Does the theory of relativity include angular motion?

[rbeale98]

Does the theory of relativity include angular motion? Say we have one body synchronously orbiting a motionless body. It can also be viewed as two motionless bodies and one is spinning while the other is not. (i.e. if you were on the moon staring at earth, you would not witness orbital motion). But we KNOW that the moon orbits the earth, so then is this kind of motion not relative? Would it be more appropriate to say that the two bodies orbit each other with some constant center of mass?

And, clearly there is a difference between a spinning object and non-spinning object (in the way of centrifugal forces) so there is evidence that rotation is not relative. Any thoughts on this?

 

[CompuChip]

One could say that "the theory of relativity" includes angular motion, because that term includes general relativity. However, if you are referring to special relativity exclusively, the answer is no. Angular motion involves forces (e.g. objects in stable orbit around another object are accelerated) hence the different frames are no longer equivalent (e.g. you could discern between them by simply putting an accelerometer in each). Therefore, special relativity does not apply, as you already concluded.

 

[atyy]

Special relativity applies to angular motion, so long as the centripetal force is not provided by gravity (SR doesn't work any time there is gravity).

Constant velocity means constant speed and direction, so angular motion is accelerated motion. In SR, accelerated motion is absolute, just as in Newtonian mechanics.

In General Relativity, there is a slight change of view - some accelerations are no longer absolute. Observers moving at constant velocity or accelerating under the influence of gravity only (ie. no other forces) are equivalent - these "inertial" observers experience no gravity (in sufficiently small regions of spacetime). Rotation remains absolute even in GR, in the sense that a rotating observer is not "inertial", and does experience gravity.

 

[DrGreg]

Does the theory of relativity include angular motion? Say we have one body synchronously orbiting a motionless body. It can also be viewed as two motionless bodies and one is spinning while the other is not. (i.e. if you were on the moon staring at earth, you would not witness orbital motion). But we KNOW that the moon orbits the earth, so then is this kind of motion not relative? Would it be more appropriate to say that the two bodies orbit each other with some constant center of mass?

And, clearly there is a difference between a spinning object and non-spinning object (in the way of centrifugal forces) so there is evidence that rotation is not relative. Any thoughts on this?

In special relativity there is a big difference between inertial motion (free-falling objects with no forces acting on them) and non-inertial motion (accelerating objects -- remember rotation is a form of acceleration).

It is only inertial observers that are considered equivalent to each other.

You can tell if you are moving non-inertially. E.g. in a car you can sense whether you are accelerating, braking or cornering even with your eyes closed. What you can feel is your "proper acceleration" which can be measured using an accelerometer.

So if we consider two masses attached to each other by a spring and the whole system rotating around its centre of mass, we cannot consider either mass to be stationary as they are both undergoing proper acceleration.

You are right that rotation is not relative in special relativity. Special relativity can cope with rotation but you cannot treat a rotating object as if it were stationary.

Your example of the earth-moon system is a bit more complicated because gravity is involved and you need to use general relativity instead of special relativity. If you are learning the subject, it's best to get your head around special relativity first before getting into general relativity.