In his attempt to formulate the laws of Physics in a form independent also of non-Galilean reference frames, Einstein formulated the chrono-geometrical theory of gravity, namely the General Theory of Relativity, within the framework of which the shape of space and the flow of time are determined by the motion of matter.
Einstein's theory of gravity constituted, as is well known, the mathematical framework for creating cosmological models which, despite the local character of Einstein's theory, aim to explain both the birth and the evolution of the Universe.
Dominant today is the quasi-metaphysical model of the Big Bang (referred to ironically as such by Hoyle).
Let me know if you want any part further clarified!
Yes, there are limits to GR-based cosmology due to General Relativity's local character, primarily because GR is a classical theory that breaks down at singularities and doesn't fully incorporate quantum mechanics.
Yes there are limits, obviously for the quantum world, however depending on who you ask, some people believe it is incomplete to describe much larger things such as the flat rotational curve of galaxies. I personally believe it is in need of some tweaking. It's something I am currently working on rather than they need to add new particles.
Right from the beginning (Einstein,Lemaître,Friedmann), general relativity was applied to the universe as a whole. It is definitely not a "local" theory, ebate.though the introduction of averages of the metric on large scale still raises some debates (Cf. Thomas Buchert).
Elaborating Νοtes:
1. On local nature of GR: General Relativity is a local theory that describes gravity as the curvature of spacetime governed by local laws. Einstein’s field equations relate the distribution of matter and energy to curvature at each point of spacetime.
2. On its application in cosmology: Although the theory is local, it has been successfully used to build cosmological models describing the evolution of the entire Universe, relying on the assumptions of large-scale homogeneity and isotropy (e.g., the Friedman-Lemaître-Robertson-Walker model).
As cosmology is the study of the entire Universe, it typically requires additional assumptions or frameworks (e.g., the cosmological principle, symmetries) to apply GR on a universal scale
Both SR and GR have been shown to be absolutely baseless in published papers in peer-reviewed journals which are available in my profile on ResearchGate. Furthermore there is an open challenge to SR and every theory based on it including Big Bang theory which is also available in my profile.
Indeed, there are restrictions on the straightforward application of the local theory of General Relativity (GR) to the highest scales of cosmos. When it comes to explaining solar system gravity and comprehending phenomena like black holes, General Relativity is remarkably effective. However, there are certain conflicts and unanswered problems when applied to the entire observable universe:
• Dark Matter and Dark Energy: In order to account for observed galactic rotation curves and the universe's accelerated expansion, GR demands the existence of these unidentified elements. They can be accommodated by GR, but it doesn't explain their nature or genesis. This implies that GR might not be comprehensive. • Singularities: GR predicts that the laws of physics will break down at the Big Bang and inside black holes. This suggests that in severe circumstances, GR might need to be changed or replaced. • The Horizon Problem and Flatness Problem: To account for the observed homogeneity and flatness of the cosmos, the conventional GR-based Big Bang model necessitates extremely precise beginning conditions, or fine-tuning. Frequently used to address these issues, inflation is an addition to GR rather than a direct result of it.
• Quantum Gravity: Quantum mechanics is not incorporated into GR, which is a classical theory. It is anticipated that a theory of quantum gravity would alter GR at very small scales and very high energies, potentially impacting cosmology. This is one of the main unresolved issues in reconciling GR with quantum mechanics. • Alternative Theories: In an effort to explain cosmic phenomena without referring to dark matter or dark energy, some cosmologists investigate alternative theories of gravity, such as f(R) gravity and modified Newtonian dynamics (MOND). Conclusion: Although GR offers a strong foundation for cosmology, its shortcomings encourage the pursuit of extensions or substitute theories that can resolve the ambiguities and contradictions at the highest energies and largest scales.
Yes, there is a conceptual limit to GR-based cosmology that stems from the local character of General Relativity (GR). GR is formulated as a local, geometric theory: the Einstein field equations relate the curvature of spacetime at a point to the energy–momentum content at that point. This locality underpins its mathematical consistency and its experimental successes in solar system tests, gravitational waves, and astrophysical dynamics.
However, cosmology inherently deals with global properties of spacetime — the expansion of the universe, the topology of spatial sections, the global energy budget, and causal horizons. Extending a strictly local theory to describe these global features requires additional assumptions, such as the cosmological principle (homogeneity and isotropy at large scales), choices of boundary conditions, or effective averaging procedures over inhomogeneities. These go beyond what GR itself strictly dictates.
