Why do astrophysical and cosmological theories accept the merely mathematically thinkable ISOTROPY (the principle that all directions in the cosmos are alike, and hence no direction is preferred in any manner than any other) in large regions of the cosmos as the general empirical case and as the absolute case in the cosmos? I think the most important reason is the dogmatic faith of physicists and mathematicians in the statistical "counts" / "measurements" of particular regions of the universe.
In fact, the reason why statistical measurements are being used is that there are differences between every two regions, subregions, etc. everywhere and in every direction in the universe. This fact is forgotten in the dogmatic faith in the power of mathematics!
If there are local differences here, and local differences there, and the same everywhere, then we cannot generalize the same local differences into supra-regional overall isotropy! But, for mathematical purposes, some theories generalize these details statistically, but this is never the absolute case anywhere, in any direction!
Even in the pages of RG, I have had discussions where some have continued to insist on the power of mathematics over physics and that those who cannot take the statistical average as the general case (and hence as the absolute case) are being stupid, because mathematics does wonders!
Let me now take the simple example of a balloon in order to discuss the cosmological aspect of identity of parts, ISOTROPY (of course, this is not identity), simultaneity of processes, cyclic cosmic evolution, etc.
I consider them all as very simplistic and silly, ad hoc, meant only for ideal mathematical consumption, and not meant for physics and cosmology. For example, how can anything absolutely cyclic, spherical etc. be the real case, if there are ANISOTROPIES everywhere in the universe?
A balloon may be inflated with air at a measurably very stable and constant rate. But between any two points of it there must be some difference of rate of expansion. This is the natural case. Nothing else can come and stop this process in the cosmic case. If not, all the points in it would naturally have to be made of the SAME thing, which is impossible.
Similarly, all our measurements and the predictions of isotropy and related equalities of potentially measurable and comparable spacetimes, may be good in theory. But these cannot be as equal as we may conclude from the theories that result.
Merely because of the minute but naturally true difference between their existence in terms of the different potentially measurable spacetimes, it should naturally be concludable that there is no absolute identity of physical existence, structure, evolution, etc. between any two parts in the cosmos.
NATURALLY, THE MINUTE DIFFERENCES IN PARTS OF THE COSMOS, IN THE COURSE OF TIME, SHOULD EXPRESS THEMSELVES AS GREAT DIFFERENCES AND RESULT IN THE MANY COSMIC ANISOTROPIES THAT WE SHOULD FIND AND THEORETICALLY PRESUPPOSE, NOT ONLY IN SOME OBJECTS OF THE COSMOS BUT ALSO IN VAST REGIONS OF THE COSMOS. NATURALLY, THIS MUST BE THE CASE EVEN IN THE VARIOUS UNIVERSES WITHIN THE COSMOS, IF THE COSMOS IS AN INFINITE-CONTENT CONGLOMERATION OF AN INFINITE NUMBER OF FINITE-CONTENT UNIVERSES.
This then becomes a pre-physically self-evident fact. This shows something interesting: Concluding CONSTANCY OR EQUALITY OF RATE OF EVOLUTION from the values concluded “at present”, “a few times”, that seem to be “constant" CAN AUTOMATICALLY BECOME A SELF-GOAL IN PHYSICS, ASTROPHYSICS, AND COSMOLOGY.
Hence, in my opinion, any sufficiently big portion of the cosmos, under expansion or contraction, should at some time experience some sort of contraction or expansion as the opposite evolutionary case. This evolutionary case is not a recurrence of everything as such, but a forward process!
This must be the case also in the infinite number of parts of the cosmos, if the cosmos is of infinite matter-energy content.
Penrose and some of his colleagues seem to have held a sort of CONFORMALLY CYCLIC COSMOS theory. On the other hand, we have the miracle-feeder theories of CONSTANT INFLATION WITH RESPECT TO OUR LOCAL UNIVERSE. I consider these theories, too, as fads INVENTED TO EXPLAIN SOME COSMIC DISCOVERIES.
In the case of Penrose, it was the recent discovery of circles (spheres) of the CMB which they claim are "around the big bang universe of ours".
