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mcjosep
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Just wondering if you are observing someone from a far out distance and they are in a gravitational field going at a high speed would the time dilation from their speed add on to the gravitational time dilation?
In some simple cases they are approximately multiplicative. However, even then it is an approximation and it doesn't work in more complicated spacetime. I prefer not to split them up.mcjosep said:Just wondering if you are observing someone from a far out distance and they are in a gravitational field going at a high speed would the time dilation from their speed add on to the gravitational time dilation?
That's an interesting though, but it does not sound convincing to me, as upon a short reflection, I can't find the problem.Matterwave said:[..] In more complicated situations, you might not be able to just add the effects like you are suggesting. Esp if the gravitational field is not static/stationary.
You can do this precisely to the extent that gravity adds linearly (to the desired precision) and thus can be represented by a scalar potential. That is, no body is too massive, and relative motion between massive bodies is small compared to c.harrylin said:That's an interesting though, but it does not sound convincing to me, as upon a short reflection, I can't find the problem.
It is possible to synchronize clocks on Earth with geostationary clocks in space by correcting for rotation and gravitational time dilation; these clocks can in turn be synchronized to more distant clocks that co-move with the Earth, with negligible gravitational time dilation. Is there a problem with a Lorentz transformation to those clocks from a distant reference system that is moving relative to the Earth?
Thanks!
OK, I see that there is an issue with the casual expression "add the effects"; and I had not thought about the title of this thread. The equations obviously require a multiplication of the time dilations and not a literal addition, although this is approximately correct for terms close to 1. It appears to me that that is all there is to it, as the OPs' question concerns a single gravitational field.PAllen said:You can do this precisely to the extent that gravity adds linearly (to the desired precision) and thus can be represented by a scalar potential. That is, no body is too massive, and relative motion between massive bodies is small compared to c.
Maybe I'm not understanding your question. Matterwave stated that separations and simple ways of combining effects break down for significantly non-stationary situations. Non-stationary implies motion of stress/energy beyond rotation of an ideal body. Thus, if by 'single gravitational field' you mean a single massive body, possibly rotating, and reasonably idealized (no wild density variations, axial symmetry), then matterwave's caveat doesn't apply. The most important real world case it does apply is closely orbiting bodies of sufficient mass (e.g. compact binary (neutron) stars).harrylin said:OK, I see that there is an issue with the casual expression "add the effects"; and I had not thought about the title of this thread. The equations obviously require a multiplication of the time dilations and not a literal addition, although this is approximately correct for terms close to 1. It appears to me that that is all there is to it, as the OPs' question concerns a single gravitational field.
Thus, my question to Matterwave remains.
Time dilation is a phenomenon in which time passes at different rates in different reference frames, as predicted by the theory of relativity. It is a consequence of the fact that the speed of light is constant in all reference frames.
Time dilation is a fundamental concept in general relativity. According to the theory, the presence of massive objects in space causes a curvature of spacetime, which results in the slowing down of time for objects in their vicinity. This effect is known as gravitational time dilation.
Yes, according to the theory of relativity, time dilation due to both gravity and special relativity is additive. This means that the total time dilation experienced by an object is the sum of the individual time dilation effects caused by gravity and special relativity.
Time dilation can affect the measurement of time in several ways. For example, it can cause clocks to run slower in the presence of a strong gravitational field, or when an object is moving at high speeds. This can lead to discrepancies in time measurement between two observers in different reference frames.
Yes, time dilation is a real phenomenon that has been observed and measured in various experiments, such as the Hafele-Keating experiment and the Pound-Rebka experiment. However, the effects of time dilation are typically only noticeable at extremely high speeds or in the presence of very strong gravitational fields, and are not noticeable in everyday life.