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Why is it often said that "time itself started with the Big Bang"?

If you take the scale factor in the Friedmann–Lemaître–Robertson–Walker metric to zero, then the spatial component goes to zero, but not the temporal one. In other words, space contracts, but nothing happens to time. Or, in the words of A. Zee, "In our current description, space is created at the Big  Bang, but not time." (Zee, A. Einstein Gravity in a Nutshell: p. 787).

So, any idea from where the notion of beginning of time in BB comes from?

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3 hours ago, Genady said:

Why is it often said that "time itself started with the Big Bang"?

If you take the scale factor in the Friedmann–Lemaître–Robertson–Walker metric to zero, then the spatial component goes to zero, but not the temporal one. In other words, space contracts, but nothing happens to time. Or, in the words of A. Zee, "In our current description, space is created at the Big  Bang, but not time." (Zee, A. Einstein Gravity in a Nutshell: p. 787).

So, any idea from where the notion of beginning of time in BB comes from?

The model it's based on takes us back to a point just after t=0, but nothing about either model or theory says that's when time itself started. It's just the beginning of a universal evolution from an extremely hot, dense state to our present configuration. Beginning of an era, rather.

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31 minutes ago, Genady said:

Why is it often said that "time itself started with the Big Bang"?

You can say, rather that 'time as we know it' started then - the temporal frame and linear units-elapsed in which measure all the events in our universe.

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If I'm allowed to speculate here, I could imagine that in that hot dense particle soup, before Higgs and before symmetry breaking, all particles were massless. Thus, time was "frozen", like the time of a photon is.

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Markus usually uses the analogy of "What is north of the North Pole ?"

Myself, I would think geometry is needed for time and space.
Without geometry, at 10-43, Planck scale/time, there is no geometry.

This would be what J A Wheeler termed 'quantum foam'.
As 

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Ignoring particles and staying with geometry for now. As we go back in time, the three spatial dimensions of spacetime collapse, but the temporal dimension survives. So, at the BB the 4D spacetime geometry is replaced by 1D time geometry (there are no many choices for geometry in 1D.)

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1 hour ago, Peterkin said:

You can say, rather that 'time as we know it' started then - the temporal frame and linear units-elapsed in which measure all the events in our universe.

Bingo! Space and time,  (as we know them) started at the BB.

One cannot exist without the other and are two sides of the same coin.

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6 hours ago, Genady said:

If you take the scale factor in the Friedmann–Lemaître–Robertson–Walker metric to zero, then the spatial component goes to zero, but not the temporal one.

The FLRW metric is a solution to a classical field equation, using classical fluid dynamics as boundary conditions. The problem is that beyond a certain point in the past, quantum effects (both within the primordial plasma, and within gravity itself) become too large to be neglected - hence, taking the FLRW metric beyond that point would mean you are extending GR beyond its domain of applicability.

The alternative approach is to treat the universe in its entirety as a quantum wave-function, even if you don’t know the precise laws of quantum gravity; it then satisfies an evolution equation not dissimilar to the Schroedinger equation, which is called the Wheeler-deWitt equation. Finding solutions to this is, for technical reasons, very difficult - however, one solution we do know of is the Hartle-Hawking state. In this state, neither time nor space have a boundary at the beginning, but instead have ‘poles’. These poles do not coincide, so there would have been an initial region that was just 3D space. The poles themselves are not boundaries, in the sense that you cannot extend geodesics ‘beyond’ them, even though geodesic completeness is maintained. What this means for time is that, if you were to extend a geodesic into the past, there eventually comes a turning point past which you can go back no further; instead, whatever direction you choose to go to will be the future again. It’s like the North Pole on Earth, from which all directions are south, without it being a boundary of any kind. In the same way, a pole in time is a point at which all temporal directions are necessarily the future. Something similar would be true for space as well. Hence, in the Hartle-Hawking state, space and time would be unbounded, yet still finite (in the past).

Note though that this is only one specific solution to the Wheeler-deWitt equation; others are possible, which lead to different scenarios.

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9 hours ago, Markus Hanke said:

The FLRW metric is a solution to a classical field equation, using classical fluid dynamics as boundary conditions. The problem is that beyond a certain point in the past, quantum effects (both within the primordial plasma, and within gravity itself) become too large to be neglected - hence, taking the FLRW metric beyond that point would mean you are extending GR beyond its domain of applicability.

The alternative approach is to treat the universe in its entirety as a quantum wave-function, even if you don’t know the precise laws of quantum gravity; it then satisfies an evolution equation not dissimilar to the Schroedinger equation, which is called the Wheeler-deWitt equation. Finding solutions to this is, for technical reasons, very difficult - however, one solution we do know of is the Hartle-Hawking state. In this state, neither time nor space have a boundary at the beginning, but instead have ‘poles’. These poles do not coincide, so there would have been an initial region that was just 3D space. The poles themselves are not boundaries, in the sense that you cannot extend geodesics ‘beyond’ them, even though geodesic completeness is maintained. What this means for time is that, if you were to extend a geodesic into the past, there eventually comes a turning point past which you can go back no further; instead, whatever direction you choose to go to will be the future again. It’s like the North Pole on Earth, from which all directions are south, without it being a boundary of any kind. In the same way, a pole in time is a point at which all temporal directions are necessarily the future. Something similar would be true for space as well. Hence, in the Hartle-Hawking state, space and time would be unbounded, yet still finite (in the past).

Note though that this is only one specific solution to the Wheeler-deWitt equation; others are possible, which lead to different scenarios.

Thank you for the detailed answer. As a synopsis, classical GR doesn't lead to a "start of time". Quantum GR might, albeit not necessarily.

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13 hours ago, Genady said:

As a synopsis, classical GR doesn't lead to a "start of time".

Yes, GR simply doesn’t have anything to say about the earliest moments - that’s outside its domain of applicability.

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