I I want a good reference to a discussion of the meaning of "the speed of light is constant"

[PeterDonis]

Your answer is because the expansion has a negligible effect on the local curvature.

No, that was not my answer. My answer was that "local" means "over a small enough region of spacetime that the effects of curvature are negligible". That is not the same as saying "the expansion has a negligible effect on local curvature".

You are thinking of it backwards. The "expansion" is an "effect" of curvature; it's not a cause of curvature. The cause of the curvature is the distribution of matter and energy. Over a small enough region of spacetime (spacetime, note, not "space"), the effects of curvature are negligible--that includes the expansion itself. But redshift observations do not involve a small enough region of spacetime, so the effects of curvature, of which the redshift is one, are not negligible.

 

[gnnmartin]

What "difference"? The redshift is certainly not negligible.


But it does not have a negligible effect on the redshift.


What "underlying problem" are you talking about?

It is my assumption when asked 'what is the local effect of the expansion of the universe' is that the enquirer seeks to find some difference in local physics, due to (to use your words) the deviation from 'flat' of space time in our neighbourhood consistent with an expanding universe.

My answer is that the differences are negligible. Your answer is the same, but expressed in terms of curvature.

 

[Ibix]

My answer is that the differences are negligible. Your answer is the same, but expressed in terms of curvature.

The point is that this answer is a tautology. The definition of "local" in this context is that curvature is negligible over the "local" region. So the answer to the question in your point 5:

5: An illustration of the problem is the question often asked "What is the local effect of the expansion of the universe". The answer often given (including by me) is that the local effect is so small that it can be ignored, but that ducks the real issue.

should be "local is defined as the region where the answer to your question is 'nothing' - so either you are confirming the definition of local or you don't understand what you are asking". (Possibly phrased more tactfully.)

So I, at least, don't really understand what "underlying issue" you think is being ducked.

 

[PeterDonis]

It is my assumption when asked 'what is the local effect of the expansion of the universe' is that the enquirer seeks to find some difference in local physics, due to (to use your words) the deviation from 'flat' of space time in our neighbourhood consistent with an expanding universe.

My answer is that the differences are negligible. Your answer is the same

Not really. My answer is "none", because "local" by definition means "no effects from spacetime curvature".

 

[gnnmartin]

The point is that this answer is a tautology. The definition of "local" in this context is that curvature is negligible over the "local" region. So the answer to the question in your point 5:should be "local is defined as the region where the answer to your question is 'nothing' - so either you are confirming the definition of local or you don't understand what you are asking". (Possibly phrased more tactfully.)

So I, at least, don't really understand what "underlying issue" you think is being ducked.

You might assert here that 'local' means flat, but the person asking the question doubtless just uses 'local' in the everyday sense given in an English/American dictionary. We detect gravitational waves 'locally'. What you think of as flat becomes not-flat as your ability to measure improves. If you give the answer you suggest, then it will prompt the question 'How far out do you have to look in order to detect the difference between stars getting further away, and the space between us and the stars expanding?'. In other words, you will eventually say 'We don't know' or perhaps 'I don't know', or 'we can't detect any effect'.

 

[PeterDonis]

If you give the answer you suggest, then it will prompt the question 'How far out do you have to look in order to detect the difference between stars getting further away, and the space between us and the stars expanding?'.

Ok, then why don't you ask that question?

In other words, you will eventually say 'We don't know' or perhaps 'I don't know', or 'we can't detect any effect'.

How do you know without asking the question and seeing what responses you get?

 

[PeterDonis]

We detect gravitational waves 'locally'.

We detect anything we detect "locally" in the sense that we can only make measurements where we are. We can't directly measure what is happening in some galaxy far away.

However, many things we detect "locally" involve effects that are not "local" in the sense you appeared to be trying to use that term in your item 5; redshifts due to the expansion of the universe are an example.

If you're going to quibble over what "local" means, then let's stop using the word, and you rephrase your item 5. using some other words that more clearly express what you mean. Can you do that?

 

[gnnmartin]

Many thanks to all for your replies. I'm disappointed that nobody seems to have any sympathy with what I am trying to ask/say, but that in itself is useful to know. I'll continue to monitor this thread, and will respond to any post that adds something I find useful, but will otherwise retire from the thread.

Thanks again to all.

 

[PeterDonis]

I'm disappointed that nobody seems to have any sympathy with what I am trying to ask/say

I don't think it's a matter of "sympathy", it's a matter of not understanding what issue you think is being "ducked". None of us know of any such issue, so when we see someone saying they think there is, we want to know what that issue is.

 

[pervect]

It is my assumption when asked 'what is the local effect of the expansion of the universe' is that the enquirer seeks to find some difference in local physics, due to (to use your words) the deviation from 'flat' of space time in our neighbourhood consistent with an expanding universe.

My answer is that the differences are negligible. Your answer is the same, but expressed in terms of curvature.

Consider the Milne universe, if you're aware of it. https://en.wikipedia.org/wiki/Milne_model

It expands, but in the region of validity of the Milne universe, t>0, there is a diffeomorphism to the standard "Minkowskii" flat space-time of special relativity which does not expand.

My not-very precise resolution of this issue is to conclude that expansion, per se, does not cause physical effects. It's basically the result of a coordinate choice, though the expanding coordinates are lacking in complete coverage of the space-time.

However, acceleration or deacceleratio of the expansion DOES have physical effects. But these effects can be analyzed in terms of the effects of the matter, dark matter, energy, or dark energy that is causing the rate of expansion to accelerate or deaccelerate in the first place. The cause can ultimately be traced back to normal and dark matter/energy distributions.

Fore example, without dark energy, "gravity" causes the expansion of the universe to de-accelerate (slow down), this gravity has physical effects. Dark energy is the only one of the four that causes an accelerating expansion.

Orodruin wrote an article on some of this recently, with much more precision than what I wrote above, but I wasn't able to locate it.

 

[gnnmartin]

Consider the Milne universe, if you're aware of it. https://en.wikipedia.org/wiki/Milne_model

It expands, but in the region of validity of the Milne universe, t>0, there is a diffeomorphism to the standard "Minkowskii" flat space-time of special relativity which does not expand.

My not-very precise resolution of this issue is to conclude that expansion, per se, does not cause physical effects. It's basically the result of a coordinate choice, though the expanding coordinates are lacking in complete coverage of the space-time.

However, acceleration or deacceleratio of the expansion DOES have physical effects. But these effects can be analyzed in terms of the effects of the matter, dark matter, energy, or dark energy that is causing the rate of expansion to accelerate or deaccelerate in the first place. The cause can ultimately be traced back to normal and dark matter/energy distributions.

Fore example, without dark energy, "gravity" causes the expansion of the universe to de-accelerate (slow down), this gravity has physical effects. Dark energy is the only one of the four that causes an accelerating expansion.

Orodruin wrote an article on some of this recently, with much more precision than what I wrote above, but I wasn't able to locate it.

Thanks, very helpful.