What happens to time as space is expanding?

[PAllen]

The short answer is that the expansion of space is measured with respect to time.

The slightly longer answer is that the whole space-time is described as a single 4-dimensional manifold, and that manifold is then sliced. The specific slice we pick when describing the expansion is the one where there average background radiation temperature is the same across the entire slice. Then we label each slice, and measure time across them.

The really nice thing is that it all behaves very regularly. It's so simple that we can even derive the matter-only expansion in exactly the same way using simple Newtonian gravity. Thus nothing at all weird happens with the time coordinate.

But the really weird thing is that General Relativity isn't covariant to transformations that affect all four dimensions at once. I used to think it was. But apparently it isn't! I believe the name of the transformation is the Weyl transformation. Alternatives to GR have been proposed which respect this symmetry, but they usually predict the exact same dynamics in nearly all cases.

This stuff gets seriously technical in any event, and I'm not sure it's yet been explained in an approachable way.

A Weyl transformation is not a diffeomorphism, and not an isometry. That is, it produces a different (scaled) metric for the same topological manifold. It really has nothing to do with the number of dimensions affected - a 'random' diffeomorphism affects all 4 dimensions but remains an isometry.

 

[eltodesukane]

According to general relativity, time and space form spacetime.
Spacetime is a fixed, frozen, unchanging, immutable 4-dimensional block.
It includes all of space and all of time, all past and all future.
It is not expanding, it is not moving, it is not changing. It does not sit in time, time is within it.

 

[phinds]

According to general relativity, time and space form spacetime.
Spacetime is a fixed, frozen, unchanging, immutable 4-dimensional block.
It includes all of space and all of time, all past and all future.
It is not expanding, it is not moving, it is not changing. It does not sit in time, time is within it.

You are NOT really describing GR, you are describing the deterministic "block universe" interpretation of SR. Since it's an interpretation, it's more philosophy than physics.

https://www.physicsforums.com/threads/the-block-universe-refuting-a-common-argument-comments.843000/

 

[PeterDonis]

You are NOT really describing GR, you are describing the deterministic "block universe" interpretation of SR.

Not necessarily. He's describing what a mathematical model of a spacetime is, whether the spacetime is flat (SR) or curved (GR). As statements about the mathematical model, what he says is correct. I've said similar things in other threads to clarify what a "spacetime geometry" is.

The "block universe" interpretation is a claim about what parts of the mathematical model are "real". But that's separate from the model itself.

 

[PeterDonis]

According to general relativity, time and space form spacetime.
Spacetime is a fixed, frozen, unchanging, immutable 4-dimensional block.
It includes all of space and all of time, all past and all future.
It is not expanding, it is not moving, it is not changing. It does not sit in time, time is within it.

While all of these statements are correct as statements about the mathematical model, it is also true that in some spacetimes, such as the FRW spacetimes that are used to describe our universe, there is a natural notion of "space" (because there is a natural split of the spacetime into "space" and "time") and a natural notion of "space expanding". Those natural notions are what the OP is asking about. (By "natural" I mean "arising from symmetries that are present in the geometry".)

 

[aperakh]

One intuitive way to put the answer is this:

Time is a dimension, same as space (to be more precise, it's one arbitrarily specially-selected dimension from a 4-dimension spacetime manifold, but never mind that right now).

When space expands, the new expanded space is measured same as before. A mile of expanded space is still same as a mile of unexpanded space (you can just think of it as there being "more" miles now, to the degree that such a term has any meaning in an infinite space)

Likewise, a second in time is still a second of time.
And even if a future event was now further in the future and a past one further in the past, how would you know?
I mean given that you can't see either past of future and there is no meaninful frame of reference to determine it by?

 

[andrew s 1905]

While all of these statements are correct as statements about the mathematical model, it is also true that in some spacetimes, such as the FRW spacetimes that are used to describe our universe, there is a natural notion of "space" (because there is a natural split of the spacetime into "space" and "time") and a natural notion of "space expanding". Those natural notions are what the OP is asking about. (By "natural" I mean "arising from symmetries that are present in the geometry".)

Can you explain why there is a natural notion of "space expanding" and why that cannot aply to time or point me at a reference where I can look it up?

Thanks Andrew.

 

[kimbyd]

One such theory would be the distant clock run slow another is that the scale factor changes. You can't measure either directly. What you can measure is the red shift.

I don't think that's a good way of looking at it.

First, consider for a moment what an observer would see in the far-away galaxy. Even if we see their time as running slow, they can't notice any difference. They'll just view time moving forward at one second per second.

