I Time dilation for two observers in relative motion

[Raytele]

If time dilates differently for two observers in relative motion, how is this possible when both observers can claim that it is the other's time that is passing more slowly? Doesn't this create a contradiction? And how does the famous twin paradox explain or complicate this issue?

 

[Ibix]

Frames in relative motion don't agree what "at the same time as I stopped my clock" means. So you and I can zero our clocks when we pass and stop them some agreed time later and say the other's clock ticked slowly, but I say you stopped your clock late and you say I did. It's called the relativity of simultaneity.

The twin paradox is a different situation because one twin turns around. They can't both use "his clock ticks slowly", because that simple statement contains an assumption that the one making it has not accelerated, but the twin who returns has accelerated.

 

[PeterDonis]

how does the famous twin paradox explain or complicate this issue?

https://www.physicsforums.com/threads/when-discussing-the-twin-paradox-read-this-first.1048697/

 

[Nugatory]

If time dilates differently for two observers in relative motion, how is this possible when both observers can claim that it is the other's time that is passing more slowly? Doesn't this create a contradiction? And how does the famous twin paradox explain or complicate this issue?

The twin paradox is not a paradox when properly analyzed. It only becomes a paradox if we make the mistake of incorrectly applying the time dilation formula and erroneously conclude that something is wrong because traveler sees earth twin's clock running slow so earth twin should be younger, earth twin sees traveler's clock running slow so traveler should be younger. But when we analyze it properly the apparent contradiction disappears: the traveler is aged less when the twins reunite, and this has nothing to do with time dilation.

So the twin paradox neither explains nor complicates the issue - it's just not relevant to your question. For more about it, check out the sticky thread at the top of this forum: https://www.physicsforums.com/threads/when-discussing-the-twin-paradox-read-this-first.1048697/

The key your question about the apparent contradiction in time dilation (you say my clock is running slower than yours, I say your clock is running slower than mine, we're somehow both right) is explained as @Ibix says above by the relativity of simultaneity. For a more detailed explanation, try https://www.physicsforums.com/threads/time-the-special-theory-of-relativity.846242/#post-5307390 or https://www.physicsforums.com/threa...on-question-w-spaceships.883303/#post-5552719

 

[PeroK]

If time dilates differently for two observers in relative motion, how is this possible when both observers can claim that it is the other's time that is passing more slowly? Doesn't this create a contradiction? And how does the famous twin paradox explain or complicate this issue?

If two people walk away from each other, they both look smaller relative to the other. Each might say that eventually the other is only about as big as his or her own thumb.

The lesson is that relying on a superficial analysis is not sufficient. Many things might appear contradictory at first sight. You always have to think things through.

 

[Orodruin]

Try reading this: https://www.physicsforums.com/insights/geometrical-view-time-dilation-twin-paradox/

It explains how symmetric time dilation relates to the corresponding statement in Euclidean (“normal”) space.

 

[robphy]

(from my post that was split off with others into another thread)

I think a spacetime diagram of the situation and its Euclidean analogue would help the OP.
For example, look at
https://www.physicsforums.com/threa...procity-of-time-dilation.1057792/post-6973393

 

[Nugatory]

A valuable but tangential discussion has been moved to https://www.physicsforums.com/threads/a-better-way-of-talking-about-time.1068101/

 

[Orodruin]

Considering OP has not been seen since posting the thread, I think we can assume we are just piling on at this point …

 

[Raytele]

Thank you very much to everyone who responded, you were able to help me understand this fabulous and complex topic.

 

[Herman Trivilino]

If time dilates differently for two observers in relative motion, how is this possible when both observers can claim that it is the other's time that is passing more slowly?

Einstein is said to have claimed that the resolution of this dilemma occurred to him while in bed, causing him to sit upright. It's the relativity of simultaneity that makes it possible.