The possible combinations of "limits" and "boundaries" in nature are [1]: 1) "limited and bounded'; 2) “limited and unbounded”; 3) "unlimited and bounded”; 4) “unlimited and unbounded”. Here the object of "limit”can be geometric size, matter, energy, etc., and the object of “boundary”can be regarded as space-time boundary. We need to pay attention to two points here, first, what is the 'space-time boundary'; second, the static 'boundary' and dynamic 'boundary' of the essential difference. For the first point, usually the boundary of space can only be constituted by geometric points, lines and surfaces [2], which ensures that there is no indeterminate space on both sides of the boundary. If set time is the boundary in another dimension, the endpoints of such a boundary are zero-dimensional if they exist at all. For the second point, the Koch snowflake, a fractal curve, is often used in mathematics to express 'infinite perimeter, finite area', which presupposes that the 'boundary' is dynamically progressing infinitely. But once it is stationary at a fixed N(≠∞) [3], it becomes 'limited and bounded’.
‘Symmetry dictates interaction’is a motto of modern physics [4]. Symmetry is in some sense invariance. Coordinate symmetry reflects energy conservation, momentum conservation [5]; charge conservation reflects gauge invariance [6] ....... If time Displacement invariance, and space Displacement invariance, are globally applicable to any individual, do they thereby determine that the entire universe must be unconditionally time Displacement and space Displacement symmetric? Does this dictate that the entire universe must be unbounded in time and space? If there are boundaries to the universe, how can symmetry be maintained at such special places as boundaries? If the universe is anything like "limited and unbounded" [7], how does it support the finiteness of space if conservation of momentum applies globally, when the universe is viewed as a whole object? If conservation of energy is globally applicable, how does it support the finiteness of time? Either way we have to deal with some kind of 'boundary' violation. And if time is cyclic, then the universe must form an 'Ouroboros' [8]. Therefore, if the laws of nature are required to apply globally, it is impossible to face any 'boundary'.
Suppose a finite set, whatever its nature, can we always assign it a centre, as with a tangible entity, we can define its centroid, centre of mass, center of gravity, and so on. Can a finite universe then avoid the existence of a centre? If there is a centre, the universe must have boundaries. At this point, are the time and space boundaries symmetrical? And if we assume that the universe is, infinite in space, infinite in time, and infinite in energy, what would be the catastrophe for our cosmology, or would it be a convenient and useful gateway for research?
---------------------------------------------------
Notes
* It has been said that the universe is limited and unbounded similar to the surface of the Earth, where clearly no boundaries are defined.
** Multiverse theories are receiving more and more attention, and it is more appropriate to think of them as subuniverses within an entire universe.
---------------------------------------------------
References
[1] Chian Fan, "Supersymmetry : Light String and Light Ring". https://www.researchgate.net/publication/369527872_Supersymmetry-Light_String_and_Light_Ring.
[2] Can This Be an Argument for 3-D Space? https://www.researchgate.net/post/NO1_Can_This_Be_an_Argument_for_3-D_Space2.
Yang, J. (2016). The Boundary of A Boundary is Null. https://jeffycyang.github.io/the-boundary-of-a-boundary-is-null/index.html .
[3] Weisstein, Eric W. "Koch Snowflake." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/KochSnowflake.html.
[4] Yang, C. N. (1980). Einstein's impact on theoretical physics. Physics Today, 33(6), 42-49.
Symmetry, Invariance and Conservation (1) - Who is the Primary? https://www.researchgate.net/post/NO20Symmetry_Invariance_and_Conservation_1-Who_is_the_Primary
[5] Kosmann-Schwarzbach, Y. (2011). The Noether Theorems. In Y. Kosmann-Schwarzbach & B. E. Schwarzbach (Eds.), The Noether Theorems: Invariance and Conservation Laws in the Twentieth Century (pp. 55-64). Springer New York. https://doi.org/10.1007/978-0-387-87868-3_3 .
[6] Brading, K. A. (2002). Which symmetry? Noether, Weyl, and conservation of electric charge. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 33(1), 3-22. https://doi.org/https://doi.org/10.1016/S1355-2198(01)00033-8 .
[7] Einstein, A. The Collected Papers of Albert Einstein [爱因斯坦文集] .
Hawking, S. W., & Hertog, T. (2018). A smooth exit from eternal inflation? Journal of High Energy Physics, 2018(4), 147. https://doi.org/10.1007/JHEP04(2018)147
Taming the multiverse: Stephen Hawking’s final theory about the big bang, https://www.cam.ac.uk/research/news/taming-the-multiverse-stephen-hawkings-final-theory-about-the-big-bang#:~:text=Hertog%20and%20Hawking%20used%20their%20new%20theory%20to%20derive%20more
[8] https://mythology.net/others/concepts/ouroboros/
Chian Fan
Yes, the entire universe has a symmetrie and no specific center.