So I think the question that needs answering here is whether you are asking if General Relativity is wrong here, or what General Relativity says is happening.

For General Relativity to be wrong in this situation, the universe would need to be highly non-uniform: we would have to occupy a very special place in the universe where properties like matter density change radically with distance. This is sufficient to me to discount the possibility entirely. And such models tend to be ruled out very easily by some combination of observations (CMB, BAO, supernovas, etc.).

As for what General Relativity says, I think the case of galaxies moving outside of our horizon paints an informative picture.

Every galaxy that isn't gravitationally-bound to us will eventually cross our horizon. When this happens, light from that galaxy will no longer be able to reach us. So all the light that we will ever observe from it is light that was emitted before that crossing. The image we see redshifts more and more, and the time we see approaches the moment of crossing but never passes it. The galaxy itself, however, keeps going. Its time continues on into the future. But because that light can never reach us, we never see it.

While General Relativity is notoriously difficult to pin down to a single, simple description, then it is clear that either the statement that redshift is the same as time dilation is either not true or meaningless. It's not true in the sense that time for an observer on that galaxy continues. It's meaningless if we define time dilation as the pace at which we see clocks tick on the far-away universe. Because in that case it's trivially true, but then you would also get time dilation from non-relativistic velocities too. So either way I don't think it works.

 

[andrew s 1905]

Thanks @kimbyd , I had naively thought that a scale factor impacting time might be analogous to that for space. As a scale factor for space does not cause issues I had not realized one for time would. However, I am looking forward to a reply by @PeterDonis to my post #42 as it promises to explain why given his post #40.

Regards Andrew

 

[PeterDonis]

Can you explain why there is a natural notion of "space expanding" and why that cannot aply to time

See my posts #14 and #15.

 

[andrew s 1905]

See my posts #14 and #15.

Thank you. Could you suggest a more expansive text on this I could educate myself with as the terminology in your posts is beyond me. However, I am willing to learn.

Regards Andrew

 

[PeroK]

Thank you. Could you suggest a more expansive text on this I could educate myself with as the terminology in your posts is beyond me. However, I am willing to learn.

Regards Andrew

If you want to learn cosmology, then a good starting point is this Insight:

https://www.physicsforums.com/insights/inflationary-misconceptions-basics-cosmological-horizons/

For more, try An Introduction to Modern Cosmology by Andrew Liddle, which is a proper introductory undergraduate course, and quite accessible. It does require undergraduate level mathematics.

Note, however, that questions like the one in the OP (IMHO) are more idle, speculative questions than questions with real substance. If you understand the model of the expanding universe, then a question like "why doesn't time expand" is not interesting. If you study a subject academically, then you end up with a different set of questions from the questions that you might think important while reading a popular science account.

 

[andrew s 1905]

Thanks @PeroK I have that book, read that Insight and have a reasonable understanding of current cosmology. I was looking for a better understanding of the geometric points made by @PeterDonis.

What is or in not interesting is a personal issue. I am interested in why time and space are in some way related and in others different. I agree it is not of interest to current cosmology. However, for me it is an interesting foundational problem.

I am not basing my interest on popular science accounts but, in this case, I am seeking a better understanding of the geometry of space time at graduate/post graduate level. I have a postgraduate degree in physics but much has changed since then. Now retired I am relearning but fortunately I am not constrained by a specific curriculum.

Regards Andrew

 

[PeterDonis]

Could you suggest a more expansive text on this I could educate myself with as the terminology in your posts is beyond me.

This Wikipedia article will at least give you a start on the terminology:

https://en.wikipedia.org/wiki/Congr...atical_decomposition_of_a_timelike_congruence

The references given in that article are all good ones to learn more. The toolkit involved here, the kinematic decomposition of a timelike congruence, is very useful (there is also one for a null congruence that is also useful), but seems to be regarded as an "advanced" topic so it isn't discussed much (if at all) in more basic presentations.

 

[PeterDonis]

I am interested in why time and space are in some way related and in others different.

Probably the first thing to learn in this regard is to stop thinking in terms of "time and space" and start thinking in terms of "spacetime", a single 4-dimensional geometric object. Spacetime does have timelike curves and vectors and spacelike curves and vectors (it also has null curves and vectors, which have no counterpart at all in the ordinary conceptual scheme that the terms "time" and "space" are part of), but there is no one single aspect of spacetime that corresponds to "time" or "space".

