of GR). In the case of the solar system, the coordinate system in which the Sun is at rest has the feature that the spacetime metric (which encodes the gravitational field) becomes assymptotically Minkowskian at large distances from the solar system (the Minkowski metric is the metric of flat spacetime, where there is no gravity present). By contrast, using the coordinate system in which the Earth is at rest the metric does not become Minkowskian at large distances, but includes constant terms related to the relative rotation of the Earth and Sun. The physical and absolute (not coordinate dependent) fact that the gravitational field of the Sun decreases with distance is therefore better "captured" using the first system. It's up to your philosophy of physics whether you view this as merely a "pragmatical convenience" of the first system or a license to say "the Earth really goes around the Sun". I prefer to say the latter.

Posted by: Alejandro February 9, 2006 04:20 PM

Another way of explaining it, perhaps clearer. If one goes at far distances where the physical gravitational field is too weak to be noticed, one can remain at rest relative to the Sun without any rockets turned on. The reference frame of the Sun becomes assymptotically inertial. The reference frame of the Earth does not; if you try to stay at rest relative to the Earth at large distances of the Solar System, one needs to turn on the rockets and make the spaceship go in circles (from the point of view of an external, inertial observer). I take this as meaning that the Earth "really" moves, while others will (bringing up the valid point that one can use either system to describe the situation) regard it as a convenient, pragmatically useful fact of the Sun-centered system.

Of course all this discussion neglects effects of other stars, the motion of the Sun around the galactic center, the relative motions of the galaxies and the expansion of the Universe. But the essential points remain valid.

Posted by: Alejandro February 9, 2006 04:32 PM

To make the second comment clearer: the important thing is not that to stay at rest relative to the Earth one has to go in circles, because this is a coordinate system dependent fact (in the Earth-centered system one is at rest). The important thing is that to stay at rest in the Earth-centered system one needs the rockets turned on, and in the other one not. This shows that relative to a distant, inertial observer it is the Earth that moves and not the Sun.

• I happen to be the proud "fellow physics student" who made it into the late porteñan night discussing this issue with His Bloggisty, and now made it all the way up his Blog.

(I have to say, though, that this is not the first but the second time I make it to a blog. The previous one, even includes a link to my webpage (under "chico de exportación"...)).

Even if I'm immersing in the study of Little Light (or Quantum Optics), and away from the bends of time, I do have an opinion on His Bloggisty's opinion:

How is it possible to neglect "the motion of the Sun around the galactic center", or to neglect any motion at all?

Or: What if "the motion of the Sun around the galactic center" is just opposite to the motion of the Earth around the Sun, in such a way that they cancel, and it's with a steady Earth that the space is flat far away?

Shouldn't we take into account the whole thing, matter, energy, and the like, then generalrelativistically sum up, divide, and go far away from that to make the space go flat?

• Hi Alejo, good to see you commenting! It's kind of weird to reassume our discussion again after so long (about 3 years and half, if memory serves me right). I guess it was an "unfinished business" between us.

My answer: If you want to discuss the question in a completely realistic fashion, we don’t need to speculate about whether global movements of the Sun or the Galaxy are cancelling te Earth’s movement, because the answer is known. The global metric of the universe at largest scales is not Minkowski but the expanding Friedmann-Robertson-Walker, and the privileged frame for it is the CMB frame in which the cosmic background radiation is isotropic (with very small random anisotropies). The movement of the Earth induces a dipolar anisotropy in our measurements of the CMB, and from it the “absolute” velocity of the Earth with respect to this frame has been determined. It turns out that the Earth and Sun and the whole solar system, and in fact the whole galaxy, are moving together at 300 kilometers per second towads a “Great Attractor” cluster of galaxies. And superimposed to this, one sees… I’ll quote it from this page, where I found all this information:

“The COBE DMR observations clearly show the change in velocity at the 30 kilometers per second - a 10% effect - due to the motion of the Earth around the Sun. One can see a clear sinsusodial pattern in the amplitude and direction of the dipole with a one year period in the four years of COBE DMR data. Differencing maps taken six months apart produces the familar dipole pattern with the amplitude and direction of the Earth's motion. This is good evidence that Galileo is right - the Earth does go around the Sun.”

So: If you moved very, very, very far away from the solar system, the galaxy, and the great attractor, kept yourself at rest relative to the CMB frame, and looked in our direction, you would see our galaxy moving with everything in it towards the great attractor, the solar system within it very slowly orbitating the galaxy center, and within the solar system the Earth going around the Sun. If you wanted to keep at rest (at rest, that is, discounting the expansion of the universe) relative to the Earth, you would need to turn on your rockets and do a lot of pirouetting with them, including make them rotate at a 1 year rate. If you wanted to keep at rest relative to the Sun, you would need the same program in your rockets minus the 1 year rotation. This is why it makes sense to say the Earth goes around the Sun and not the other way round.

• I'm also a physics student. I agree with your conclusion that the earth "really does" move around the sun. I don't think you stated your argument very well, however. I'm not a relativist, but i don't think that the extra term (or terms?) in the metric far away from an geocentric frame would be qualitatively different from those in a heliocentric frame. I think that the big difference is that the extra term in the geocentric frame is a lot bigger than the other terms from the rotation of the sun around the center of the galaxy and other such motions. I think the most convincing argument is that the CMB frame is as close to an "absolute" frame we have, and that our motion relative to this frame has a not insignificant contribution from our motion around the sun.

• In my view everyone have to glance at it.
metal buildings

By  Brice, at 4:11 PM, November 05, 2011