Doubt about the relativity of simultaneity

[Ideassimples]

TL;DR Summary

The cosmic microwave background questions the relativity of simultaneity.

(I hope my English is understood). Hello, I have a question regarding the relativity of simultaneity.

The mean temperature of the cosmic microwave background tells us how big the universe is with respect to the recombination epoch. If I now measure that the mean temperature of the cosmic microwave background is 3 Kelvin, and I know that at the time of recombination it was 3000 Kelvin, then I can deduce that the universe is now (3000/3 = 1000) 1000 times more larger than in the recombination era. From then until now the universe has been expanding to multiply by 1000 its size.

The mean temperature of the cosmic microwave background is the same for two observers who measure it simultaneously, regardless of their relative motion. Two observers with relative movement between them, by Doppler effect, may not agree on the temperature of the cosmic microwave background in a certain direction, but if they both make the measurements simultaneously, they will both measure the same mean temperature of the cosmic microwave background.

And this is problematic. Let me explain, let's imagine two radio telescopes with no relative motion between them, radio telescope 1 and radio telescope 2. Both radio telescopes can measure the mean temperature of the cosmic microwave background with great precision. Radio telescopes are turned on by hitting their switch with a beam of light.

Right in the center is a light source, with no relative motion relative to radio telescopes. The light source sends a beam of light to each radio telescope, hits the switch, turns them on. Both radio telescopes measure the mean temperature of the cosmic microwave background. It turns out that both radio telescopes get exactly the same result.

Observer A is not moving relative to the system. From the reference frame of observer A, the light rays reach both radio telescopes at the same time. Therefore observer A sees that both radio telescopes are turned on at the same time. Observer A is told that both radio telescopes measured exactly the same mean temperature of the cosmic microwave background. Since observer A saw that both radio telescopes measured the mean temperature of the cosmic microwave background at the same time, he understands that the data agrees with his observation.

Observer B does move relative to the system. From the reference frame of observer B, first a ray of light arrives at radio telescope 1, and then a ray of light arrives at radio telescope 2. Therefore observer B sees that radio telescope 1 turns on first and radio telescope 2 later. Observer B is told that both radio telescopes measured exactly the same mean temperature of the cosmic microwave background. Observer B understands that there is a conflict between his observations and the measurements from the radio telescopes.

Since from the reference frame of observer B, radio telescope 1 is turned on first and then radio telescope 2, observer B expects that the measurement of the mean temperature of the cosmic microwave background of radio telescope 1 is higher than that of radio telescope 2. Without However this does not happen, both measures are identical.

Then observer B reaches the following conclusion:
-Or for a certain period of time, from its reference frame, the universe stopped expanding.
-Or the simultaneity is not relative, but absolute.

What do you think?

 

[phinds]

Observer B has drawn a frame dependent conclusion from frame independent data. When he is told that they got the same measurement, he should have calculated whether or not they made the measurements at the same time in THEIR reference frames and of course the answer is that they did so of course they got the same measurement.

 

[Ibix]

If observer B chooses a coordinate system in which the two telescopes are not activated simultaneously then he has chosen a coordinate system in which the temperature of the CMB is not the same at all points at a given time. So he should not be surprised that telescopes measuring at different times can measure the same temperature. In fact, in such a system the CMB isn't isotropic and doesn't have a single defined temperature, so even describing what the telescopes are doing is more complicated in this coordinate system.

The usual comoving coordinate system, where the CMB is isotropic is a frame like the Earth's surface frame in every day life. It picks out a notion of simultaneity in the same way that the Earth's surface frame picks out a notion of "ar rest". But it has no fundamental significance. It's just convenient.

 

[Dale]

Summary:: The cosmic microwave background questions the relativity of simultaneity.

The mean temperature of the cosmic microwave background is the same for two observers who measure it simultaneously, regardless of their relative motion.

I don’t think this is true.

You can transform from your actual measurement to get the temperature in the local rest frame of the CMB, but that is not the same the mean temperature that you actually measure.

Since both observers have to transform their measurements to the same frame I fail to see the problem.

Then observer B reaches the following conclusion:
-Or for a certain period of time, from its reference frame, the universe stopped expanding.
-Or the simultaneity is not relative, but absolute.

