Hello everyone,
I’m opening this new thread following some really satisfying answers I recently received here about galaxy properties and metallicity scaling. Those explanations were great, and they’ve definitely made me much more confident in the idea of a static and eternal universe. However, I have a doubt regarding the geometry and mechanical stability of such a universe.
Philosophically speaking, I’m deeply attracted to the idea of a spatially infinite universe. I really dislike the concept of a closed universe, even if that universe were static and eternal. The problem is that I haven’t been able to find a rigorous relativistic model that allows space to be infinite while also remaining completely stable.
As we all know, General Relativity does, in principle, allow for a static universe, but only if a cosmological constant is introduced and carefully fine-tuned to exactly balance gravitational attraction. Einstein originally adopted this solution because he wanted a universe that was eternal and unchanging on large scales. However, this equilibrium is extremely delicate. As Eddington later showed, even the smallest perturbation would cause the universe to either begin expanding or collapsing, which makes the static solution fundamentally unstable. On top of that, Einstein’s static universe is closed, which isn’t what I’m looking for. So my question is: does there exist any modified version of General Relativity that preserves Einstein’s space-time structure while also accommodating a stable, static and spatially infinite universe?
I’d really like to preserve General Relativity, at least in some form, because there are several observational and theoretical reasons that make it hard to abandon completely. On the observational side, there are phenomena that seem to strongly support General Relativity, such as gravitational lensing, time dilation, the perihelion precession of Mercury, the two photos of the supermassive black holes at the center of Messier 87 and the Milky Way, and especially the direct observation of gravitational waves, which appear to confirm that space-time behaves dynamically in the way Einstein predicted. On the theoretical side, General Relativity offers some fascinating possibilities. For example, it allows for faster-than-light travel through the warping of space-time.
So it would be awesome to find a framework that preserves Einstein’s dynamic space-time structure while also allowing for a spatially infinite, static and stable universe. Do any of you know of alternative relativistic models that could reconcile all of those features?
@luisenrique-arch,
The premise of your question is incorrect. Einstein’s version of General Relativity does not contain a space-time structure. A mid 20th century revision of GR added a space-time structure but Einstein explicitly rejected that revision.
Essentially Einstein is stating that space and time are relational concepts, not substantival entities that causally interact with matter and energy. Modern cosmology simply ignores that distinction because the expanding universe model requires an expanding space to mitigate what would be physically catastrophic consequences if galaxies were actually receding at the near light-speed velocities attributed to them by the model.
No, it does not. Relativity Theory does not have a universal frame. Models like the FLRW expanding universe that is the basis of the standard model of cosmology first assume a universal frame then solve the field equations of GR for that frame. The resulting Big Bang model is a non-relativistic model that does not fit the Cosmos we observe. Your understandable desire to ditch the expanding universe model runs into immediate difficulty however by retaining the fundamental error of the model - the existence of a universal frame.
The Cosmos we observe is consistent with GR in that we do not and cannot observe a universal frame - static or dynamic. We can not observe a universal frame because the finite maximum speed of light does not allow us to observe the “whole universe” simultaneously. The light speed maximum also means that the “whole universe” is not, to borrow from John Bell, a beable; it’s existence is precluded by basic physics.
The only frame we have is our local frame which extends outward from our cosmological location in all directions to the limits of our current observational technology. That local frame has a local clock that has no “universal” significance - it is not marking time for the “whole universe”.
Other observers in other galaxies will have their own local frame with their own local clock ticking that will be as independent of our frame as ours is of theirs. Those frames may overlap but with a significant time lag such that the concept of “now” has no common meaning. That is the essence of Relativity Theory on the cosmological scale, unlike the Big Bang model, there is no universal “now”.
The concept of the “whole universe” with a Universal clock ticking away does not fit with a relativistic cosmological model because it contradicts the basic premise of Relativity Theory. The Cosmos we observe is consistent with a relativistic model without a universal frame. “Universal models” that assume a universal frame are not consistent with the Cosmos we observe; they have to imagine something that cannot be observed- a universal frame. In the case of the Big Bang, the model then has to imagine other undetectable things in order to fit itself to cosmological reality.
