The discussion centers on the concept of time dilation as described by special relativity and its implications in general relativity. It establishes that velocity-based time dilation is symmetric, meaning two observers in uniform inertial motion perceive each other's clocks as running slow. The conversation also clarifies that the Doppler effect influences how time is observed between moving observers, particularly when one observer is moving away or towards the other. Additionally, it emphasizes that time dilation in general relativity differs from special relativity due to the curvature of spacetime.
PREREQUISITESPhysicists, students of relativity, and anyone interested in the effects of high-speed travel and gravitational influences on time perception.
Your question reveals a fundamental misunderstanding of time dilation.AdvaitDhingra said:If time slows down for an observer traveling at some speed relative to your proper time, shouldn't the traveling observer also see your time slow down relative to his proper time? Or does the observer see your time speed up relative to his proper time.
Yes, because both people can regard themselves as "at rest in an inertial frame". Note that what you actually see is that a clock moving away slows down and a clock moving towards you speeds up because the Doppler effect due to changing distance dominates the time dilation effect. But if you correct for that, both observers will calculate that the other's clock runs slow in either direction. Also note that if one observer turns round and comes back they were not always at rest in an inertial frame and the results are not symmetric.AdvaitDhingra said:If time slows down for an observer traveling at some speed relative to your proper time, shouldn't the traveling observer also see your time slow down relative to his proper time?
No. Special relativistic results rely on spacetime being flat, and thus they do not usually generalise to curved spacetimes. Sometimes you can get away with it, but some experience is needed to know when you can do it.AdvaitDhingra said:Also, is dilation exactly the same in general relativity?
Ah ok. thanksPeroK said:Your question reveals a fundamental misunderstanding of time dilation.
Velocity-based time dilation is symmetric: two observers in uniform inertial motion measure each other's clock to be running slow, according to the frame of reference in which they are at rest.
Ok thanks for clearing that up.Ibix said:Yes, because both people can regard themselves as "at rest in an inertial frame". Note that what you actually see is that a clock moving away slows down and a clock moving towards you speeds up because the Doppler effect due to changing distance dominates the time dilation effect. But if you correct for that, both observers will calculate that the other's clock runs slow in either direction. Also note that if one observer turns round and comes back they were not always at rest in an inertial frame and the results are not symmetric.No. Special relativistic results rely on spacetime being flat, and thus they do not usually generalise to curved spacetimes. Sometimes you can get away with it, but some experience is needed to know when you can do it.
...assuming you are in a stationary spacetime where time dilation can be defined so casually. And being aware that the Doppler effect is different in the two cases. And noting that the gravitational time dilation formula applies between clocks at rest at different heights, not clocks free-falling from infinity at those heights.Myslius said:The ratio is the same.
This, on the other hand, is meaningless.Myslius said:Both observers see proper time slowing down,
Myslius said:Both observers see proper time slowing down
If I squint just right I can read that [overly] pithy sentence to mean:Ibix said:This, on the other hand, is meaningless.
Maybe. Generalising your comment slightly, to be clearly written, the sentence needs to state whose proper time is being talked about and as compared to what time standard by what methodology.jbriggs444 said:If I squint just right I can read that [overly] pithy sentence to mean:
Each observer observes that elapsed proper time for the remote observer is less than elapsed coordinate time for the remote observer, measured using the local observer's inertial rest frame.
Ahh ok thanks for clearing that upMyslius said:Let's say a spaceship moves away from you at the 0.8 speed of light. Time slows down by the factor of
1 /sqrt(1 - 0.8^2)=5/3. Let's say you have a very powerful telescope and are able to see the clock on the spaceship very far away. After 1 year what time would you see on the spaceship? 3/5 year? Not really, the clock actually shows sqrt((1 + 0.8)/(1 - 0.8) = 1/3 year, this is because of relativistic doppler effect and the fact that it takes some time for light to travel back at you. If after 1 year ship turns away and travels towards you with velocity of 0.8c, for some time (not 1 year) through the telescope you would see the clock running 3 times faster than your own clock. The combination of both seeing time running slower and seeing time running faster gives 5/3 ratio when the ship travels back to where it started. When you say a word "see" you have to include doppler effect. Classical doppler effect * relativistic time dilation = relativistic doppler effect.
Escape velocity on the surface of the Earth is 11186 m/s, time on Earth ticks slower in the gravity well for an observer far far away by 1 /sqrt(1 - (11186 m/s/c)^2) = 1.0000000007 times slower.
Let's say you're are in flat spacetime and someone is moving 11186 m/s away from you:
1 /sqrt(1 - (11186 m/s/c)^2) = 1.0000000007 times slower
The ratio is the same.
Both observers see proper time slowing down, and both observers see time speeding up when traveling towards each other when looking thru telescope.