Anomalous contribution to galactic rotation curves due to stochastic spacetime

This is exactly what Sabine Hossenfelder is talking about for years now.

To be fair, everything that astrophysics comes up with will be massively under constrained. For all intents and purposes we work with a single datapoint and try to infer dynamics.

I'm far from an expert, and I'm still struggling my way through this paper, but from what I can see they are only intruducing one new free parameter, the same number as lambda CDM.

I agree with your point in general, but in this case specifically I strongly disagree.

The idea worked out by Oppenheim and his colleagues/students is a fairly concrete theory which aims to marry quantum mechanics and general relativity. They're working on a bunch of approaches to turn their model into testable predictions in different regimes.

They have a bunch of different papers with different ways their model could be falsified. None of them are at the level where you could falsify their model with current technology but they're seriously working on the theory required to make their ideas potentially testable.

I went to a talk a couple of years ago at a conference by Oppenheim and he is very clear that what they're looking for is to make concrete predictions which can be tested.

Edit: you can see here for another paper where they try to push their theory towards producing some testable predictions

https://arxiv.org/abs/2203.01982

Correct me if I am missing something, but it seems like the speculative bit was Milgrom noticing that coincidence in 1983, and now they are trying to explore the consequences of assuming that it's not just a coincidence... hopefully with testable predictions coming out of this ?

How else should they go about it ?

I think you're missing the point: you can say this about any theory. At least ones that attempt to deal with something significant and difficult.

It's therefore not a very perceptive critique to make to say the problem with this specific theory is that it is one of many possible ones. It's more meaningful to compare such wide-aperture theories like this to their actual alternatives, rather than distrust them on principle because the space of potential hypotheses in which they carve out a specific model is so large.

Funnily, your observation could be said to be an instance of itself: in that it is an overly general appraisal unrooted in pertinent specifics, therefore mostly divorced from explanatory power - akin to what you're misjudging this theory to be.

I don't know if this theory will pan out, but it seems more interesting than you say. While different to the paper, I have the following related thoughts to offer: I've often thought gravity makes sense, not as a fundamental force, but as an emergent metric, rooted in randomness (perhaps the informational content of matter, for which mass is, normally but not always, useful proxy?), similar to how temperature is merely an emergent property that we can measure that arises from (and reflects) the microstates/ensembles of gigantic numbers of particle interactions, owing to their energy content.

I wonder if a "time" or "age" factor could be needed in revised calculations of gravity to account for the plausible way in which information increases over time (if we assume, without trying to understand, that the history is recorded somewhere, somehow), and if that's why these very old and very distant galaxies bork our normal (non dark matter fudged) calculations of gravity, because they are so old that the time accrual of information is an effect which begins to come into play.

Thank you, this is much more accessible for me.

That sounds very unconvincing. Afaik there are several found galaxies with more than normal amounts of dark matter, and less. How would these fit into ANY modified gravity theory?

This type of theory seems to only handle the common case, but the universe is full of edge cases...

The Guardian headline stands in contradiction to this statement from the paper’s abstract: “We caution that a greater understanding of this effect is needed before conclusions can be drawn”.

Only if we've constrained ourselves to take inflation as true.

Yes and also in gravitational lensing. The most famous example of this is the Bullet Cluster [1], which displays a pattern of lensing that doesn’t line up with the distribution of light (visible matter) but does line up with where we might expect dark matter to end up after a collision.

[1] https://en.wikipedia.org/wiki/Bullet_Cluster

Could we infer these effects to be from an average distribution of matter across multiversal spacetime, and how would we test for that?

From the preprint link at the top's page 6, after Eqn (23): "While this study demonstrates that galactic rotation curves can undergo modification due to stochastic fluctuations, a phenomenon attributed to dark matter, it is important to acknowledge the existence of separate, independent evidence supporting ΛCDM. In particular, in the CMB power spectrum, in gravitational lensing, in the necessity of dark matter for structure formation, and in a varied collection of other methods used to estimate the mass in galaxies. These now form an important set of tools with which to test [our] theory".

Other lines of evidence like the one at your link just increase the ability to test their theory (which is meant to solve some quantum gravity problems at very small length scales) at very large length scales.

They are not motivated by the desire to prove MOND is correct or that cold dark matter doesn't exist. Rather they can show that in certain restricted circumstances their theory allows for nearly-MOND-like orbits. So their theory survives a small but important hurdle imposed by our observations of nature (we observe MOND-like orbits).

