Time Dilation: Exploring Effects of Relative Motion

[mananvpanchal]

Suppose, there are two inertial frame first is in motion with constant speed and second is motionless. We can say that two frames are relatively in motion with each other with constant speed. So time would slowdown for each frame referenced by other frame. But after some long journey first frame feels some force and start coming back, after long journey first frame is now standing near second frame with less aged.

Time slowdown for both frames but it is maintained only for first frame. why..?
What do the force render its roll in the scenario...?

Why the Length Contraction cannot be maintained..?

 

[HallsofIvy]

This is just another statement of the "twin paradox" that has been done here over and over again. The answer is that the force, and so acceleration (and acceleration is NOT relative), applied to one frame, breaks the symmetry.

 

[BruceW]

Yeah, you could probably make a search in physics forum for 'twin paradox', and you would get the answer.

The first time I saw this problem, I thought that it would require general relativity, since the 'first frame' is non-inertial. But you can work out what happens using only the 'second frame' (i.e. the one that does not accelerate).

It can all be explained by thinking of the world-lines of the two people according to 'second frame'. We also know that $d \tau ^2 = dt^2 - \frac{1}{c^2} dx^2$ (for motion only along x axis). and $\tau$ is the proper time.

So for the person staying still, $d \tau = dt$ In other words, the proper time for the person who stayed still will be greatest. So the proper time experienced by the person who accelerates will be less than for the person who stayed still.

We can think of a person's age as a kind of clock, so that for every year of proper time, it 'ticks' once more and they are a year older! The proper time experienced by the person who accelerated was less, so he will be younger.

 

[ghwellsjr]

Suppose, there are two inertial frame first is in motion with constant speed and second is motionless. We can say that two frames are relatively in motion with each other with constant speed.

It's always dangerous to convolute two frames at the same time. You should pick one inertial frame and describe all observers, objects, clocks, etc in that one frame, then if you want to see what all the relevant events look like in another frame moving with respect to the first one, you need to use the Lorentz Transform.

So time would slowdown for each frame referenced by other frame.

This doesn't make any sense. What does make sense is to talk about the same observer/object/clock in one frame and then in the other frame. All frames include all observers/objects/clock. A frame is just a coordinate system.

But after some long journey first frame feels some force and start coming back, after long journey first frame is now standing near second frame with less aged.

All frames stretch out infinitely in all directions and cover all time, past, present and future. There is no sense in which you can say that one frame is nearer to another frame or that one frame ages. Frames don't feel anything and are not subject to forces, they are coordinate systems.

Time slowdown for both frames but it is maintained only for first frame. why..?
What do the force render its roll in the scenario...?

Why the Length Contraction cannot be maintained..?

Time dilation is a very simple concept, just like speed is, if you use one Frame of Reference to specify the locations and speeds of the observers/objects/clocks that you want to consider.

The way you should think about the Twin Paradox is start with one Frame of Reference with two twins located at the same place. Time progresses equally for both of them. Then one leaves at some speed. This speed determines his time dilation which always causes time to slow down for him. After awhile he comes back to his original location and stops. Now he has aged less than his twin. Is that so hard to understand?

If you want some more detailed explanation, I recently expanded on these ideas in this post.

 

[Naty1]

Why the Length Contraction cannot be maintained..?

which length?? ...it depends on the relative speed measured at each instantaneous time.

The time dilation is a cumulative, ongoing, measure of duration...not an instantaneous one.