-Or the universe is not isotropic in B’s frame, which is well known

 

[Ideassimples]

Observer B has drawn a frame dependent conclusion from frame independent data. When he is told that they got the same measurement, he should have calculated whether or not they made the measurements at the same time in THEIR reference frames and of course the answer is that they did so of course they got the same measurement.

Yes, observer B understands that both radio telescopes obtain the same result because from THEIR reference systems (radio telescope reference systems) they make the measurements at the same time.

But that both radio telescopes get exactly the same result indicates that the universe was exactly as big and old when both measurements were made.

If simultaneity is relative, observer B is entitled to say that radio telescope 1 made a measurement first, and radio telescope 2 did a measurement later, even though he understands why both radio telescopes obtain the same result. But that would mean that from the reference frame of observer B, for a certain period of time the universe did not expand.

Is it correct to interpret that two exactly equal measurements of the mean temperature of the cosmic microwave background may not be simultaneous for an observer? Can the universe be the same size for a given observer at two different times?

Is it correct to interpret that two different measurements of the mean temperature of the cosmic microwave background can be simultaneous for an observer? Can the universe have two different sizes for a given observer at the same time?

If we start from the postulate that the entire universe is just as old, then not all reference frames are valid for determining whether two events are simultaneous.

If we understand that two events are simultaneous only if at the moment they occur the universe is the same size, then the only frame of reference that simultaneously sees two events that actually occur at the same time is the one that sees the same temperature of the cosmic background microwave in all directions.

Special relativity does not distinguish between two events that correspond to the same size / age of the universe and two events that correspond to different size / age of the universe.

But I interpret that this does not mean that simultaneity is relative, but that special relativity does not distinguish between simultaneous and non-simultaneous events if they are not causally connected.

That is my position, at least it is what I understand so far, waiting for what they tell me. It is not a technical question, it is a philosophical question, of interpretation, or so I think.

 

[PeterDonis]

that would mean that from the reference frame of observer B, for a certain period of time the universe did not expand

No, it doesn't; it just means that, at a given time in B's frame, different parts of the universe have expanded to different extents. Surfaces of constant time in B's frame are not surfaces of constant scale factor of expansion.

Note, btw, that you are implicitly assuming that "B's frame" is something like an inertial frame in which B is at rest, as it would be in SR. But the spacetime of our universe is curved, not flat, so there are no global inertial frames as there are in SR; there are only local inertial frames. So what you are calling "B's frame" is not well-defined except for a reasonably small region of spacetime around B. This in itself doesn't invalidate your thought experiment; you just need to stipulate that the two radio telescopes are close enough together that they both fit inside the same reasonably small region of spacetime. But it's good to be aware of the limitations of what you are doing.

 

[Ideassimples]

If observer B chooses a coordinate system in which the two telescopes are not activated simultaneously then he has chosen a coordinate system in which the temperature of the CMB is not the same at all points at a given time. So he should not be surprised that telescopes measuring at different times can measure the same temperature.

Observer B need not be surprised by the measurement data, he simply interprets it. I start from the postulate that the whole universe is just as old, from this it follows that the temperature of the CMB is the same everywhere at any given time. However, observer B sees that the temperature of the CMB is not the same everywhere at any given time. Then observer B starts to think. He interprets that although from his reference system he sees two events as non-simultaneous, from the reference system that measures the same CMB temperature everywhere at the same time, these events could be simultaneous.

If we start from the postulate that the entire universe is just as old, then only the reference system that sees the same temperature of the CMB everywhere at once sees two simultaneous events corresponding to the same age / size of the universe.

Therefore the simultaneity would not be relative. Simultaneity would be absolute, even if special relativity does not distinguish between two simultaneous events and two non-simultaneous events that are not causally connected.

 

[Dale]

But that would mean that from the reference frame of observer B, for a certain period of time the universe did not expand.

No. That is not the only explanation.

If we start from the postulate that the entire universe is just as old, then only the reference system that sees the same temperature of the CMB everywhere at once sees two simultaneous events corresponding to the same age / size of the universe.

