# I Is the relativity of simultaneity the reason for time dilation?

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1. Dec 28, 2015

### MachPrincipe

2. Dec 28, 2015

### Orodruin

Staff Emeritus
This depends on what you put into the concept of time dilation. In the most common approaches, the answer is yes. And it does cause people to have conceptual problems ...

3. Dec 28, 2015

### Staff: Mentor

I think that "the" reason is too strong of a claim, but certainly understanding the relativity of simultaneity is important for understanding time dilation. Failure to understand the relativity of simultaneity is the key conceptual problem faced by students of SR:

http://arxiv.org/abs/physics/0207081

Last edited: Dec 28, 2015
4. Dec 28, 2015

### Vitro

Metaphorically you could say length contraction and time dilation are two sides of the same coin. That coin is the relativity of simultaneity.

5. Dec 28, 2015

### Staff: Mentor

That the question is poorly formulated.

Both follow from assuming a particular structure to the universe (pseudo-Riemannian, locally Minkowski) so we can't have one without the other. That doesn't mean that either one has to cause the other.

I'm looking at a 3-4-5 right triangle. Does the fact that one side is of length three and the hypotenuse is of length five "cause" the other side to be of length four? Or does the fact that the two sides have the lengths they do "cause" the hypotenuse to be of length five?

6. Dec 28, 2015

### Mister T

Time dilation and relativity of simultaneity each follow from the postulates, so in that sense neither is the cause of the other.

7. Dec 28, 2015

### pervect

Staff Emeritus
I don't see how the statement can be justified offhand, and no supporting argument has been presented.

One can make a case that the existence of time dilation, combined with the isotropy of space time and the principle of relativity, implies the relativity of simultaneity. Which is the reverse of your original statement. The principle of relativity, combined with isotropy, means that if A is moving at some velocity relative to B, if A sees B's clock time dilated, B must also see A's clock time dilated. This is only possible if the means for comparing clocks depends on the frame of reference, if the method of clock were frame-independent (as it is in Newtonian mechanics), if A's clock ran slow relative to B's clock, it would logically follow that B's clock ran fast relative to A's clock.

Perhaps there is some way to justify the argument in the other direction, but I'm not aware of it offhand.

8. Dec 28, 2015

### MachPrincipe

The bad wording of the question is intentional. I wanted to see some reference to the mutual time dilation. Basically, one observer can say that it is the other obserrver who sees her moving and time dilated because of relativity of simultaneity, so, in this sense, relativity of simult. can be seen as a «reason» for time dilation. From this case you extrapolate to every single inertial frame, forget that in your calculations you first introduce some time dilation too, and you are done: simultaneity has to do, entirely, with time dilation.
I have seen so many times that I am glad to see the No responses.
In special, I would like to know the arguments of the first response to say Yes, and the exceptions mentioned.

9. Dec 29, 2015

### Staff: Mentor

That is not acceptable.