Thoughts and questions about the CMBR.

[Endervhar]

Recently it occurred to me that my mental image of the CMB radiation, gleaned from a range of popular science books, was probably completely wrong. I set about some thinking. The following notes outline my thoughts so far, and I would appreciate the comments of others more knowledgeable than I.

Thinking about the CMB

What is the cosmic microwave background? Put simply; it is the remnant radiation from the Big Bang.

The theory is that the Universe, up to almost 400,000 years after the Big Bang, was so hot and dense that it was effectively a plasma within which photons were prevented from traveling any distance, light could not travel through it, so it was opaque.

At a little less than 400,000 years (some references give this as 300,000 years), at what is referred to as the photon decoupling event (also known as the period of last scattering), the Universe had cooled sufficiently for protons and electrons to combine into atoms. This changed the state of the Universe such that photons were able to move freely through the it. It became transparent. These photons have been traveling ever since, but are no longer in the wavelengths of visible light. There energy has decreased, and, correspondingly, their wavelength has increased, so that they now appear as microwaves, with a temperature of about three degrees above absolute zero (almost 3K).

Some questions must arise from this, for instance:
1. Where is the radiation coming from?
2. Where is it going?
3. It is traveling at the speed of light, so why had it not passed us long ago?
4. If its origin is in a small spot that must be central to the Universe, does this give a preferred direction to the Universe?

Attempting to answer these questions challenges the lay person's intuitive image of the Big Bang, the expanding Universe and the CMB radiation.

1. Where is the radiation coming from? This implies another question: Where did the Big Bang happen? The answer to this is that it happened everywhere in the Universe. At the first instant, the Big Bang was the Universe; the Universe was the Big Bang. There is no part of the Universe today, nor will there ever be, however long it continues to expand, in which the Big Bang did not occur. The Big Bang was everywhere; so the radiation must be coming from everywhere.

2. Where is it going? If it originated everywhere in the Universe, it follows that it must be going everywhere in the Universe. It is moving at the speed of light from every point in the Universe to every other point in the Universe, without exception.

3. It is traveling at the speed of light, so why had it not passed us long ago? To some extent, this question has already been answered, but if by "us" we mean the point in the Universe at which the Earth is situated, we must accept that it has been passing us ever since the original radiation was able to move freely through the Universe, and it will continue to pass us, and every other point in the Universe, as long as any energy remains in the waves.

4. If its origin is in a small spot that must be central to the Universe, does this give a preferred direction to the Universe? As mentioned earlier, we have to abandon the image of the Big Bang happening at the centre of the Universe, and the radiation emanating from there and moving outward. Viewed from the Earth, the radiation would be seen to be coming from every direction. This does not mean that the Earth is at the centre of the Universe, because, if that image were right, the radiation would appear to be moving away from Earth, and would, therefore, not be visible. Also, the Earth's position is not special. Whatever viewpoint in the Universe an observation might be made from, the radiation would still be observed to be coming from every direction towards that point. Therefore, no preferred direction can be identified by observation of the CMB radiation.

I said that radiation that is receding would not be visible, yet we are all familiar with doing something like shining a powerful flashlight into the sky and seeing a beam of light that is obviously moving away. This is due to the fact that some of the light is reflected back from water molecules, dust particles etc in the atmosphere. The clearer the air, the less visible would be the beam of light. In space, we would not see it at all unless it were shining straight towards our eyes. For this reason, only the CMB radiation moving directly towards a detector can be detected.

One might also ask if the CMB, because it fills the Universe, can be regarded as a "fixed" reference against which motion in the Universe can be measured. If this were the case, motion would no longer have to be regarded as solely relative. Absolute motion could be demonstrated.

The first thing to recognise is that the CMB is electromagnetic radiation, and as such it is observed as moving at the speed of light, irrespective of the position and (relative) motion of the observer. It seems unlikely, therefore, that the CMB could be regarded as an absolute frame of reference, any more than can any other electromagnetic radiation, including visible light.

 

[Drakkith]

I'm not an expert, but that looks like a pretty good overview of the CMB to me.

