[Eternal Student]

Thanks @yor_on
  I should probably be getting on with something useful like washing my dishes and doing the laundry but I spend some time reading or writing some stuff in here and hoping the housework will do itself.

Best wishes to you.

[Halc]

There is a local CMB frame at every point in the universe, so there are a lot of CMB frames.

OK, that's a different usage of the term than my usage of it. I think perhaps yours is used at least as often as mine, and neither is 'wrong'.

The coordinate system I am referencing is not inertial and foliates, as I said, most of the entire universe. This coordinate system (the ordering of almost all events) can be determined independently by any number of observers despite no common reference for the origin of spatial coordinates or the current time, the latter of which is dependent on a given observer's relative depth of gravitational field.

If the real universe in which we find ourselves was an FRW universe,

I can think of few alternatives that are not FLRW solutions, including all the viable interpretations that claim some kind of preferred coordinate system.

then the set of CMB frames at all points and times would cover the entirety of spacetime.

No they wouldn't. At the spacetime events that are not ordered by the comoving coordinate system, there is no CMB frame defined. And even if they did collectively cover all events, no one CMB frame defines universal ordering, so they're quite irrelevant to the task. Any pair of CMB frames might order events A and B differently, so they cannot be used to define any sort of absolute ordering.

However, the real universe is not an exact match for the cosmological model that is an FRW universe (it's lumpy with high density regions like stars and planets, rather than a homogeneous cosmological fluid).

Local variations don't contradict the FLRW models. It is a model of large scale structure, not of details.

If you (Halc) have some spare minutes then I'd like to hear what you had in mind as a point or region of spacetime where a CMB frame cannot be identified.

Beyond the event horizon of a black hole for starters. Despite relativity theory having no trouble describing physics at such regions (it's still locally Minkowskian, so the principle of relativity still applies, and therefore you can't tell when you cross), any absolute interpretation is forced to deny even the existence of such events. This is a problem, since I pass through a coordinate singularity all the time without ill effects. It's just an abstract singularity, not a physical one.  Oh yes, a physical one is not abstract, and physics falls apart there, and one does not observe.

If you suggest points in the vicinity of a Schwarzschild black hole then you know what I'm going to say next -  can you really say that General Relativity has "no trouble with such spaces".  Where a space is geodesically incomplete then I'll agree that there can be some "directions" from which no radiation can be received by an observer

That would be weird physics.  If I scatter fireflies all around me as we all pass into a black hole, I will continue to see all of them in every direction. There is no direction where they become undetectable. As I said, I will not be able to tell that something new has happened. I'm assuming a large black hole, because just like on Earth, there are tidal forces that are measurably different than those in spacetime that is not flat at non-local scales.

(but a geodesically incomplete space is plenty of trouble for GR in my opinion).

Not sure what that is.

If we consider a point in the vicinity of a less extreme gravitational source, the CMBR may be impossible to observe isotropically in intensity

Perhaps, but the cosmological coordinate system still orders the events, as does the absolute interpretation. It's why I don't prefer the 'CMB isotropy' definition, based on local appearances as it is. The coordinate system has a very formal definition under FLRW, and it very much orders events in the vicinity of a gravitational source. Just not inside the event horizon. One is forced to make a different abstract choice of coordinates to describe what it is like for an observer there.

[Eternal Student]

Hi Halc.
   Thanks for taking the time to reply.

There's a few points that might be worth making now:

You took this quote from one of my earlier posts:
Where a space is geodesically incomplete then I'll agree that there can be some "directions" from which no radiation can be received by an observer

  and then grumbled about how that can't be true by taking fireflies with you into a black hole.  So you'll have to forgive me if I grumble about taking the quote completely out of context.   I was talking about the CMBR in that post and that's the "radiation" which I was referring to.   The CMBR does not originate from any local source (although it was right here where I am now but that radiation has long since moved on travelling at the speed of light and/or interacted with some matter in the region).  The CMBR is radiation that was from the early universe.  I will call it  "CMBR" based purely on it's origin - it came from the early universe and has been travelling through space since then.  Anyway the CMBR that we observe is radiation that has travelled for about 13 billion years and therefore came from a spatial location that we would describe as being a long way away given the state of expansion of the universe now.

