From the Relativity Theory perspective, how does one know which object(s) are moving and which are stopped.?

Question

I have always been puzzled by this....assuming that two objects are being taken into consideration, and that both objects are moving in the opposite directions <-----> . How would one judge the velocity of each of the objects (again only considering these 2 objects). For instance, if both object's velocity where just under the speed of light...couldn't we consider one of the objects to be stopped (0 velocity) and the other to be moving well over the speed of light?

To Harrypete: I believe there is a flaw in your " radio transmission from a rocket" analogy...the message sent from rocket A to rocket B only has to overcome rocket B's velocity, since it is sent from a fixed point in space...it doesnt have to travel at the combined relative velocity of both rockets...the message wouldnt even have to go through earth.

Also to Harrypete or anyone who could answer this: how do we know which object is accelerating...how did Einstien prove which object was accelerating in his theory?

Answer 1

The key here is frame of reference.
The Flash and Superman head off in opposite directions from you at 0.8c. To YOUR eyes, they are moving apart at 1.6c, and the relative velocity of one to the other should be well over c. However, THEY are not in your frame of reference; velocities don't add linearly under relativity, they add according to this formula:
v = (s - f)/(1 - sf/c^2)
where s is Superman's velocity relative to you, and f is the Flash's. If we were to ask Superman, he would say that the Flash is in fact moving at:
v = (0.8c - -0.8c)/1-(0.8c*-0.8c)/c^2) = 1.6c/1.64, or 0.98c.

Answer 2

Excellent questions!

The theory of special relativity, which applies to objects moving at constant speeds, really does say that there is no way to determine which object is moving, which object is still, or if both objects are moving. In fact, scientists objected to the Theory precisely for this reason. The Twin Paradox says that if you take two identical twins, send one on a space ship that can travel nearly the speed of light and leave one twin on the earth, while the twin on the space ship is moving away from the earth, both twins will observe the other twins' clocks to be running SLOWLY. The critics of the theory said this cannot be right, because when the twin on the ship returns to the earth, one of the twins will have aged at a different rate. Well, Einstein pointed out that the absolute difference between the two frames of reference of the two twins happened during the acceleration of the twin on the rocket. THAT twin's reference frame was accelerated, while the one on the earth was not. (Neglecting earth's rotation.) Einstein's Theory of General Relativity describes accelerating reference frames and resolves the Twin Paradox.

On your question about "adding" velocities, Galileo would have agreed with your approach of adding the velocities with respect to a common reference point to get the velocity of one object with respect to the other. But in Special Relativity, velocities, especially when they approach the speed of light, do not add that simply. You can look up the formula for how velocities add. (The equations are called Lorentz Transformations.) But to give you a troubling thing to think about to refute your intution that two rockets speeding away from the earth in opposite directions, each moving at 75% the speed of light, are essentially moving away from each other at 150% the speed of light, consider this:

The two rocket ship captains have radios. If the two ships recede from each other at a speed greather than the speed of light and radio waves, then the two should not be able to communicate via radio. But you know that ship A can communicate with the earth and so can ship B, so if there was a person with a reciever speaker held up to a microphone on the earth, the signal from ship A could reach earth and the reciever speaker, go to the microphone and transmitter and then reach ship B. The fact that the two ship can communicate using a method that travels at the speed of light means that they cannot be receding from each other at greater than the speed of light.

Answer 3

Well, the key point of relativity is that you can always claim you are stopped, and everything else is in motion. The only element that makes some object motion special is acceleration, as you are then changing referential.
And two objects speeding towards one another at a speed close to that of light will NOT add their velocities. For each one, it will appear the other one is a bit closer to the speed of light than as seen from a 3rd "immobile" observer (only immobile relative to himself, actually). Relativity's effect in changing both space (length contracts from the perspective of the other observer) and time dilatation (slow clock for those in motion) ensures that everyone will always agree on one thing: noting gets faster than light, no matter from who's perspective the measurement is taken.

Answer 4

In our universe everything is moving in a spiral. Spirals have beginnings and ending; no matter how indefinite. If an object is 'not moving' it is 'not moving' with respect only to our universe. An object that does not move relative to our universe must disappear for the duration of its "not moving'. Our universe, galaxy, solar system does not stop, however, so when the period of an objects 'not moving' is over; the object must reappear at a distance from its' beginning.

Answer 5

Everything is always moving, but I see your point. Very interesting...the combined speed of 2 objects traveling apart could be greater than the speed of light. I like that.

Answer 6

1. Relativity means that everything is relative. Are you moving? Or is the rest of the universe moving and you are the only one standing still? For the purpose of solving the equations, it doesn't matter.

2. That's because of the Lorenz contraction. v1 + v2 = (v1 + v2) is Newtonian. In relativity, v1 + v2 = (v1 + v2)/(1 + (v1*v2/c^2))

So as v1 and v2 approach the speed of light, the divisor goes closer and closer to 2.