 

[Mordred]

I certainly cannot see anything wrong in that overview as well

 

[Bandersnatch]

Looks good, except for the last paragraph. It is perfectly possible to determine the frame of reference "at rest" with respect to the CMB.
It's just that instead of trying to measure the variation in speed of the incoming radiation, which as you've correctly noted is always c, we look for doppler shift "spots" in the otherwise uniform spectrum of CMB. There will be a blueshifted spot in the direction the observer is moving w/r to the CMB-rest frame, and a corresponding redshifted spot in the opposite direction.
Our current speed in that frame of reference has been measured to be around 630 km/s.

 

[Endervhar]

Thanks folks.

My apologies to the Mods for having posted in the wrong place. I would blame senile dementia, but I can't remember what that is. :)

Bandersnatch, I see what you are saying; but would I be right in thinking that this doesn't establish absolute motion?

 

[Bandersnatch]

You are right. The frame of reference at rest with respect to the CMB is by no means privileged from the point of view of relativity.
It's a special frame of reference in the same sense that e.g. the geocentric one is. I.e. "something" is at rest in both of them - the Earth in one, everything in the early universe in the other.

 

[Mordred]

Is the CMB usually modeled as a early De Sitter?

 

[Chronos]

The CMB is well accommodated by a Friedman model - http://cds.cern.ch/record/407395/files/9911177.pdf

 

[Mordred]

Thanks Chronos Ill have to look at the paper tomorrow. The link isn't loading on my phone atm

 

[Mordred]

Got the paper to load thanks again its definitely a good read

 

[Endervhar]

Can we assign a rest frame to the CMBR?

To a non-scientist there does seem to be a circular argument.

We cannot assign a rest frame to a photon. The CMBR is composed of photons; therefore it cannot be assigned a rest frame.
However, an observer who is moving at sufficient speed relative to the CMBR will see its spectrum blueshifted in the direction of motion, and redshifted in the other direction.
Thus, an observer can claim to be at rest relative to the CMBR if the radiation is measured as being isotropic.
Because an observer can be judged to be at rest relative to the CMBR, relativity holds that it must be equally valid to say that the CMBR is at rest relative to the observer.

How does this differ from assigning a rest frame to the CMBR?

 

[Drakkith]

Because you can assign a rest frame that is based on the redshift or blueshift of the cmb relative to yourself. You cannot assign a rest frame to a single photon.

 

[Endervhar]

Thanks Drakkith.

That's roughly where I started; but then I reasoned that if I were dealing with a beam of light rather than the CMBR; although I would not be able to tell which way I was traveling relative to the direction of the light by measuring relative speeds, I could tell by the Doppler effect.

My next questions were:
Why can I not do that with a single photon?
What is the smallest number of photons with which I could measure the Doppler effect?

The only answer I could think of was that in order to be measured, a photon must be "destroyed". Therefore, in order to make a measurement that has any ongoing relevance, there must be more photons than would be observed in taking the measurement.

Deciding that a single photon was Doppler shifted would be a bit pointless, even if I could do it, because it would no longer exist

Am I on the right track?

 

[Drakkith]

My next questions were:
Why can I not do that with a single photon?

You can assign a reference frame to an observer based on the measured frequency of the photon, but you cannot assign an inertial frame of reference to the photon itself. It just isn't possible. An inertial frame is one where you aren't accelerating and if you have one you will measure all light as moving at c. Trying to use c as your velocity in SR math leads to nonsensical results because light ALWAYS travels at c in a vacuum when measured from an inertial frame of reference.

What is the smallest number of photons with which I could measure the Doppler effect?

If you knew the frequency of the emitting source beforehand, as little as one. If not, then two. One to establish the initial frequency, and one to compare where you are now. (This ignores a few practical considerations, but I believe it is essentially correct)

The only answer I could think of was that in order to be measured, a photon must be "destroyed". Therefore, in order to make a measurement that has any ongoing relevance, there must be more photons than would be observed in taking the measurement.

Deciding that a single photon was Doppler shifted would be a bit pointless, even if I could do it, because it would no longer exist

Am I on the right track?

