Stationary Relativity

[WWLabRat]

This should be an easy question to answer... I'm curious. I know that time is relative between moving objects. I also understand that as an object's velocity approaches the speed of light, that difference in time is made more apparent proportionally. So my question is this: Is time relative between two stationary objects/people? For example, say there were two observers sitting in a room across from each other. Assuming neither is substantially closer to the center of a large mass than the other, would time still flow at a constant? Would they both experience time in the same way?

 

Follow up: What if they were both moving at the speed of light (as if the room were part of a "faster than light shuttle"? Would it still be the same if they were in separate shuttles?

[TrappedLight]

All matter experiences time. Two observers sitting at opposite ends of a room are no different, the time they experience is asymptotic time. That is the time we all come to agree on.

 

Two inertial observers can not move at the speed of light. And things that do move at the speed of light don't even have reference frames to speak about, so you can't even talk about time in that respect.

[ajb]

So my question is this: Is time relative between two stationary objects/people? For example, say there were two observers sitting in a room across from each other. Assuming neither is substantially closer to the center of a large mass than the other, would time still flow at a constant? Would they both experience time in the same way?

So you assume that there are no effects due to some background gravitational field, which is why you speak of the large mass. Okay, then as the two obsevers are co-moving, that is they can be seen as moving at the same velocity as measured by some third inertial observer, they see no effects like time dilation or length contractions with respect to each other.

 

Follow up: What if they were both moving at the speed of light (as if the room were part of a "faster than light shuttle"? Would it still be the same if they were in separate shuttles?

No third inertial obsever will see them move with a speed equal to the speed of light. So the question is ill-posed. However, the fact that the two are co-moving is independent of the relative velocity of the third observer.

[WWLabRat]

I know it's an poorly phrased, or otherwise, question. It basically boils down to this: I have been wondering at what point there couldn't possibly be any time dilation. Obviously between two observers, one moving at a constant velocity, the other remaining stationary, the one in motion will experience time differently than that of the stationary observer. So we slow the velocity of the one in motion. And we keep slowing him. Mathematically, we could keep cutting his speed in half to an infinitesimally small amount to where as far as we could tell he would be stationary. By all measurements he would still be moving, so there must be some time dilation between the two. Am I right? However to the stationary observer, he would appear stationary as well, until a substantial amount of time had passed for him to have any noticeable movement.

[ajb]

So we slow the velocity of the one in motion. And we keep slowing him. Mathematically, we could keep cutting his speed in half to an infinitesimally small amount to where as far as we could tell he would be stationary.

Okay, so relative to the stationaty observer we slow the moving one down, but with a very small deceleration so that we can keep things in terms of inertial observers to a first approximation. Eventually we could get to a situation where the velocity is very small and we can ignore any terms we have in any expressions like v^{2}.

 

If you do this you see no time dilation. So you would have to keep higher order terms. So we get

 

[math]dt' = dt + \frac{1}{2} \frac{v^{2}}{c^{2}}dt + \cdots[/math],

 

so we get smaller and smaller corrections.

 

By all measurements he would still be moving, so there must be some time dilation between the two. Am I right?

Right, if there is some velocity that is non-zero between the two objects then there will be time dilation effects. If that that velocity is infinitesimal, so nilpotent, then there are no time dilation effects!

[Strange]

Obviously between two observers, one moving at a constant velocity, the other remaining stationary, the one in motion will experience time differently than that of the stationary observer.

 

A couple of points.

 

When you say one is moving and the other is stationary, that is purely a relative statement. You could say the first is stationary and the second is moving.

 

Also, the one who is considered to be moving will not experience time differently. Their time will be seen as different relative to the other observer. (And, because we can consider either as moving, the reverse is true: observer A sees B's clock running slow and B sees A's clock running slow.)

Edited September 25, 2013 by Strange

[WWLabRat]

 

Obviously between two observers, one moving at a constant velocity, the other remaining stationary, the one in motion will experience time differently than that of the stationary observer.

A couple of points.

 

When you say one is moving and the other is stationary, that is purely a relative statement. You could say the first is stationary and the second is moving.

 

Also, the one who is considered to be moving will not experience time differently. Their time will be seen as different relative to the other observer. (And, because we can consider either as moving, the reverse is true: observer A sees B's clock running slow and B sees A's clock running slow.)

 

You do realize that both statements that you made are the exact same as what I had said. And the time experienced is going to be different. This is because he is moving. As AJB stated above, the moving observer's velocity is a non-zero number and therefore he will experience a time dilation. Being that this is a discussion on relativity, it's implied that everything said will be dealing with how everything is relative to which observer is being discussed.

[Strange]

I just wanted to make sure that someone reading the thread would not be misled by the word "experience" and get the idea that someone moving at high speed relative to something else (as we are ourselves) would feel time pass differently.

 

We feel time ticking away normally even though we are stationary with respect to our neighbor, travelling at 15 km/s relative to Voyager and 99%c relative to cosmic rays. It is only from those other frames of reference that our clocks would appear to run slow.

[ajb]

As AJB stated above, the moving observer's velocity is a non-zero number and therefore he will experience a time dilation.

By experiences, I really mean that the two observers will notice a difference when the clocks are compared. Each individual obsever does not think anything "strange" has happened to himself.

[WWLabRat]

I just wanted to make sure that someone reading the thread would not be misled by the word "experience" and get the idea that someone moving at high speed relative to something else (as we are ourselves) would feel time pass differently.

By experiences, I really mean that the two observers will notice a difference when the clocks are compared. Each individual obsever does not think anything "strange" has happened to himself.

 

Sorry, that was poor phrasing on my part.