Time Dilation Dilemma: Exploring A & B's Questions

• phylove
In summary: Length contraction: The x'=0 line in the white frame is shorter than the x=0 line in the black frame. Similarly, the t'=2 lines in the white frame are shorter than the t=2 lines in the black frame.
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?

thats where relativity of simultaneity comes in

Hi phylove, welcome to PF
phylove said:
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.

1. What is time dilation?

Time dilation is a phenomenon in which time appears to pass at different rates for observers in different frames of reference. This is due to the effects of gravity and speed on the flow of time.

2. What is the Time Dilation Dilemma?

The Time Dilation Dilemma is a thought experiment that explores the concept of time dilation in a scenario where two observers, A and B, are moving at different speeds and experiencing different gravitational forces.

3. How does time dilation affect the passage of time?

Time dilation causes time to pass slower for objects that are moving at high speeds or in strong gravitational fields. This means that time appears to move faster for an observer in a lower frame of reference compared to an observer in a higher frame of reference.

4. Can time dilation be observed in real life?

Yes, time dilation has been observed and measured in various scientific experiments, such as with atomic clocks on airplanes and satellites. It is also a key factor in the theory of relativity.

5. How does time dilation affect our daily lives?

In most cases, time dilation is too small to have a noticeable effect on our daily lives. However, it is important to consider when dealing with extremely precise measurements, such as in GPS technology, and in understanding the behavior of objects moving at high speeds, such as particles in particle accelerators.

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