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Eitan_Zohar comments on Open Thread, Apr. 13 - Apr. 19, 2015 - Less Wrong Discussion
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I discovered, today, a letter by the Lubavitcher Rebbe in which he claims that the sun revolves around the Earth:
Does anyone understand what this is trying to argue? I suspect he's saying something analogous to, you know, the universe shifting around the Earth in sync with the sun, which technically makes the sun revolve around the Earth (in a semantical sense). But I'm not confident of that.
That the Bible was always right and even science doesn't really contradict it. Yay, Bible!
The steelman version is that (ignoring all other bodies in our solar system), both Sun and Earth actually revolve around their common center of gravity. Saying "Earth revolves around Sun" brings the connotation that the Sun is not influenced by the gravity of Earth, which is not true.
Except that this is unrelated to the theory of relativity (you could get the same conclusion using Newtonian mechanics), and I believe the common center of gravity still happens to be inside the Sun (please correct me if I am wrong).
The common center of gravity is inside the sun. However, the Earth-Sun system also revolves around the center of the galaxy. From that perspective, the main trajectory of the Earth is around the center of the galaxy, but the sun's gravity is deflecting it this way and that. If you plotted the Earth's motion, it would look something like a sine wave wrapped around a giant ellipse around the center of the galaxy. Saying the Earth went around the Sun wouldn't make much sense from this perspective.
The argument being made is that the theory of relativity doesn't give a preferred coordinate system for the Earth-Sun system, so saying "The sun goes around the Earth" is an accurate statement for an observer located on Earth.
In fact, the theory of relativity would say that the question of whether the Earth goes around the Sun or the Sun goes around the Earth is meaningless unless you specify a reference frame ahead of time. There has to be some observer who is observing the motion from a certain reference frame, and if we know the reference frame then we can decide whether the observer sees the Sun going around the Earth, the Earth going around the Sun, both of them going around Mars, etc.
That too.
Under special relativity, the laws of physics are conserved under translation and Lorentz transformations. There is no privileged position, orientation, or velocity. You could argue that we can't prove that there isn't a specific reference frame that's fundamentally true and that it doesn't just happen to be a specific one you think is cool, but that's almost certainly false.
Under general relativity, the laws of physics are conserved under continuously differentiable functions so long as the spacetime metric is altered accordingly. You can't stick cartesian coordinates in space in a sensible way no matter what, so there's no niceness to preserve. You could pick a reference frame (or whatever they call the general relativity version) where the Earth is in the center and not rotating, and you can't prove that that reference frame isn't fundamental. If you built a computer model of the universe, you could set that as the reference frame and you wouldn't need to add code to make sure it works like you'd have to with special relativity. But even if there really is some fundamentally true point of reference, which isn't necessarily true, it's not going to happen to be that one.
Not actually valid. You can only shift non-accelerating reference frames without introducing extra gravity sources or fictitious forces. The reference frame of Earth falling around the Sun, and the Sun falling around the Earth, are not equivalent in the way that a frame moving 1000 km/s relative to another is.
If you're dealing with general relativity, there's no way to avoid gravity. You can pick a reference frame where you're not accelerating at the origin, but if you look at a path epsilon away then it will be accelerating against the tidal forces.
It is funny that he invokes relativity because Galileo invented it specifically to argue that the Earth goes around the Sun.
The laws of physics work in any reference frame (Principle of Relativity). You will make the exact same predictions in a geocentric system as you would in a heliocentric system. The change of coordinates may introduce certain inertial forces and will likely complicate any calculations you wish to perform, but it's perfectly valid.