B Does the CMB give us absolute space and time in practice?

[vanhees71]

We can compare it to the clock rate realized by an atomic clock as defined in the definition of the second of the SI. In fact we can check our cosmological model by measuring the temperature of the CMBR at different times. For an example, see (open access):

https://www.nature.com/articles/s41586-021-04294-5

 

[S Holtom]

There is no spatial variation for the CMB "clock" since it defines "at the same time" as "observing the same CMB temperature", so obviously anyone anywhere in the universe will see the same CMB "clock" reading at the same "time" by this clock.

I think you misparsed what I wrote. I was trying to ascertain whether you were referring to the CMB varying over time or over space.
The CMB isn't perfectly uniform over space, but pretty close to it.
I wasn't trying to make a claim about the clock varying over space.

Only if we have a different clock to compare the CMB "clock" to. If the only "clock" we have is the CMB clock, we won't have any way of knowing the variation in its "tick rate".

We might be talking past each other on this too.

Many of the thought experiments related to relativity include "alice" and "bob" observing a different amount of time having passed, or disagreeing about whose clock was ticking faster or slower. But ISTM that either observer can measure the temperature of the CMB and, in principle, know the "true" time and relative rate of time passing. Yes, this includes comparing to a physical clock but that's largely the point, not a constraint / limitation.

Thinking about it though, I guess it doesn't matter, because, in all those hypotheticals, the observers already know whether their frames were inertial or not. So it's not a "disagreement" in the sense of being an ambiguous situation (let alone a contradiction). We know that Bob's clock was ticking slower, relatively, because of his acceleration, say.

 

[PeterDonis]

The CMB isn't perfectly uniform over space

We have no way of actually measuring this, because we can't travel to a far distant galaxy and measure the CMB there.

We do know that the CMB is not perfectly isotropic (the same in all directions at our particular point in space); its average temperature is the same in all directions but its actual temperature varies from the average by up to about 1 part in 100,000. But that's not the same as varying in space.

 

[PeterDonis]

ISTM that either observer can measure the temperature of the CMB and, in principle, know the "true" time and relative rate of time passing.

That's not what this measurement would tell them. The CMB "clock" is just another "observer", call it "Charlie", in addition to Alice and Bob. It is no more "privileged" or "true" than Alice's and Bob's clocks are.

However, the CMB "clock" is worse than Alice's and Bob's because it does not directly measure proper time. That is, it does not directly measure arc length along a timelike worldline. That is the point of the "rate variation" I mentioned. In all of the relativity scenarios you mention, Alice's and Bob's clocks are assumed to directly measure their proper time (and with our best clocks of today, we have clocks that can do that to 1 part in a trillion or better).

 

[S Holtom]

That's not what this measurement would tell them. The CMB "clock" is just another "observer", call it "Charlie", in addition to Alice and Bob. It is no more "privileged" or "true" than Alice's and Bob's clocks are.

The difference is though, that everyone everywhere has access to "Charlie's" POV.
I mean, put it this way: if there was a literal, visible grid overlaid over the whole universe we could call that "just another" frame of reference too. We would still likely consider it "special" though. And that's all I'm saying.

However, the CMB "clock" is worse than Alice's and Bob's because it does not directly measure proper time.

It doesn't matter if it's direct or not. Even if it allows us to indirectly infer a time interval then it seems to be a kind of universal clock.

 

[Orodruin]

Because they'll see each other redshifted, and the distance between them growing.

Well … it is not really that simple. At ”relative rest” is convention dependent and therefore not physical for observers that are not colocated.

 

[Nugatory]

Even if it allows us to indirectly infer a time interval then it seems to be a kind of universal clock.

There is no such thing as a “time interval” that does not correspond to the proper time along some timelike worldline.

 

[Vanadium 50]

The difference is though, that everyone everywhere has access to "Charlie's" POV.

Again, that's a statement that its big, not that it is preferred.

I a race of beings were to build a galaxy-zied clock that everybody had access to, would that be the same or different?

 

[russ_watters]

univeral, not Universal.

I am aware that we can choose any arbitrary reference frame. The point was, the CMB seems "special" in that anyone, anywhere in our universe can use it and agree on relative velocity.

