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## What does SR say about the expanding universe?

You have it backwards, time slows in higher gravity field relative to lower gravity fields.

 Quote by Chronos You have it backwards, time slows in higher gravity field relative to lower gravity fields.
actually the phrase I used is the same on wikipedia
http://en.wikipedia.org/wiki/Gravita..._time_dilation

I wish I could find any relation demonstrating this difference in time rate on earth
in different eras (if exists)

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 Quote by marcus There is no reason that the acceleration of distance growth cannot continue forever. Distance growth is not like ordinary motion and is not governed by SR and is not limited by c.
I would like to expand on this point because it is so often a source of confusion.

Even in SR, and using standard inertial coordinates, the distance between to bodies can grow by up to twice the speed of light if each is going near c in opposite directions relative to some observer (the distance being that measured by this observer). This does not contradict that an observer moving with either body will measure the other having a velocity relative to them of less than c.

Further, 'standard inertial coordinates' are not a physical observable, and are not required by SR. The only requirement for a simultaneity convention is that it connect events with spacelike separation. In terms of light cones, a simultaneity surface intersects the world line of body between its forward and backward pointing light cones. If the initial observer in the scenario above chooses to use a time dependent simultaneity convention, that starts out 'just outside' its backward light cone, changing over time to approach its forward light cone, then the proper distance between two separating bodies in this valid SR coordinate system can grow by any multiple of c at all! This can be exploited to model many features of an expanding universe in SR, without curvature.

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 Quote by galaxion1 Is there any relation to measure this slight difference of time rate on earth in terms of gravitational time dilation due to expansion of the universe? thanks
Hmmm. I see I did not understand your question the first time round. I thought when you said "this slight difference" you were referring to something another poster had already mentioned which had to do with speed of motion, not with depth in a gravitational field.

So I responded that the time rate difference due to motion was very small.

But you are asking about gravitational time dilation. Has that changed since the formation of the solar system?

I don't think it has appreciably changed. Expansion of U would not cause Earth distance from Sun to increase appreciably. We might actually be closer now because of other effects, but all very tiny.

 Quote by galaxion1 Ok... let me rephrase the question ....Does the expansion of universe result in experiencing a different gravitational potential on earth than that experienced 4.5 billion years ago when earth was formed (as it is farther apart now from the sun, the center of the galaxy, etc)? If yes...then as "the gravitational time dilation" says "Clocks at higher gravitational potentials run faster, and clocks at lower gravitational potentials run slower"....and that means that the time rate at certain point in the universe did change since the big bang till present...
I don't think the Hubble law expansion of distances would make the solar system get farther from the center of the galaxy.

We're talking about miniscule effects which would have negligible effect on passage of time. Roughly speaking Hubble expansion DOES NOT CHANGE THE SIZE OF BOUND SYSTEMS. whether they are gravitationally bound or crystal lattice bound, like rock and metal, or whatever. Galaxies don't change size because of Hubble expansion.

But there are other effects which cause orbits to decay. So we may be slightly CLOSER to the center now than when the sun and planets formed.

If that is true then our clocks would now be running a wee bit slower than they were 4 billion years ago.

I would say these effects of time of changing orbit radius are so small, though, that one might as well ignore them. Just my two cents. Someone else may have a different opinion.

 Quote by galaxion1 Does the expansion of universe result in experiencing a different gravitational potential on earth than that experienced 4.5 billion years ago when earth was formed (as it is farther apart now from the sun, the center of the galaxy, etc)?
No.

One thing about the expansion of the universe is that it assumes that the universe is almost smooth. Once you get to a region of space in which this is not true, then the expansion calculations don't work any more.

One way of thinking about this is to imagine the universe to be a gas. You can take a gas and image it to be a continuous fluid. The gas expands and contracts. However, the expansion of the gas doesn't affect the atoms, because if you are looking at individual atoms, then the assumptions you are making about the gas being smooth are wrong.

 If yes...then as "the gravitational time dilation" says "Clocks at higher gravitational potentials run faster, and clocks at lower gravitational potentials run slower"....
That may not be a good way of describe the situation. I've often found that talking about clocks running faster or slower leads to all sorts of confusion. Especially around black holes.

The problem is that if you think that gravity makes clocks run slow, then once you get close to the event horizon you start thinking that "time stops" which it doesn't.

 Quote by galaxion1 actually the phrase I used is the same on wikipedia http://en.wikipedia.org/wiki/Gravita..._time_dilation I wish I could find any relation demonstrating this difference in time rate on earth in different eras (if exists)
I'll fix the article later. It's worded badly.

Gravitation potentials are negative so "lower" potentials (in the context of the article) means "stronger gravity" (or "higher potential" if you are looking at the absolute value of the thing).
 Recognitions: Gold Member Science Advisor The Wiki article is clear, if taken in context. It is less clear if you omit the caveats. I admit I fell for that one.