Time Dilation

[Strange]

Thanks, Studiot;

But there is a rub, from this point of view two bodies are moving literaly with superlucent speed relative to each other while the math is saying they are not.

 

 

You are mixing frames of reference.

 

From your point of view, as someone who sees the two frames moving apart at near c, you will see the separation speed as near 2 x c.

 

However, each frame of reference will see the other moving at just less than c, as Janus explained.

[Delta1212]

Thanks, Studiot;

But there is a rub, from this point of view two bodies are moving literaly with superlucent speed relative to each other while the math is saying they are not.

Let say an observer was put at a point where the two moving frames began their journey. This third person, stationary one, would have all the right to say that each frame move away from him at speed close to the speed of light, but moving observers would argue that they are not.

Speeds do not add linearly, although this is really only noticeable at very high speeds unless you are talking about really crazy levels of precision.

 

The maximum speed that anyone can every measure anything as traveling at is c. The maximum separation speed that anyone can measure between two objects that are both moving in your frame of reference is 2c.

 

There is no frame in which any object will be measured as moving faster than c relative to "rest" in that frame.

[Janus]

Hi Janus;

What happens when two moving frames move in opposite direction and each of the two frames moves with the speed of very close to the speed of light? Also to this point, let us say that observer on each of the frames shooting a beam of light towards receding frame. Imagining such a situation, one would reckon that relative velocity between the two frames is approaching twice the speed of light C. Yet the fundamental precept of the Relativity precludes such a possibility, asserting that no physical bodies can move with respect to each other with the speed greater than the speed of light C.

 

Let's assume that we have three observers. Two are traveling at 0.99c relative to the third but in opposite directions. Now let's assume that they meet while right next to the third observer (for one brief moment, all three are in the same spot.). At that moment a flash of light is set off from that location, What happens according to the three observers? Since each observer measures the speed of light as being c relative to himself, they will all see the flash of light expand outward from them at c in a spherical front with themselves at the center.

 

So the third observer sees the light expand out from him at c and the other two move away from him at 0.99c and thus they all stay inside the sphere of light.

If we consider either of the other observers, we have to take into account that, if one of the observers concludes that the they all stay inside the sphere of light, they all must come to this same conclusion. This means that if you are the first observer, you remain at the center of the expanding sphere and the other two are chasing after the edge of the sphere. The third observer is traveling at 0.99c relative to you, and thus obviously trailing behind the edge.

 

What about the second observer? According to both the third observer and himself, he never leaves the sphere of light. This means that he can't leave the sphere of light according to the first observer either. The only way he remains inside the sphere according to the first observer is for him to be traveling at less than c relative to the first observer. The addition of velocities formula gives us the answer as to just how fast he is moving relative to the first observer, (0.9999495c).

 

It is this combination of all the reference frames measuring the same speed for the light and the fact that all three frames must agree that all our observers remain inside the expanding sphere that leads to this conclusion of how the observers each measure their respective relative motions.