Moreover, GR has no built-in mechanism to address certain nonlocal or emergent aspects of cosmology:
- The cosmological constant problem (linking local vacuum energy to global expansion).
- The horizon and flatness problems, which motivated inflation.
- Possible infrared modifications of gravity that might emerge only at cosmological scales.
Thus, while GR provides the indispensable local framework for spacetime dynamics, its extension to cosmology relies on global hypotheses that are not uniquely prescribed by the theory itself. This tension motivates alternative or complementary approaches (effective field theories of dark energy, nonlocal gravity, holographic principles, quantum cosmology), which attempt to bridge the gap between GR’s local formulation and the universe’s global structure.
The answer to thread question
“Is there a limit to gr-based cosmology given General Relativity's local character?”
- is : the GR can be used only at description and analysis of rather simple systems of gravitationally coupled cosmological objects, and only in the weak Gravity case. It is fundamentally non-applicable if Gravity force is extremely strong, including at description and analysis of matter’s state in, though till now rather exotic, extremely dense objects, which are some QM systems; on macroscale the GR equations have rather evidently scientifically senseless solutions – “black”, “white” , “worm”, “holes in spacetime” etc.
That is because of, as that rigorously proven in the Shevchenko-Tokarevsky’s Planck scale informational physical model, more sees Preprint Planck scale informational physical model and fundamental pr...
, Matter’s spacetime is fundamentally absolute, fundamentally flat, fundamentally continuous, and fundamentally “Cartesian”, (at l east) [4+4+1]4D spacetime with metrics (at least) (cτ,X,Y,Z, g,w,e,s,ct), which fundamentally cannot be impacted by anything in Matter, and cannot impact on anything in Matter. I.e. it is fundamentally nothing else than an infinite “empty container”, where Matter is placed and constantly evolves.Gravity is fundamentally nothing else than some fundamental Nature force, which is similar to Electric Force; though on Planck scale Matter is rather simple logical system, and so at least Gravity, Electric, and Nuclear/Strong Forces act bt the same scheme; more see the link above, section 6 “Mediation of the fundamental forces in complex systems”
Though, if we say about cosmology, the cosmology itself has rather numerous problems, really [if we don’t touch fundamentally non-elaborating scientifically in mainstream physics the Matter’s Beginning problem at all] flaws,
- first of all since in the cosmology – and in whole mainstream physics, though – Matter’s spacetime is Minkowski/pseudo-Riemannian spaces with metrics (ict,X,Y,Z), where real space cτ-dimension is [mathematically] imaginary time dimension.
What is fundamentally wrong, and so really this spacetime contradicts with thje well reliable “Big Bang” hypothesis, since in this spacetime the “he cosmological principle” acts that exclude the fixed “Big Bang” initial point in the space, which, if the hypothesis is true, of course exists;
- while so cosmologists really observe Space as through some strange double convey lens.
More see the really scientific SS&VT initial cosmological model in the linked paper above, section 5 “Cosmology” .
To read reDzennn comment, 4 passages, in/to https://phys.org/news/2025-05-dark-evolving-energy.html it is useful as well.
Cheers
Yes, General Relativity is a fundamentally local theory — its field equations describe spacetime curvature determined by local energy-momentum. This works extremely well for many scales, but it also creates a limitation when one tries to construct a fully global cosmology: the universe as a whole is not just the sum of local patches.
In my recent work on QTIP (Quell-based Tick-type Information Processing) Cosmology, I argue that what GR misses is an absolute information framework beyond local spacetime. GR describes how information is expressed locally (through curvature), but QTIP suggests that there is an underlying absolute domain (an "imaginary space" of information) which governs global consistency and self-maintenance of the universe.
In short: GR is local by construction, but cosmology demands a global structure. QTIP provides one possible way to bridge this gap.
It looks here as it is necessary to note that the absolutely fundamental phenomenon/notion “Information”, which – as all other fundamental phenomena/notions also are - is fundamentally transcendent in mainstream philosophy and sciences,
- as it is rigorously scientifically defined in 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
- really is very general phenomenon – in the conception it is rigorously proven that there exist nothing besides some informational patterns/systems of the patterns that are elements of the absolutely fundamental and absolutely infinite “Information” Set.