Yes. That is correct. But it is also an assumption, one that is not required. General relativity works perfectly fine with coordinates that violate this assumption

 

[Ideassimples]

I don’t think this is true.

You can transform from your actual measurement to get the temperature in the local rest frame of the CMB, but that is not the same the mean temperature that you actually measure.

Since both observers have to transform their measurements to the same frame I fail to see the problem.

I believe that it is true. If we start from the postulate that the entire universe is just as old at any given time, the only difference between measurements is due to the Doppler effect.
An observer can see the temperature of the CMB more or less hot in a certain direction by its relative motion, but I understand that the mean temperature of the cosmic microwave background is the same at any given time, everywhere.

-Or the universe is not isotropic in B’s frame, which is well known

If we start from the postulate that the whole universe is just as old then saying that the universe is not isotropic in the frame of B is wrong. It would have to be said that from the reference frame of B the universe does not look isotropic, although it is.

 

[Dale]

I believe that it is true.

Do you have a reference that agrees with your claim that the mean Doppler shift of the CMB is invariant?

If we start from the postulate that the whole universe is just as old

Yes, but that assumption is kind of circular here. Yes, if you assume that only one simultaneity convention is valid then simultaneity is not relative. That assumption is not part of either SR or GR and it is not needed to explain any data.

 

[Ideassimples]

No, it doesn't; it just means that, at a given time in B's frame, different parts of the universe have expanded to different extents. Surfaces of constant time in B's frame are not surfaces of constant scale factor of expansion.

If the mean temperature of the cosmic microwave background is the same, the size of the universe is the same. I understand that if different parts of the universe expanded to different degrees, then some parts expanded and others contracted, which cannot have happened.

Note, btw, that you are implicitly assuming that "B's frame" is something like an inertial frame in which B is at rest, as it would be in SR. But the spacetime of our universe is curved, not flat, so there are no global inertial frames as there are in SR; there are only local inertial frames. So what you are calling "B's frame" is not well-defined except for a reasonably small region of spacetime around B. This in itself doesn't invalidate your thought experiment; you just need to stipulate that the two radio telescopes are close enough together that they both fit inside the same reasonably small region of spacetime. But it's good to be aware of the limitations of what you are doing.

It is an interesting nuance but I understand that it does not affect the question we are dealing with.

 

[Ideassimples]

Yes. That is correct. But it is also an assumption, one that is not required. General relativity works perfectly fine with coordinates that violate this assumption

The postulate that the entire universe is just as old seems difficult to question. Obviously general relativity does not need this assumption.

 

[PeterDonis]

If the mean temperature of the cosmic microwave background is the same, the size of the universe is the same.

Yes. But in B's frame, the mean temperature of the CMB is not the same everywhere at a given instant of time in that frame.

I understand that if different parts of the universe expanded to different degrees, then some parts expanded and others contracted

That is not correct. In B's frame, at a given instant of time in that frame, the scale factor of expansion is different in different places because the expansion is not isotropic in that frame; the rate of expansion is different in different places (and changes with time at different rates in different places).

The postulate that the entire universe is just as old seems difficult to question.

You are misunderstanding what that postulate does. It does not tell you anything invariant about the universe. It only tells you that you have picked a particular frame--in your scenario this is A's frame.

 

[Dale]

The postulate that the entire universe is just as old seems difficult to question.

No. It is easy to question.

The actual assumption that is made in the derivation of our cosmological models is that there exists a coordinate system where the universe is isotropic and homogenous. This is a far weaker assumption than yours but this assumption explains the data and is compatible with SR and GR.

 

[Ideassimples]

Do you have a reference that agrees with your claim that the mean Doppler shift of the CMB is invariant?

We agree that there is a frame of reference in which the same temperature of the cosmic microwave background is seen in all directions. If an observer sees different temperatures of the CMB in different directions, it is because it is moving relative to the first reference frame. I understand that the mean CMB temperature must be the same in all reference systems.

Yes, but that assumption is kind of circular here. Yes, if you assume that only one simultaneity convention is valid then simultaneity is not relative. That assumption is not part of either SR or GR and it is not needed to explain any data.

Yes, it is not necessary for either SR or GR, I agree. However I understand that it is difficult to question that the entire universe is just as old.

