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Since we found $T_0$, the origin of the line/ the absolute zero of ..Time with the Big Bang, can we consider that the absolute time, the same as we do with absolute temperature?

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  • $\begingroup$ The so called Big Bang is a classical singularity, which has to be avoided in the full (quantum) theory. The very nature of time is actively debated in the field of quantum gravity. So it is very much probable that your question does not make sense. $\endgroup$ – Prof. Legolasov Sep 18 '16 at 5:25
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    $\begingroup$ @SolenodonParadoxus, I imagine your proposition does not make sense, unless quantum gravity is the absolute truth. Which is not. $\endgroup$ – user104372 Sep 18 '16 at 5:45
  • $\begingroup$ What is absolute truth then? $\endgroup$ – Prof. Legolasov Sep 18 '16 at 16:41
  • $\begingroup$ @SolenodonParadoxus, the truth is that a comment should be relevant and constructive. You say it is still debated, good!, so it is not decided, fair enough, then, when it will be, it will be according to quantum gravity, right? what has that got to do with the question here, that refers to the standard/accepted/ ordinary indisputed notion of time? $\endgroup$ – user104372 Sep 19 '16 at 8:45
  • $\begingroup$ You are asking a question which lies outside the domain of applicability of standard/accepted approaches. Why do you expect that it makes sense then? $\endgroup$ – Prof. Legolasov Sep 19 '16 at 8:53
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One of the lessons of relativity is that there is no unique way to specify the time axis. Indeed, this is why time dilation occurs - moving observers differ about their definitions of the time axis so they measure different times between the same events.

So there is no unique definition of the elapsed time between the Big Bang and the present. Different observers may measure different elapsed times since the Big Bang, and therefore we can't use the Big Bang to define an absolute time.

However there is a natural way to choose a time axis. There is a choice of coordinates in which the universe is isotropic and these are called comoving coordinates. These are effectively the coordinates in which you are at rest with respect the universe as a whole. In these units every comoving observer everywhere in the universe will agree about the time since the Big Bang. We generally call the time measured in this way the comoving time. This is the nearest you'll get to an absolute time, though it's important to be clear that this isn't an absolute measure of time, just a convenient one.

There are several related questions that go into more depth on this subject. If you're interested have a look at:

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  • $\begingroup$ Yes, that is what I meant, even if I didn't know the exact term: 'comoving' $\endgroup$ – user104372 Sep 18 '16 at 10:18
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To start some answer to this question I will refer to previous posts by myself . The first illustrates how the Friedman-Lemaitre-Robertson-Walker (FLRW) cosmology can be pretty closely approximated with Newtonian physics. I also point to another Stack Exchange post of mine on the origin of gravitation.

These provide some background for what I will say here. The de Sitter cosmology has the line element in stationary coordinates $$ ds^2~=~\left( 1~-~\Lambda r^2/3\right)dt^2~-~\left(1~-~\Lambda r^2/3\right)^{-1}(dr^2~+~r^2d\Omega^2). $$ Here $\Lambda~\simeq~10^{-52}m^{-2}$ is the cosmological constant. There is an event horizon at $r~=~\sqrt{3/\Lambda}$, called the cosmological event horizon. This occurs at about $1\times 10^{26}m$ or $10^{10}$ light years. We then have a holographic screen associated with the universe at large. I reference the books “ Black Holes, Information, and the String Theory Revolution, Holographic Universe” by Leonard Susskind on the subject of the holographic principle, and this paper by Susskind and Witten. This applies largely to black holes, but Raphael Busso found the entropy bound by holography applies to cosmology as well.

In the case of black holes the dynamics of any objects in a classical setting as seen by a distant external observer is time dilated and the coordinate extension of that object transverse to the horizon is extended. If one is observing a relativistic quantum field falling towards the black hole it will be compressed along the radial direction, time dilated and extended across a region near the horizon. The physics will then appear nonrelativistic. I illustrate that in the second SE post of mine I reference here. Particle physicists employ relativistic quantum field theory (QFT) that is formulated according to equal time commutators on a spatial surface. The commutators occur according to the Wightman condition inside light cones. In this way QFT is formulated according to local amplitudes or fields. This is useful for practical reasons. In the LHC the production of a $W^+~W^-$ particle pair is an entangled state, which is a nonlocal quantum physics. However, the $W^{\pm}$ is only stable for a distance of $10^{-16}cm$ or for a time of $10^{-26}sec$. There is no practical way that one could perform the sort of quantum optical type of experiments that measure nonlocality on an optical lab bench, or now across distant fiber optical lines. Quantum nonlocality is not of any significant consideration in high energy physics. This is until one observes the production of these flavor changing particles near the event horizon of a black hole. If such an observation could be made the high energy physics would appear according to the non-relativistic physics, such as the Schroedinger equation.

Returning to the universe at large. The reason that Newtonian physics works remarkably well is related to this. The spacetime has the symmetry of $SO(3,\mathbb R)$ for the spatial surface, which reflects a rotational symmetry according to an observer in an O-region bounded by the cosmological event horizon. This means that physics obeys this symmetry if the observer witnesses no anisotropy of redshifting of the distant universe. In other words the cosmological microwave background has no large scale anisotropy. We in fact measure a small anisotropy that is due to some local motion of the Milky Way and due to something called the big attractor, which is some clumping of matter not far from the Virgo cluster. This symmetry is ultimately enforced by the holographic principle, which is also a reason the FLRW cosmology is pretty well approximated by Newtonian physics. The classical structure is a signature of the holographic principle.

This does mean, returning to the paragraph above, that there is a duality between nonlocal physics of quantum mechanics (plain vanilla QM of Schrodinger equation etc) on a holographic screen and the local physics of relativistic QFT on the surrounding bulk spacetime. In the $AdS/CFT$ correspondence something similar is found. The gravitational physics of the $AdS_n$ bulk is nonlocal and this is equivalent to a conformal field theory $CFT_{n-1}$ on the boundary of the $AdS_n$. This means the nonlocal physics of QM with entanglements and apparent “spooky action at a distance” is dual or equivalent to QFT in one dimension larger.

That cosmology has this apparent “preferred frame” has some deep implications, and it is something that has bothered me for years. I thought early on this was significant of something, and not dismissed as some breaking of general relativity (I have heard this) and further this is beyond our imposed solutions to the Einstein field equations.

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