    One simple example of what I was talking about might be placing an observer close to a black hole with a directional microwave detector.   See the simple diagram below:

                                            (CMBR from above)
                                                       |
                                                       |
                                                      \/
  (CMBR from the left) - - - - >  (Observer)             (Black Hole)   < - - - -   (CMBR from the far right)
                                                      /\
                                                       |
                                                       |
                                                  (CMBR from below)

   The observer can detect Cosmic Microwave Background radiation (ok, it might be shifted in frequency) coming from most directions but they cannot detect the CMBR when they point the detector at the singularity.    (Well... to be honest they may detect a little if the black hole was considered to be an eternal black hole but let's keep it simple and assume the black hole formed later in the development of the universe from the collapse of a star).   This is simply because the observer cannot detetct radiation coming from space that lies beyond the black hole (labeled as CMBR from the far right in my diagram).  Radiation that tried to take a straight line path from beyond the black hole, through the singularity and to the observer will fail to arrive at the observer, all such geodesics terminate at the singularity of the black hole.  (This is the essence of what it means to be geodesically incomplete but it's hardly worth discussing a precise definition of geodesic incompleteness here).  There may be some rays from the far right that are curved around the black hole and strike the observer but these would appear to be incoming from a slightly different angle (not straight from the black hole).  (To most this would seem perfectly reasonable, black holes are black because you detect no radiation at all coming out of them or travelling across them but Halc and maybe a few others are discerning enough to realise this may not be the end of the story).

     Why did I say  "to be honest they could detect a little CMBR from the direction of an eternal black hole?"    It's because we need to remember that the CMBR is radiation that was everywhere in the universe at an early time.  If the black hole is what we describe as an eternal black hole (it was always there)  then there would have been some photons that were just outside the event horizon of the black hole but were on the observer's side of it and travelling toward the observer.  Spacetime is so warped near the event horizon that those photons could take 13 billion years (by the observers clock) to get away from the event horizon and reach the observer.  None the less those photons were from the early universe, just like CMBR from any other direction and they have struck the observer from the direction of the black hole.  Assuming the black hole was NOT eternal but formed later removes most of this technicality but not all of it:  If it formed, let's say 7 billion years ago, then there could have been cosmic background radiation near the new event horizon that came from 7 billion light years away and now the problem starts again (spacetime is so warped ... the next 6 billion years... to reach the observer).  However, we can assume that dense matter blocks most radiation with frequencies below X-ray, so there doesn't have to be any radiation from the early universe with the correct velocity (moving away from the horizon and toward the observer) on the observer's side of the black hole horizon.

(Too long, stopped typing and went to bed.  Bye for now).

[Eternal Student]

(Awake again).  Hi all.

Continuing / Closing the discussion with Halc.
     Most of the rest of what you said seems to focus around a differing understanding of what a CMB frame is and may not be worth discussing.  Thanks for your time and attention though.

Here's a minor thing you said, which may trouble me if I said nothing about it at all:

Local variations don't contradict the FLRW models. It is a model of large scale structure, not of details.

     How can you say this?   Yes, an FRW universe is a model and yes, it holds well against what seems to happen in the real universe on the largest astronomical scales.      However A FRW universe is NOT one with lumps in it,  it is one where there is a homogeneous cosmological fluid.   There cannot be local variations and regions of high density like planets and stars in an FRW model, it would be an immediate violation of the assumptions on which the model is based.   As a consequence there won't be any interesting objects like black holes in a FRW universe.
     I know what you were trying to say.... an FRW universe is only intended to model the universe on the largest scales - but that is very different from saying local variations don't contradict FRW universe models.

A minor side note:
   It is, in my opinion, almost a miracle that an FRW universe models our real universe as well as it does.    We know that the Einstein Field Equations are non-linear (unlike, for example Maxwell's equations):  If we identify a solution for a space with one stress-energy tensor,  and also another solution for another stress-energy tensor,  then adding the two sources of stress-energy together in one space gives us a solution that is (in general) NOT the sum of the two separate solutions.  It is apparent then that if we had AVERAGED (just add and divide by 2) the two stress-energy tensors we would not have produced a solution that was the average of the two separate metrics.    An FRW universe represents the stress-energy of the contents of the universe as an ideal fluid with parameters of density and pressure.  This is like averaging the actual momentum-energy of each individual particle in the universe.  So it is, in my opinion, surprising that we produce a solution that does actually work as a large scale ("an average") description of our universe.

Halc said this:

(Quote from me was...)
    then the set of CMB frames at all points and times would cover the entirety of spacetime.
(Reply from Halc was....)
No they wouldn't. At the spacetime events that are not ordered by the comoving coordinate system, there is no CMB frame defined. And even if they did collectively cover all events, no one CMB frame defines universal ordering, so they're quite irrelevant to the task. Any pair of CMB frames might order events A and B differently, so they cannot be used to define any sort of absolute ordering.

   I wouldn't like to say that this wrong, so I won't.  It's just not entirely right.  You seem to be worrying about something that you don't need to.  A CMB frame isn't a Cosmological truth frame, it never claimed to offer an absolute ordering of all events if they are outside of each others light cones etc.  A CMB frame is one where an observer at rest and at the origin in that frame would see the Cosmic Background radiation isotropically.  (see the next section, below).

