# Assuming that the Cosmological Principle is correct, does this imply that the universe possess an empirically privileged reference frame?

OK...before everyone blasts this with references to the relativistic invariance of the physical laws, time dilation, etc let me add some context. Also, I am an amateur with an interest in physics, so I don't know the details of the physics. However, I have read enough about the cosmological principle and cosmic time to develop this "confusion" .

Based on evidence gathered to-date, it appears that the universe is both isotropic and homogenous to a high degree, as evidenced by observations and the usefulness of the Freedman-Lemaitre-Robertson-Walker (FLRW) metric. This principle, when combined with the FLRW metric, allows space-time to be divided into non-intersecting slices and therefore establish a "cosmic time."

Now, the existance of such a time in no way suggests that it is the "right" time or a true "now", hence violating relativity -- although some presentist philosophers (e.g., W.L. Craig) have tried to make this argument, but it is not generally accepted in philosophical circles.

However, this leaves me confused about an apparent disconnect between relativity and the cosmological principle:

Isotropy only holds if we are at rest relative to the cosmic microwave background radiation (universal rest frame), o/w anisotropy is present - yet each reference frame is supposed to allow equally valid observations. How can these two be reconciled when most reference frames would lead us to conclude that the universe is NOT isotropic?

It seems that only by appealing to the idea of being at rest relative to "universal rest frame" can we explain away any discrepancies from isotropy as due to "peculiar motion". However, doesn't this give this "universal rest frame" and its associated time an empirically privileged status, even though physical laws work just fine in every reference frame?

For example (pardon any abuse of astronomy): if look off in some part of space and see only quasars, and then in another part of space and see only brown dwarfs, but I measure both as apparently the same distance from me, then can I conclude that we are in motion, since otherwise we would have an empirical contradiction (kind of like finding dinosaur and human remains in the same strata)?

Any help on where I am going wrong would be helpful. Intuitively, I don't think there should be a way to establish absolute ordering between space-like separated events, but the above reasoning suggests otherwise.

• See also this – David Z Nov 15 '13 at 18:21
• Wow...yes, that was a great discussion. Ill need some time to fully read through, but it is very much along the same lines. – user31580 Nov 15 '13 at 18:30
• Ok..I feel the mental gaps closing. One last thing: Doesn't fact that we can describe our universe using comoving coordinates iimply that the universe is fundamentally isotropic/homogenous? I say this becasue I can imagine spacetimes where you cannot make simple corrections to the peculiar velocity to get to an isotropic frame. In that case, every observer will agree that the universe is not isotropic. Seems like a very special thing that we can make such "inertial" corrections, suggesting again that the most accurate way to look at our world is from a comoving frame – user31580 Nov 15 '13 at 18:46
• John and David: Thanks to you both for your helpful explanations. I've moved the above comment regarding isotropy to a different thread, as its too off topic for this. Thanks again!! – user31580 Nov 16 '13 at 0:34

Your mistake is to assume that the cosmic microwave background constitutes a universal rest frame, because it doesn't.

In an FLRW universe there is a frame called the comoving frame or proper frame that is particularly mathematically convenient. This is the frame in which the comoving distance between all inhabitants of that frame is constant, so all the "stuff" in the universe is mutually stationary (the comoving frame factors out the Hubble expansion). Given that we expect all the "stuff" in the universe to be created in a similar way we would expect it to be approximately stationary (in a comoving sense) so the sum total of everything, matter and energy, acts as a reference point for the comoving frame.

So there's nothing special about the CMB. If you ignored the CMB and measured the Earth's velocity to all the galaxies we can see then you'd expect to get the same result as measuring the Earth's velocity relative to the CMB. The CMB occupies the same frame as everything else because it was created in basically the same way. The only special thing about the CMB is that gravitational interactions haven't given it various peculiar velocities as has happened for large aggregations of matter.