Elsewhere in the comments someone asked the good question of (highly paraphrasing) whether this success is wiped out if a distribution of dark matter is added to their SdS-like universe as the generator of some of the observations normally taken as proof of \Lambda-CDM. That question is closely related to the final sentence in the quote above, and answers are hard to guess at.

> Can dark matter and [the author's theory of gravitation] fit together...?

Nobody knows yet. The authors aren't seeking to overthrow the concordance cosmology; this paper is essentially trying to see if their theory is quickly killed by being unable to model a stable spherically symmetric galaxy in an expanding universe. Their theory predicts significant differences from the Schwarzschild-de Sitter (SdS) metric in General Relativity, with SdS serving as a proxy for an isolated galaxy. The paper in part investigates whether those differences can be "hidden" by removing the cold dark matter which otherwise would be the standard source of outer orbit anomalies.

They don't go deeper than that, and at this stage just can't: "To make it tractable analytically, we have restricted ourselves to spherically symmetric and static spacetimes". They restrict themselves in other ways too.

> The evidence for dark matter

From just after Eqn (23) in the preprint:

"While this study demonstrates that galactic rotation curves can undergo modification due to stochastic fluctuations, a phenomenon attributed to dark matter, it is important to acknowledge the existence of separate, independent evidence supporting ΛCDM. In particular, in the CMB power spectrum, in gravitational lensing, in the necessity of dark matter for structure formation, and in a varied collection of other methods used to estimate the mass in galaxies"

I think there's a bit of language problem here. In the way physicists use the word in 2024, making gravity "quantum" means something very different to just having discrete "quanta" particles.

It means a theory with stuff like superpositions of classical states,interference and entanglement. It also means having a theory which can consistently interact with other quantum stuff.

The standard through experiment goes something like this. Take a particle with some mass (maybe am electron, maybe a bowling ball), general relativity tells us what its mass does to space-time around it. Now take that particle and put it in a superposition of being located at point A and point B (you can do this if the particle is quantum). What the heck is it doing to spacetime now? GR doesn't tell us, because GR can't deal with quantum particles. Naively it seems like space-time should also be in a superposition, but we tried to make theories like that and they didn't really work.

Is that the "postquantum" bit? i.e. not that spacetime is quantized as such, but that it's not a uniform continuous medium at all scales, that classical mechanics would assume.

I can imagine that wobbliness comes from chaotically passing strong gravity waves of very high wavelengths coming from outside of the observable universe and from before times of Big Bang.

There's no specific reason that forces us to believe that Big Bang was the actual beginning of everything. It might have been "local" high energetic event happening in much larger structure.

For example try to imagine how the collision of two dense clusters of trillions of black holes each traveling at nearly light speed would look like from the point of view of the dust swirling in-between and around them. I can't imagine it would be very different from what we observe in our universe.

No one can explain the Bullet Cluster.

> Good.

Is it, or isn't it, and why? You don't say.

The authors asked themselves how their quantum gravity theory differs from General Relativity, and whether the successes of General Relativity in astrophysical settings would be fatal if their theory has strong differences, and that's the basis for this paper. The tl;dr is that their theory predicts different trajectories outside of large central masses, but that might not conflict with evidence from galactic-dynamics astronomy.

This is the second paper released in the past few days by the University College London Oppenheim group. It's a preliminary investigation of the longer length scale features of their classical stochastic theory. The central question is how its version of Schwarzschild-de Sitter (SdS) differs from standard General Relativity.

The first paper, and I think the more interesting one, is about the short length scale aspects of their asymptotically free theory, in which the gravitational interaction weakens as distances between interacting sources decreases. The asymptotic freedom means the theory is amenable to renormalization, unlike perturbative quantum gravity and a number of other approaches. That paper is at <https://arxiv.org/abs/2402.17844>. Note that they do not know how to make the gravitational part quantum mechanical without introducing problems (i.e., it is haunted by "bad" ghosts in the sense of <https://en.wikipedia.org/wiki/Ghost_(physics)>); their classical and stochastic gravitational sector is ghost-free (a point also made at the end of Appendix A in the large-scale paper), and it is reasonable for them to believe that could be good enough that it's worth continuing to investigate what the theory predicts and how its parameters are set.

The second paper was motivated by the first: "The theory was not developed to explain dark matter, but rather, to reconcile quantum theory with gravity. However, it was [noted] that diffusion in the metric could result in stronger gravitational fields when one might otherwise expect none to be present, and that this raised the possibility that gravitational diffusion may explain galactic rotation curves".

That MOND-like effects might arise in their approach to the problem of small-scale quantum gravity is at least interesting. It was not the starting point.

