Gravitational Time Dilation and Twin Paradox ?'s

[Apophenia]

Please stop randomly throwing in irrelevant topics. You posted about time dilation. Stick with that.

If you have questions about virtual particles please post them in the QM forum, and if you have questions about string theory please post them in the beyond standard model forum. When you post them here it seems that you are just trying to deflect the discussion.

Deflecting is not my intent. I should just shut it sometimes. As for the discrepency: It seemed that some had the impression that you can say 1) and not mean 2) when now it seems 1) = 2) ... (until I read the next post). But other than that seeming to be an argument of semantics it is really saying that when you say 'time' you are inherently referring to all processes (anything that can be used to measure time) which I agree with you is seemingly too coincidental but how things 'seem' has no effect on what we observe. I think the next response clears this problem and put's me back into confusion though.

Maybe If we cleared up something about gravitational time dilation it will help.

It seems to me that so far you have been thinking of it as being the relative strength of the gravitational field at different heights that results in the clocks running at different rates. It isn't. It is the difference in gravitational potential.

So why does this make a difference? Let's consider the following scenario:

Imagine we have a uniform gravity field. By uniform, I mean one in the the strength of the field doe not change with height. An object at one height experiences exactly the same gravity force as an object at a different height.

Now let's say that we have two identical pendulum clocks. We put them side by side and they tick in perfect sync. Now we put one of these clocks at a different height from the other. The clock that is higher will tick faster.

The only thing that physically effects the operation of the mechanism is the force of gravity, but both clocks experience the same force of gravity. Yet, the clocks will tick at different rates from each other.

You are basically saying that there is NO physical effect on the mechanism which changes it's operation (other than gravity which is same for both so it does not matter within the context of what is being discussed). Get's back to my confusion of how the operation of a mechanism could change without something "physically effecting" (as you put it) it. You can simply say time changes (there is no physical effect) but I don't know what that means, anyone can't know what that means, but we may just have to take it and look at the whole thing mathematically. idk.

 

[Dale]

It seemed that some had the impression that you can say 1) and not mean 2) when now it seems 1) = 2) ... (until I read the next post).

1) and 2) are experimentally indistinguishable. Since they are experimentally indistinguishable there is no scientific way of choosing between the two. They are philosophically distinct, but many people regard experimentally indistinguishable positions as being the same in some sense.

Personally, I recognize them as being distinct, but feel that the distinction is unimportant.

 

[Apophenia]

1) and 2) are experimentally indistinguishable. Since they are experimentally indistinguishable there is no scientific way of choosing between the two. They are philosophically distinct, but many people regard experimentally indistinguishable positions as being the same in some sense.

Personally, I recognize them as being distinct, but feel that the distinction is unimportant.

...and certainly unimportant for GPS design. By the way, is there a straightforward method for calculating GTD? Also, a geosynchronous satellite would be considered a coincident frame with the Earth so are there exclusively GTD effects acting upon them?

I understand your sentiments.

 

[mfb]

By the way, is there a straightforward method for calculating GTD?

If you know the gravitational potential, yes.

Also, a geosynchronous satellite would be considered a coincident frame with the Earth

Something rotating together with Earth is not an inertial frame. No. You have to consider the velocity as well.

 

[Dale]

...and certainly unimportant for GPS design. By the way, is there a straightforward method for calculating GTD? Also, a geosynchronous satellite would be considered a coincident frame with the Earth so are there exclusively GTD effects acting upon them?

Where curvature is unimportant you can use this approach: http://hyperphysics.phy-astr.gsu.edu/%E2%80%8Chbase/relativ/gratim.html

If curvature is important and you are dealing with time outside a non-rotating spherically symmetric mass then you need to use:
http://en.wikipedia.org/wiki/Gravitational_time_dilation#Outside_a_non-rotating_sphere

In more complicated situations it is not generally possible to split the time dilation into a "gravitational" and "motion" part. In such cases, the overall time dilation can usually still be defined. There are two typical processes for doing that. One is to simply calculate the frequency shift of signals sent, and the other is to calculate the ratio of proper time to coordinate time. The first doesn't work when signals cannot be exchanged and the second doesn't work if your coordinate system doesn't have a timelike coordinate.

 

[A.T.]

Also, a geosynchronous satellite would be considered a coincident frame with the Earth so are there exclusively GTD effects acting upon them?

Something rotating together with Earth is not an inertial frame. No. You have to consider the velocity as well.

How would you combine the two TD effects. Is it just multiplication? The clean way to deal with the rotating common rest frame of Earth and geosynchronous satellite is to use the Schwarzshild metric for the rotating frame:
http://en.wikipedia.org/wiki/Geodetic_effect#Formulae
However, when I simply multiply the TD-factor from the non-rotating metric with the movement TD in the inertial frame, I get something else than the TD-factor from the rotating metric.

Also, what does dt in the rotating frame metric represent physically? In the non-rotating frame dt is the time of a clock at rest at infinity. But in the rotating frame we can't have an clock at rest at infinity. Is this still the time of an inertial clock.