Sure, it's universal but not Universal. special, but not Special.

 

[PeterDonis]

The difference is though, that everyone everywhere has access to "Charlie's" POV.

This isn't a difference; you could construct global "frames" for Alice and Bob as well.

Even if it allows us to indirectly infer a time interval

You're missing the point: it doesn't. The only way to know the variation in the "tick rate" of the CMB "clock" is to already have another clock that directly measures proper time. Which means you can only "indirectly infer a time interval" from the CMB clock if you already directly know the time interval you are "inferring". Which means the CMB "clock" is pointless.

 

[S Holtom]

Again, that's a statement that its big, not that it is preferred.

I a race of beings were to build a galaxy-zied clock that everybody had access to, would that be the same or different.

It would be the same. (well, actually galaxy scale and universe scale are two different things. But I'll assume you meant to say universe scale)
But the point is, the CMB frame does exist, and no others do that we're aware of.

It's like if I were to say that the Earth's magnetic field is special, as (almost) anywhere on Earth it can be used to find the direction of the north magnetic pole, and you were to say it's not special, because someone could construct another global magnetic field.

 

[PeterDonis]

the CMB frame does exist

As far as any "frame" is concerned, they "exist" only in the sense that we humans define them.

and no others do that we're aware of.

This is not correct. We humans can define any frame we like.

If you said that the CMB has certain physical properties independent of any choice of "frame", that would be true, but that is also true of any physical system. In short, the distinction you are trying to draw simply does not exist.

It's like if I were to say that the Earth's magnetic field is special, as (almost) anywhere on Earth it can be used to find the direction of the north magnetic pole

The Earth's magnetic field is a physical system with physical properties, just like the CMB. Neither one is any more "special" than the other.

and you were to say it's not special, because someone could construct another global magnetic field.

No, it's not special because no physical system is "special" in terms of being preferred by the laws of physics.

 

[S Holtom]

The only way to know the variation in the "tick rate" of the CMB "clock" is to already have another clock that directly measures proper time. Which means you can only "indirectly infer a time interval" from the CMB clock if you already directly know the time interval you are "inferring". Which means the CMB "clock" is pointless.

This is the thing I am still not getting.
Let's imagine that you're put into stasis. You wake up, and discover that the CMB now has a wavelength of 5cm.
You can be pretty confident that you've been asleep a hell of a long time, but the question is, can you use this observation to know roughly how long ago the big bang was?

If the answer is "no" only because our model of dark energy is incomplete, or we still haven't solved the "crisis in cosmology" then fine, but if those are the only objections, then that implies that the CMB is a kind of clock, just not one we can use until our cosmological models are more refined.

 

[PeterDonis]

You can be pretty confident that you've been asleep a hell of a long time, but the question is, can you use this observation to know roughly how long ago the big bang was?

Not if that's the only information you have, no. You can tell by what ratio the scale factor of the universe has changed since the CMB was emitted (since that's just the ratio of temperatures), but you can't tell how much time that took without knowing the specific expansion history of the universe. And that will require having access to different (non-CMB) clocks that directly measure proper time.

 

[S Holtom]

The Earth's magnetic field is a physical system with physical properties, just like the CMB. Neither one is any more "special" than the other.

I think this is being a bit silly.
Upthread I said that even if the universe had a visible grid overlaid, then that would techically-speaking also just be an arbitrary frame. However, no-one would deny that it would be special, as a single frame visible to everyone in the whole universe.
You seem to be biting the bullet and actually claiming that an overlaid grid would indeed not be special. No more important than the frame of reference where the tower of london is the origin.

 

[PeterDonis]

You can tell by what ratio the scale factor of the universe has changed since the CMB was emitted (since that's just the ratio of temperatures)

Perhaps this is another way of getting at what is missing from the "CMB clock": what the CMB temperature is actually measuring is the ratio of scale factors from CMB emission to "now", and that, in itself, does not carry any information about time, only about space.

 

[PeterDonis]

I think this is being a bit silly.

I think you are not thinking carefully about what you are saying.

You seem to be biting the bullet and actually claiming that an overlaid grid would indeed not be special.

That's correct. No "overlaid grid" is special. And that includes the "overlaid grid" you are constructing using the CMB as a reference.