In the case of Alan Guth and others, the inflation theory has been a contrivance to keep astrophysics and cosmology away from some speculations, which Guth recently admitted to be not a very realistic solution!
The extent of inapplicability involved in the concept of isotropy may be extended also to theories of the overall shape of the outermost realms of each expanding universe. Some speak of empirical evidence for the outermost layer of such a universe to be spherical. From this conclusion, they even proceed to emphasize that it is absolutely spherical, citing again the same “empirical” evidence! They do not forget to claim that all cosmic shapes are such! But the question to be put at them is whether the so-called spherically exact expansion of our universe would mean also that the clusters of galaxies, galaxies themselves, stars, planets, etc. should also expand as do the universe in a spherical manner as they claim!
The perhaps controversial viewpoint presented in this short discussion text is of wide-ranging consequences. The thesis is clear and works against accepting mathematically presupposed perfection as such in physics and other sciences. I invite critiques on my arguments.
thanks Dr Raphael Neelamkavil for pointing out this question. However, I've another one regarding the calculations of the background radioactivity that traced from the big bang event, can we find that origin point of the coordinates (0,0,0) through numerical methods?
regards,
What you said is true. Naturally, it is a facility necessitated by the mathematics. For that matter, even the concept of a singularity in black holes and maybe of many other cosmic bodies! In the physics, the mathematically correct asymptotic approach of infinite time, infinite density, and zero volume can never be realized. To exist, there should be some Extension. Hence, a strict singularity does not exist in the black holes and has not existed at the central black hole of the "big bang" universe.
If it had existed, it would have existed for an infinite time, and in that case its expansion is a paradox.
All these are because of the partial extent of incompatibility of mathematics to physics. See:
https://www.researchgate.net/post/Source_of_Major_Flaws_in_Cosmological_Theories_Mathematics-to-Physics_Application_Discrepency
https://www.researchgate.net/post/Infinite-Eternal_Multiverse_Implications_to_Physics_and_Cosmology
https://www.researchgate.net/post/Gravitational_Coalescence_Paradox_GCP_Introduction_to_Gravitational_Coalescence_Cosmology_GCC
https://www.researchgate.net/post/Is_Mathematics_an_Exact_Science_If_Yes_and_If_Not_Why
https://www.researchgate.net/post/Mathematics_and_Causality_A_Systemic_Reconciliation
https://www.researchgate.net/post/If_the_cosmos_is_1_finite-content_or_2_infinite-content_Is_there_finite_or_infinite_creation
https://www.researchgate.net/post/Can_the_cosmic_or_local_black_hole_singularity_be_of_infinite_density_and_zero_size
A 3-sphere with all its remarkable properties is a perfect model for the structure of our universe. The most remarkable property is that a 3-sphere does not have a surface. It has a homogenous scalar space curvature of 1/R² and a finite volume of 2π²R³. It cannot collapse because every point is the centre of gravitation of the whole volume.
The metric of a 3-sphere is isotropic. Now many people think that this proves, that a 3-sphere also is isotropic. But a 3-sphere has an orientation. As long as we consider that orientation as arbitrary, we can keep our assessment of isotropy. But a concrete 3-sphere has a definitive orientation.
How can we see that a 3-sphere has an orientation? We consider the geodesics. The geodesics in a 3-sphere are great circles of radius R. If we link any two points, which are not antipodes, with great circle arcs, we can rotate those arcs around the straight connection of the two points. But from this rotational symmetric bunch of arcs, only one arc is a geodesic. Without this specific selection, the image of the second point would appear as a circle. This would lead to a blurred image of distant galaxies.
But this specific selection of the geodesic arc, from all possible great circle arcs connecting two points, disturbs the isotropy and proves that a 3-sphere has an orientation.
The proof with the blurred image also shows that a homogenous and isotropic space expansion cannot lead to a concrete 3-sphere structure.
Cosmologists do not want this being true, because they proudly can proof that the isotropic space expansion, they are postulating, leads to the 3-sphere metric. But the geodesic argument unrefutably shows that a concrete 3-sphere has an orientation, which disturbs isotropy.
This confirms Raphaels initial assessment in that thread.
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