There is also a hard limit to our observational range that is a consequence of the cosmological redshift. If the Cosmos extends far enough from our location in all directions then eventually there will reach a point where light from the most distant galaxies is redshifted beyond detectability.
Alternatively, if the Cosmos is vast enough, there could be a point where the galaxies completely cover the night sky ala Olber’s Paradox and the night sky should be bright - the paradox being that the sky isn’t bright. But, the night sky is bright - at 2.7K, the CMB. Olber just didn’t take the cosmic redshift into account, otherwise his logic seems consistent with observations.
The two previous considerations address the concept of infinity as it pertains to cosmological matters. Essentially infinity is only a metaphysical or mathematical concept, not a scientific one. It is not useful to scientific considerations because it is not an observable. Infinity lies beyond the boundary of empirical reality. Like the whole universe, it is not something that can be found in empirical reality.
The disadvantage you put yourself at @luisenrique-arch is that you are trying to fit cosmological reality to a metaphysical premise - an infinite, static universe - that is discordant with the empirical evidence. On the other hand if you adopt as your mental framework, Einstein’s version of Relativity Theory you will find that it is logically coherent and also consistent with empirical observations. The only downside is you’ll have to get along without the metaphysical baggage of a simultaneously existing Universe and therefore you will not wind up with a simplistic model of a Universe that does not exist.
General Relativity is dubbed as our greatest gravity theory, yet it is not without its own problems. From your post:
Gravitational lensing is based on a mutual attraction between mass and light (energy). In the metric, energy should self-gravitate but I don’t know if any evidence has been found for this. Therefore, the lensing can also be explained with a basic refraction model.
GR gives a better calculation for Mercury’s precession than Newton but did you know it is still not 100% correct? There is a small extra precession component for Mercury that still eludes GR.
On a galactic scale GR needs Dark Matter to remain valid. We’re not going to find Dark Matter but because GR remains the only ‘accepted’ gravity theory, Dark Matter must be ‘real’.
On a cosmic scale GR needs Dark Energy to remain valid. Same problem as point before.
Gravitational waves, yes
The complex tensor mathematics mean we have only a few basic solutions to the equations. Intricate systems are near-impossible to solve with GR. Compare this to electrodynamics and QFT where calculations and equations are precise for multi-particle interactions. Not saying the solutions are not in there, but maybe we shouldn’t have jumped from Newton directly to 4D tensors.
There are many better alternative theories. Some within these pages. The struggle is to find evidence of anomalies, that has not already been fudged into the existing, and to gain a wider acceptance.
@luisenrique-arch if I remember correctly a relativistic “stable” static universe can be achieved in Einstein-Cartan torsion gravity. https://arxiv.org/abs/1401.7639
https://www.tandfonline.com/doi/abs/10.1080/21672857.2013.11519725
A few days ago, while browsing through various discussions on the forum, I came across a comment by @RedshiftDrift mentioning something called “Hubble Force”. It was described as something that could supposedly balance gravitational attraction and therefore keep a static universe stable. The problem is that the comment I found was really short, so I couldn’t really understand what it actually means or how it’s supposed to work.
If @RedshiftDrift could explain it in more detail, I’d be really interested, especially if this is something that remains compatible with General Relativity and could realistically allow for a spatially infinite, flat universe that stays static.
Also, I have the strong feeling that somewhere out there there might be a MOND-like theory that doesn’t just eliminate the need for dark matter, but also somehow manages to keep the universe static. There are so many MOND-style theories floating around that it’s likely that at least one of them could, in principle, do all of that at once.
@luisenrique-arch could you give the link to the comment mentioning “Hubble force”? This doesn’t seem like an expression I would use, but I may not remember writing it.
However, it is argued here https://royalsocietypublishing.org/doi/10.1098/rspa.2022.0045 that light-dust interactions produce a ‘pressure term’ in the Einstein equations which make the solution stable. (It can be a ‘local’ solution anywhere you wish. I don’t interpret this as meaning “the infinite universe is stable”.) I have argued in a poster that the STz light–electron interaction also produces a ‘pressure’, but on electrons. I suggest that this pressure is sufficient to stabilize the Einstein equations, but I haven’t calculated that pressure yet.
