wikipedia quote on gravitational time dilation

[enfield]

While gravitational redshift refers to what is seen, gravitational time dilation refers to what is deduced to be "really" happening once observational effects are taken into account.

When using special relativity's relativistic Doppler relationships to calculate the change in energy and frequency (assuming no complicating route-dependent effects such as those caused by the frame-dragging of rotating black holes), then the Gravitational redshift and blueshift frequency ratios are the inverse of each other, suggesting that the "seen" frequency-change corresponds to the actual difference in underlying clockrate. Route-dependence due to frame-dragging may come into play, which would invalidate this idea and complicate the process of determining globally agreed differences in underlying clock rate. [/b]

http://en.wikipedia.org/wiki/Gravitational_redshift#Gravitational_redshift_vers us_gravitational_time_dilation

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So is *all* the perceived gravitational time dilation due to the gravitational redshifts??

Because when a clock is traveling away from you, and its light is redshifted, part of the reason why you perceive the clock to have slowed down is because the light (which contains the information of the clock ticks) takes longer and longer to get to you, but the tick rate doesn't change*

It's easy to visualize if you imagine the clock is moving away at relativistic speeds. Of course there is also the "innate" time dilation due to the speed of the clock. The twin paradox wikipedia article goes into all of that in amazing detail. But I guess this is not the case for gravitational time dilation (?)

*well it actually does get shorter. but even if it did not, this would still be a source of perceived time dilation (the fact that the light from it is redshifted because it's moving away from you). and I'm wondering if this is the sole source of gravitational time dilation or not.

[pervect]

What is your question exactly?

The Wiki article strikes me as well-meaning, but rather confuisng. Your own remarks cover a lot of different questions, many of them interpretational in nature.

Interpretation is a difficult subject - for instance, I find it convenient to follow in the footsteps of Misner (see for instance http://arxiv.org/abs/gr-qc/9508043) and replace the concept of "the observer" with the idea of "making a map of space-time". In this view, space-time is populated by events. Events have coordinates, which give them a location on the space-time map. The space-time map represents both raw events, and the signals they emit (usually electromagnetic in nature) which we perceive directly or via insturments.

In this view, time dilation, of whatever sort, is simply the relation between coordinate time (which is defined by the particular space-time map we are using, it defines the time coordinate we assign to an event to tell us when it happened), and proper time, which represents the readings an actual physical clock would have if it follows a particular worldline. Proper time can be thought of as a "length" on our space-time map.

People can and do use all sorts of coordinate systems (i.e. different maps of space-time), so there is some ambiguity in talking about where time dilation comes from in general, though it's not ambiguous if one refers to a specific map / coordinate system.

[atyy]

So is *all* the perceived gravitational time dilation due to the gravitational redshifts??

Yes. Gravitational time dilation is defined by red shift. This is a different definition from time dilation in special relativity where time dilation is red shift plus correction for the travel time of light.

http://casa.colorado.edu/~ajsh/schwp.html: "That the redshift factor is the same as the time dilation factor (well, so one's the reciprocal of the other, but that's just because the redshift factor is, conventionally, a ratio of wavelengths rather than a ratio of frequencies) is no coincidence. Photons are a good clocks. When a photon is redshifted, its frequency, the rate at which it ticks, slows down."

[enfield]

ah thanks so much for that link :smile:.