• I see. I guess its just that comoving frame seem particularly embedded with our overall universe, which makes me think that if a comoving observer existed at t=0+$\epsilon$ their clock would always run faster than any other clock in the universe. I have no theory to back this up, and it could very well be wrong. If so, then i would be less confused. – user31580 Nov 15 '13 at 18:15
• I'm not sure what you mean by a comoving observer existed at t=0+ϵ, but if you wanted to post a separate question on this I'd be happy to look at it. – John Rennie Nov 15 '13 at 18:26
• Sorry, just that it seems that clocks attached to observers who have always moved with only the hubble flow should have the fastest clocks relative to anyone else. – user31580 Nov 15 '13 at 18:30
• @Eupraxis1981: well, no. An observer with a peculiar velocity of 0.999c would see everyone else's clocks running slow. We're back to the point I raised above: if you see 99.999% of clocks running slower than yours then you would probably assume it was your clock that was unusual even though it's perfectly valid to regard yourself as stationary and everything else as moving. – John Rennie Nov 15 '13 at 18:33
• There it is! Ok, so I am incorrectly privileging what seems like the "most likely" scenario (i.e., I am moving, others are at rest) when in fact all we know is that our relative motion is opposite at the point I am making the observation. – user31580 Nov 15 '13 at 18:39

The universe not being isotropic is a perfectly valid observation, as far as relativity is concerned.

However, doesn't this give this "universal rest frame" and its associated time an empirically privileged status, even though physical laws work just fine in every reference frame?

Yes, it does, but that's not a problem. Relativity doesn't prohibit a physical system from selecting certain reference frames that are "preferred" in the sense that they're more convenient to work with. In fact, this doesn't happen only with the universe. Even for a small system, like two particles, there is one empirically privileged reference frame, the center-of-energy frame in which the total momentum is zero. (This is a spontaneous breaking of Lorentz symmetry, if you appreciate such terms.)

But the fact remains that the fundamental laws of physics are perfectly valid whether you're in that empirically privileged frame or not. The only sense in which it's empirically privileged is that it's convenient, but it's not a necessary choice.

• Thanks for that explanation. I have no truck with all reference frames being relativistically valid. I just want to know if an observer who concludes that the universe is NOT isotropic is factually wrong. If so, how do we know that or demonstrate that to the observer. – user31580 Nov 15 '13 at 18:01
• No, an observer who concludes that the universe is not isotropic is not (necessarily) factually wrong. Isotropy is a frame-dependent conclusion, so observers in one frame will conclude that it is isotropic and those in other frames will conclude that it's not, and both are valid. – David Z Nov 15 '13 at 18:05
• I see. So the Cosmological principle is only correct if you are at rest wrt CMBR. Wouldn't that establish spacetime itself as a reference frame in the sense that two observers moving only with the hubble flow would have synchronized clocks whilst another moving with particular motion wrt hubble flow would run slower relative to either of the others? Sorry if this is gettng off topic, perhaps we can set up a chat. – user31580 Nov 15 '13 at 18:09
• Ordinarily I would love to chat about this but I'm quite busy today so I won't have time. You can bring this up in Physics Chat and someone else could expand on it, perhaps. – David Z Nov 15 '13 at 18:23
• @Eupraxis1981: it depends on your definition of isotropic. If 99.999% of observers measure the universe to be isotropic, but you don't, then either the 99.999% of observers could be moving relative to you or you could be moving relative to them. Either choice is valid, but the latter is mathematically simpler. – John Rennie Nov 15 '13 at 18:24

I am an engineer who has played with relativity and cosmology as a hobby ever since I retired. It seems to me that Einstein was never fully comfortable with Relativity whenever acceleration was involved. In 1920 he said,

“Newton might no less have called his absolute space ‘Ether’; what is essential is merely that besides observable objects, another thing, which is not perceptible, must be looked upon as real, to enable acceleration or rotation to be looked upon as something real.”

Einstein, Albert: "Ether and the Theory of Relativity" (1920), Sidelights on Relativity (Methuen, London, 1922)

The Twins Paradox (one twin aging more than other, even though neither has a preferred reference) gets explained as due to one experiencing acceleration when turning around. As best as I can tell nothing in Relativity justifies this explanation. On the other hand, if effects are dependent on motion relative to the universe as a whole, the acceleration explanation is unnecessary. Although most things can be explained using a two body only version of Relativity, many others fail with just two body Relativity - especially if acceleration is involved. I have come up with a multi-body mathematical representation of Relativity that appears to resolve this. However, this does give the inertial reference, for which the cosmological principle holds, special status.

In addition, Einstein stated that while velocity is relative, acceleration is not. The interpretation of acceleration as the time derivative of velocity just does not work for a two body interpretation. However, a summation of multi-body relationships solves this. interestingly, when Einstein's method of deriving classical physics from Relativity is applied to gravitational energy, the multi-body interpretation presents itself in an obvious and hard to deny way.