I can't manage to understand the quasi-schizofrenic way we should believe that our universe started at a certain time point called Big-bang while at the same we must never admit that in order to say that it follows that an absolute time (and an absolute frame) must be distinguished, (the CMB rest comoving frame). We at most can call it "preferred" frame-even if many people uses "preferred frame" as the one where physics is different, wich is a notion forbidden by reativity. I think it is one way or the other, if we must think something extraordinary happend exactly 13.7 bly (with fractions of a second precision) ago then we are using an absolute clock, and therefore we shoud admit an absolute frame. If no such frame exists and that frame is only preferred in an arbitrary way, those 13.7 bly are also an arbitrary number and there's not anything absolute associated to that "age" and we could as well say something singular happened an infinite (if our universe was infinite) time ago or yesterday or an infinite number of different ages ago fom some other point in the universe. Please someone take me out this interpretational swamp.
There is nothing schizophrenic about it. It is straight out of the Einstein Field Equations and differential geometry. The problem is trying to describe the math in english. If you are frustrated and confused by the verbal descriptions then you really need to learn the math. Otherwise you are "blind" to the overall picture. http://en.wikisource.org/wiki/The_poems_of_John_Godfrey_Saxe/The_Blind_Men_and_the_Elephant
Thanks for the poem but I don't think the confusion comes in this case from the verbal description, I know the math and is precisely from the math that I gather the verbal description of my last post, in any case you could try and describe (in english or mathematically) which way of the two I described in the second paragraph do you think is the correct one.
If you know the math then what is the problem? 1) The big bang is a feature of the FRW metric. 2) The FRW metric is a solution of the EFE. 3) The EFE are manifestly covariant. 4) Covariance implies the lack of a prefered frame. 5) Therefore, there the big bang does not imply a prefered frame.
I agree with those 5 points, that's the problem. So is the "age" of the universe just an arbitrary figure?
The "age of the universe" refers specifically to the proper time experienced by an observer which is passing next to us now and has been at rest in the FRW coordinates since the big bang. It is arbitrary, but well-defined.
Two things, if t=0 is a real singularity, that is "outside physical theories realm", an exact age can't be that well-defined since we can't know how our theory behaves at the limit when t tends to zero, as far as we ñnow time could behave weirdly there and became asymptotic or...whatever, that what a true singularity does. Second, I agree with the " refers specifically to the proper time experienced by an observer which is passing next to us now and has been at rest in the FRW coordinates since the big bang", but a proper time in relativity is a purely local measure (with the caveat I referred to above on top of it), it can never be generalized to a "universe age" in any sense other than our local non-centric or non-special location in any way, right? (if you respect the cosmological and Copernican principles at least).
Agreed, similar issues happen with defining the proper time of an observer falling to the singularity of a black hole. Usually the singularity is simply excluded from the manifold, which makes the limits all behave nicely (and is actually required mathematically). This is what is meant by the proper time of an observer going into or coming out of a singularity. Of course, GR probably diverges from reality well before reaching the singularity. Science is full of bad terminology that persists despite good reasons for it to be dismissed. It sounds like you actually understand everything, and simply object to the terminology. Your objection is reasonable, but changing common terminology is nearly impossible. However, I personally don't think that the terminology is as bad as you seem to feel it is. The above definition certainly can be generalized to a "universe age" simply by adopting the same convention at every point in the universe. Since the FRW metric is homogenous it is reasonable to do, IMO.
As I said I disagree that it is simply a terminology issue, it is about logical consistency and avoiding contradictions. The FRW metric is homogeneous only spatially and to adopt the same convention at every point in te universe wrt a "universe age" i.e, sharing the same clock for the BB event, it would be necessary to either have a not FRW universe spatially and temporally homogeneous which seems not to be the case or do without the relativity of simultaneity (you are basically demanding absolute simultaneity for the BB event for every point in the universe no matter how distant).
I'm no cosmologist but the only maybe useful observation I can make is that as real universe is lumpy not spatially homogeneous, temporal 'lumpiness' is also present to some extent. So higher gravitational potential inside a cosmic void region implies experiencing more relative total time since BB than inside a clumped region. And of course considerably less time has passed at the surface of an ancient neutron star say. But guessing that is not your concern here, as it seems from your earlier remarks we are assuming homogeneity.
The FRW model does not say that every observer sees the same "universe age" regardless of their state of motion. It only says that *comoving* observers all see the same "universe age". We here on Earth are not comoving observers, so the universe age we measure will actually be slightly different than the universe age that would be measured by a comoving observer just passing through the Solar System right now. Our instantaneous hypersurface of simultaneity on Earth right now is also not the same as the hypersurface of constant comoving time passing through Earth right now.
Huh? Any event (including the BB) is in fact simultaneous with itself absolutely. So yes, I am demanding that, and that is noncontroversial. I think I must be severely misunderstanding your point.
Ok, I guess you mean that the BB is supposed to have occurred not in a single location but in every location, and that's what you find noncontroversial. So it's no problem for you to do without the relativity of simultaneity for this particular event. You do realize that all this implies an absolute frame, right?
Sure, since we are using the FRW model I'm idealizing a little and assuming perfect homogeneity (wich is expected anyway at certain scale) so that "all observers are basically comoving".
We are observers and we are not comoving. Let me describe a slightly different way of constructing this coordinate system. First, recall that in order to define a geodesic you need an event and a tangent vector (i.e. velocity). So, take any event in the universe, and at that event find the one unique velocity at which there is no CMB Doppler shift. Using that event and tangent vector construct a geodesic that goes back in time to the BB, called the comoving geodesic. At each event along the geodesic calculate the length of that geodesic from the BB to the event (with the aforementioned caveats). Assign that number as the t coordinate of each event along the geodesic. Because the universe is spatially homogenous you can do this procedure at every point in the universe, assigning 3 different coordinates to identify the different comoving geodesics. This will result in the standard FRW coordinate system, with corresponding hypersurfaces of simultaneity. However, there is nothing that requires you to use that procedure. You could just as well choose a different method for assigning coordinates. You can have simultaneity without having absolute simultaneity.
I said I'm assuming the idealization of the FRW model, the universe age we as observers measure will actually be slightly different than the universe age that would be measured by a comoving observer, if that is a problem for you here I guess you wouldn't accept the FRW model because we as observers are not comoving and therefore the universe must not be homogeneous. Frankly, that's feeble, we are looking at the big picture here.
Ok, so if we can choose a different methd for assigning coordinates, you then admit there is nothing special about the age (13.7 bly) we usually assign to the universe right?
I am assuming the same idealization of the FRW model. In the ideal FRW model we observe a Doppler shift to the CMB, therefore we are not comoving observers. This is certainly not correct. I have no problem with the FRW model as a very close approximation. What you do not seem to realize is that the FRW model, at each spatial location, identifies one particular worldline as the worldline of a co-moving observer, and it is not our worldline.
Correct. I said as much back in post 6. It is a very reasonable convention, but a convention nonetheless.
No, all observers are *not* comoving, not even in an idealized, perfectly homogeneous and isotropic model. Only observers who *see* the universe as homogeneous and isotropic are comoving. Even in the idealized model, there are plenty of observers who do not see the universe as homogeneous and isotropic and so are not comoving.