Is Time Dilation Creating an Infinite Loop Between A and B's Observations?

[phylove]

I have a question.

There are 2 men, A and B.

A is on the earth’s surface and B is in a spaceship traveling at a speed comparable to the speed of light. Both A and B have a light clock each, that is, a pair of parallel mirrors a fixed distance apart and a pulse of light being reflected between the 2 mirrors.

At A’s end: 10 oscillations have occurred in the light clock on earth. He also sees that only 8 oscillations have occurred in the space ship.

At B’s end: 8 oscillations have occurred in the light clock in the space ship. Shouldn’t the number of oscillations he observes on the light clock on Earth be lesser than 8?

In that case wouldn’t this form something like an infinite loop.? Wherein the number of oscillations each perceives for the other decreases for a set time? I’m not sure where I’m going wrong. It may be that I not have understood the fundamentals of time dilation, so could you please explain this?

 

[granpa]

thats where relativity of simultaneity comes in

 

[Dale]

Hi phylove, welcome to PF

I’m not sure where I’m going wrong. It may be that I not have understood the fundamentals of time dilation, so could you please explain this?

Here is a diagram I made a while ago showing two different observers moving at 0.6 c relative to each other. If you look carefully at this diagram you can see how all three effects (length contraction, time dilation, and the relativity of simultaneity) work together symmetrically. In this diagram time is vertical and space is horizontal in the black frame, and the lines of constant time and constant position are drawn for both the black frame and the white frame.

Time dilation: Follow the white x'=0 line up from the origin, note that it crosses the black t=2 line before it reaches the white t'=2 line, meaning that the white clock runs slow in the black frame. Similarly, follow the black x=0 line up from the origin, note that it crosses the white t'=2 line before it reaches the black t=2 line, meaning that the black clock runs slow in the white frame.