About MOND: a natural acceleration comes out of the STz framework. It is the average acceleration of electrons interacting with the light field of the MBR. That acceleration is $a_{STz} = 7.15 \times 10^{-10} {\rm m/s}^2 = 2\pi a_0$, where $a_0$ is the MOND acceleration. So MOND is a manifestation of STz, but how this happens is rather complex (I submitted a paper explaining this but it was rejected… I’ll try again some other time.)
P.S. @ExpEarth uses “Hubble luminosity”, is this what you have in mind @luisenrique-arch ?
Note that expansion is generally materialized as the Hubble flow https://arxiv.org/abs/astro-ph/0609271 Not sure of the distinction with Hubble law.
Another key parameter is the scale factor https://en.wikipedia.org/wiki/Scale_factor_(cosmology) Which evolve in this cyclic universe
https://arxiv.org/abs/1904.08022
@RedshiftDrift I tried searching the forum to find the comment I was talking about, but I can’t track it down anymore. Still, I clearly remember you mentioning something called the “Hubble Force”, which supposedly counterbalanced the gravitational attraction of the universe and kept it stable.
In any case, if I’m not mistaken, this whole stability problem only really exists if the universe is assumed to be isotropic on very large scales. If isotropy only holds up to a certain scale, and beyond that the universe becomes anisotropic, or even fractal in its large-scale structure, then the classical gravitational instability problem of a static universe basically disappears altogether.
In the thread that @RedshiftDrift mentioned, he refers to Sahil’s model as having a Hubble force. I mentioned in another thread that my model has something like that too, the Hubble luminosity (or Lambda luminosity).
Thanks @ExpEarth for mentioning a discussion with @sahil5d… I found the post where I wrote “Hubble force” here at https://github.com/orgs/a-cosmology-group/discussions/58#discussioncomment-6746942
@luisenrique-arch This “Hubble-force” was a term to name Sahil’s model and is related to the pressure to keep the Einstein equations stable. But this is not standard nomenclature, and the post is short because I had not calculated anything three years ago, and I still have not calculated that pressure yet, so I don’t know anything about it except that it should exist.
@luisenrique-arch . >Is it possible to have an infinite, static and stable universe in relativistic physics?
I think you should definitely take notice of my newest thread (which by the way has been motivated by your current activity): The Variable Mass Theory and Gravitational Paradoxes. Of interest to you might be the following quote: >It has been shown [ .. ] that General Relativity (GR) can be effectively replaced by Variable Mass (VM) in a Static Euclidean Universe (SEU).
Thus General Relativity is so much not rejected, as it is made redundant on a cosmic scale. This is done by a sort of a coordinate transformation that effectively replaces GR by a Variable Mass equivalent that works in common geometry. The main advantage of this approach is simplicity.
I have not invented the VM theory myself. A lucid introduction to it is provided by this video: Variable Mass Theory: Intrinsic Red-Shift. Basic reference is the paper by Halton Arp and Jayant Narlikar: FLAT SPACETIME COSMOLOGY: A UNIFIED FRAMEWORK FOR INTERGALACTIC REDSHIFTS. Quoting from the abstract: >It is known that the standard Friedmann cosmology with k=0 can be described equivalently in a conformal frame in which the spacetime is Minkowskian but all particle masses uniformly scale with epoch.
I’m familiar with the variable mass theory proposed by Arp and Narlikar. The reason I didn’t mention it is because I find it rather inelegant.
I’ve always preferred models where the laws of physics are stable and universal. A static and eternal universe should, in my opinion, be governed by consistent principles that apply everywhere in the same way. Once you start proposing that particle masses change across different regions of the universe, or that physical constants are not truly constant, the entire structure begins to feel messy and overly flexible.
Ironically, there is a relativistic tired-light cosmology that manages to keep the universe stable: David Crawford’s Curvature Cosmology. Even though it proposes a closed universe rather than an open and infinite one, it manages to stabilize Einstein’s static universe through various mechanisms. The problem is that Curvature Cosmology appears to have been falsified by some recent observations. In particular, objects have been identified with candidate redshifts exceeding the maximum values allowed by the model.
