# Relativity and the Dark Energy question

1. Nov 22, 2004

### aokrongly

Relativity and the "Dark Energy" question

I am an amateur and I am looking for help in answering the following question concretely - with numbers.

Time passes more slowly in a gravity well. This we know.

Regarding the expansion of the universe, and the increasing rate of expansion. If time passes more quickly outside the influence of gravity, then can't we quantify the expansion of the universe as a function of the time difference between galactic (and galactic cluster) gravity wells and time outside of those well - i.e. the empty voids of space.

Stated another way, for every tick of the universal clock space expands. If the clock ticks faster in the voids between the galaxies, then space expands faster in those voids - pushing the galaxies farther apart and creating the foam like stucture of the universe. AND as those voids increase in size the cumulative effect of the differing expansion rates increases - thus creating an acceleration of cosmic expansion - which has been observed.

Would this not account for the "dark energy" issue? I don't have advance mathematical training and I don't even know the volumes and formulas that would be involved. Can you help me explore this question?

The difference would be very small, but a very small difference of a vast distance and vast timespan may just account for "dark energy".

Thank you,

Anthony Okrongly
aokrongly@yahoo.com

2. Nov 22, 2004

### 4newton

You are making the assumption that clocks record universal time. You should consider that your clock changing has nothing to do with real time any more than moving the dial on the clock moves you back and forth in time.

I think you should soon get some different viewpoint.

3. Nov 22, 2004

### Garth

Welcome to these Forums Anthony!!
Actually time passes at the rate of one second per second! One can only speak of the observed difference between clock rates. The clock at the bottom of a gravitational 'well' is observed to 'tick' more slowly than one at the 'top'. This effect is observed as gravitational red shift.
For galaxies and normal stars the differences in clock rates would amount to only one part in 10^-10 or so, and this would not explain the observations. Gravitational time dilation is observed as a local or peculiar red shift, also caused by peculiar motions, over and above the cosmological red shift a distant luminous object exhibits caused by Hubble flow. Such objects would be the Type Ia Supernovae, from which the deduction of an accelerating cosmological expansion has been made.
Other objects might have significant gravitational red shift such as quasars, however if so then their spectral lines would be smeared out by the gravitational well, and this is not observed. So summing up, local gravitational red shifts probably do not account for the “dark energy” issue.

Garth

Last edited: Nov 22, 2004
4. Nov 1, 2005

### aokrongly

Garth,

I appreciate your response. I'm still wondering though, about such a small difference over such vast volumes. First, I'm sure your number (10^-10) is right, can you tell me where I might read more on it, though? Also, I'm interested in what happens when you take into consideration the volume. It's similar in my mind to the Neutrinos with mass issue. They needed very very miniscule mass to address the entire dark matter issue. If I were to try to translate this difference in time to an equivelent amount of energy (or mass), how would one go about doing that? Is there a calculation that takes time, energy and mass into relation?

Thanks

5. Nov 1, 2005

### Garth

Hello again aokrongly! LTNS.

First the 10-10 actually applies to gravitational fields in deep space. For stellar and galactic fields the time dilation is about 10-6, still very tiny and unable to explain DE.

At a distance r from a spherical mass M the time dilation factor (as observed by an observer at infinity) is

$$\frac{2GM}{rc^2}$$

Typical orbital velocites as a fraction of the speed of light are

$$v^2 = (\frac{GM}{rc^2})$$

so to find the OOM typical gravitational time dilation as observed by a distant observer well out of the gravitational field you simply square the circular velocity expressed as a fraction of c.

Example: Galactic orbital velocities are around 10-3c therefore the time dilation is around 10-6. You might find "Space Time and Gravity" by Robert Wald (a small paperback) an interesting read - others may recommend alternative books to you.

Neutrinos will only account for about 1% of the closure density, the standard theory requires about 23% in total, there are plenty of ideas as to what this might be but nothing has been discovered yet.

Garth

Last edited: Nov 2, 2005
6. Nov 5, 2005

### aokrongly

thanks. If you ever need help with poker, let me know. I'm an expert at that.