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

[S Holtom]

TL;DR Summary

Relativity teaches that space/time is relative, but in practice, does our cosmos have a grid and clock?

Another noob relativity / cosmology question (although at least this time won't turn out to be a coding bug, as no code is involved...)

AIUI, according to relativity, there is no privileged reference frame, and any inertial reference frame is as "correct" as any other.

But...

In practice, in our universe, observers can compare their velocity to the CMB, right? So there is something like a universal reference frame.

And time too. If I measure the CMB's temperature accurately enough, can it be used as some sort of universal clock? Can I compare the speed of my physical clock ticking to the speed that the CMB is redshifting (obviously this would require ludicrous precision, I'm speaking theoretically for this part).

 

[Vanadium 50]

No more so than setting your coordinate system origin at the time and place Lincoln was shot, Charlie Bucket found his Golden Ticket, or the Greenwich medidian and the equator 2022 years ago.

 

[PeterDonis]

In practice, in our universe, observers can compare their velocity to the CMB, right?

Yes.

So there is something like a universal reference frame.

No. This frame is not picked out by the laws of physics. It's picked out by a particular physical property of the particular solution to the laws that we happen to live in (namely, the presence of background radiation that is isotropic to observers in a particular state of motion). That will be true for practically all solutions to the laws that are of any interest at all, since in practically all cases of interest there is some kind of distribution of matter and energy that defines, at least to a good enough approximation, a particular frame.

 

[PeterDonis]

If I measure the CMB's temperature accurately enough, can it be used as some sort of universal clock?

Not really, since its "tick rate" will not be the same as the "tick rate" of proper time for the observers at rest in the "CMB frame". The "tick rate" of the "CMB temperature clock" depends on the rate of expansion of the universe, which is not constant.

 

[Dale]

In practice, in our universe, observers can compare their velocity to the CMB, right? So there is something like a universal reference frame.

In practice we can also compare our velocity to Mt Everest. The CMB is just a thing in the universe like any other. Velocities relative to the CMB are just as relative as velocities relative to Everest.

 

[256bits]

As @PeterDonis mentioned the CMB can be isotropic for an observer in a particular state of motion.
A Mt. Everest, would be an anisotropic condition of motion for all observers in any state of motion.
Doesn't that hamper the comparison?

 

[PeterDonis]

As @PeterDonis mentioned the CMB can be isotropic for an observer in a particular state of motion.
A Mt. Everest, would be an anisotropic condition of motion for all observers in any state of motion.
Doesn't that hamper the comparison?

No. You can adopt a frame in which Mt. Everest is at rest the same way you can adopt a frame in which the CMB is "at rest". Neither one is picked out by the laws of physics.

Also, even though the CMB is isotropic in the "CMB rest frame", other things are not. If you were sitting in a spaceship somewhere in the solar system, with your state of motion just right to see the CMB as isotropic, you would still have the Sun in one particular direction, not to mention the planets, nearby stars, and the Milky Way galaxy in general.

 

[256bits]

You can adopt a frame in which Mt. Everest is at rest the same way you can adopt a frame in which the CMB is "at rest". Neither one is picked out by the laws of physics.

That is the part I do not get.
The CMB comes from all directions, so how could it be at 'rest' in all directions regardless of the frame.

 

[PeterDonis]

The CMB comes from all directions, so how could it be at 'rest' in all directions regardless of the frame.

The CMB is not "at rest" in any frame; it's light, and light is never at rest.

An observer in one particular frame, the one we have been calling the "CMB rest frame", will see the CMB as isotropic--its temperature is the same in all directions. So the CMB is isotropic in that frame. But only in that frame; the CMB is certainly not isotropic in every frame.

 

[Ibix]

That is the part I do not get.
The CMB comes from all directions, so how could it be at 'rest' in all directions regardless of the frame.

