# Time dilation or length contraction

## Main Question or Discussion Point

Hi, i asked some quesitons about this before but i need a clarification. Generally we use vertical light clocks and compare the distances taken by light and since c is constant the longer path taken by the light means a dilation in time, from here we say every other type of clcok dilates in same ratio because if they differ in dilation we have a way of understanding who is "moving".
We use this dilation and apply to the horizontal "moving" clock and we have the length contraction formula, but here i need some clarification, when we try to prove time dilation from horizontal clock we first have to accept that the length contracts along the direction of motion, so this time time dilation occurs as a result of length contraction. But we accept lenthg contraction from the vertical clocks' time dilation which brings us back to time dilation . so we use the result of time dilation if we try to prove time dilation by horizontal clock. Isn't this a paradox?Obviosly not but i couldn't get it.
I hope i could define my problem well, thanks.

Related Special and General Relativity News on Phys.org
we first have to accept that the length contracts along the direction of motion, so this time time dilation occurs as a result of length contraction.
Consider the width, as opposed to the length, it does not contract while clocks still dilate right? Thus could you still conclude that time dilation occurs as a result of length contraction?

Consider the width, as opposed to the length, it does not contract while clocks still dilate right? Thus could you still conclude that time dilation occurs as a result of length contraction?

Time dilation and length contraction work in tandem, one is not the result of the other, instead they both happen because there is a relative velocity.

Saw
Gold Member
Hi, i asked some quesitons about this before but i need a clarification. Generally we use vertical light clocks and compare the distances taken by light and since c is constant the longer path taken by the light means a dilation in time, from here we say every other type of clcok dilates in same ratio because if they differ in dilation we have a way of understanding who is "moving".
We use this dilation and apply to the horizontal "moving" clock and we have the length contraction formula, but here i need some clarification, when we try to prove time dilation from horizontal clock we first have to accept that the length contracts along the direction of motion, so this time time dilation occurs as a result of length contraction. But we accept lenthg contraction from the vertical clocks' time dilation which brings us back to time dilation . so we use the result of time dilation if we try to prove time dilation by horizontal clock. Isn't this a paradox?Obviosly not but i couldn't get it.
All concepts in SR (time dilation, length contraction, relativity of simultaneity and the invariance of the speed of light) are intertwined and you cannot have one without the others. The system is a package, its elements work in tandem, as passionflower said. For example:

- You use the invariance of c to derive the TD formula, but different observers would not agree on c if there were no TD (and LC and RS).
- An observer A measures a time lapse between two events that he witnessses (proper time) and argues that the time measured by two clocks in frame B that he has successively seen (one at each event) is too short, it is "dilated", but frame B argues that the first event was simultaneous with A lining up with another clock, at an earlier time, so it is A who suffers TD... Thus TD involves RS, which is another way to say that it involves LC...

What the thought experiments do is trying to build that whole step by step. Authors start with the display of the vertical clock because in that context there is no length involved (I mean, length in parallel to the relative motion) and thus you can derive TD isolatedly. Then they add a further complication with the horizontal clock, but building on already conquered land (TD)...

Yes, if you start directly seeking TD in the horizontal display, you get TD by the wrong factor, a factor of (1-v^2/c^2) [if v = 0.5c, that is 0.75], instead of sqrt(1- v^2/c^2) [= 0.86]. But that would mean that if you make a Michelson Morley experiment in the frame in question, a horizontal pulse would return to the origin later than a vertical pulse. And that is against the principle of relativity, which is a postulate of the thought experiment.

You have to understand that the thought experiments by themselves do not prove anything. They make assumptions or postulates and explore their consequences. In particular, their postulates are the principle of relativity + an invariant c. What proves the latter is empirical evidence.

JesseM
Not sure if this is relevant to the question, but here's an old thread with a discussion of why length contraction in the direction perpendicular to the direction of motion would contradict the postulates of SR: