January 16, 2014

Philosophy of time

The nature of time has had extensive attention in part down through the ages, such as Plato, St. Augustine, Pascal, Leonardo, Newton etc. For example, Newton considered time to flow uniformly, as if it were a separate manifold (1-surface) from the 3-surface of his mechanics described universe.

‘Absolute, true, and mathematical time, of itself, and from its own nature, flows equably without relation to anything external…’   Newton’s Principia

For a manifold, this would give a product space description M3 x M1 , the simplest fiber bundle description. Hence such description would be universal; that is the same common time for throughout the universe. Subsequently, the relativistic model refers to time as the interval between events, wherein clocks are associated with respective observers. However an event such as the Big Bang, and concomitant Big Expansion of our manifold (i.e. 3-surface), does not have such a General Relativity Theory description; nor is ‘initial’ 3-expansion (i.e. Hubble expansion) limited by velocity of light, as in Special Relativity. Hence the possibility of further modeling in regards to how our 3-space and contents evolves.

Might there be another common time description as to how our 3-volume evolves? Just as Gauss described curvature of a surface intrinsic to such 2-surface, Riemann described curvature of a 3-surface as intrinsic to such 3-surface. Might not one analogously describe time as intrinsic to our 3-surface? Could the nonlinear Hubble expansion be utilized as such common time description for our 3-surface, and perhaps for a set of such 3-surfaces (i.e. 3-volumes, 3-manifolds); that is for misnomer, ‘multiple universes’? Universe, denotes all inclusiveness, rather than multi-universe which implies a set of such all inclusiveness. Hence better to refer to a set of 3-volumes i.e. 3-manifolds. Also non-linearity to Hubble expansion might even be of an always exponential nature, if it is just a specific example of the more general case: all declining explosiveness is of an exponential nature.

Do all locations of our 3-volume and for a possible set of 3-volumes, share the same common time i.e. common cosmic time? That is, perceiving the same Big Bang ~13.8 billion years ago; and thus the same ~2.7 degree kelvin temperature of cosmic background radiation for our now i.e. common positive definite modified global instant; with mapping of a set (domain of function) of such instants to co-domain integers? Hence are integers analytical? Also then no necessity for inflation models?  see above blog.

Also for a set of 3-volumes, contained in an array of planes, spherically symmetrical about modified central force,  might one also have a concomitant common cosmic time description intrinsic to the System i.e. array of planes consisting of 3-volumes? That is, might one utilize a spherical shell intersecting respective centers of all 3-volumes, denoting such common cosmic time for all 3-manifolds? This might be referred to as Modified Global Simultaneity (MGS). Such set of successive concentric MGSs (each of positive definite thickness) would be matched to the integers. Also such set of MGSs could be rendered as always exponentially changing; matching to an exponential curve. Likewise for changing rate of Hubble expansion, intrinsic to each and all changing 3-volumes.

Thus in such modeling, would one have two concomitant descriptions of an overall common cosmic time; the Hubble expansion, intrinsic to changing 3-volume, and MGS, intrinsic to an endlessly evolving dynamic System?  Apeiron

Further elaboration

Also see blog: Integersanalytical?


1 Comment »

  1. Thus in such modeling, would one have two concomitant renditions of an overall common cosmic time; the Hubble Expansion, intrinsic to changing 3-volume, and MGS, intrinsic to an evolving dynamic System, described as an analytical engine, consisting of an entangled array of manifolds, endlessly evolving?  apeiron    

    Comment by zankaon — January 21, 2016 @ 2:11 pm

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