Time Dilation: Self-Consistency Problem Explained

In summary, the conversation discusses the concept of time dilation in special relativity, particularly in the context of two frames of reference moving at a relative velocity. The first statement is that a clock in frame A will be time dilated with respect to a clock in frame B, and vice versa. However, it is clarified that this is only true for events that occur at the same location in both frames. For events at different locations, the full Lorentz transformations must be used to accurately calculate the time difference between the frames. Therefore, it can be seen that both statements are not entirely true and depend on the specific conditions of the events being measured.
  • #1
mathman44
207
0
Hi all.

I'm having trouble getting an intuitive understanding for the following situation. Let frame A and frame B be moving with relative velocity v.

It's true that a clock in frame A will be time dilated with respect to a clock in frame B, but also that a clock in frame B will be time dilated with respect to a clock in frame A.

i.e. any time between two events measured in frame A must be multiplied by gamma to get the corresponding time measured between those two events in frame B, and correspondingly, that time as measured in frame B must be multiplied by gamma to get the corresponding time as measured in frame A. Obviously this would mean that

[tex]t_a = \gamma^2{t_a}[/tex]

Can anyone explain this apparent contradiction?
 
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  • #2
mathman44 said:
i.e. any time between two events measured in frame A must be multiplied by gamma to get the corresponding time measured between those two events in frame B,
In general, that's not true. You need the full Lorentz transformations to translate the time between two arbitrary events from one frame to another.

In the special case of events that take place at the same location in A, which could be measured with a single collocated clock in A, then the simple time dilation formula would apply. (Note that events that take place at the same location in A must of necessity take place at different locations in B; so it's true that ΔtB = γΔtA, but ΔtA ≠ γΔtB.)
 
  • #3
Ah... yes, if the events occur at one location in space in one frame, they must be separated in space in the other frame.

Cheers!
 
  • #4
Mathman, now that Doc Al has addressed the second part of your post, can you explain how that impacts the earlier part where you said:
"It's true that a clock in frame A will be time dilated with respect to a clock in frame B, but also that a clock in frame B will be time dilated with respect to a clock in frame A."

Specifically, does his answer mean that one or both of your "true" statements are not true?

It appears to me that he was focusing on just your first statement and it appears that what you call "a clock in frame A" is what he is calling "a single collocated clock in A" but I'm wondering that if you still consider this to be a true statement, where is the clock in frame B or what clock in frame B were you talking about?
 

1. What is time dilation?

Time dilation is a phenomenon that occurs in the theory of relativity, where time appears to pass differently for different observers depending on their relative motion or gravitational field.

2. How does time dilation relate to the Self-Consistency Problem?

The Self-Consistency Problem is a paradox that arises when considering time travel. It questions whether a person traveling back in time and changing events could create a paradox or contradiction. Time dilation is often used to explain how this paradox can be avoided.

3. Can time dilation actually occur?

Yes, time dilation has been observed and measured in various experiments, such as with atomic clocks on airplanes or in space. It is an important concept in the theory of relativity and has been confirmed through numerous experiments and observations.

4. Is time dilation the same as time travel?

No, time dilation and time travel are two different concepts. Time dilation refers to the difference in the perceived passage of time between observers, while time travel involves physically moving between different points in time.

5. How does time dilation affect our daily lives?

While time dilation is a well-established concept in physics, its effects are only significant at very high speeds or in strong gravitational fields. In our daily lives, time dilation is not noticeable and does not have a significant impact on our experiences of time.

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