Relativity of simultaneity and cosmology

  • #1
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Main Question or Discussion Point

According to SR relativity of simultaneity, the temporal order of events depends on the frame of reference from which the observer watches the events and different observers with a spacelike separation between them or at relativistic speeds won't agree in the order of events.

Now , in standard cosmology, there is a set of so-called "fundamental or comoving observers" that are supposed to move with the "cosmological Hubble flow" and that act as observers that wouldn't register motion wrt the CMBR. This is a fundamental premise(a.k.a. Weyl's postulate) for the construction and use of FRW metric. These fundamental observers define a common temporal order of events for everyone that uses this metric regardless of how distant apart they are or their speeds.
It would seem at first sight that if the relativity of simultaneity,(due to the finiteness of c and equivalence of inertial frames for physical laws), forbids that an omniscient observer be able to define the order of events in different frames, then the fundamental observers of cosmology shouldn't be allowed since that is exactly what they do.
It' looks like if we were subtly introducing an absolute rest frame or aether with the fundamental observers comoving with the CMBR , but this set of observers is needed to build the hypersurfaces or homogenous density slices defined by the FRW metric and to interpret redshift as expansion.
There seems to be an arbitrariness here, is the SR relativity of simultaneity no longer valid in GR and cosmology? or is there any other explanation to clear this up?
any comments?
 

Answers and Replies

  • #2
JesseM
Science Advisor
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Relativity of simultaneity says the fundamental laws of physics don't pick out a "preferred frame", and that's still true in general relativity, the equations of GR will work just the same in any coordinate system regardless of whether its definition of simultaneity matches the most common cosmological coordinates system based on proper time of comoving observers (likewise, in any infinitesimal patch of spacetime the laws of physics will reduce to those of SR in the local inertial frame of any freefalling observer, even if this observer is moving relative to the comoving observers). The cosmological coordinate system based on comoving observers is only "preferred" in the weaker sense that the metric takes a particularly simple form due to the symmetry of how matter is distributed and spacetime is curved, but when physicists talk about there being no preferred frame (and no preferred definition of simultaneity), it seems like they generally mean preferred relative to the basic laws of physics, regardless of how matter happens to be distributed.
 
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  • #3
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Relativity of simultaneity says the fundamental laws of physics don't pick out a "preferred frame", and that's still true in general relativity, the equations of GR will work just the same in any coordinate system regardless of whether its definition of simultaneity matches the most common cosmological coordinates system based on proper time of comoving observers
That is my understanding too, and certainly the GR equations don't pick out a "preferred frame".
What I am hinting at is the fact that the GR equations when solved with a determined boundary condition such as defining this set of comoving observers (Weyl's postulate), like in the FRW metric, might be in some sense going against the spirit of relativity of simultaneity, this might not be bad in itself but we should be aware of it, because by choosing this particular "preferred frame", regardless of if we do it for "practical" or simplicity reasons as you say, we are in fact introducing an absolute rest frame (any common "cosmic time" introduces it) that might lead us to wonder why our particular presumed distribution of matter is simplified precisely when we introduce an absolute rest frame(CMBR).
(likewise, in any infinitesimal patch of spacetime the laws of physics will reduce to those of SR in the local inertial frame of any freefalling observer, even if this observer is moving relative to the comoving observers).
True, only the word "infinitesimal" is problematic IMHO when we talk about observers in GR.
Because the moment we introduce real particles like say electrons, they have mass, however small, and that small mass curves spacetime in a very small amount, but not infinitesimal in the mathematical sense, sure it can be neglected in a first linear approximation, but GR non-linearity might put a constraint for any not idealized massless observer.

The cosmological coordinate system based on comoving observers is only "preferred" in the weaker sense that the metric takes a particularly simple form due to the symmetry of how matter is distributed and spacetime is curved, but when physicists talk about there being no preferred frame (and no preferred definition of simultaneity), it seems like they generally mean preferred relative to the basic laws of physics, regardless of how matter happens to be distributed.
Sure, but note that the notion of how matter is distributed is a also introduced "by hand" in the GR equations as a boundary condition in the form of the cosmological principle, which is neither directly observed nor derived from any law of physics, supported basically-leaving aside philosophical reasons-by the redshift interpreted as expansion (interpretation that is curiously very often justified either by elimination of the rest of hypothesis or by the particular distribution of matter of our universe, in a sort of circular reasoning).
 

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