Is Time Dilation Affected by Varying Mass Density in Identical Universes?

[PFanalog57]

Relativists have told me that the only acceptable metrics discovered for an expanding universe, so far, are the conformal "Robertson-Walker" type metrics:


ds^2 = a(t)^2 [ -dt^2 + dr^2 ]


where t is the "conformal time".


the theoretical and experimental investigation of a(t)
(the expansion scale factor) It's form for mass dominated and radiation dominated regimes is well known... as are the phenomenal "phase change"... "inflation" scenarios.

The conformal time of the Robertson - Walker metrics, naturally lead to the following quesions:

Take two "linearized" Riemannian metrics, g and h, on a smooth manifold M, then of course they are referred to as being "conformally equivalent", if, g = uh for a positive function u on M. What is needed is a quantum gravitational manifesto, generalizing classical GR and QM.

As a thought experiment Let's Assume a cosmological model with a constant mass density, Take for example, a homogenous universe filled with a motionless dust. Will a clock run at a different rate if the mass density parameter is varied?

Make the supposition of two identical Universes having only one difference between them, which is the mass density. That is to say, one universe with mass density X and another with mass density Y. Will the the clocks appear to run at different rates in the two Universes? Will they have different time dilation factors? It seems that they should.

 

[juju]

Hi,

A mapping between two separated universes would be difficult. There would be no commonality as a basis for comparison unless both universes emerged from the same higher space/time. However, if the two density regions were part of the same universe with a zero density state separating them, then I would say that according to GR, there would be a clcok rate difference between them.

juju

 

[R0man]

The concept of time dilation is a fundamental principle in the theory of relativity, stating that time can appear to pass at different rates for observers in different frames of reference. This is due to the fact that the speed of light is constant and the perception of time is relative to the observer's frame of reference. So, in theory, the mass density of a universe should not affect the concept of time dilation, as long as the speed of light remains constant.

The Robertson-Walker metrics you mentioned are used to describe the expansion of the universe and they are based on the assumption that the speed of light is constant. Therefore, any variations in mass density within a universe should not affect the concept of time dilation, as long as the speed of light remains constant.

However, the thought experiment you propose raises an interesting question. If we have two identical universes with only one difference being the mass density, will the clocks in each universe appear to run at different rates? This is a complex question and the answer is not straightforward.

On one hand, the concept of time dilation is based on the relative motion between two frames of reference. In this case, the two universes are identical, so there should not be any relative motion between them. Therefore, time dilation should not be affected.

On the other hand, the mass density of a universe can affect the curvature of spacetime, which in turn can affect the perception of time. This is seen in the phenomenon of gravitational time dilation, where time appears to pass slower in a stronger gravitational field. In this case, the two universes have different mass densities, so there could potentially be a difference in the perception of time.

In conclusion, while the concept of time dilation should not be affected by varying mass density in identical universes, the specific scenario you propose raises some interesting questions that would require further investigation and analysis. It is possible that there could be subtle differences in the perception of time in these universes, but it is difficult to say for certain without further research and understanding of the effects of mass density on spacetime. A quantum gravitational manifesto, as you mentioned, could potentially shed more light on this topic.