Back to some discussion of the CMB frame as a special frame of reference
    Well, it is.   Assuming a FRW universe we can always identify a CMB frame at every point in space.  I've reduced the scope down to an FRW universe because we just don't want black holes or other strange local variations which might hide some of CMBR away from an observer at that point.
   Halc was unduly concerned that a CMB frame allows for some universal ordering of all events throughout the universe.   Any co-ordinate system specifies events with co-ordinates and (as Halc implied) you can choose to look at the time co-ordinate as a number and order the events according to that number, if you wish.  There's no reason why you should do this, that co-ordinate system doesn't have to be "better" or more truthful than any other co-ordinate system.  In particular, it doesn't remove the need to consider light cones when considering causality (and as a result of this, there is still the possibility to find co-ordinates that are equally good and can reverse the ordering of the time of the two events).  To say this another way, the existence of the CMB frame is interesting but it doesn't break special relativity.
    The essence of Special Relativity is NOT that we can't single out one inertial reference frame as being "preferred" or unique among other frames.   Instead, Special Relativity only requires that the laws of physics are the same in all inertial reference frames.
     Cosmology often challenges a few ideas that were part of the established beliefs for Physics and the identification and study of the CMBR is no exception.  I have no doubt that students of special relativity were taught that SR prevents us from identifying one inertial reference as being preferred over another but the modern emphasis should be different:  Special Relativity only demands that the laws of physics are the same in all inertial reference frames and in this sense no frame is preferred or "better" than any other.  There are some empirical observations that can be made in the real universe which can differentiate between reference frames.

OK.  I've probably already gone on too long.  Best wishes to everyone.

[Halc]

OK, I know what you mean by geodesically complete now. I think that mathematically one can see CMB radiation in the direction of a black hole. The thing formed at some point, and a steady stream of CMB light was suddenly severed, but the trailing end of it is still coming at us, just like you never stop seeing a light dropped into a black hole. From a distance, yes, it is insanely redshifted, but it's there. Just food for thought. Not suggesting that means there's isotropy in any frame. If I look at the CMB in the direction of a distant black hole, I will very much notice the distortion there regardless of my motion. The CMB will not be isotropic.

However A FRW universe is NOT one with lumps in it,  it is one where there is a homogeneous cosmological fluid.

So the standard model is wrong because it disallows rocks? I would say it simply doesn't attempt to describe local details.

Halc was unduly concerned that a CMB frame allows for some universal ordering of all events throughout the universe.

That wasn't my concern at all. My observation was that no known coordinate system orders all events, covering both large scale (events outside our event horizon) and local variations (lumps as you put it). This seems to be a problem in need of solving by any metaphysical assertion of there being a preferred ordering of events. It is of no actual concern to me because I propose no such metaphysical premise.

Any co-ordinate system specifies events with co-ordinates and (as Halc implied) you can choose to look at the time co-ordinate as a number and order the events according to that number, if you wish.

Not any coordinate system. One one that defines a coordinate to both events being compared.

There's no reason why you should do this

Totally agree, but not everybody does. I'm currently conversing with someone who very much cannot even conceive of a universe where there isn't a co-ordinate system that is truthful to the exclusion of all others.

the existence of the CMB frame is interesting but it doesn't break special relativity.

SR is a local theory, so the CMB is irrelevant to it. If SR is to be applied to the universe as a whole (as occurs if one approaches the zero-energy-density limit of the FLRW model), then one prediction that follows is a lack of CMB. Hence the demise of the Milne solution which proposed just that: SR for large scales and GR only for local variances.

I have no doubt that students of special relativity were taught that SR prevents us from identifying one inertial reference as being preferred over another

Only in Minkowskian spacetime, and the universe at large scales is apparently not Minkowskian. So all one needs to do is a non-local test.

[Eternal Student]

Hi and thanks Halc.

   You don't need to spend any more time here by the way but I have enjoyed reading what you've said.

SR is a local theory, so the CMB is irrelevant to it.

   Yes to the essence of what you were saying next.... SR shouldn't be applied to the whole universe and SR is not going to explain how the CMBR came to be there in the first place.    However, there's nothing much wrong with applying SR to the real universe as just a local theory.  At any point in the real universe we usually do observe CMBR and locally we can use SR.  Among all the inertial frames that can be centred around that point in space, there should be one where the CMBR is isotropic (subject to all the limitations previously discussed in earlier posts).  It's not as if this frame of reference is "better" than another but it's just interesting that there is a frame which can be singled out from the others.  The only thing of any cosmological interest about a CMB frame is that in that frame the universe should be as symmetric as you can get it to be  (for example, the CMBR is isotropic).
    You may have spelt Milne incorrectly.  I'm not all that familiar with the Milne universe.  The Wikipedia entry on the Milne universe has been "challenged" for accuracy at the time when I glanced at it.  The discussion I've seen in Carroll's book only treats it as a trivial example.  I imagine there was some history much as you described.