The ideal FLRW spacetime is filled with matter (etc) at the same density everywhere. The frame where the CMB is isotropic is the frame that is at rest with respect to the matter around you. Reality is a bit messier because the tiny anisotropies of the CMB have grown a bit and local velocities of matter can vary somewhat from the isotropic CMB frame, but it's still a rest frame for local matter as long as you average over a large enough area.

It's much the same as your local Earth surface rest frame. It's important because of all the matter that is at rest in that frame, but it's not special in terms of any physical law.

 

[Orodruin]

That is the part I do not get.
The CMB comes from all directions, so how could it be at 'rest' in all directions regardless of the frame.

The CMB is a photon gas. The rest frame of a gas is the frame where the macroscopic momentum density of the gas is zero.

 

[256bits]

The CMB is a photon gas. The rest frame of a gas is the frame where the macroscopic momentum density of the gas is zero.

That's another way of putting it neatly.
Tks

 

[256bits]

thanks guys - you know who you are! :)

 

[vanhees71]

The CMB is not "at rest" in any frame; it's light, and light is never at rest.

An observer in one particular frame, the one we have been calling the "CMB rest frame", will see the CMB as isotropic--its temperature is the same in all directions. So the CMB is isotropic in that frame. But only in that frame; the CMB is certainly not isotropic in every frame.

The CMB is a equibrium distribution of em. radiation, and as such this situation defines a preferred reference frame, i.e., the rest frame of this "heat bath". For an observer at rest in this frame the CMB spectrum is a Planck spectrum with a isotropic temperature, i.e., no matter in which direction you look you always measure a Planck distribution with the same temperature. If you are moving with an arbitrary four-velocity $u$ relative to this frame this radiation is subject to the usual Doppler effect. Since photons are massless this implies that at any direction you again see a Planck spectrum but with a direction-dependent temperature, i.e., it's blue shifted if you look in the direction of $\vec{u}$ (i.e., the angle between $\vec{u}$ and $\vec{k}$ is $<\pi/2$ and a red shift otherwise. This refers to the dipole part of the expansion of the temperature field in terms of spherical harmonics and is usually subtracted first from the usual pictures of the CMBR to investigate the really interesting fluctuations of temperature with direction (with $\Delta T/T \mathcal{O}(10^{-5})$).

The usual coordinates to describe the large-scale-course-grained universe, which is assumed to be homogeneous and isotropic, the Friedmann-Lemaitre-Robertson-Walker metric, define the local rest frame of the CMBR heatbath for any observer at rest in this frame.

 

[S Holtom]

No more so than setting your coordinate system origin at the time and place Lincoln was shot, Charlie Bucket found his Golden Ticket, or the Greenwich medidian and the equator 2022 years ago.

In practice we can also compare our velocity to Mt Everest.

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. For specific events (including India slamming into Eurasia and making Everest), different observers can disagree on when it happened and even whether it happened (that event will forever be unobservable to some frames).

 

[S Holtom]

Not really, since its "tick rate" will not be the same as the "tick rate" of proper time for the observers at rest in the "CMB frame". The "tick rate" of the "CMB temperature clock" depends on the rate of expansion of the universe, which is not constant.

Do you mean it doesn't change in a linear way over time, or a uniform way across space?
If it's the former, then of course we can factor that into our calculations, and still have a universal clock.

If it's the latter...well, I guess that constrains the accuracy of this hypothetical clock.

 

[Orodruin]

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. For specific events (including India slamming into Eurasia and making Everest), different observers can disagree on when it happened and even whether it happened (that event will forever be unobservable to some frames).

They will agree on the local relative velocity to the CMB.

An event cannot be unobservable to an observer in one frame and observable to them in another frame. The causal structure of the spacetime is unaffected by the choice of coordinates.

 

[PeroK]

The point was, the CMB seems "special" in that anyone, anywhere in our universe can use it and agree on relative velocity.

There's an assumption in physics that the laws of physics should apply in any reference frame.

The CMB is not special in the sense that the laws of physics have to be written in relation to the CMB.

If you want to can choose a different frame. E.g the rest frame of the Earth's surface. The laws of physics may then be applied without reference to the velocity of the Earth relative to the CMB frame.

