Does motion break existing symmetries?

oldman

Observations suggest that the observable universe is spatially flat and, on the largest “cosmic”scale, highly symmetric. On this scale it is modeled as always isotropic and homogeneous. In this situation Birkhoff’s theorem tells us that “exterior” matter, i.e. matter in the universe at large, exerts no gravitational influence on local masses. (In a spherically symmetric Newtonian universe this is also true, because there is no gravitational field inside any uniform spherical shell of matter, due to that shell).

Now the Cosmic Microwave Background (CMB) displays tiny deviations from spherical symmetry, the most prominent of which is its dipole character. This is interpreted as showing that in a local frame of reference at rest with respect to the CMB (a CMB frame) we happen to be moving with a velocity of about 600 km per second.

Can the Relativists in this forum tell me if such motion breaks the assumed perfect symmetry of the universe we observe, so that its symmetry takes on a (very slightly) uniaxial character, with concomitant observed density enhancements (due to observed Lorentz contractions) fore and aft, as it were, along the axis of motion? And is not Birkhoff’s theorem (very slightly) perturbed in this case? In the case of uniform motion, does it still preserve its essential conclusion (since the Lorentz contraction is the same fore and aft)?

If the answers to these questions are “yes”, then the kinematic nature of uniform motion (Newtons first law) in our observed universe seems natural. But what then of more complex motions, for instance accelerations or rotations, which must also break the high symmetry of our observed universe and perturb Birkhoff’s theorem in more complex (higher multipolar) ways?

Finally, might such symmetry breaking have a connection with Mach’s principle and the origin of inertia from the gravitational influence of remote masses, if Birkhoff's theorem is perturbed and its conclusion modified in such cases?

country boy

Our motion with respect to the universe does not violate any symmetry principles. As we move through the universe we see a relative motion with respect to other objects, including the CMB. Nothing wrong with that. The symmetry comes in when we say that every location in the universe is equivalent, i.e., that the physical laws are the same everywhere (and everywhen). A locally observed asymmetry in the doppler shift of the CMB does not imply a cosmic asymmetry.

oldman

Thanks for your comment -- what you say is correct, especially the bit about physical laws being the same everywhere and everywhen. But there is a deeper point here. In my post I tried to stress that I was talking of the observed universe. Now each of us has her/his own such universe, and this, for the person concerned, is what counts, what "is", or "is real" for him/her. This is what relativity teaches. Relativity relates one person's universe-that-is to another's.

For example, consider the decay of a fast-moving cosmic-ray particle. It is observed to be slower than that of a similar particle at rest in your laboratory. Its longer lifetime is part of your observed universe, and must be taken into account when considering the physical consequences of this decay, like one's measurements.

If one is in motion with respect to the CMB (as we are), the universe that "is" has a (very slightly) different symmetry from the FRW model considered by cosmologists. And this may have some physical consequences, like those speculated about.

The universe we observe in one direction is not necessarily the same as the universe we observe in another. It is the symmetry breaking of this universe, the observed universe, that I was talking about. In principle one should accept the observed universe as "real" -- e.g. that the CMB shines hotter ahead than behind, and would fry one's face if one moved fast enough!

Mentz114

The assumptions of homogeneity and isotropy in cosmological models can be seen as rotational and translational symmetry respectively. But the FRLW type of universe does not include the CMB. The CMB must represent the rest frame of matter at the time the universe became transparent which we could assume was dustlike, homogenous and isotropic.

oldman

Could you explain why not? I thought that the CMB is assumed to be relic radiation from the (everywhen, always, eternally FRW) model universe used by cosmologists...

Mentz114

Sorry, that's not accurate. The way it works is that one can derive the line element of an isotropic, homogenous universe purely from symmetry, without reference to Einstein's field equation. If we now want to add dust like matter to the model, the components of the Einstein tensor must be set equal to the energy-momentum tensor of the matter. This gives us the famous relation between energy density and expansion rate, two observable (in principle) quantities.

To add the CMB to the equation, one just uses the energy-momentum tensor of matter plus CMB radiation. I feel sure this has been done and I can look for it in arXiv if you want to follow up.

oldman

Yes, I agree with what you say, and thanks for the offer to find references, but I'm reasonably familiar with how the FRW model is set up. Correct as your comments are, I can't quite see what bearing they have on the sort of questions I was asking, particularly w.r.t. my crazy speculations on the origin if inertia that, as far as I know, is still completely opaque.

Mentz114

Since my previous post, I have read that the only matter compatible with the RW metric is a perfect fluid. Adding a radiation part is not an option.

But, as you say that's off topic.

In Lagrangian and Hamiltonian formalisms, invariance under rotation gives conservation of angular momentum, and translational invariance gives conservation of translational momentum. But in cosmology these formalisms aren't used, so the 'symmetry breaking' is you refer to isn't familiar to me.
I don't think Birkhoff's theorem applies in the world because there's no real spherical symmetry.
The origin of inertia is indeed obscure, but if Mach's principal is invoked, it only requires average homogeneity and isotropy on a very large scale which may be a fact.