We seem to have drifted a long way from the OP and they have gone quiet, so I'm going to stop writing now.

Best wishes to all.

[yor_on]

Hmm. I agree in that the CMBR, or CBR as I tend to call it, is observer dependent. To make it simple, which is what I like, I don't think one can avoid that conclusion. We're all 'local', our experiments, even if they agree, are also 'local'. What's funny with that local definition is that it contains something of both. Your wrist watch relative your life span is locally defined the same, invariant, and that is also the way we define physics and science by repeatable experiments. That locality is correct and locally a 'invariant'. And using those local agreements we reach a global definition of f.ex 'constants'. Well, the way I look at it.

The confusion comes when one apply locality on a global 'system'. Because then it suddenly becomes observer dependent, if I by my 'system' f.ex define it as 'the universe'. So logically I don't think I can do both, I can't both see the universe as being 'globally defined' observer dependent at the same time as I define it to have some objective 'golden standard' globally. That is, I don't think I can make my coordinate system cover both simultaneously, if that now makes sense?

But when we look out we all see 'the same thing', the same stars and the same universe and that is what I think this idea of a global definition comes from. You can reach it locally, which actually is what we do, but we need something more than locality to explain why the night sky exist.
=

Another way to express it is that by stating that my clock never goes wrong I can rely on it, and my other means of measurement, to define this universe. You can do the same, and if our experiments are shown to be equivalent we reach a agreement.

But if we move from that to a global definition they are observer dependent, as there is no guarantee that my clock, or measuring stick, is the exact same as yours. Einstein found a way of avoiding it using ideal 'frames of reference' and ideal 'test particles'. Frames of reference are coordinate systems as I read it, but they also become a metaphor for something else. You can imagine yourself sharing the same 'frame of reference' with something a million light years away, without any object in between doing the same.

Actually, the only 'golden standard' that exist in relativity (globally defined) is abstract, as shown by Lorentz transformations.

Well, and this

And no, the reason why they aren't the same is not due to miscalculations of length, time etc. It's a question of 'scaling' your frame of reference down, the further down you go, defining your system, the more exact your 'time' should be, etc, and the more it should differ from your macroscopic wrist watch, which means that you no longer share the same frame of reference. Doesn't matter how you define that frame of reference before scaling.. (What creates time dilation's and length contractions is mass/energy  'speeds', and accelerations which in relativity becomes a equivalence to 'gravity'. And by defining a new scale or 'system' you will change parameters)  Until it breaks down into uncertainty. Although that is my take on it, it depends on what you think a clock or 'time' is. If you set it as a equivalence to 'c', then it breaks down at Planck scale.

So yes, looking at it this way there might be a sort of ''golden standard' to our universe, but it's not macroscopic. You can define frames of reference differently but to be precise, assuming it to be correct, you should need Planck scale. And once you're there its all uncertainty.

Thinking this way there becomes a difference between a 'clock' and 'time'. 'Clocks' becomes discrete, 'ticking', whereas 'time' somehow should relate to HUP and decoherence. And I don't know if this last part (under the video link) is correct. I think the equivalence is correct though, locally defined. The rest, more or less, follows from it. One thing is true though, this universe is observer dependent, no matter what, or how, you look at (it).

alternatively you can think of that clock and 'time' as being equivalent,  'flowing' all the way down, to where it dissolve into uncertainty. But if you use it the way I do it actually seems to become 'discrete' as it allows me to "split"  'c'  (becoming a perfect local clock)  all the way down to Planck scale.

You could see it as we exist inside two limits. A regime defined by 'c' on one side and Planck scale on the other, that is if you accept the main stream definition in where our known physics breaks down under it. The same can be said for 'c' as it becomes a limit no 'normal' (proper) mass can reach

And yes, looking at it this way also opens for questioning the whole concept of lights 'propagation' as it is about questions of what scales and decoherence do this universe we find existing macroscopically. So this last part belongs actually to 'New Theories' I'm afraid :) Nevertheless, the part above the video link is main stream science, although formulated differently than physics normally do..

[yor_on]

If you want both parts to be true you will need to introduce new concepts. Four dimensions doesn't cover it. That we locally become 'invariants' while globally becoming 'observer dependent'
=

It's just a logical extension of relativity. And a question of how to keep the cake while eating it. I do not doubt the genius of
Einstein, neither relativity. But there is something missing.