Is there a known parametrization for time dilation in the FLRW metric?

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Discussion Overview

The discussion revolves around the parametrization of time dilation in the Friedmann-Lemaître-Robertson-Walker (FLRW) metric. Participants explore the implications of different time coordinates and metrics in cosmology, particularly in relation to time dilation effects and the nature of cosmic expansion.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant questions whether the metrics (1) and (2) are equivalent and if a substitution of coordinates can yield a known parametrization.
  • Another participant introduces the concept of conformal time as an alternative, suggesting that changing coordinates can alter the perception of time dilation, which may not have physical significance by itself.
  • A different viewpoint emphasizes that while the FLRW metric may not reflect time dilation in the same way as the Schwarzschild metric, there are still relevant effects, particularly concerning redshift and remote observations.
  • Participants discuss the Milne metric and its relationship to time dilation, questioning whether flat metrics inherently avoid time dilation.
  • There is a distinction made between velocity time dilation and gravitational time dilation, with some participants expressing confusion over the applicability of gravitational potential in a non-stationary spacetime like FLRW.
  • Concerns are raised about the ambiguity of gravitational potential in cosmology, with participants debating its relevance and how it might be reflected in the metric.
  • One participant argues that gravitational potential can be defined in stationary spacetimes, but this definition does not extend to the FLRW metric, which is not stationary.

Areas of Agreement / Disagreement

Participants express differing views on the nature of time dilation in the FLRW metric, with no consensus reached on whether a suitable parametrization exists or how gravitational potential should be interpreted in cosmological contexts.

Contextual Notes

There are unresolved questions regarding the definitions and implications of gravitational potential in non-stationary spacetimes, as well as the relationship between coordinate choices and perceived time dilation effects.

  • #31
ah gotcha, thanks for the clarification on the Milne universe. I was under the understanding that it was a matter removed model only. Not sure where I picked that mistake up from, it certainly wasn't in any of my textbooks lol
 
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  • #32
Peter: if something is different from the FRW metric that doesn't mean it is in conflict with GR. Your statement is in effect: there is no gravitational time dilation, because it is not in the FRW metric. That doesn't mean it does not exist. This is precisely the point a raised in my original post. I think it's not there, because we simply don't know (yet) how to calculate the cosmic potential and how it evolves. But I believe their are some clues, as I indicated before, which could help us moving forward on this, all within GR context. FRW model is not free from interrogation as long as we have no acceptable answer to what dark energy is supposed to be.
 
  • #33
Vincentius said:
if something is different from the FRW metric that doesn't mean it is in conflict with GR. Your statement is in effect: there is no gravitational time dilation, because it is not in the FRW metric. That doesn't mean it does not exist.

Ok, then show me another metric that correctly describes the universe as a whole but also allows a meaningful "gravitational time dilation" to be defined. Just waving your hands and saying "cosmic potential" doesn't mean any such metric consistent with GR does exist.

Vincentius said:
I think it's not there, because we simply don't know (yet) how to calculate the cosmic potential and how it evolves. But I believe their are some clues, as I indicated before, which could help us moving forward on this, all within GR context.

None of the clues you have mentioned so far are "within GR context"; they are either speculations on alternative theories to GR that didn't pan out, or dealing with other theoretical frameworks altogether (such as quantum mechanics).

Vincentius said:
FRW model is not free from interrogation as long as we have no acceptable answer to what dark energy is supposed to be.

Modeling dark energy in the FRW model is easy: it's a positive cosmological constant. If that's not enough for you because we don't know what microphysics produces a positive cosmological constant, that's not a problem with the FRW model; *any* large-scale model that produced the same predictions would be open to the same objection.

Also, I don't see what dark energy, or the observations that lead us to incude it in the standard cosmological model, have to do with any "cosmic potential". None of the suggestions you have made about how that might be the case were valid alternatives to the standard FRW model with a positive cosmological constant; they were misunderstandings of how the FRW model works.
 
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  • #34
Vincentius said:
The increase of total mass within the expanding particle horizon

Btw, I haven't commented on this before: according to the best current model of the universe (the one with a positive cosmological constant, aka "dark energy"), the total mass within our particle horizon is *decreasing*, not increasing. That's because the expansion of the universe is accelerating, and the effect of the accelerating expansion (which moves matter outside the particle horizon) outweighs the effect of the increasing age of the universe (which increases the distance to the particle horizon).
 
  • #35
One quick question on a com-moving observer...

if an observer is in relative motion to the fundamental observer and to the fundamental observer the universe is homogeneous and isotropic. Am I correct in thinking that the com-moving observer would not see the universe as isotropic?
 
  • #36
Mordred said:
if an observer is in relative motion to the fundamental observer and to the fundamental observer the universe is homogeneous and isotropic. Am I correct in thinking that the com-moving observer would not see the universe as isotropic?

What you are calling the "fundamental observer" is what is usually called a "comoving observer". Those observers see the universe as homogeneous and isotropic. An observer in relative motion to the comoving observer in his vicinity will *not* see the universe as homogeneous and isotropic.
 
  • #37
thanks that's what I thought but wanted to make sure
 

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