If we include peculiar motions in a cosmological model it may be possible to write a Lagrangian where all the potental at time t=0 is converted to peculiar motion ( motion off the comoving geodesics).

I wouldn't take any of my ramblings too seriously, but I'm surprised none of the relativists have tried to answer your questions.

Ich

Radiation is a perfect fluid, there's no problem with it.
Anyway, I did not really get the OP's point. The universe is thought to be isotropic and homogenous on large scales, and there is no evidence that we should believe otherwise. On the other hand, it is not thought to be Lorentz-invariant, so it makes a difference whether you're move relative to the surrounding matter (and radiation) distribution or not. However, this does not break symmetries of the universe: "isotropic" does not mean isotropic in every frame (that would be isotropic and Lorentz-invariant, like vacuum energy), it means isotropic only in the frame where matter is at rest.

Mentz114

Thank you, Ich. Enough said.

oldman

I'm afraid my OP was much more obscure than I had hoped. My fault. But now that posts by others in this forum have helped clear my mind (a bit), I hope I can do a better job of asking a question.

First, Ich, I don't disagree in the least with what you say so clearly here, namely:

It is the subject that we're discussing that I have difficulty with. When you say "the universe", I believe you mean a model universe, which observation shows approximates closely to what you may accept as the "real" universe - a universe that is, as you say, isotropic and homogeneous on a very large scale, but not Lorentz invariant. It follows that Birkhoff's theorem applies strictly here, and that this "universe at large" has no gravitational influence on local observers.

But I believe , and stress again, that relativity teaches that there is no such thing as a unique reality, as you are perhaps assuming in your post.

For example, consider observers in a frame in which matter is at rest. These observers partake of the Hubble flow, and for them the "real" universe is just as you describe "the universe" to be. In this case "the universe" means no more than "the observed universe", which corresponds to the model FRW universe.

Now consider observers like us. The dipole we observe in the CMB shows that we are moving relative to such a frame. For us, the "real" , or observed, universe has a (very slight) axial symmetry. I guessed earlier that this does not invalidate the strict application of Birkhoff's theorem.

But I don't know whether this would be true if we were accelerating or rotating. This was the rather silly question I was asking. Maybe that's "Enough said." as Mentz114 commented.

Ich

It seems that I am still not understanding what you mean. Birkhoff's theorem maks a statement about the gravitational field outside a spherical mass, and says nothing about the universe as a whole. But I'll come back to this.

That's some interpretations of quantum mechanics; relativity says that there is one and only one four dimensional reality, which is perceived differently by different observers.

The universe or reality is definitely not in the least impressed by the presence of accelerating, rotating or otherwise fidgety observers. But that does not mean that these observers may experience different things, depending on their relative motion. For example, the CMB could get blueshifted to gamma rays with unpleasant consequences.
Or, relating to Birkhoff's theorem, an extended observer would start contracting (or at least experience a force acting this way) under certain circumstances, becaus the mass flow inside him act differently than a stationary mass. This effect can be attributed to spatial cuvature.
I'm not an expert in GR, you might want to read Baez's tutorial, from where I got the following quote:
Maybe that is what you mean. But I'm afraid I don't know enough tho answer deeper questions.

oldman

Ich: Now I can see where we don't agree -- it's in our different definitions of reality. You claim that:

I think you are talking of a four dimensional model or concept, rather than reality.

wheras I claim that what a person observes (in the sense of an observer in relativity) is his reality (nothing to do with quantum mechanics!). All I can do is to quote Einstein, who said:

But such disagreements take us too far towards philosophy to be easily resolved, I suspect.

Thanks for the BAEZ URL. He is a indeed a useful source of clarity about relativity.

oldman

As I pointed out in the previous post, our ideas of what is meant by "the universe" are rather different.

The universe you are considering in the quote above is after all only a model universe, perhaps like the cute one set out by Baez you refer to. And models certainly aren't impressed by fidgety observers, as you so nicely put it.

The model universe that Baez discusses, in particular, is one in which the uniform and isotropic "cosmic fluid" of the model flows uniformly past and though his ball of test particles, so that there is a flux of momentum through the ball, and so that the energy density in the ball changes. This is what makes it shrink, just as he states.

There is nothing wrong with this model --- it is just not even remotely like an observer who, I claim, judges for himself what to call "real" about the universe. The universe any observer takes to be real for himself is not a model or a concept, it is part of his experience (like for example designing and building a cyclotron that has to take into account the changing observed masses of the particles it accerates). I speculate in this thread that a observer may experience physical phenomena in his observed universe, due to rotating or accelerating motion relative to the CMB.

Finally,you concluded:

I reply: Neither do I!