 

[Dale]

I understand that the mean CMB temperature must be the same in all reference systems.

Please be aware that personal speculation is not permitted on PF. If a reference is requested for support of a claim then either the claimant must produce such a reference or cease making the claim.

However I understand that it is difficult to question that the entire universe is just as old.

See post 14. This assumption is easy to question

 

[Ideassimples]

Yes. But in B's frame, the mean temperature of the CMB is not the same everywhere at a given instant of time in that frame.

When an observer measures the mean temperature of the CMB he only gets a number.

That is not correct. In B's frame, at a given instant of time in that frame, the scale factor of expansion is different in different places because the expansion is not isotropic in that frame; the rate of expansion is different in different places (and changes with time at different rates in different places).

Even so. If the mean temperature of the CMB did not change, the universe did not expand, or it expanded and contracted in different regions, which could not have happened. In any case, it is an irrelevant question for the subject at hand.

You are misunderstanding what that postulate does. It does not tell you anything invariant about the universe. It only tells you that you have picked a particular frame--in your scenario this is A's frame.

Sure, a particular frame of reference is being chosen. If the postulate that the entire universe is equally old is correct, then there is only one reference frame that sees two simultaneous events corresponding to the same size / age of the universe.

 

[Ideassimples]

No. It is easy to question.

The actual assumption that is made in the derivation of our cosmological models is that there exists a coordinate system where the universe is isotropic and homogenous. This is a far weaker assumption than yours but this assumption explains the data and is compatible with SR and GR.

At no point do I question that the universe is isotropic and homogeneous.

 

[Ideassimples]

Please be aware that personal speculation is not permitted on PF. If a reference is requested for support of a claim then either the claimant must produce such a reference or cease making the claim.

See post 14. This assumption is easy to question

I thought this was clear since Penzias and Wilson discovered the CMB in 1965.

 

[Dale]

I thought this was clear since Penzias and Wilson discovered the CMB in 1965.

That isn’t the claim being objected to (but you would still need to provide that evidence if it were). This is the claim I dispute:

Two observers with relative movement between them, by Doppler effect, may not agree on the temperature of the cosmic microwave background in a certain direction, but if they both make the measurements simultaneously, they will both measure the same mean temperature of the cosmic microwave background.

I do not believe that the mean CMB temperature measured by two observers in relative motion is the same. Do you have a source to support that specific claim?

At no point do I question that the universe is isotropic and homogeneous.

Again, that is not the necessary assumption. The necessary assumption is merely that there exists a coordinate system where the universe is homogenous and isotropic.

 

[Ideassimples]

That isn’t the claim being objected to (but you would still need to provide that evidence if it were). This is the claim I dispute:I do not believe that the mean CMB temperature measured by two observers in relative motion is the same. Do you have a source to support that specific claim?

Again, that is not the necessary assumption. The necessary assumption is merely that there exists a coordinate system where the universe is homogenous and isotropic.

It is as simple as understanding this: (x / y) * (y / x) = 1
If you measure the CMB above the mean in a certain direction, it gives below the mean in the same proportion in the opposite direction.

 

[PeterDonis]

When an observer measures the mean temperature of the CMB he only gets a number.

He can only measure the temperature of the CMB at his location. He cannot measure it at other locations.

In A's frame, observers at different locations who measure the temperature of the CMB at their location at the same coordinate time in that frame get the same temperature.

In B's frame, observers at different locations who measure the temperature of the CMB at their location at hte same coordinate time in that frame get different temperatures.

If the postulate that the entire universe is equally old is correct

That postulate can only be true in one frame. "The age of the universe" at different spatial locations is not an invariant; it depends on your choice of frame. When cosmologists talk about "the age of the universe", they are talking about the age in a particular frame (which in your scenario corresponds to A's frame).

At no point do I question that the universe is isotropic and homogeneous.

But do you understand what that statement means? Based on your posts, I strongly suspect you don't.

If you measure the CMB above the mean in a certain direction, it gives below the mean in the same proportion in the opposite direction.

Yes, and that is what observers at rest in B's frame measure. But observers at rest in A's frame do not; they measure the same CMB temperature in all directions.

