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According to relativity theory (gravitational time dilation), the observed pace of a clock depends on the strength of the gravitational field at the clock and at the observer. Isn't this at odds with the concept of cosmic time in big bang cosmology: the idea that time passes at the same pace everywhere since if it doesn’t, it makes no sense to speak about the age of the universe?

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    $\begingroup$ Nowhere in cosmology do we say that there is one cosmic time variable. We say that the universe is sufficiently homogeneous to be treated as completely homogeneous for cosmological purposes, which allows a foliation of spacetime using one global cosmological time variable... for cosmological purposes (and nothing else). $\endgroup$ – CuriousOne Jul 15 '16 at 2:10
  • $\begingroup$ While -gravitational time dilation- time passes at the same pace everywhere the gravitational field has the same magnitude; the problem is that there is no absolute, cosmic clock relative to which we can specify that pace. We only can speak about the observed pace of time somewhere: as this pace depends on the field at the observer, the pace at which time passes somewhere it is a relative quantity. If time not only passes at different paces at different places, but we only can speak about its observed pace, then the concept of cosmic time, of absolute time, makes no sense. $\endgroup$ – Anton Jul 16 '16 at 7:37
  • $\begingroup$ Put differently, if the universe cannot have any particular properties nor be in any particular state as a whole as ‘seen’ from the outside, then it also cannot have any particular properties not be in any particular state as a whole -and hence have a ‘universe-wide’ age- as seen from within. $\endgroup$ – Anton Jul 16 '16 at 7:38
  • $\begingroup$ As the electric repulsion between the parts of a finite-sized electron are so strong that it would disintegrate, it is thought to be an infinitesimal point-particle: if true, then it would be a tiny black hole, so if (please correct me if I’m wrong) time stands almost still near the event horizon of a black hole, then time would pass at wildly different paces even inside our body, so different parts would age at a different pace -so we might consider celebrating our birthday every day -which actually is not such a bad idea now I come to think of it. Cheers! $\endgroup$ – Anton Jul 16 '16 at 7:38
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In cosmology it is assumed that the universe is homogenous and isotropic for all intents and purposes.

Homogeneity means that every point in spacetime is equivalent regarding the dynamics of spacetime. Therefore we can define an observer that has a special physical meaning: the fundamental observer. It is the observer that is stationary with respect to the cosmic fluid.

Cosmic time is defined as that such an observer measured since the big bang. Hence there is no problem with the relativity of time, we have simply defined a time of a specific observer, that is a useful measure in a cosmological context.

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The gravitational time dilation and the speed-related time dilation - together with their respective twin paradox - are applying in the whole universe. That means that the age of a photon emitted at the beginning of the universe is zero, and the age of fast-moving particles is very different from what we call the "age of the universe".

You may imagine the universe as a "string curtain" of discrete strings (nothing to do with string theory): each particle is following its own worldline through time, and each particle has its own age, function of its velocity and its exposition to gravitation.

Between particles, space is timeless, because you cannot assign any velocity to points in space as long as there is no particle (at the difference to massless photons to which you can at least assign a proper time zero). This is why foliation of spacetime does not work. All you will get are sections of the "string curtain", but no continuous sheets.

However, there is a solution for the determination of the age of the universe: The age of the slow (non-relativistic) particles is the oldest age which can exist. Slow particles are approximately comoving with the cosmic microwave background, and the resulting age is higher than the one of fast moving particles. That means, the possible error due to relativistic effects with regard to the age of the universe is small.

There may be one reserve which is the early time after the big bang where all particles (even those which stars and planets are made of today) were fast and relativistic. But even in this period we may suppose that there were no particles which were much slower than the particles we are made of, and thus no particles with a longer proper time than the particles stars and planets are made of today.

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  • $\begingroup$ The problem I have with big bang cosmology (cosmic time, the age of the universe) is that the universe only can have a beginning in time, if time already passes before the bang, even though nothing much happens before the bang: if the (big bang) universe lives in a time realm not of its own making. If the universe can create itself, it always must have been able to do so. $\endgroup$ – Anton Jul 15 '16 at 7:24
  • $\begingroup$ For all fundamental questions about time, you must also take into account that any coordinate time may be reduced to some proper time, and proper time is a characteristic of mass particles. So if you ask, where does the time come from, it may help also to ask: where does mass come from. But the enigma of the origin of the universe is very far from being resolved. $\endgroup$ – Moonraker Jul 15 '16 at 7:31
  • $\begingroup$ I always think of cosmic time as "average time", i.e. The average of time at all points across the manifold (excluding event horizons). Which is similar in many ways to the flrw notion of cosmic time. $\endgroup$ – R. Rankin Jul 15 '16 at 7:49
  • $\begingroup$ Sorry, no: though (I read somewhere that) the time difference between a clock on the surface of the Sun and a clock in empty space is small, about 6 second per year, it doesn’t matter how tiny such difference it is –not to mention that a clock near the event horizon of a black hole would run much slower. You cannot sweep this fundamental difference away under your ‘average’ carpet. $\endgroup$ – Anton Jul 17 '16 at 9:41
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Laymans answer is coming.

The very simple answer: There is no absolute time in General Relativity.

(There isn't one already in the Special Relativity on a different reason).

The reason in the case of the GR (on my layman's understand) is the following: GR (and already the SR) plays not with time and points in space, it calculates distance and elapsed time between events, i.e. between points of the spacetime. This "spacetime distance" is calculated by an integration on the curved spacetime. But in the general case of the GR, this integration would be ambiguous.

But, the expanding Universe is described by the Friedmann equations. They describe essentially the curvature of the expanding Universe. This curvature is very symmetric, its space-like part is probably flat, so this is a special case, where this integration can be done. This is why we can have a "cosmic time", i.e. we can assign a "time since the big bang" to nearly every spacetime point of the Universe.

In very special situations, for example, around merging black holes, this curveture can be again not so "beautiful", I suspect the "cosmic time" is in their case again impossible.

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  • $\begingroup$ Well, I didn’t ask nor do I care about relativity theory, especially not about general relativity as it doesn’t offer any clue as to the origin of mass. You just cannot speak about the age of the universe if time passes at different paces at different places –how hard is it to understand this? $\endgroup$ – Anton Jul 17 '16 at 9:29
  • $\begingroup$ @Anton The very important second part of my post is that although generally there is no objective time in GR, the universe has a very special geometry where there is. Although you mentioned the GR only indirectly, the Big Bang and the Friedmann metric are GR things... you refer GR in your question. $\endgroup$ – peterh - Reinstate Monica Jul 17 '16 at 14:14
  • $\begingroup$ Gravitational time dilation has nothing to do with big bang cosmology -which I don't believe in, so as far as I'm concerned, Friedman describes a fictious universe. $\endgroup$ – Anton Jul 17 '16 at 15:54
  • $\begingroup$ @Anton Despite that, there is no absolute time in the GR in general sense. It is not about gravitational time dilatation (which is also another specific case in the GR), Friedman model is another. It is up to you, what you believe, but now you asked a question from us, i.e. you wanted to know what we think, and you referred in the question things what you "don't believe". $\endgroup$ – peterh - Reinstate Monica Jul 17 '16 at 16:03
  • $\begingroup$ While there may be no absolute time in general relativity, the statement of big bang cosmology that the universe has a beginning, a definite age, only makes sense if time passes at the same pace everywhere inside of it. Though by definition there is nothing outside the universe, if we speak about its age we nevertheless treat it as an ordinary object which lives in time realm not of its own making, as if we imagine to look at it from the outside and imagine things inside it to evolve at a single pace. $\endgroup$ – Anton Jul 18 '16 at 11:40

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