Details on analyzing relative motion

Question

I have been viewing some videos and reading some articles about Relativity and relative motion. My search abilities seem to be rather lacking. I am looking for articles, questions, and/or forums that describe the concept of two bodies which are moving relative to each other. For discussion let’s presume there two space ships that are far from any other body that might be used as a reference point. Further presume that they are moving apart at some significant velocity. I infer that the inhabitants of those space ships cannot determine if one of them is moving and the other stationary. Or indeed, any combination of movements that could produce the same relative motion. What principles of relativity specify that this situation is true?

Answer 1

Special Relativity builds on Galilean Relativity in that, you can always consider yourself to be at rest and that others are in motion. Einstein's innovation is of course, that the speed of light (or speed of massless particles) is frame-independent or invariant.

So, since you are unconcerned with the Twin Paradox in your example (that is, there's no "original shared frame" between the spaceships), a simple way of addressing your concerns generally can be done by allowing both vessels to use the Minkowski Metric to measure the other spaceship (this excellent exposition of how to solve the Twin Paradox by John Rennie states that the spaceship that accelerates requires a different metric to understand what they measure from their frame of reference: logically, this means your situation involves the use of the Minkowski Metric to describe what both vessels measure).

So for your situation, both vessels will determine that the other's clock is always moving slower than their own clocks. There will be no manner by which anyone can determine who is "genuinely" moving and who is at rest, unless you alter the situation to involve how these spaceships got to their speeds to begin with (and thus, the Minkowksi Metric wouldn't be used anymore to describe what either spaceship measures from their frame of reference).

In short: your situation is resolved by the idea that the same metric gets used to properly describe how each vessel measures anything regarding the other vessel.

Answer 2

You are missing a fundamental point, which is that there is no such thing as absolute position. The concept of position only makes sense if you specify some frame of reference, which means that position is necessarily relative.

Now, what is inertial motion? It means that position is changing at a constant rate with respect to time, and since position is necessarily relative, inertial motion is necessarily relative too. There is no absolute inertial motion because there is no absolute point of reference in relation to which motion can be defined.

In physics you are free to pick any inertial reference frames. Given that, if you and I are moving relative to each other, I can pick a reference frame in which I am moving and you are stationary, or one in which you are moving and I am stationary, or one in which we are both moving, and all those options are equally valid.

Answer 3

From my limited understanding of relativity and motion there is a way to determine relative motion and possibly absolute motion. Here is the basic concept. I am in my spaceship and am watching Alice and Bob in their space ships. Alice and Bob both send a 1 MHz pulse at each other once every second.

The two of them begin stationary with respect to me. Then I start Bob moving directly away from Alice at some high rate of speed.

Alice can use her radar and determine how fast Bob is moving away. She calculates the Doppler shift and checks the signal from Bob. It has slowed down due to his moving away rapidly.

However, it has slowed down more than can be accounted for by the Doppler calculations. It has slowed down some additional amount because Bob is now moving at a significant speed relative to c, speed of light. My understanding is this is called time dilation. Bob cannot detect this change, but Alice can. (That might not be true. Too much for this edit.) This indicates that Bob is moving, not Alice. Alice can make this determination.

On the other hand, consider Bob’s perspective. The signals from Alice have also slowed down. However, the signal from Alice is just a bit higher than the Doppler calculation predicts. Why is this?

It is because Bob’s clock and time perspective have slowed down. Bob cannot directly detect this. But, Alice’s clock appears to have sped up exactly the same amount that Bob’s clock has slowed down. Because Bob sees Alice’s signal appearing to be faster than expected, Bob can determine that he is the one moving rather than Alice.

This indicates that we can determine our own motion through space.

I doubt this is a brand new revelation so what is there that I don’t understand or am unaware of?