Why does rotation simulate gravity if motion is relative?

Question

In Einstein's theory of relativity, if motion is truly relative, then why would somebody in a rotating space station experience (artificial) gravity? I mean, I get why they experience gravity IF the space station is rotating, but what I do not get is how can you say it is rotating in the first place? Would you not need to define its motion in relation to another point in space?

So let's say we have two space stations and in our hypothetical universe they are the only two things that exist in the entire universe.

• In space station 1, there is no sensation of gravity.
• In space station 2, there is a sensation of gravity.

So we know that space station 2 is rotating and space station 1 is not because of the sensation of gravity we feel in station 2.

To an observer in station 2, they would feel gravity and see station 1 appearing to orbit around them. An observer in station 1 would feel no gravity and see station 2 spinning but staying in one spot. I think everyone would agree with all of those observations thus far.

But here is where it breaks down, I think, you have to have some fixed reference point in space to be able to say that station 2 is spinning and it is not station 1 orbiting in order to get the sensation of gravity on station 2. Newton seemed to have an answer to this because he said there was a fixed "at rest" but according to Einstein, I don't think there is a fixed at rest?

Does my question make sense? My confusion also applies to acceleration, it seems you have to have some fixed reference frame to say anything is accelerating at all. We know you would feel the effects of acceleration if in a space ship in deep space, but why if all motion is relative. I mean, how can you even say you are accelerating and it is not everything else in the universe accelerating and you are actually standing still without a fixed “at rest” point in space?

Answer 1

Velocity is relative. There is no special reference frame that would be "at rest".

But acceleration is not and was never claimed to be. Reference frames in free fall are special and reference frames that are accelerating relative to the ones in free fall contain inertial forces (circular motion involves acceleration towards the centre; the corresponding inertial force is called centrifugal force).

So you can distinguish which of the stations is rotating and theory of relativity never claimed otherwise.

Answer 2

Special relativity deals with "inertial" or "non-accelerating" frames. Physics in inertial frames are equivalent independent of their velocity and the velocity of inertial frames are relative. You are free to assume any inertial frame is stationary and all other frames are moving relative to it. Rotating frames are not inertial, they are accelerating frames and are therefore not relative. If a frame has no rotation then it must be maintaining orientation with the mean of the galaxies in the universe. This is an absolute. It has been conjectured, originally by Mach, that the distribution of matter in the universe sets the non-rotating frame.

General Relativity does deal with accelerating frames and discusses differences between rotating frames and gravitational accelerating frames, but that is another story.

Answer 3

In general relativity, angular motion actually does have some "relativity" to it as well. When you're in close proximity to a spinning object, you'll actually be dragged along with it. This is known as the Lense-Thirring effect, or just "frame-dragging". The most dramatic example is the ergosphere of a spinning black hole, a region where no object can remain stationary - it must rotate with the black hole. (similar to the event horizon from which objects cannot escape)

The fact that you feel a force under constant angular motion is because you're spinning relative to the background universe. (that statement may be somewhat controversial) If you were to take a large spherical mass shell, and set it spinning around yourself, you would actually begin to rotate with the shell but experience no centripetal force. If you added mass until the shell was nearly a black hole, your natural rest frame would have the same angular velocity as the shell relative to the rest of the universe.

Answer 4

General covariance applies only to freely falling observers -- once you invoke non-gravitational forces, like the inward pressure of the wall, the observer is no longer freely falling.

Answer 5

If the occupants of the space station were not aware of its design and could not look out a window then there is no way to tell if it is rotating or they are near a earth size planet that causes the gravity.

Orbiting around another space station will causes a sensation of gravity, and it seems you are contradicting yourself. If there is any rotational motion about of a body around its own axis or another space station then the occupants will feel a force you have defined as gravity. They can't feel it as in your space station 1 scenario.

That's how I see it as a non-pro.

As to acceleration, no you do not need a fixed reference point. In contrast to velocity which is defined as relative to the velocity of something else, acceleration is absolute in a sense that it is not relative to something else.

Answer 6

Easy way to distinguish between gravity and rotating space station: Throw a ball straight up in the air. If it comes straight down, gravity. If it moves away from you (behind your tangential velocity), it's a rotating space station.

Answer 7

The "reference" for acceleration, is its own previous "state". What this means is that, for linear acceleration, it is the initial point prior to the start of linear acceleration (at t = 0). And for angular acceleration, it is the imaginary line defined by the center of rotation and the initial position at t = 0 ($theta$ = 0).