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If we accept the result of big-bang theory that time does not indefinitely extend back in the past, how can this result be smoothly integrated with the common-sense view that for every time-instant there exist others prior to it?

That is, how can we re-school our common sense so that it accepts that the idea of "beginning of time" is not an outcome deemed necessary only because of the measuring limitations of experimental physics or the structural properties of the equations used to arrive at it?

Which leads naturally to another issue: why should the experimental approach re-school common sense rather than common sense re-school us with respect to our accepted mathematical methods?

EDIT: I have posted the same question in physics stackexchange. It was rightfully closed as "opinion based", but the following highly illuminating answer was given in the comments by John Rennie:
"no physicist I know really believes time started at the big bang. We believe some theory of quantum gravity will remove the singularity. You don't want to take the wilder claims of popular science media too seriously. There is no shortage of common sense amongst physicists".
See here.

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    I think yours and physicists' ideas of "common sense" are very different. Physicists believe that quantum gravity will remove the singularity because such a thing is a mathematical contrivance, not because of everyday intuitions about time instants. Physicists easily dismiss plenty of such intuitions: flat Earth, inertial forces, absolute time, determinism, etc. The "common sense" Rennie has in mind, as one can see from his link, is the experience informed by working with sophisticated mathematical models, not reflections on thinking habits.
    – Conifold
    Commented Jul 16, 2020 at 6:17
  • @Conifold -- I view Rennie as confirming my and everyone's experience with the mathematical-model approach to physics (today an odd-sounding phrase, as nothing else seems possible), namely that "the experience informed by working with sophisticated mathematical models" hasn't been able to change our normal intuition, which, even for the great minds of physics, is the same as that of "the man in the street": that for every time-instant there exist others prior to it. So there is still a formidable gap to be bridged. Popular science seems not to adequately emphasize this point.
    – exp8j
    Commented Jul 16, 2020 at 7:31
  • He is not, you are repeating Kant's mistake. If physicists were bound by "normal intuition" they'd feel that every motion requires a push and "at he same time" and Euclidean geometry have universal meaning. Common sense gets refined and evolves routinely, one does not need a "great mind" for it. You should read Peirce on common sense:"indubitable beliefs refer to a somewhat primitive mode of life... occasions of action arise in relation to which the original beliefs, if stretched to cover them, have no sufficient authority."
    – Conifold
    Commented Jul 16, 2020 at 8:46
  • @Conifold -- Agreed, but not regarding space and time. To my mind these primary categories are internally conceived and have nothing to do with the external, practically measurable quantities of physics. E.g. when velocities approach the speed of light, it's only our measuring capabilities that are altered (hence the need for the concept of relativistic spacetime) not our internal conception of space and time, which exists without need for visible light and measuring devices. So it's an issue how measuring-based physics will ever manage to enter the realm of our internal conceptions.
    – exp8j
    Commented Jul 16, 2020 at 11:43
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    @exp8j Read up on the delayed choice quantum eraser experiment if you believe that physicists can afford to trust their common sense. Keep in mind that this isn't like the singularity at the big bang, which is only predicted by models that may be an approximation. This is an experiment that has actually been performed. Our common sense evolved in a macroscopic, low-speed, low-gravity environment. It works reasonably well in that setting. Not always so well outside it.
    – Ray
    Commented Jul 16, 2020 at 14:21

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You must realize that "common sense" views about the operation of the physical world are of no use at all when considering the earliest times in the big bang. In that regime (of order ~ one Planck time) the concept of time itself loses its physical meaning i.e., it makes no physical sense to talk about time intervals shorter than the Planck time (which is about 10^-43 second). Mathematically, this fact gets smoothly integrated into the "common sense" view of time as time marches forward out of the big bang, and the Planck time is left behind in the past.

The mathematical expression of this is what drives our understanding, not the other way around. You will find that the math describing the evolution of the universe at early times is under no obligation to comport with what our everyday opinions about it might be. That regime is the province of mathematics, not philosophy.

A good reference on this topic is Stephen Weinberg's book The First Three Minutes.

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  • Planck time is an example of our current measuring limitations, not a final threshold. I have added an edit to the original question which I consider very helpful towards a correct interpretation of big-bang mathematics relative to "the beginning of time".
    – exp8j
    Commented Jul 16, 2020 at 6:03
  • you are wrong. it is not a measurement issue, it is a final threshold. have a look at weinberg's book.
    – niels nielsen
    Commented Jul 16, 2020 at 17:10
  • Our mind can in principle divide every threshold in half, therefore how can we be sure that this internal, mental action can never be transformed into an external, physical one?
    – exp8j
    Commented Jul 16, 2020 at 19:53
  • it is a direct and fundamental outcome of the math involved and it cannot be circumvented by any means. As such it is woven into the structure of spacetime. Search on "planck time", "planck length", and "planck mass" for more on this.
    – niels nielsen
    Commented Jul 16, 2020 at 21:06
  • "Common sense" is indeed very useless in that which is not common. Higher dimensions, large scales, or tiny scales, non-euclidean geometry. You need to basically train an intuition. Before that, you trust your tools, your measurements, your methodology. In fact, discarding common sense is more useful, it boxes you into what is allowed.
    – GettnDer
    Commented Jul 20, 2020 at 17:58

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