For example, in particle physics experiments at CERN, the theorists do not have to transform the experiment into the CMB frame, apply the laws of physics, then transform back to the CERN frame.

 

[vanhees71]

There's an assumption in physics that the laws of physics should apply in any reference frame.

The CMB is not special in the sense that the laws of physics have to be written in relation to the CMB.

If you want to can choose a different frame. E.g the rest frame of the Earth's surface. The laws of physics may then be applied without reference to the velocity of the Earth relative to the CMB frame.

For example, in particle physics experiments at CERN, the theorists do not have to transform the experiment into the CMB frame, apply the laws of physics, then transform back to the CERN frame.

Of course not, but nevertheless the CMBR defines a "preferred frame" in the sense that it is adapted to the physical situation at hand, i.e., an Hubble-expanding universe "filled" with thermal em. radiation. Of course you can describe anything in any frame you like, and if the CMBR doesn't play a significant role in the situation you consider, e.g., the motion of the planets in our solar system, it's much more convenient use the Sun's rest frame as a "preferred" frame for this situation.

 

[PeroK]

Perhaps every frame of reference is special in some sense!

 

[Dale]

The point was, the CMB seems "special" in that anyone, anywhere in our universe can use it and agree on relative velocity.

That actually is not true. In fact, I would say the opposite is true. If two distant observers each are at rest wrt Mt Everest then they will say they are at rest wrt each other*. If two distant observers each are at rest wrt the CMB then they will not say they are at rest wrt each other. So in the sense of your point Mt Everest is a more suitable universal reference than the CMB.

*Edit: even this statement depends on the choice of parallel transport. I am thinking of transporting within the spatial slices that are approximately flat to the best of our current measurements

 

[Ibix]

The point was, the CMB seems "special" in that anyone, anywhere in our universe can use it and agree on relative velocity.

It's a sensible choice for a standard local definition of "state of rest", just as the Earth's surface frame is a sensible choice for state of rest in everyday life. You would not get far trying to get off a speeding ticket by pointing out that you were traveling at less than 30mph with respect to other traffic, even though the frame is not specified on the speed limit signs.

In that sense, the CMB frame is a "special" frame but, critically, it's picked out by the distribution of matter, not the laws of physics. The laws of physics work in exactly the same way if you choose not to use the CMB frame as a standard of rest - there's no way to detect that you are at rest with respect to the CMB except to measure its temperature distribution. So it is not a "special" frame in the sense of physical law.

 

[vanhees71]

I thought we talk about local frames of local observers. Of course, different observers, being at rest in their local CMBR restframe, are not at rest relative to each other.

 

[Ibix]

I thought we talk about local frames of local observers.

Was wondering how long it would be before someone mentioned the ambiguity in the use of the word "frame" here.

 

[Vanadium 50]

The point was, the CMB seems "special" in that anyone, anywhere in our universe can use it and agree on relative velocity

It's not special. It's just really, really big.

 

[S Holtom]

An event cannot be unobservable to an observer in one frame and observable to them in another frame. The causal structure of the spacetime is unaffected by the choice of coordinates.

I said different observers though.
We can look at the edge of our observable universe and see events that will never be seen by an observer on the other edge.

 

[S Holtom]

If two distant observers each are at rest wrt Mt Everest then they will say they are at rest wrt each other

Well they can choose to. They can choose to use the Earth as the basis of a shared reference frame (as we obviously do every day).

If two distant observers each are at rest wrt the CMB then they will not say they are at rest wrt each other

Why's that?

 

[Ibix]

Why's that?

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

 

[S Holtom]

Ah of course

 

[PeterDonis]

Do you mean it doesn't change in a linear way over time

Yes.

or a uniform way across space?

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.

If it's the former, then of course we can factor that into our calculations

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 could, of course, use observations of variation in other physical processes with respect to the CMB "clock" to work out that the CMB "clock" tick rate was changing and by how much. But that is just another way of saying that we have a different clock to compare it to.

 

[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.