 

[PeterDonis]

The necessary assumption is merely that there exists a coordinate system where the universe is homogenous and isotropic.

Actually, it is possible to give an invariant meaning to "homogeneous" and "isotropic". But there will still only be one frame in which the homogeneity and isotropy are directly observable. I'm not sure the OP understands that.

 

[Dale]

Actually, it is possible to give an invariant meaning to "homogeneous" and "isotropic". But there will still only be one frame in which the homogeneity and isotropy are directly observable. I'm not sure the OP understands that.

Yes. I debated expressing it in terms of Killing vectors (I assume that is what you mean), but decided that the coordinate-based expression was likely to be better understood.

 

[PeterDonis]

I debated expressing it in terms of Killing vectors (I assume that is what you mean)

Yes.

 

[Dale]

It is as simple as understanding this: (x / y) * (y / x) = 1
If you measure the CMB above the mean in a certain direction, it gives below the mean in the same proportion in the opposite direction.

First, that isn’t a professional scientific reference, and second that isn’t the mean. The mean would be $$\frac{\frac{x}{y}+\frac{y}{x}}{2}\ne 1$$

 

[Ideassimples]

First, that isn’t a professional scientific reference, and second that isn’t the mean. The mean would be $$\frac{\frac{x}{y}+\frac{y}{x}}{2}\ne 1$$

I think you are joking, the average is:
[f*(x/y)+f*(y/x)]/2=f

 

[Dale]

I think you are joking, the average is:
[f*(x/y)+f*(y/x)]/2=f

Try $f=1$, $x=5$, and $y=1$. You get $2.6\ne 1$

 

[Ideassimples]

You're right! I don't even know what I'm doing anymore.

 

[Dale]

You're right! I don't even know what I'm doing anymore.

It is OK, it is easy to get turned around in discussions like these. Here is my interpretation of the issue you raise.

1) To get a single temperature at a point (instead of a Doppler shifted range of temperatures) it is necessary to transform into the frame where the CMB is isotropic and homogenous. (Or something mathematically equivalent)

2) If you do so simultaneously at multiple points in that frame then the results will be the same (by homogeneity)

3) A different frame will disagree that the measurements were simultaneous, but it will also disagree that the universe is isotropic and homogenous.

4) Both frames will be consistent with the data.

 

[jartsa]

Since from the reference frame of observer B, radio telescope 1 is turned on first and then radio telescope 2, observer B expects that the measurement of the mean temperature of the cosmic microwave background of radio telescope 1 is higher than that of radio telescope 2. Without However this does not happen, both measures are identical.

So according to B the other beam travels for a very very very very long time, and then the beam is in a universe that is not very very old.

Is this perhaps a correct rephrasing of the problem?(Let's say B travels extremely fast relative to the telescopes, and also let's say the telescopes are not so far apart that expansion of universe matters.)

 

[PeterDonis]

the other beam

What "other beam" are you talking about?

The OP's scenario doesn't include any "beams". The radio telescopes are measuring the CMB at their location; they're not sending or receiving "beams".

 

[jartsa]

What "other beam" are you talking about?

The OP's scenario doesn't include any "beams". The radio telescopes are measuring the CMB at their location; they're not sending or receiving "beams".

OP said: "Right in the center is a light source, with no relative motion relative to radio telescopes. The light source sends a beam of light to each radio telescope, hits the switch, turns them on."

 

[PeterDonis]

OP said: "Right in the center is a light source, with no relative motion relative to radio telescopes. The light source sends a beam of light to each radio telescope, hits the switch, turns them on."

Ah, ok. But these "beams" have nothing to do with the actual measurements the radio telescopes are making. They're just a way of specifying in what frame the measurements made by the radio telescopes are simultaneous (the A frame, in which both telescopes are at rest).

Everyone appears to agree that in the B frame, the measurements are not simultaneous; explaining how that comes about is not the issue. The issue is how an observer at rest in the B frame explains the fact that both measurements still give the same result for the CMB temperature, which means that the "age of the universe" under the usual definition of that term (which is not the same as "coordinate time elapsed in the B frame") is the same at both measurements, even though they are not simultaneous in the B frame.