Absolute Time in GR: Einstein Fans Unite!

[Karlisbad]

Aboslute time in GR??

:shy: although for Einstein fans this post could be a "blasphemy" .. my question is if under some assumptions we could derive (or at least an approximation to ) GR in a way so there is some kind of "absolute time-frame" of reference for every observer in the universe of inside a certain region of space time... i know it can show a bit stupid but...:shy:

 

[pervect]

One can globally assign events 4 coordinates, one of which is a time coordinate. But this assignment isn't unique, there are many possible ways of doing this. I would describe the state of affairs by saying that there isn't any single notion of "absolute time" in GR, but there are many possible notions of coordinate time.

 

[Stingray]

You can define various notions of "absolute time" using cosmology. Effectively, you use the mean behavior of matter in the universe as a clock. By happy coincidence, it's quite a nice one on large enough scales.

 

[Bos]

Actually, at a fundamental level, GR claims that there is something that everyone agrees upon, absolute space-time. Although observers in relative motion will not agree on simultaneous events or even perhaps where those events took place, they will however agree upon the objects overall trajectory through space-time. This is why Einstein didn't actually like the name general relativity, he wanted to call it Invariance theory.

 

[Chris Hillman]

Absolute time in gtr?

Hi, Karlisbad,

my question is if under some assumptions we could derive (or at least an approximation to ) GR in a way so there is some kind of "absolute time-frame" of reference for every observer in the universe of inside a certain region of space time

Possible comments include:

1. Newtonian gravitation is an approximation to gtr under weak-field slow-motion conditions, so in this sense absolute time is approximatly valid in gtr under some conditions. By the way, Newtonian gravitation has a spacetime formulation due to Cartan. In the thread on reading lists, I have been urging an autodidact to carefully compare "hyperbolic trig" and "circular trig" (the usual high school trig). It turns out that there is also a "parabolic trig", and this is the kind used in Newtonian spacetime.

2. As stringray already mentioned, in exact solutions of the Einstein field equation which feature a region containing a perfect fluid, the world lines of the fluid particles are physically distinguished, and if the fluid flow is vorticity-free (aka "hypersurface orthogonal"; see for example the book A Relativist's Toolkit, by Eric Poisson, for the connection between hypersurface forming and vorticity-free timelike congruences), then in a sense we do obtain a physically distinguished "cosmic time". Examples include the well known FRW models and "nonrotating" but inhomogeneous generalizations, but not "rotating" cosmological models. This is closely related to what cosmologists mean by saying that our solar system is moving in such and such a direction and such and such a velocity wrt the cosmic background radiation.

3. Even in something like the Schwarzschild vacuum, there is a geometrically distinguished class of observers, namely the observers ("static observers") whose world lines agree with the timelike Killing vector field. By definition, static spacetimes feature a hypersurface-orthogonal timelike Killing vector field, but I think it would be stretching a point to speak of "cosmic time" in such a case. In the more realistic Kerr vacuum, the timelike Killing vector field is no longer hypersurface orthogonal. But you can read about "chronometric observers" in the book Physics of Black Holes by Frolov and Novikov.

Actually, at a fundamental level, GR claims that there is something that everyone agrees upon, absolute space-time. Although observers in relative motion will not agree on simultaneous events or even perhaps where those events took place, they will however agree upon the objects overall trajectory through space-time. This is why Einstein didn't actually like the name general relativity, he wanted to call it Invariance theory.

I know what you mean, but this would be a good place to stress that this view needs to be filtered through the multiplicity of operationally significant notions of distance, insofar as we are thinking of "observations in practice". This phenomenon, and various others (such as multiplicity of signal paths) add up to substantial difficulty in "coordinatizing spacetime" as a practical matter. There has been some interesting theoretical work in recent years which attempts to begin to lay a theoretical foundation for extending the highly successful GPS system (which coordinatizes spacetime very near the surface of the Earth) to coordinatize spacetime in the solar system for purposes of spacecraft navigation and consistent documention of observations (we'd like to say when and where something was observed to happen by a robot explorer). Interested forum members can try for example http://arxiv.org/find/gr-qc/1/ti:+GPS/0/1/0/all/0/1

Chris Hillman