So, everything is some “information”, and really addition to some theory the word “information[al]” really has a sense only if this relates to really general and fundamental points.
Say, in the Shevchenko-Tokarevsky’s “Planck scale informational physical model” the word “informational” means only that the model is based on the conception above, first of all on that in the conception fundamentally necessary fundamental phenomena/notions case “Matter”, “Consciousness”, “Space”, “Time”, “Energy”, “Information”, which are fundamentally completely transcendent/uncertain/irrational in maimstream philosophy and sciences, are rigorously scientifically defined; and
- since the conception in this case completely rigorously scientifically legitimates the outstanding C. F. von Weizsäcker “Ur hypothesis”, and E. Fredkin “Digital Philosophy/Physics”,
- which proposed and rather rigorously grounded that rather probably Matter’s ultimate base is/are some binary [von Weizsäcker] and reversible [E. Fredkin] logical elements; however they were mainstream physicists and philosophers, and hadn’t no any explanation – for what, if non- mystical, reason, why and how, if non-mystically, these logical elements appeared in also for some if non-mystical reason appeared Matter; including both their findings are defined in the mainstream physics 4D spacetime, what really is incorrect.
Again, the SS&VT conception above makes the von Weizsäcker’s and Fredkin’s outstanding ideas quite rationally generally grounded, and so in the SS&VT model above [more see https://www.researchgate.net/publication/391209088_The_Informational_Conception_and_Basic_Physics, https://www.researchgate.net/publication/395113364_Planck_scale_informational_physical_model_and_fundamental_problems_in_physics]
- it is postulated that 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 corresponding 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.
That’s all, the word “information” really cannot be, and isn’t, concretely used in the whole model, since, again, really it doesn’t contain any concrete information about what concrete informational system “Matter” is, and the model’s concrete subjects for study and analyzis are first of all reliable experimental data and existent physical theories – as that really reliable theories and models are.
Though yeah, in physics a lot of “informational theories” appeared; and more and more appears….
Cheers
Then tell me — where does information, in its ultimate essence, dwell?
“...Then tell me — where does information, in its ultimate essence, dwell?....”
- any information, in its ultimate essence, indeed absolutely for sure dwells somewhere, not, of course in an absolute information framework beyond local spacetime, etc.
Really , again - see yesterday SS post on page 1 - in 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
- it is completely rigorously proven that there exist nothing besides some informational patterns/systems of the patterns [further IPS] that are elements of the absolutely fundamental and absolutely infinite “Information” Set. The Set exists absolutely objectively, because of it fundamentally – logically - cannot be non-existent and so exists absolutely eternally, having no Beginning and no End.
The utmost general scientifically rigorous definition of the so absolutely fundamental phenomenon/notion “Information” is:
“Information is something that is constructed in accordance with the set/system of absolutely fundamental Rules, Possibilities, Quantities, etc. – the set/system “Logos” in the conception”
Including “Matter” is an informational system /the Set’s element, while “Space”, “Time”,, “Energy”, “Logical Rules”, etc. . are “Logos” elements.
So any/every concrete IPS in the Set can dwell absolutely fundamentally only in some concrete actualization of the Logos elements “Space” as the concrete the IPS’s “space”, the concrete IPSs spaces can have arbitrary number and nomenclature of concrete “space dimensions” ,
- and change its state, including being fixed in the space, in the unique universal for all the Set’s elements actualization of Logos elements “Time” - “time dimension” .
At that any IPS in the Set can exist in two main states:
- “implicit state”, as informational pattern “this IPS doesn’t exist really”, what contains absolutely exactly and completely the IPS as : “this ….this…etc. in IPS doesn’t exist”; and
- “real state”, what appears after some portion of Logos element “Energy” impacts the “implicit state” pattern, and opens this conserve can transforming it into really existent IPS.
Say, yesterday everywhere in the Set, including in SS consciousness space, there existed an implicit pattern “there is no the SS post that will be posted in the RG thread tomorrow”, what was evidently true - yesterday there was no the post – and contained absolutely complete and exact information about this SS post.
Today this pattern in SS consciousness space got at breakfast some energy portion, has become real as the real thinking, further by corresponding electric energy portions has become real in RG server and other PC.