Moreover, they did not start with the idea of modifying General Relativity to get rid of the need for (some or all) cold dark matter. As they say: "While this study demonstrates that galactic rotation curves can undergo modification due to stochastic fluctuations, a phenomenon attributed to dark matter, it is important to acknowledge the existence of separate, independent evidence supporting ΛCDM. In particular, in the CMB power spectrum, in gravitational lensing, in the necessity of dark matter for structure formation, and in a varied collection of other methods used to estimate the mass in galaxies."

> Now explain the Bullet Cluster

This paper does not seek to do so. "To make it tractable analytically, we have restricted ourselves to spherically symmetric and static spacetimes, with metrics of the form of Eqs. (17)." Eqn 17 describes out an adapted Schwarzschild-de Sitter spacetime and leans on an argument that Birkhoff's theorem applies (in particular that their model spacetime is stable against certain perturbations, notably those concentric upon the source mass). There is further detail in Appendix B.

Studying this restricted model, the de Sitter expansion of the spacetime and MOND-like anomalous Kepler orbits at some remove from the Schwarzschild central mass are in their theory driven by entropic forces generated by the fluctuations in the gravitational field of the central mass (and they do a good job in Appendix D explaining this).

In GR's Schwarzschild-de Sitter the free-fall trajectories of test particles around the central mass are totally determined by the mass; the gravitational field doesn't fluctuate. The (Boltzmann) gravitational entropy of the region outside the central mass is everywhere very high.

In GR-SdS we can consider adaptations where with M=const. we turn the pointlike central mass into a spherically symmetric shell, or a concentric set of such shells, or even a ball of fluid, or a ball of dust, or a ball of stars and other galactic matter. None of these symmetry-preserving adaptations changes the free-fall trajectories of test particles outside the outer surface, or the gravitational entropy at any outside point.

In the author's theory, the spacetime is stochastic. It fluctuates. Close to the central mass fluctuations are unnoticeably small; the gravitational entropy is very low. Far from the central mass the gravitational entropy is very high, and gravitational fluctuations are noticeable. A sort of thermodynamics leads to a diffusive flow outwards from the central mass, from the low entropy near there to the high entropy at increasing radial distance. This diffusion is carefully constructed so that the outwards flow is only really appreciable at large-scale distances. The effect is that large-radius orbits are statistically pulled inwards by something describable as stronger gravity at larger radiuses (see around Eqn (21)). This is an "entropic force", very roughly analogous to squashing a sponge ball in your hand then releasing the pressure and watching the sponge ball expand, where the material of the sponge represents the gravitational field.

Their stochastic fluctuations are still generated by the spherically-symmetric central mass. These fluctuations break the spherical symmetry of the outside metric. Consequently they have to do some work to make the outside metric look appropriately Schwarzschild-like in their "diffusion regime", and to keep that stable against the stochastic perturbations.

The authors contend that with reasonable choices of parameters, and restricted to static spherical symmetry of the central mass (and no additional dynamics), this effect comes close to duplicating MOND's low-acceleration regime.

They don't go into anything like a backreaction upon the Schwarzschild metric by large fluctuations.

(They do have an idea about how to get the de Sitter trajectories though, but that doesn't fit very naturally into this comment, which is already long.)

> Bullet cluster

The authors know full well that the metric for a gravitationally bound cluster of galaxies isn't well-represented by their choice of SdS-like metric. A galaxy cluster is too lumpy for the Schwarzschild part.

Two gravitationally bound galaxy clusters having passed through each other (trailing collided gas and dust, and tidally stripped stars and other matter) is even less like Schwarzschild. This is because SdS solutions of the Einstein Field Equations do not linearly superpose. So their metric is a poor description of any sort of "close call" interaction between galaxies or galaxy clusters, even if the individual components are "close enough" to Schwarzschild from the perspective of an observer sufficiently large (as in cosmologically large) distances. They do not (and within this initial paper should not really be expected to) offer a more suitable metric. I'm sure they'd love to look into things like that though.

The non-linear superposeability of useful solutions of General Relativity is a problem for asking how astrophysics differ in most theories that preserve the equivalence principle (this one does, it's a metric theory of gravitation). As the replacement for the Einstein Field Equations lose symmetries (sphericity, staticity) they tend to become analytically intractable and non-numerical approximations become unreliable.

The authors -- imho in a strikingly principled way -- call attention to various difficulties in using this work to describe astrophysical systems, particulary from the middle of the fifth page of the PDF.

They are not obviously worse off than the Verlinde programme of emergent-entropic gravity, where the gravitational field is generated by entropic forces rather than vice-versa.