 

[andrew s 1905]

Probably the first thing to learn in this regard is to stop thinking in terms of "time and space" and start thinking in terms of "spacetime", a single 4-dimensional geometric object. Spacetime does have timelike curves and vectors and spacelike curves and vectors (it also has null curves and vectors, which have no counterpart at all in the ordinary conceptual scheme that the terms "time" and "space" are part of), but there is no one single aspect of spacetime that corresponds to "time" or "space".

Yes I will try to. I look forward trying to understand it better. Thanks Andrew

 

[alantheastronomer]

Summary:: When space expands, what happens to time?

I have one question I hope someone here can answer for me.

Relativity theory tells us that space and time are sort of the same thing, as a spacetime. So when space is expanding, what happens to time? I find it hard to believe that time is somehow unaffected by the expansion of space, so while space is expanding, what is happening to time? Does it expand too or contract or what?

That's a very thoughtful and insightful question...you've noticed that space and time are connected and so if space is expanding doesn't that affect time somehow?

What you are thinking of is the spacetime interval, and the way they're connected is that the interval is invariant - unchanging - whatever the relative velocity with the observer might be.

This is also true for multiple observers with different relative velocities and this is the basis for special relativity.

But this all happens in a space, in a universe, that is non-expanding (called the Minkowski spacetime).

So what happens when the space itself is expanding?

What you're asking about is a different situation - we're not looking at a particular spacetime interval to see if it remains invariant - under what transformation?...there is none! - but at the universe as a whole, which is observed to be expanding.

As PeterDonis noted in post #15 it's not necessary for the time interval to be affected at all by the expansion of space...it also does not preclude it! But if the passage of time were to be affected by the expansion of space, that would lead to a variety of effects that could be confirmed observationally.

Since these effects don't seem to be observed we can safely exclude the possibility that the passage of time behaves differently with the expansion of the universe...

 

[PeterDonis]

if the passage of time were to be affected by the expansion of space, that would lead to a variety of effects that could be confirmed observationally.

Can you give some specifics about the effects you have in mind?

Bear in mind that "time" and "space" are artifacts of a coordinate choice, and artifacts of a coordinate choice cannot have any observable consequences.

 

[PeterDonis]

we're not looking at a particular spacetime interval to see if it remains invariant - under what transformation?...there is none!

Yes, there is. In General Relativity, intervals (more precisely, arc lengths along particular curves) are invariant under any coordinate transformation whatever.

 

[alantheastronomer]

Yes, there is. In General Relativity, intervals (more precisely, arc lengths along particular curves) are invariant under any coordinate transformation whatever.

What I mean by "there is none"... is that we're not making a coordinate transformation in the situation the op is positing.

Can you give some specifics about the effects you have in mind?

Bear in mind that "time" and "space" are artifacts of a coordinate choice, and artifacts of a coordinate choice cannot have any observable consequences.

Well, I don't want to get into areas that are too speculative, but if the expansion of space were to cause clocks to tick slower with increasing distance, that would affect kinematics systematically, so clusters of galaxies would appear to have lower velocity dispersions the further they were, for instance.

 

[PeterDonis]

What I mean by "there is none"... is that we're not making a coordinate transformation in the situation the op is positing.

Ok.

if the expansion of space were to cause clocks to tick slower with increasing distance, that would affect kinematics systematically, so clusters of galaxies would appear to have lower velocity dispersions the further they were, for instance.

Apparent kinematics is affected by distance--increasing distance means increasing redshift, and apparent kinematics is affected by redshift. For example, a supernova in a galaxy at a redshift of $z = 1$ appears to take twice as long (as shown by measurement of light curves) as a similar supernova in a nearby galaxy with essentially no redshift. (Twice as long because the Doppler factor is $1 + z$ for redshift $z$.)

It seems to me that you are trying to take two incompatible viewpoints. On the one hand, you recognize that the spacetime of our universe is not flat Minkowski spacetime; "expansion of the universe" is spacetime curvature. But on the other hand, you are trying to use intuitions that only work in flat Minkowski spacetime.

 

[alantheastronomer]

Ok.Apparent kinematics is affected by distance--increasing distance means increasing redshift, and apparent kinematics is affected by redshift. For example, a supernova in a galaxy at a redshift of $z = 1$ appears to take twice as long (as shown by measurement of light curves) as a similar supernova in a nearby galaxy with essentially no redshift. (Twice as long because the Doppler factor is $1 + z$ for redshift $z$.)

Yes, but this would be an effect that would be evident even after redshift is taken into account.

Something more speculative and the result more uncertain, would be the effect on local thermodynamics and how that would impact star formation, structure and evolution.