Note that the “implicit” absolutely true and exact pattern above existed not only yesterday, but always, including, say, before Matter Creation, as absolutely true and exact pattern “there is no a Set’s element “Matter”, where in near 13 billions of years after its creation SS will post that…”
– in the Set’s whole space that have at least “simply infinite number” of space dimensions of all the Set’s elements, where [partial] Matter’s and humans consciousness spaces always existed/exist/will exist.
Etc. more see the conception.
Cheers
The question of where information fundamentally exists is indeed crucial. In my independent research on the QTIP (Quell-based Tick-type Information Processing) framework, I define this domain as the Imaginary Realm (absolute information domain) — a real structural basis where information is stored and processed before its expression in spacetime. If you are interested in a comparative perspective, you may find it worthwhile to take a look.
Einstein's system, developed before the Hubble result, is incompatible with a Hubble universe.
Curved spacetime theory tells us that if a region contains lots of sources of positive curvature (=stars), the curvature is cumulative, making the region increasingly positively-curved. As we look at larger spaces, for a sufficiently large space, it curves right around on itself.
That is, every time a signal passes through another gravity-well, it comes away a little more redshifted.
Snag is, that's a result that corresponds to "Newtonian" gravity, ==not== the Einstein version.
With C19th "Newtonian" gravity a recession redshift is given by
E'/E = (c-v)/c
, and the roundtrip blueshift-and-redshift of a gravity-well is
E'/E = (c-v)/c * (c-(-v))/c = 1 - v2/c2
, Lorentz-squared over a round trip.
That's the basis of the "Newtonian" Hubble redshift: each star redshifts light passing through a region by a little bit more, and over large expanses, assuming a uniform distribution, the redshift becomes distance-dependent..
With the Einstein system the SR recession redshift formula is instead
E'/E = sqrt[ (c-v) / (c+v) ]
, and there is no round-trip gravitational redshift, because the SR formula inverts perfectly when we switch the velocity signs from positive negative. In Einstein's universe, a signal crossing a gravity-well ends up back at its original height with precisely the same energy that it started with.
This chimed with Einstein's conviction that the basic laws of physics must be time-symmetrical. SR was time-symmetrical, and so was Schwarzschild. Hence no energy-loss in forward time. Einstein used the same argument to prove that there could be no such thing as gravity-waves, because they also generate time-asymmetrical energy-laws.
But the SR / Schwarzschild result makes no sense from the point of view of curved-spacetime theory. So in 1917, Einstein was faced with the problem that his equations predicted no cumulative redshift, but curved spacetime predicted a real redshift. How could he get rid of the geometrically-required cumulative redshift to allow Schwarzschild and SR to be correct?
He did it by inventing Lambda, whose purpose is to cancel long-range cumulative curvature, so that SR-Schwarzschild could be correct.
But then the Hubble result came along and said that Hubble shifts were real, and physics was NOT time-symmetrical.
This basic incompatibility has never been resolved.
“....The question of where information fundamentally exists is indeed crucial. ..., I define this domain as the Imaginary Realm (absolute information domain).....”
- again – see SS posts above – any information absolutely fundamentally cannot, and so
doesn’t, exist somewhere in some “the Imaginary Realm (absolute information domain)”. Absolutely complete information about absolutely everything, and in all times, exists as absolutely infinite “Information” Set that contains absolutely infinite “number” of elements;
- while the Set exists not in some transcendent/strange “domains”, it exists, and mostly everything in the Set changes, in the Logos set elements “Space”, and “Time” actualization in the Set’s self spacetime that has at least “simply infinite number” of space dimensions, which is the sum of concrete space dimensions of completely all concrete the Set’s elements.
At that, again, the Set exists absolutely for sure always – “in absolutely infinite time interval”, having no Beginning and End, since absolutely for sure – logically – cannot be non-existent.
Though moreover – every the Set’s elopement exists as the bit-superposition “I/not I”, where “I” is the element/informational pattern/system really existent in concrete time moment, while “not I” contains absolutely complete information about everything in the Set, and the element itself in other time momentums, in the implicit form. So really every the Set’s element exists in whole the Set’s space. The “Time”, again, is actualized absolutely fundamentally as the fundamentally unique universal for everything in the Set time dimension, where every element moves fundamentally only in positive/ahead direction at every its change.
More see the SS posts above and li nks in the posts.
Cheers
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