B Does the expansion of space influence the passage of time across the universe?

[Vincent Neave]

We are told that space is expanding and that the rate of expansion is speeding up. However, as relativity shows that space and time are inextricably linked, does this mean that time is expanding too?

 

[Drakkith]

However, as relativity shows that space and time are inextricably linked, does this mean that time is expanding too?

Not as far as I know. Space and time may be linked together into spacetime, but as far as I know the metric expansion of space has no effect on time. But I could be incorrect, as I'm not as familiar with GR and cosmology as I'd like to be.

 

[PeterDonis]

We are told that space is expanding

No, we are told that the universe is expanding: that galaxies and galaxy clusters are moving away from each other. This does not mean that "space" is expanding. See below.

relativity shows that space and time are inextricably linked

More precisely, relativity shows that "space" and "time" depend on how you choose coordinates, and that the fundamental object, independent of your choice of coordinates, is spacetime, the four-dimensional geometry. "The universe is expanding" can be more precisely expressed as a property of the four-dimensional geometry that describes our universe.

does this mean that time is expanding too?

Since "time", as above, depends on your choice of coordinates, the answer to this question will depend on that choice as well. In the standard coordinates used in cosmology, all of the properties of the four-dimensional geometry of our universe that are referred to as "the universe expanding" are put into the "space" part of the coordinates, and none of them are in the "time" part. So in those coordinates, one can say that "space" is expanding but "time" is not.

However, it's important to keep in mind that that is a property of the coordinates. You could choose coordinates in which "space" was not expanding, or in which "time" was. But that would not change the fact that galaxies and galaxy clusters are moving apart, that the light we see coming from faraway galaxies is redshifted, etc. That's why it's preferable to focus on the actual observables, the things that don't depend on your choice of coordinates.

 

[Vincent Neave]

this article is interesting and bears on my question.
http://www.theregister.co.uk/2017/05/16/quantum_fluctuations_universes_expansion/

 

[PeterDonis]

this article is interesting and bears on my question

The paper linked to in the article is certainly interesting, but I don't think it bears on the specific question you are asking. Nothing in that paper changes what I said in post #3.

A link to the arxiv preprint of the paper is here:

https://arxiv.org/abs/1703.00543

 

[karthik kamath]

If the universe stops expanding, will time come to a standstill?

 

[PeterDonis]

If the universe stops expanding, will time come to a standstill?

No.

 

[Chronos]

It would be equally valid to ask whether all motion [spatial coordinate displacement] would come to a halt if the universe stopped expanding. What exactly would that mean and, more importantly, what might be the observational consequences? Hint- even assuming expansion came to a screeching halt, there is no reason to believe it would have any effect on peculiar motion.

 

[lomidrevo]

The same question was answered in the following thread, maybe it helps you:
https://www.physicsforums.com/threads/expanding-space-and-time.905277/

 

[Niwrad]

V.N.
1. If you pay very special attention you will discern that there is no definition for space. No one can give you a non mathematical definition of space. One could say that space is created by necessity. Space-time is a Bandersnach.
2. Still if space came to a standstill there would still be a time between points.

Space/time will prove to be the Bandersnach (no good) of Physics.

 

[Drakkith]

1. If you pay very special attention you will discern that there is no definition for space.

I'm sorry but this is entirely incorrect. Space is integral to spacetime and is very well defined by General Relativity.

No one can give you a non mathematical definition of space.

This is also incorrect. The most precise definition of space relies heavily on mathematics, but it is not the only definition of space. Heck, you can look at the wikipedia article on space to get a decent overview of it, including a definition.

2. Still if space came to a standstill there would still be a time between points.

This makes no sense. Space isn't moving and cannot move.

Space/time will prove to be the Bandersnach (no good) of Physics.

Neither does this.

 

[Khashishi]

When we say space is expanding, what we mean is that it is bigger at later times. What does it mean for time to be expanding? For time to be bigger at later times makes no sense.

 

[stoomart]

We are told that space is expanding and that the rate of expansion is speeding up. However, as relativity shows that space and time are inextricably linked, does this mean that time is expanding too?

Based on my understanding of the relativity of simultaneity, I believe time has elapsed the same at all points in the universe, and will continue to do so unless expansion somehow reverses course and compresses at a higher rate.

 

[PeterDonis]

Based on my understanding of the relativity of simultaneity, I believe time has elapsed the same at all points in the universe

What is your logic here?

 

[stoomart]

What is your logic here?

My logic comes from the Minkowski diagram in the link and my understanding of the special principle of relativity:

If a system of coordinates K is chosen so that, in relation to it, physical laws hold good in their simplest form, the same laws hold good in relation to any other system of coordinates K' moving in uniform translation relatively to K.​

 

[PeterDonis]

My logic comes from the Minkowski diagram in the link and my understanding of the special principle of relativity

How does this get you to "time has elapsed the same at all points in the universe"?

 

[stoomart]

How does this get you to "time has elapsed the same at all points in the universe"?

That was my initial assumption from intuition, which comes from another assumption that there are infinite inertial frames or points in the universe.