The physical properties of a specific physical system can be described independently of any "overlaid grid", so in that sense they are different from "frames". But specific physical systems are not "special" either in the sense we are discussing; none of them is preferred over any other by the laws of physics. Different physical systems have different properties, and that's all there is to it.

no-one would deny that it would be special, as a single frame visible to everyone in the whole universe

No, it's not. It's a physical system with particular properties that happens to be homogeneous (at least as far as we can tell) throughout the whole universe. (But, as I have pointed out already, we have no way of verifying that it actually is homogeneous by measurement, since we can't travel to far distant galaxies to measure the CMB there.) That doesn't make it "special" in the sense we are discussing, since it gives no preferred status in terms of the laws of physics. It's just a particular physical system with particular properties that happen to be convenient for certain purposes. That's all there is to it.

 

[Vanadium 50]

But the point is, the CMB frame does exist

True.

and no others do that we're aware of.

False.

While I suppose it's technically true, in the sense that there was only one Big Bang, the CMBR is just a thing, like any other thing. The frame where it is at rest is no more and no less special than the frame that any other object is at rest.

It is also probably the case that the frame where the neutrino background is at rest is ever-so-slightly different from the frame where the photon background is at rest. The fact that they are not identical (but very, very close) poses you with a big problem - which CMBR? The fact that our eyes evolved to see photons and not neutrinos - how can that possibly be significant?

I think this is being a bit silly.

On that we can agree.

 

[PeroK]

This is the thing I am still not getting.
Let's imagine that you're put into stasis. You wake up, and discover that the CMB now has a wavelength of 5cm.
You can be pretty confident that you've been asleep a hell of a long time, but the question is, can you use this observation to know roughly how long ago the big bang was?

I believe you've asked a good question and made some valid observations, but rather than digest the answers you have been given you are now pushing a dubious idea too far.

Better to take stock. There is so much to the theory of general relativity that you are missing with your simplistic reduction of the CMB as a universal frame.

 

[vanhees71]

No, it's not special because no physical system is "special" in terms of being preferred by the laws of physics.

But there are preferred frames for a given physical situation. Here we discuss "the Universe" in the sense of cosmology, i.e., a very coarse-grained point of view, where we can assume the cosmological principle (homogeneity and isotropy) and choose the corresponding "preferred frame" in terms of the various coordinates where the Friedmann-Lemaitre-Robertson-Walker metric (FLRWM) looks simple. Choosing the version with the proper time of co-moving frames (and I mean always local frames of course)
$$\mathrm{d}s^2 = \mathrm{d} t^2 - a^2(t) \left (\frac{\mathrm{d} r^2}{1-Kr^2} + r^2 (\mathrm{d} \vartheta^2 + \sin^2 \vartheta \mathrm{d} \varphi^2 )\right ).$$
How can one now determine an observer, which is at rest in such a frame (a socalled co-moving or fundamental observer of cosmology) physically?

The most simple answer, of course is, that it is an observer who measures the CMBR spectrum as an isotropic black-body spectrum, i.e., physically the (local) rest frame of the CMBR thermal radiation defines such a fundamental observer.

 

[S Holtom]

I believe you've asked a good question and made some valid observations, but rather than digest the answers you have been given you are now pushing a dubious idea too far.

What? I'm asking the question as a means of trying to digest the answers given so far.
Let's be clear: I have no agenda on this. I'm quite happy with the idea that the CMB cannot be used as a universal clock. What I am trying to get is an idea of why.

I wouldn't have started this thread if I just wanted to believe some position forevermore, right or wrong.

 

[Ibix]

What I am trying to get is an idea of why.

You can use it to define a universal definition of "now". What you cannot do is oblige anyone to use it, or show anything in the laws of physics to make anyone prefer to use it. Also, if I gave you a series of photos of the CMB taken over millions of years you could use CMB temperature to order them, but you could not use it to put a time stamp on any of them, not without other measurements that would depend on standard issue clocks.

 

[PeroK]

I'm quite happy with the idea that the CMB cannot be used as a universal clock. What I am trying to get is an idea of why.

