Ems57fcva

Revision as of 11:42, 24 May 2005

Revision as of 15:50, 24 May 2005

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I am so curious about that because in SR one of the characteristics of inertial motion is that the time-relationship with the surroundings remains the same during inertial motion. I am curious whether, under special circumstances, that characteristic can also occur in curved space-time.<BR> --[[User:Cleon Teunissen|Cleon Teunissen]] | [[User talk:Cleon_Teunissen|Talk]] 11:42, 24 May 2005 (UTC)

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Cleon - You wrote:

: Proper time, it seems, is a ''resultant'' of the scalar time minus a "reverse time" due to motion through space.

[[Proper time]] is time as experienced locally by an observer. Each observer can use that proper time to set up a [[coordinate system]] with a temporal coordinate defined by clocks synchonized with their own clock. In addition, the observer can use rods or parallax to set up a spatial coordinate system (preferably a system of linear orthogonal ''x'', ''y'', and ''z'' coordinates) such that there are four coordinates being used to map '''[[spacetime]]''' (not just space).

Special relativity fundamentally is a means of converting between the coordinate systems of different observers, all of whom have used the above means to set up their own coordinate system. Proper time for another observer who is in motion with respect to myself is given is given by '''my''' proper time minus how that observer is moving through space '''and''' time in '''my''' coordinate system. Similarly, the other observer figures out my proper time with respect to '''his''' coordinate system. Time dilation is one observer finding another observer's clock running slow with respect to that observer's temporal coordinate system.

You have to do this on the basis of coordinate systems. That way there is no absolutism to it. (Absolutism would violate the principle of relativity).

Now step back. All inertial observers in SR see spacetime as being described by the [[Minkowski metric]]. In fact, there are 10 isotropies of spacetime (or ways that you can change your view but still have the spacetime look the same) in SR: Four translations (one for each axis, including time), three rotations (''x''-''y'', ''x''-''z'', and ''y''-''z''), and three velocities (which act as rotatations with time). Note that while a rotation is OK, rotational velocity is not: The metric for an observer co-rotataing with a Sagnac interferometer is not the Minkowski metric, after all. (See my part of the [[Sagnac effect]] page if you doubt that.)

Of course if spacetime is curved the Minkowski metric goes out the door, but curved spacetimes still have metrics, and the [[proper time]] formula still applies. For your observer falling towards a massive object from a distant position, it turns out that his time dilation due to velocity from the free-fall is the same as the time dilation for an object at rest with respect to the central object at that position. The two effects multiply, and so his pulse rate with be determined to be 1 - 2''m''/''r''. Note that this is with respect to the distant observer's temporal coordinate system (as set up using synchonized clocks). The observed pulse rate will be less due to each pulse being emitted from further away, and I am not interested in computing that right now.

--[[User:Ems57fcva|EMS]] | [[User_talk:ems57fcva|Talk]] 15:50, 24 May 2005 (UTC)