 

[PeterDonis]

That was my initial assumption from intuition

But then it isn't a logical argument based on anything, let alone the Minkowski diagram and SR.

which comes from another assumption that there are infinite inertial frames or points in the universe

I don't understand how this gets you to "time has elapsed the same at all points in the universe" either. Coordinate time is different in each frame; it's not the same in all frames. And in any case, spacetime in our actual universe is curved, so there are no global inertial frames, only local ones.

 

[stoomart]

But then it isn't a logical argument based on anything, let alone the Minkowski diagram and SR.

No argument here, just stating my opinion based on my understanding of this stuff.

I don't understand how this gets you to "time has elapsed the same at all points in the universe" either. Coordinate time is different in each frame; it's not the same in all frames. And in any case, spacetime in our actual universe is curved, so there are no global inertial frames, only local ones.

My understanding comes from the concept of absolute time described by Newton:

Absolute, true and mathematical time, of itself, and from its own nature flows equably without regard to anything external, and by another name is called duration: relative, apparent and common time, is some sensible and external (whether accurate or unequable) measure of duration by the means of motion, which is commonly used instead of true time ...​

 

[PeterDonis]

My understanding comes from the concept of absolute time

Sorry, absolute time isn't a valid concept in relativity. We're talking about relativity here, not Newtonian physics.

 

[ChrisVer]

What does it mean for time to be expanding? For time to be bigger at later times makes no sense.

Obviously you can say that (well not exactly, as it's not exactly like that for space too: https://www.physicsforums.com/insights/balloon-analogy-good-bad-ugly/ ), since time is just a coordinate. Eg space wasn't small at time t and bigger at time t+dt... There are easy-to-grasp examples by looking at actual shapes you can draw and see how a coordinate can change relative to itself...
afterall in general relativity g_{\mu \nu} can be a function of all coordinates g_{\mu \nu} (x^\rho).

That was my initial assumption from intuition, which comes from another assumption that there are infinite inertial frames or points in the universe.

Also in general you shouldn't try to understand GR from SR... For example Lorentz covariance holds only locally in case of GR, while it's a global feature in SR.

 

[stoomart]

Sorry, absolute time isn't a valid concept in relativity. We're talking about relativity here, not Newtonian physics.

My understanding is relativity and all its complexities is only necessary for an observer to accurately perform measurements; but like the tree falling in the woods thought experiment, the absence of observation does not negate the existence of an absolute time/simultaneity, it just makes it of little practical value to science.

I think we could agree that at any given moment, any two CMB radiation waves that decoupled simultaneously have existed for exactly the same duration, regardless of their energy level or traveled path.

 

[PeterDonis]

My understanding is relativity and all its complexities is only necessary for an observer to accurately perform measurements

Your understanding is incorrect if you think this implies that absolute time is still possible. See below.

the absence of observation does not negate the existence of an absolute time/simultaneity, it just makes it of little practical value to science

We don't just have an "absence of observation" of absolute time. We have direct observations that contradict absolute time. If absolute time were correct, "twin paradox" type observations would be impossible, but we have such direct observations.

 

[PeterDonis]

I think we could agree that at any given moment, any two CMB radiation waves that decoupled simultaneously have existed for exactly the same duration, regardless of their energy level or traveled path.

You think incorrectly. This statement is obviously dependent on a choice of simultaneity convention ("at any given moment"), so it is not absolute.

You might be confused by the fact that there is in fact a standard choice of simultaneity convention in cosmology, namely the one that is made in standard FRW coordinates. But the fact that there is a standard choice that everyone uses does not make it absolute.

 

[stoomart]

We don't just have an "absence of observation" of absolute time. We have direct observations that contradict absolute time. If absolute time were correct, "twin paradox" type observations would be impossible, but we have such direct observations.

I wasn't aware we had direct observations of time dilation, which I agree does seem damning for the idea of absolute time/simultaneity. Going back to your post #3, is it accurate to say expansion affects the passage of time for any observer relative to another across the universe?

 

[Drakkith]

I wasn't aware we had direct observations of time dilation, which I agree does seem damning for the idea of absolute time/simultaneity.

Here are a few experimental tests. All of them agree with SR/GR.
http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html#Tests_of_time_dilation

 

[stoomart]

Here are a few experimental tests. All of them agree with SR/GR.
http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html#Tests_of_time_dilation

Thanks Drakkith, the Hafele and Keating experiment was the most understandable and convincing to me.

 

[PeterDonis]

I wasn't aware we had direct observations of time dilation

The term "time dilation" is ambiguous. It can refer to the proper time of a given observer vs. coordinate time, which depends on the choice of coordinates (or, equivalently, simultaneity convention), or it can refer to the difference in proper time experienced by two observers who take different paths through spacetime between the same starting and ending events. I mentioned the twin paradox to make it clear that I was referring to the latter, which is directly observable and does not depend on your choice of coordinates.

is it accurate to say expansion affects the passage of time for any observer relative to another across the universe?

It depends on what you mean by "the passage of time". You can set up twin paradox scenarios--in which two observers have different elapsed proper time between the same starting and ending events--in any spacetime, including flat spacetime. The exact difference in proper times between the two observers will of course depend on the details of the scenario, including the exact geometry of the spacetime. But given a spacetime geometry and the two different paths for the two observers, the difference in proper time between them is an invariant, independent of any choice of coordinates.

Any other meaning to "the passage of time" will depend on your choice of coordinates.