suppose you have two objects moving parallel in the same direction. One is at a constant speed; the other is accelerating and reaches the same speed as the first object just as it passes it. In other words, for that instant the two objects are side by side and moving at the same speed; only difference is that one is accelerating and one is not. Does General Relativity say that the two objects are in two distinguishable states, and if so how is the difference determined? If both emit a pulse of light at that moment, does the light they emit differ in any way?
TThe light shouldn’t differ. That about exhausts my knowledge of things relitivitical.
I am not a physicist, but I am not sure you can answer your question without more details.
A pulse of light has a duration. During that duration the velocity of one object will change in the reference frame of the other, therefore there will be a change of doppler shift throughout the pulse.
Now, if the pulse of light is magic single photon pulse, what information about the craft do you need if you are object C receiving both pulses to distinguish which pulse came from which craft? Obviously if you know the entire set up and know “the one on the left is accelerating” then you have enough information to distinguish the light pulses when they arrive.
Without that I believe you are stuck evaluating the specific magic method of synchronization the objects will use to create the pulses. I believe the idea of inertial frames of reference has to obey Heisenberg uncertainty principle just like everything else… A moment where their velocities are exactly the same and their positions line up exactly simply does not exist – if their velocities are exactly the same they do not have much of a position in relation to each other.
This is a thread on GR, so we have to either ignore quantum mechanics, or shrug our shoulders and say “I dunno”. The latter isn’t very useful, so I’ll take the former approach.
In terms of pulses of light, whether between the two spaceships or between a spaceship and a third party, the two ships will be momentarily indistinguishable. In fact, in terms of anything not interacting directly with the ships via non-gravitational forces, they’ll be indistinguishable. So if I shoot a bullet from each spaceship, for instance, the bullets will also behave indistinguishably. In fact, the way you derive things for accelerating reference frames is by comparing the accelerating frame with a set of inertial frames, each one of which matches the accelerating frame at a single moment.
The big difference will be with their interactions (read: forces) with other things. First and foremost, something must be exerting a force on the accelerating ship, and the accelerating ship is therefore also exerting a force on that something. So if that force has any detectable effects (and it will, such as a plume of hot exhaust coming out of a rocket engine, or a string pulling thee nose, or whatever), that can be used to distinguish the two spaceships. Also, the spaceship (or something) will also be exerting forces on anything else in its frame (for instance, the contents of the spaceship). So an observer might notice that in the accelerating spaceship, people are walking around on the floor, while in the non-accelerating ship, they’re just floating.
Well, you’re the boss, but it seems to me that posing a question that has two events occuring at the same time and place already starts mixing things up. I think to be more meaningful you have to give up one. So either the objects A and B both send a pulse when they are traveling at the same velocity relative to observer C, or they both send a pulse when they are lined up. In my non-physicist view claiming both makes things lean towards mixing quantum and GR in ways they cannot be mixed.