The question you are raising just hits the main point of current cosmology.
But the answer is given by differential geometry. The proposed structure for the universe is called S³ or 3-sphere. Mathematically it is the three dimensional surface of a four-dimensional ball.
Physically it is a structure without a surface and with a constant spatial Ricci curvature. The curvature is given by 1/R² with a volume of 2π²R³. Every point in this volume is a centre of gravity of the whole volume.
Such a structure is immune against compressional (gravitational) or expansive pressure because pressure forces cancel out at any location. The missing surface is the reason for that property.
Chian Fan
It's simply a sphere which has a radial oscillation. The Universe is situated inside an infinite void and there are most likely other similar Universes.
JES
Any really scientific answering the question
【 “NO.50】Should the Entire Universe Have any Symmetry? Can a Finite Universe Avoid a Centre?”
- really is impossible in mainstream physics, since in the mainstream all really fundamental phenomena/notions , first of all in this case “Matter” [in the mainstream “Universe”] – and so everything in Matter, i.e. “particles”, “fundamental Nature forces” – and so “fields”, etc., “Consciousness”, “Space”, “Time”, “Energy”, “Information”, are fundamentally completely transcendent/uncertain/irrational, and so in the mainstream only some , and rather numerous, really scientifically non-grounded “answers” are possible – and are, though.
At least scientifically rational elaboration of the question problems really can be only in framework of the Shevchenko-Tokarevsky’s really philosophical 2007 “The Information as Absolute” conception, recent version of the basic paper see
https://www.researchgate.net/publication/363645560_The_Information_as_Absolute_-_2022_ed
and more concretely in the Shevchenko-Tokarevsky’s Planck scale informational physical model, which is based on the conception, two main papers are
https://www.researchgate.net/publication/354418793_The_Informational_Conception_and_the_Base_of_Physics and
https://www.researchgate.net/publication/383127718_The_Informational_Physical_Model_and_Fundamental_Problems_in_Physics
- where the phenomena/notions above are rigorously scientifically defined, and so on the model quite scientifically rationally, i.e. in complete accordance with existent experimental data, and basing on the really outstanding foundational von Weizsäcker Fredkin-Toffoli findings, it is postulated that the Matter’s ultimate base is the (at least) [4+4+1]4D dense lattice of primary elementary logical structures – (at least) [4+4+1]4D binary reversible fundamental logical elements [FLE], which is placed in the Matter’s fundamentally absolute, fundamentally flat, fundamentally continuous, and fundamentally “Cartesian”, (at least) [4+4+1]4D spacetime with metrics (at least) (cτ,X,Y,Z, g,w,e,s,ct).
FLE “size” and “FLE binary flip time” are Planck length, lP, and Planck time, tP, the utmost universal “kinematical” space dimensions are “von Weizsäcker’s” XYZ, and “Fredkin-Toffoli” cτ, dimensions, ct is real time dimension.
Everything in Matter, i.e. particles, fundamental Nature forces’ mediators, etc., are some specific disturbances in the lattice, which constantly and always move in the 4D space with metrics (cτ,X,Y,Z) [which directly now is observable as the 3DXYZ space] with 4D speeds of light, c, c= lP/tP; and, in parallel, simultaneously move with the speed of light in the ct-dimension.
In the mainstream Matter’s spacetime is 4D with [in classic physics, including Newton Gravity] Euclidian metrics (cτ,X,Y,Z), and [in the cosmology] pseudo Riemannian metrics (icτ,X,Y,Z), “i”is the imaginary unit, where the really space cτ-dimension is postulated as the time dimension;
- what, again, really is some illusion, and so in the mainstream development of the really adequate to the reality topology of Matter is principally impossible.
Including, say, anything in this
“…If the universe is anything like "limited and unbounded" [7], how does it support the finiteness of space if conservation of momentum applies globally, when the universe is viewed as a whole object? If conservation of energy is globally applicable, how does it support the finiteness of time? Either way we have to deal with some kind of 'boundary' violation. And if time is cyclic, then the universe must form an 'Ouroboros…..”
- cannot be answered, while in the quote are quite legitimate in the mainstream “finiteness of space”, “finiteness of time” , “time is cyclic”, what fundamentally isn’t correct: Matter’s space dimensions by definition are fundamentally infinite, and in the space infinite number of other Matters can exist, even would be infinite; time dimension is absolutely infinite; and by no means can be some “cyclic times” and “'Ouroboros”.
The post is rather long, so now
Cheers
Sergey Shevchenko "The post is rather long..."
