How are the ways in which time is dialted unified?

[enfield]

I know I spelled dilated obscenely wrong in the title. I'm sorry!

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Is the connection that in both time dilation due to faster movement through space, and time dilation due to movement into lower gravitational potentials, the flux of "gravitons" through the object increases?

(of course that is time dilation with respect to the clock on an object that is moving slower, or in a higher gravitational potential).

Or is that a totally wrong are harmful way to "unify" them in one's mind? or is loosely correct and impotent? (btw, i know this all must fall beautifully out of general relatively, but I'm just not really at the point yet where I can understand the phenomena at that level. If they can only be understood on that level, then I'll gladly take that for an answer).

 

[torquil]

Is the connection that in both time dilation due to faster movement through space, and time dilation due to movement into lower gravitational potentials, the flux of "gravitons" through the object increases?

There are no "gravitons" involved in uniform relative motion in flat Minkowskian spacetime. Despite this, time dilation still occurs between different observers.

Btw, there is no evidence in physics for the existence of gravitons, at this time.

 

[pervect]

The short answer is that this seems harmful. Following is the longer answer.

I would forget about gravitons for a while - classical relativity doesn't use them. You won't need gravitons for a long, long, long time, if ever.

Worrying too much about time dilation tends to get one off on the wrong track. This is especially true if one tries to conceive of there being some sort of "master time" and that "measured time" is dialated, or changed, relative to the hypothetical "master time". There isn't any such concept of master time in either special or general relativity.

Time dilation can be understood as the relation between coordinate times, which are the labels that one assigns to events, and proper time, which is the time measured by clocks.

Most of your questions seems to be oriented around the issue of calculating proper time, the time measured by a clock. In GR, what you need to do this are the following:

1) A coordinate system that defines the locations of events, for instance (t,x,y,z) or more commonly (t,r,theta,phi)

2) A set of metric coefficients which serve as a map of space-time that uses these coordinates

The purpose of the metric coefficients is to convert changes in coordinates into proper intervals. In your case, you seem to be generally interested in measuring proper time, rather than proper distance.

Suppose at some event E, your clock is located at (t,x,y,z). And at some subsequent E', yoru clock is located at (t+dt,x+dx,y+dy,z+dz). You can apply the same techniques if your coordinates are (t,r,theta,phi), the later being more likely the case

The elapsed proper time ds (which is more generally the invariant Lorentz interval) is given by:

ds^2 = g_tt dt^2 + g_xx dx^2 + g_yy dy^2 + g_zz dzz^2 + g_tx dt dx + g_xt dx dt + g_ty dt dy + g_yt dy dt + g_tz dt dz + g_zt dz dt + g_xy dx dy + g_yx dy dx + g_yz dy dz + g_zy dz dy

You may notice that this is just the long-written out version of what Aty was saying in the previous thread. So perhaps your original question was the one you were leading up to all along, how to calculate time in generalized coordinates. I.e.

$$ds^2 = g_{ij} dx^i dx^j$$

For real ds to represent time, g_tt must be positive. If g_tt is unity, one second of proper time represents one second of coordinate time. g_tt is normally scaled so that it's one at infinity, and it then gives you "gravitational time dilation". The other g_ij's, give you the effect of velocity, as per the equation, and well be negative.

Compare and contrast the above to the situation in special relativity using Minkowski coordinates where we write:

ds^2 = dt^2 - dx^2 - dy^2 - dz^2

I suppose I might have mentioned it before, but I've simplified things a bit by assuming c=1. Otherwise you need to put a c^2 in front of every dt^2, which mostly serves to confuse more than enligthen, though it does allow you to use SI units.

 

[enfield]

It's going to take me awhile to digest your answer. but thank you so much! Even if I can't extract everything from your answer I feel it's given me some direction. I think i need to soundly understand Lorentz transformations first.

Yeah, if understanding how time is calculated in generalized coordinates can explain the various sources of time dilation (or all the ways in which discrepancies in measured time can arise, etc.) then that was what I was wondering about all along.

 

[pervect]

You might also try looking at http://www.eftaylor.co/download.html#general_relativity , there are a couple of downloads there that talk about the space-time interval in the context of both sr (chatper 1, speeding), and gr (chapter 2, curving).