The strength of the electromagnetic force would be the same, while temperatures would be lower. Main sequence stars of the same mass would have systemically lower luminosities. It would take more mass to reach the Chandrasekar limit. In our own globular clusters, there's be less x-ray sources because in the past less of the high mass stars would have gone supernova and left neutron star remnants behind...

 

[PeterDonis]

this would be an effect that would be evident even after redshift is taken into account.

I can choose coordinates in which there is an effect after redshift is taken into account. So what you are describing is just a coordinate artifact, as I said before.

Something more speculative

Too speculative for PF. The rest of your post is personal speculation and off topic.

 

[alantheastronomer]

I can choose coordinates in which there is an effect after redshift is taken into account. So what you are describing is just a coordinate artifact, as I said before.

I'm not sure I understand...these are observations made from Earth! How can you choose to observe from any other location?

If you mean hypothetically, then if the universe is isotropic, the redshift you're measuring would be different which would account for your result, but if you chose to observe a different object at the former redshift you'd still find the same effect due to the increase in the time interval...

 

[PeterDonis]

these are observations made from Earth!

You can't observe "what time it is" at a distant location from Earth; that is a convention that depends on your choice of coordinates. You can only observe the redshift and Doppler shifted observations like the lengthened supernova light curves. Any effect you claim is "after redshift is taken into account" is a coordinate artifact. This fact is often obscured in discussions of SR because of the naturalness of adopting inertial frames and their associated simultaneity conventions. But however natural they are, they are still conventions, not observations.

 

[PeterDonis]

If you mean hypothetically, then if the universe is isotropic, the redshift you're measuring would be different

I don't understand what you mean. Our actual universe is isotropic, to a very good approximation.

 

[PeroK]

The strength of the electromagnetic force would be the same, while temperatures would be lower. Main sequence stars of the same mass would have systemically lower luminosities. It would take more mass to reach the Chandrasekar limit. In our own globular clusters, there's be less x-ray sources because in the past less of the high mass stars would have gone supernova and left neutron star remnants behind...

Are you implying some local test as an absolute measure of the passage of time? E.g. put a certain mass in a given region and if it forms a star of some characteristic and eventually goes supernova, then time is flowing at a "default" rate. And if it doesn't, then time locally is flowing "slow" or "fast"?

If time locally is measured using natural processes (e.g. a caesium clock), then wouldn't everything appear to be "normal" locally? Wouldn't all the physics locally be the same?

Alternatively, what could be a test on Earth to verify that time is flowing at the same rate year after year? I suggest this can't be tested - because, as the passage of time hypothetically slows or quickens, then our mechanism for measuring its passage changes along with it.

 

[alantheastronomer]

I don't understand what you mean. Our actual universe is isotropic, to a very good approximation.

Just affirming that it is...

You can't observe "what time it is" at a distant location from Earth; that is a convention that depends on your choice of coordinates. You can only observe the redshift and Doppler shifted observations like the lengthened supernova light curves. Any effect you claim is "after redshift is taken into account" is a coordinate artifact. This fact is often obscured in discussions of SR because of the naturalness of adopting inertial frames and their associated simultaneity conventions. But however natural they are, they are still conventions, not observations.

You can compare observations of clusters of galaxies at different redshifts and see if there are systematic trends over and above what could be accounted for by the Hubble relation, though admittedly any effect I might attribute to an increase in the time interval with redshift could also be attributed to evolutionary effects...but what would I attribute a lack of these effects to...?

 

[PeterDonis]

any effect I might attribute to an increase in the time interval with redshift could also be attributed to evolutionary effects

What's more, attributing them to evolutionary effects is making use of a well known model, whereas attributing them to "an increase in the time interval with redshift" is just meaningless words since there is no model to correspond to them.

The plain fact which you are refusing to acknowledge is that "the time interval" as you are using the term is not a physical quantity. It's an artifact of coordinates. Proper time along a particular worldline is a physical quantity, but that is not what you are describing. There has been research done looking for variation over cosmological times of dimensionless physical constants like the fine structure constant, but no such variation has ever been found, and even if it were, interpreting such variation as "a change in the time interval" would still be an artifact of a particular choice of coordinates (and other choices of convention such as the gauge used for the EM field); one could always make different choices that would keep "the time interval" the same and put the variation somewhere else.

what would I attribute a lack of these effects to...?

A lack of what effects? There is nothing that requires "evolutionary effects" over and above the Hubble relation to always be present. So if they aren't, that's fine; there's nothing to explain.

 

[alantheastronomer]

Proper time along a particular worldline is a physical quantity, but that is not what you are describing.

I thought I was...I'm attempting to describe a model where proper time varies as a function of redshift.

one could always make different choices that would keep "the time interval" the same and put the variation somewhere else.