Unfortunately it also is nothing than hot air without any substantial fact.
After the preface in SS post above let continue more concretely relating to the thread question
“Should the Entire Universe Have any Symmetry? Can a Finite Universe Avoid a Centre?”
Firstly note that from the rigorous scientific definition in the SS&VT really philosophical 2007 “The Information as Absolute” conception of the fundamental phenomenon/notion/informational system – element of the absolutely fundamental and absolutely infinite “Information” Set - “Consciousness” , and from existence of seems quite well observable “Consciousness on Earth” version “human’s consciousness”,
- which, using fundamentally specific any real “Consciousness’s” ability to obtain and logically analyze, some information about her environment, often and rather adequately to the reality, rationally explore the really transcendent for her material environment, and, using also transcendent for her “energy” makes, say, a lot of things that don’t exist in the environment, etc.,
- it looks as quite rational to assume, that in the Set a lot of other consciousnesses exist, including which can have much more abilities to make something, and, at that, know – what is the mystic for humans absolutely fundamental phenomenon/notion “Energy” is.
Including, say, such Consciousness(es) could design and make the really smartly beautifully designed informational system “Matter”, that is based on a simple binary logics, however exists as practically infinite diversity of material objects, in Matter the energy conservation law acts, and so it is well closed system in the Set, etc.
So that is assumed in the SS&VT initial Planck scale cosmological model, more see 3-rd link in the SS post 2 days ago now, above.
This, first of all means, that such points as what is Matter’s creation, from where and how the unbelievable portion of energy was spent at the creation, including also why, and spending of what energy, at that Matter “expanded” at first steps [inflation epoch] of creation and why, and spending of what energy, it “expands” till now; etc. like,
- all these points, including the last one that in mainstream cosmology is called “dark energy” and /|-term, are outside physics that really can “non-transcendently” study only observable by instruments matter., i.e. what is on Planck scale and above.
Though, again, Matter is rather simple logical system, and so humans can, in principle, to develop some models/theories that scientifically at least rationally could answer if not “Why and how really was/is?”, but at least “How that could be?”
An example is the SS&VT Planck scale initial cosmological model [see 3-rd link in SS post above, 2 days ago now, section “Cosmology”], where well scientifically rationally it is assumed that Matter’s creation indeed started from some points as creation of possibly one FLE, on next step this FLE – and the next FLEs - was/were by some program “divided”, and so in the 8D space of Matter’s infinite spacetime with metrics (at least) (cτ,X,Y,Z, g,w,e,s,ct), which “appeared” absolutely obligatorily [see in this case, say SS post https://www.researchgate.net/post/what_is_the_most_important_problem_in_the_theoretical_physics_now#view=6664575e41c39451ce08b623/1680/1681/1680/1683/1683/1683/1683/1684/1683/1685/1685/1686/1685/1685/1686/1685/1687/1686/1685/1689/1689/1688/1690/1691/1700/1758/1758/1759/1764/1765/1764/1765/1766/1768/1768/1769/1768/1769/1769/1769/1770/1769/1770/1769, page 1769, 4 days ago now] at first FLE creation.
That resulted in exponential creation in the space of first version of the uniform and isotropic in the space FLE lattice [“inflation epoch”], the lattice had the center, including in 3DXYZ space, – the point, where the first FLE appeared.
At next step in the lattice uniformly and isotropically globally, but not uniformly locally [so, say, galaxies were formed] the main portion of energy was pumped, what resulted in creation of eventually observable now matter, which formed the observable globally uniform/isotropic – and in this sense “having this “symmetry”” Matter/ “Universe”.
All/every created particles – and so all/every material structures – because of the energy conservation law always and constantly move isotropically in the utmost universal 4D space with metrics (cτ,X,Y,Z) with the 4D speeds of light, and so absolutely obligatorily simultaneously in the time ct-dimension, i.e. Matter at every time instant exists as a 4D hyperplane in ct=ct time ct-dimension point that has thickness one Planck length, while matter moves isotropically in the 4D – really observable 3DXYZ - space in rather probably 4D hypersphere’s [as that Feynman suggested in 1960s] surface in the 5D spacetime.
The 5Dsystem has the center in the space, which is the first FLE point above, however in the hypersurface above there is no center, and so the observable now Matter is again uniform and isotropic; while the sphere’s utmost universal 4D volume, which has radius be equal ct, below the surface is rather probably empty.
More see the pointed “Cosmology” section.
Cheers
Dear @All
Many thanks to everyone for their responses, even though everyone has a different point of view.
For me personally, learning is not about accepting a particular answer, but about respecting each point of view and thinking about their rational basis.
Best Regards, Chian Fan
- Badges
- Science topic
- Similar topics
- Higher Education
- Universities