The Little Red Dots observed by the JWST are a good example of this problem. If you interpret their surface brightness within the framework of a static universe using a tired-light mechanism, you could theoretically argue that these are relatively normal galaxies rather than exotic ultra-early objects. However, doing so would require assigning them redshifts on the order of z ≈ 30. That’s incompatible with Curvature Cosmology, because the model only allows redshifts up to about z ≈ 22.
So even though Crawford’s model manages to create a stable relativistic universe, it ultimately seems unable to accommodate the observational data. And that’s unfortunate, because it’s probably one of the best alternative cosmological models.
@luisenrique-arch . >I’m familiar with the variable mass theory proposed by Arp and Narlikar.
Appreciated. >The reason I didn’t mention it is because I find it rather inelegant.
Okay, that’s your own choice, with decent underpinning as far as I can see. >That’s incompatible with Curvature Cosmology, because the model only allows redshifts up to about $z\approx 22$.
That’s typical, because in the section named G. de Vaucouleurs at my (! safe !) website it is argued that the maximum possible cosmological redshift is $\approx 28.5$ . More details are found in With other words. Material for my next publication in the VM series.
@luisenrique-arch . >On the observational side, there are phenomena that seem to strongly support General Relativity, such as gravitational lensing,
Gravitational lensing can be completely described in the Newtonian way. The only difference being half the deflection as predicted by General Relativity. Twice as much mass is required for the same result.
See the thread Time Dilated Past hypothesis at this forum.
Was Newton misled by Kepler?
The well known pictures of black holes are fake!
Have we really measured gravitational waves?
When it comes to gravitational waves specifically, I don’t think it’s necessary to criticize the methodology used by LIGO or other gravitational wave observatories. If one adopts an ether-based framework, it’s perfectly possible to argue that gravitational wave observatories are really detecting something, but that what they interpret as gravitational waves are actually oscillations of the ether generated by massive cosmic events, such as collisions between stars and compact objects (black holes). The real challenge is building a detailed ether model that can quantitatively reproduce the observed signals and make accurate predictions that match the data as well as General Relativity does.
As for gravitational lensing, yes, I know that Newtonian gravity already predicts it. The problem is that, as you yourself pointed out, the Newtonian prediction accounts for only about half of the observed light deflection. To make the numbers work, you’d have to postulate some additional invisible mass, which looks very much like the same kind of trickery that Big Bang cosmologists resort to when they invoke dark matter to explain everything that doesn’t fit. It’s not exactly the most elegant way to solve the problem.
In general, I know that non-relativistic explanations have been proposed for essentially every phenomenon that is usually presented as evidence for Special Relativity or General Relativity. The issue is that many of these alternatives tend to become increasingly complicated and contrived once you try to make them account for the full range of observations. That’s one of the main reasons I still lean toward Relativity. It simply provides a more coherent and economical framework for explaining what we see.
There’s also a more personal reason. From a theoretical standpoint, General Relativity leaves room for concepts like warp drives and wormholes. Whether any of that will ever prove physically achievable is another question entirely, but at least the possibility is there. On a purely personal level, I’d rather live in a universe where interstellar travel might be feasible, because I enjoy imagining a galaxy filled with advanced civilizations moving between the stars rather than being permanently trapped around their home worlds.
@luisenrique-arch . >When it comes to gravitational waves specifically, I don’t think it’s necessary to criticize the methodology used by LIGO or other gravitational wave observatories.
Read this: How to measure a distance of one thousandth of the proton diameter? The detection of gravitational waves. This one too: Gravitational Waves and LIGO.
Really? On the time lags of the LIGO signals. In thread 274 a discussion about LIGO starts here. It’s about the wrong use of statistics in LIGO and elsewhere. My argument is that the variance of the sample means is NO way better than the variance of the samples themselves.
It’s the other way around. People deduce invisble mass from gravitational lensing according to GR. What difference does it make?
Agreed !!