I'm not sure what you mean. Let's say you are traveling at a certain velocity relative to me. I shoot a photon and you detect it and measure its frequency. Then you accelerate for 10 seconds and I shoot another photon at you. This photon arrives after you have stopped accelerating. You can measure the frequency of the photon and find your change in velocity.

The nature of detecting and measuring photons means that we very rarely work with single photons, so in reality it would be more than one.

 

[Endervhar]

you cannot assign an inertial frame of reference to the photon itself. It just isn't possible... An inertial frame is one where you aren't accelerating and if you have one you will measure all light as moving at c.

Eureka (?)

Could be the missing bit!

I reasoned: Two things are in the same F of R if they are stationary relative to each other. Two photons would be stationary relative to each other, so why are they not in the same F of R?

What I had not considered was that neither could measure the other as traveling at c.

Does that deserve a "eureka", or am I still off track?

 

[Drakkith]

Eureka (?)

Could be the missing bit!

I reasoned: Two things are in the same F of R if they are stationary relative to each other. Two photons would be stationary relative to each other, so why are they not in the same F of R?

What I had not considered was that neither could measure the other as traveling at c.

Does that deserve a "eureka", or am I still off track?

It's more than that. See the following.

From wiki: http://en.wikipedia.org/wiki/Inertial_frame_of_reference

In physics, an inertial frame of reference (also inertial reference frame or inertial frame or Galilean reference frame) is a frame of reference that describes time and space homogeneously, isotropically, and in a time-independent manner.[1]

All inertial frames are in a state of constant, rectilinear motion with respect to one another; they are not accelerating in the sense that an accelerometer at rest in one would detect zero acceleration. Measurements in one inertial frame can be converted to measurements in another by a simple transformation (the Galilean transformation in Newtonian physics and the Lorentz transformation in special relativity). In general relativity, in any region small enough for the curvature of spacetime to be negligible, one can find a set of inertial frames that approximately describe that region.[2][3]

Einstein's theory of special relativity, like Newtonian mechanics, assumes the equivalence of all inertial reference frames, but makes an additional assumption, foreign to Newtonian mechanics, namely, that in free space light always is propagated with the speed of light c₀, a defined value independent of its direction of propagation and its frequency, and also independent of the state of motion of the emitting body. This second assumption has been verified experimentally and leads to counter-intuitive deductions including:

Note that you cannot transform measurements from a frame which is moving at c. Such a thing is not possible and calculations using c as the velocity end up giving us nonsensical results. It's not really that the photon can't measure another photon, it's that the concept of a photon measuring anything at all makes no sense. Heck, talking about what the photon may be doing between emission and absorption doesn't even make any sense. None of our laws that we use to govern the movement of objects at a velocity below c apply. Photons are utterly different than anything else in the universe and trying to apply normal laws to them results in nonsensical results such as "time not passing for a photon" and "photons traveling no distance". Obviously they do travel through space, and the only reason we get these weird results is because we try to apply rules for massive objects to them. It doesn't work and will only confuse you if you try to.

 

[Endervhar]

Note that you cannot transform measurements from a frame which is moving at c.

Just as I think I'm getting the hang of things, something throws a spanner in the works!

I'm confused by the concept of "a frame which is moving at c."

 

[Drakkith]

Just as I think I'm getting the hang of things, something throws a spanner in the works!

I'm confused by the concept of "a frame which is moving at c."

From my point of view a car's frame of reference is moving at 60 mph. I can do calculations to transform my frame to theirs and back again and everything we see will make sense. We will both agree that physics hasn't changed just because one of us is moving relative to the other. Attempting to do the same thing to a frame which is moving at c gives us nonsense. It cannot be done. There is no such thing as a frame which is moving at c. To my knowledge at least.

 

[marcus]

Endervhar the way this discussion is going it seems to me (I could be wrong of course) that you have the mental image of bolting a "frame of reference" onto the CMB. Of some how "attaching" a reference from to something that is moving. That's not such a helpful idea, I think.

The CMB simply gives us a criterion of rest
so we can say what it means for an observer to be at rest
and that observer could have a reference frame associated with him.