Take the point I made earlier. Why would you use CMB time for particle physics experiments at CERN? Why not use local atomic clocks on Earth?

 

[S Holtom]

Take the point I made earlier. Why would you use CMB time for particle physics experiments at CERN? Why not use local atomic clocks on Earth?

I don't know what the relevance of these questions is.
My answer to both would be: "Use whatever clock you like". I'm not a lobbyist for the CMB consortium.

The OP is just about how, while in theory time intervals are relative, in practice there is a universal (lower case u) reference. One that doesn't require prior synchronization. That's all.

 

[Ibix]

The OP is just about how, while in theory time intervals are relative, in practice there is a universal (lower case u) reference. One that doesn't require prior synchronization. That's all.

But that's a false dichotomy. There is no universal reference built into the laws of physics, and this is true both in theory and in practice to the best of our knowledge. In your wording, all intervals are relative both in theory and in practice.

However, there can be ways to pick a simultaneity standard that depend on an accident of history. The CMB frame is one, correct. As V50 points out, however, we expect a Cosmic Neutrino Background which would probably define a slightly different frame (in any non-perfectly-ideal model). Which one is the "right" one?

 

[S Holtom]

There is no universal reference built into the laws of physics, and this is true both in theory and in practice to the best of our knowledge.

This objection doesn't make a lot of sense.
If something was explicitly laid out in the laws of physics then it would necessarily be true in theory.

So when I suggest that X might be true only in practice, not in theory, it seems strange to point out that X is not in the laws of physics as a kind of refutation. Because my statement already implies that.

 

[PeroK]

The OP is just about how, while in theory time intervals are relative, in practice there is a universal (lower case u) reference. One that doesn't require prior synchronization. That's all.

That's the $t$ in the conventional FLRW metric. See post #50.

 

[Ibix]

So when I suggest that X might be true only in practice, not in theory,

...then you are suggesting that theory is inconsistent with reality. Is that what you intended to suggest?

The theory says that there is no privileged frame, and that is also what we see in reality to the best of our knowledge. You are confusing a privileged frame with a frame that is well chosen to describe the universe. This is exactly the same mistake as confusing the Earth center-of-mass rest frame with a privileged frame. This frame is not privileged. It is simply extremely convenient for describing a range of physical phenomena near Earth, and two people on opposite sides of the Earth could arrive at this conclusion independently. It is a useful frame because there is a lot of mass on average at rest in the frame, and that has a lot of effects that are easier to describe in this frame. But there is no experiment that can detect this frame other than to measure the speed of the Earth - so it is not privileged.

All of that is also true of the CMB frame. Two disconnected observers can certainly arrive at the conclusion that it's a useful frame, and they will do so because there's a lot of mass at rest in that frame. But there is no experiment they can do to detect the frame other than measure the CMB dipole, and there is no consequence to choosing to use another frame.

 

[PeterDonis]

The OP is just about how, while in theory time intervals are relative, in practice there is a universal (lower case u) reference.

And this claim is false. The CMB "clock" you describe is not a time reference in the required sense. It does not reflect proper time along timelike worldlines, and you cannot infer proper time from it alone; you have to already have a different clock that does reflect proper time along timelike worldlines in order to know how to transform CMB "clock" readings into proper time readings. I have already explained this.

I'm quite happy with the idea that the CMB cannot be used as a universal clock. What I am trying to get is an idea of why.

I have explained that. See above.

Perhaps this will help: the CMB can be used as a universal simultaneity convention. You can adopt a convention that says "events at which the observed CMB temperature is the same happen at the same time, no matter where in space they are located". There is nothing wrong with that. Simultaneity conventions are conventions, and no such convention is preferred by the laws of physics, but particular conventions can be picked out by physical properties of particular physical systems. The CMB is an example of that.

But that is not the same as a "universal clock". The latter also requires a "tick rate" that matches proper time or can be used, without any other information, to infer proper time. The CMB "clock" doesn't meet that requirement, for the reasons I have already explained.

 

[Ibix]

Simultaneity conventions are conventions, and no such convention is preferred by the laws of physics, but particular conventions can be picked out by physical properties of particular physical systems.

@S Holtom - this is a shorter way of saying what my last two paragraphs say in my last post above.