I think I see...like attributing it to a variation in distance or curvature?

A lack of what effects?

The hypothetical variation of cluster velocity dispersion with redshift that I posited, which admittedly was based on the tacit assumption that redshift was entirely due to distance...

There is nothing that requires "evolutionary effects" over and above the Hubble relation to always be present. So, if they aren't that's fine; there's nothing to explain.

So I was alluding to the fact that a lack of any of these observational effects means that there is no variation in proper time with distance, which is what the op was asking about...or are you saying that there still could be, with the right change in coordinate system?

 

[PeterDonis]

I'm attempting to describe a model where proper time varies as a function of redshift.

Then you need to give a specific reference to such a model, so we can understand what "proper time varies as a function of redshift" even means. As it stands those words make no sense.

like attributing it to a variation in distance or curvature?

Like attributing it to "variation" in some coordinate other than time. Either way it's an artifact of your coordinate choice.

The hypothetical variation of cluster velocity dispersion with redshift

Which, as I pointed out, is not hypothetical; it is actually observed, and would be expected given what the redshift means physically.

I was alluding to the fact that a lack of any of these observational effects means that there is no variation in proper time with distance

Which, as I said above, makes no sense as it stands. You need to give a reference. Otherwise what you are saying is just personal speculation and is out of bounds here.

which is what the op was asking about

The OP's question was based on the same confusion you keep exhibiting: confusing coordinate artifacts with actual physical effects. That was cleared up for the OP before you joined the thread. You are just obfuscating it again.

are you saying that there still could be, with the right change in coordinate system?

I'm saying that "variation in proper time with distance" is just word salad as it stands. If you want us to make sense of it, you need to give a reference to an actual model that explains what it is supposed to mean.

 

[alantheastronomer]

Then you need to give a specific reference to such a model, so we can understand what "proper time varies as a function of redshift" even means. As it stands those words make no sense.

I'm saying that "variation in proper time with distance" is just word salad as it stands. If you want us to make sense of it, you need to give a reference to an actual model that explains what it is supposed to mean.

I was in the process of trying to develop such a model when I realized that redshift is not time independent and would also be affected by any type of time variation;

I had erroneously thought that the light curves and velocity dispersions would diverge at larger redshifts but I see that's not true and so redshift can always be interpreted as being due to the expansion of space - is this what you mean by being just a coordinate artifact?

What about gravitational time dilation - that's not also coordinate dependent, is it?

Are you implying some local test as an absolute measure of the passage of time? E.g. put a certain mass in a given region and if it forms a star of some characteristic and eventually goes supernova, then time is flowing at a "default" rate. And if it doesn't, then time locally is flowing "slow" or "fast"?

If time locally is measured using natural processes (e.g. a caesium clock), then wouldn't everything appear to be "normal" locally? Wouldn't all the physics locally be the same?

Globular clusters formed between 10 and 12 billion years ago, and so if any physics was different back then, it should have ramifications and have left anomalies with local physics that we can observe today within the Milky Way...

 

[PeterDonis]

I was in the process of trying to develop such a model

When I asked for a reference to an actual model, I meant an actual model that already exists somewhere in the literature, not one you are trying to develop yourself. The latter would be personal research and would be off topic here.

I had erroneously thought that the light curves and velocity dispersions would diverge at larger redshifts

What do you mean by "diverge"?

redshift can always be interpreted as being due to the expansion of space

Redshift can be "interpreted" as a variety of things depending on how you choose your coordinates. But doing that is getting things backwards. Redshift is the direct observable; you don't need to "interpret" it at all. You just need to look at how redshift is related to other direct observables, such as luminosity and angular size. "Interpretation" of the redshift is a calculational convenience and is not necessary at all; you can do cosmology entirely in terms of direct observables and the relationships between them.

What about gravitational time dilation - that's not also coordinate dependent, is it?

Gravitational time dilation is not even a well-defined concept in an expanding universe. It is only well-defined in stationary spacetimes. In stationary spacetimes, it is true that it is not coordinate-dependent; it has an invariant definition.

Globular clusters formed between 10 and 12 billion years ago, and so if any physics was different back then, it should have ramifications and have left anomalies with local physics that we can observe today within the Milky Way...

Certainly; for example, if the fine structure constant were different back then, that should in principle have observable consequences when we look at such objects. So far no such observable consequences have been found. But testing for them does not require any "interpretation" of redshift or any other observables.

 

[PeterDonis]

The OP question has been thoroughly discussed, and speculations are off limits at PF. Thread closed.