But neither he nor his reference frame would be attached to the CMB.
To me the idea of attaching a frame to a bunch of moving light seems confusing a a bit wacko. It is not what I mean, or I think others mean, when we talk about observers at CMB rest.

CMB rest means the TEMPERATURE of the CMB light is the same (approximately) in all directions.

CMB is a thermal glow, so it has a temperature. and it happens that if you move towards a glow it raises the perceived temperature.

The solar system is moving about 1/10 of one percent of speed of light in the direction of constellation Leo.

So the perceived temperature of the CMB is about 1/10 of one percent HOTTER in that direction. we see a hotspot in the CMB sky, surrounding the Leo constellation.

If you compensate all the data for that motion then the hotspot goes away and it is AS IF your data had been collected by an observer who is at rest (at CMB rest according to the criterion).

Just don't think of bolting a frame onto some moving light---focus mentally on the criterion of rest itself---and maybe things will clear up.

 

[Endervhar]

There is no such thing as a frame which is moving at c.

It's better than I thought! I was just approaching the point where it seemed that a F of R moving at c was not on, when you mentioned "that you cannot transform measurements from a frame which is moving at c." I misinterpreted that as saying that such a frame was possible.

 

[Endervhar]

CMB rest means the TEMPERATURE of the CMB light is the same (approximately) in all directions.

Given that; would it make any sense to say that the reference frame of the CMB was about 2.7K, or would that be the reference frame of the observer, relative to the CMB?

Could be I'm just tying myself in unnecessary knots!

 

[Drakkith]

Given that; would it make any sense to say that the reference frame of the CMB was about 2.7K, or would that be the reference frame of the observer, relative to the CMB?

Could be I'm just tying myself in unnecessary knots!

Technically I think it would be the frame of an observer that is measuring the temperature of the CMB to be approximately 2.7k. However, you will see times where something is compared to the CMB frame, which I think just means that they compare a frame to the one where the CMB is 2.7k. If you stick to making frames have a "real" observer, IE an observer that has mass, such as a person or a proton then I think you will be fine. Trying to give the CMB a frame may be confusing because it is made of photons, but if you just make the frame from the point of view from a hypothetical observer instead it should make sense.

Note that the CMB is not special in this way of doing things. I can come up with a hypothetical observer for the center of mass for the solar system. That doesn't mean the actual center of mass is doing anything, it just means that I am using an observer that is following the center of mass.

Does that make sense?

 

[Endervhar]

Does that make sense?

I think so but it may take a while to percolate.

If the frame from the neutrino background radiation is confirmed, does that mean that there will be a second frame at 1.95K; or does it not work like that?

 

[Mordred]

I'll let those more knowledgeable than I answer your question on a neutrino thermal frame of reference. I would say yes but I am no authority lol. Anyways found a related paper on CNB thought you may enjoy it.

http://arxiv.org/abs/1212.4855

 

[Drakkith]

I think so but it may take a while to percolate.

If the frame from the neutrino background radiation is confirmed, does that mean that there will be a second frame at 1.95K; or does it not work like that?

I believe that's correct.

 

[marcus]

Given that; would it make any sense to say that the reference frame of the CMB was about 2.7K, or would that be the reference frame of the observer, relative to the CMB?

Could be I'm just tying myself in unnecessary knots!

You may be creating unnecessary mental knots, as you say. I don't think anything is gained by attributing a temperature to an observer.

Do you understand how light coming from a hot or warm object can have a temperature? That's very important to understanding the CMB.
Corresponding to every temperature there is a characteristic mix of wavelengths given off by a black body (or pretty much any rough/dull nondescript surface) at that temperature. So by analyzing the light you can determine the temperature that it is characteristic of.

An observer who is AT REST RELATIVE TO CMB will see the CMB having approximately the same 2.7 K temperature in every direction (with only very tiny fluctuations that are like 1/1000 of one percent).

If there is some chosen reference frame of xyz coordinates, it belongs to the observer.
If there is a temperature, it belongs to the the CMB light which the observer sees.
My advice would be to keep trying to formulate your thoughts as simply and concretely as possible, and this apparent temporary confusion will just blow over.