B Gravitational red shift and gravitational time dilation

[Ahmed Samra]

How does the gravitational red shift causes time dilation?

 

[Nugatory]

That's too vague of a question to answer easily - the two phenomena are related but it's not clear that one causes the other. If you could point to whatever you're reading about red shift and time dilation and ask a more focused question about exactly what's confusing you, you'll get a better answer.

 

[Ahmed Samra]

I mean what's the relationship between gravitational red shift and gravitational time dilation?

 

[Ahmed Samra]

Is there any relationship between the gravitational red shift and gravitational time dilation? What is it?

 

[Nugatory]

Is there any relationship between the gravitational red shift and gravitational time dilation? What is it?

Google them both and you'll find some pretty decent explanations. If after you've done that it's still not clear, come back with a more focused question about exactly what's not clear and we'll be able to come up with a more helpful answer.

 

[Ahmed Samra]

I searched them in google but still I can't understand. I want to ask a question? Does the gravitational redshift causes the time dilation? And how??

 

[Ahmed Samra]

I am totally confused. I am going to tell you an example. If there is a tower with two clocks in the first floor and the last floor. In the last floor the clock will be ticking more quickly than the other in the first floor. What if there is a light source in the first floor it will be redshifted in the last floor and the light's frequency is going to be reduced. However, the clock is ticking faster in the last floor. Is there any relationship between gravitational time dilation and the gravitational redshift from this example? And what is this relationship. I hope you understand me and explain it to me.

 

[PAllen]

I do think they are related. Redshift is the observational analog of time dilation. You can't see time flow; and time dilation is defined in terms of coordinates, which are arbitrary. However, the coordinate dependent time dilation must represent two observable phenomena: differential aging and redshift = observed slowdown of physical processes.

Let me expand a little: different coordinate choices will disagree on which clock is fast or slow compared to coordinate time, and by how much. However, any coordinate choice will 'encode' the predictions that a clock slowly raised and lowered in gravitational field will elapse more time than one that stayed put; and that an observer at a higher elevation viewing a lower elevation will see light from known source (e.g. a particular emission line of hydrogen) red shifted, and all physical process slower than theirs. It will always be true that observed slow down and redshift show the same factor; this flows from the fact that there exists a common mathematical basis (in GR) to all redshifts (including simple Doppler between inertial observsers) and observed slowdown. Since they all flow from one mathematical basis, I view them as all manifestations of a single phenomenon(which I prefer to call Doppler in curved spacetime). Other knowledgeable people view them as different phenomena even though they can be mathematically unified.

 

[Dale]

Here is a good page to start with. http://www.ast.cam.ac.uk/~ybahe/Time.pdf

Time dilation is a ratio between proper time and coordinate time. It depends on the coordinates chosen.

Redshift is a ratio between an emitted frequency and a received frequency. I.e. It is a ratio between two different proper times. It is independent of the choice of coordinates.

 

[1977ub]

someone at the wikipedia had this to say:

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.

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.

- http://en.wikipedia.org/wiki/Gravit...l_redshift_versus_gravitational_time_dilation

 

[PAllen]

someone at the wikipedia had this to say:
- http://en.wikipedia.org/wiki/Gravit...l_redshift_versus_gravitational_time_dilation

That is a pretty reasonable statement. The only further thing to add is that the separation between gravitational redshift and ordinary Doppler is itself coordinate dependent, thus I don't view them as separate phenomena. To see this consider how SR or GR analyzes redshift between the front and back of an accelerating rocket: front sees redshift from and slower clocks on the bottom; back sees blueshift from and faster clocks on the top. Sounds like gravitational redshift. However, in an inertial frame it is absolutely nothing but ordinary Doppler (by the time light from the back has reached the front, the front is moving away faster, so it is seen redshifted; by the time light from the front reaches the back, the back is moving towards it faster, so it is blue shifted). Gravitational redshift is ultimately nothing but Doppler between non-inertial emitter and receiver that maintain a constant distance. In the case of static observers at different elevations on earth, if you analyze using normal coordinates for a free fall observer, you see pure Doppler with tiny corrections on the order of tidal forces (unmeasurable compared to the primary effect which is pure Doppler).

Similarly, in reference to the link Dalespam provided, Rindler coordinates for a rocket in pure SR have g00 as a function of position. You can call this gravitational redshift, but it is removable by coordinate transform. Similarly, almost all of the g00 difference between a pair of static observers near Earth is removable by coordinate transform to normal coordinates of a free fall observer (the amount left is undetectable even by today's super sensitive clocks). What's left is just Doppler between non-inertial world lines.

 

[Dale]

the separation between gravitational redshift and ordinary Doppler is itself coordinate dependent, thus I don't view them as separate phenomena

I agree.

 

[P.Schuurmans]

Doesn't Doppler work on different velocities whereas Gravitational redshift works only in gravitational fields ? (or according to EEP to accelerating frames)
That is an important difference, I think.

I agree with Topicwriter that Timedilation and Gravitational Redshift seem to work opposite in stead of in similar direction.

 

[PAllen]

Doesn't Doppler work on different velocities whereas Gravitational redshift works only in gravitational fields ? (or according to EEP to accelerating frames)
That is an important difference, I think.

I agree with Topicwriter that Timedilation and Gravitational Redshift seem to work opposite in stead of in similar direction.

Please read my last post. All questions you ask are fully answered there. Given an emitter and receiver at the top and bottom of a tall building, analyzed from the point of view of a free falling observer you find the detectible effect is 100% due to velocity difference between the emitter at emission time and receiver at reception time. Thus, who is observing (more precisely, which coordinates you use) determines whether a given observation is explained by Doppler, gravitational red shift, or any mixture.

The best way to summarize this is that there is one underlying phenomenon, which manifests as gravitational redshift or Doppler (or a mixture) depending on coordinates chosen.

 

[PeterDonis]

The OP's question has been sufficiently addressed. This thread is closed. Related questions should be posed in a new thread.