Lee Smolin has a new paper on quantum gravity including the proposition that modified gravity rules giving rise to the effects summarized in the MOND toy-model should arise in Loop Quantum Gravity theories based upon a couple of different arguments, neither of which are rock solid, but both of which are basically plausible. Sabine Hossenfelder discusses the paper and related issues in a recent post at her blog, and also wrote an article for the general public on a hybrid of a gravity modification and dark matter proposal.

I share Smolin's optimism that MOND-like gravitational laws will arise out of quantum gravity, although I've been more attracted to the reasoning of Alexander Deur who sees that coming out of the self-interaction term of the graviton. But, that doesn't mean that equivalent phenomena couldn't arise out of a space-time based quantization of gravity. It is nice to see room for this arising from quantum gravity in either approach.

In Deur's approach, some dark energy effects arise from a shielding effect in the dark matter effects (also nicely explaining the "coincidence" phenomena that I am loathe to call a "problem"). In Smolin's approach, the cosmological constant is integral in giving rise to the MOND-like effect, so the chain of causation is in the opposite direction.

Why is Deur's approach so attractive?

Occam's Razor: it explains more, with a simpler theory, than the alternatives.

1. It can reproduce the flat rotation curves and Tully-Fisher relationship for spiral galaxies recovered in other theories with dark matter and/or modified gravity.

2. More generally, essentially all arguments for modified gravity theories relative to dark matter theories are also arguments in favor of this theory (e.g. the close relationship between luminous matter distributions and dark matter distributions and the low scatter of this relationship, the contrived assumptions necessary to make N-body dark matter simulations work, etc.).

3. It explains why satellite galaxies tend to arrange themselves in a plane of rotation around a galaxy.

4. It explains the variation in the proportion of dark matter amongst elliptical galaxies, which almost all other modified gravity and dark matter particle theories fail to do.

5. Unlike MOND which ceases to be predictive beyond the galactic scale, it correctly predicts the approximate proportion of dark matter in galactic clusters.

6. It can explain the bullet cluster entirely without resort to supplemental dark matter.

7. It naturally explains why the proportions of ordinary matter, dark matter and dark energy in the universe at this moment are of the same order of magnitude in the lamdaCDM model of cosmology (the "coincidence problem").

8. It likewise explains why the apparent cosmological constant is so small (i.e. there actually isn't any dark energy or cosmological constant and the observational evidence is a function of gravitational fields between non-elliptical galaxies being weaker than one would expect because gravitons tend to stay within gravitationally bound galaxies more often than they would if gravitons did not interact with each other).

9. It explains all dark matter phenomena and much if not all dark energy phenomena with a single, widely assumed hypothetical particle beyond the Standard Model, the graviton, without having to hypothesize additional new physics particles or additional fields or extra dimensions that are not observed.

10. It has just one experimentally determined constant (the gravitational coupling constant) rather than the three experimentally determined constants (G, the cosmological constant lambda and one constant related to dark matter such as the dark matter particle mass) of General Relativity with a cosmological constant and cold dark matter. Relativistic MOND theories such as TeVeS also need three (the MOND acceleration constant, G and the cosmological constant).

11. Its mathematical conclusions are well motivated by experimentally confirmed consequences of QCD in circumstances where the gravitational equations and the quantum gravitational equations are similar.

12. The respects in which Deur's approach differs from conventional general relativity (e.g. it localizes gravitational energy, it effectively includes gravitational fields in the stress-energy tensor, it conserves mass-energy, it considers higher order terms that are natural in a graviton formulation) involve issues that have been the subject of considerable scholarly discussion over the last century, while it does realize the Einstein equations as its classical limit for a sufficient set of simplifying assumptions.

13. Unlike other modified gravity and dark matter theories which are generally purely phenomenological, Deur's approach is well motivated theoretically from a fundamental physics perspective.

14. It would not lead to significantly different predictions around time of the Big Bang because the Big Bang is widely assumed to have been spherically symmetric.

15. It would not lead to very different predictions about the properties of black holes which are also widely assumed to be spherically symmetric. In general, in the spherically symmetric limit, which is a good approximation of most situations involving strong gravitational fields, it reduces to General Relativity in a domain where the predictions of General Relativity have been rigorously confirmed.

16. It would not lead to very different predictions at the solar system scale where mass distributions around the Sun are very spherically symmetric and the mass of the total system is very small compared to galaxies.

17. This is the basis of two peer reviewed published articles in respectable journals by a professional physicist. Whether or not it is correct, it is not a crackpot theory. Indeed the author's primary background in QCD, rather than general relativity, may explain why he was able to see mathematical possibilities that others in the seemingly unrelated fields might not, and to appreciate what simplifications of the naively intractable equations could make them workable without sacrificing their accuracy greatly.

18. In this theory it is natural that space-time is extremely close to being topologically flat as is observed.

19. There are serious problems with most dark matter theories and the few that remain viable are close to being overconstrained by the observational evidence.

20. The apparent shortcomings of this approach (failure to explain inflation - although it might if a cosmology on this basis were developed, and failure to explain baryogenesis and leptogenesis) are shared by almost all of its competitors, but unlike those theories it doesn't also have to explain where dark matter comes from as the emission and absorption of gravitons on an ongoing basis over the life of the universe is well explained.

In short, the Standard Model and a Deur type quantum gravity theory involving just one additional tensor boson beyond the Standard Model, suffice to explain all observed phenomena in the Universe, delivering us to the "end of physics" at the fundamental level, except for the very early parts of Big Bang cosmology and the deeper relationships between the component parts of the core theory in some kind of unification of the forces and particles.

**Why Deur's approach?**Why is Deur's approach so attractive?

Occam's Razor: it explains more, with a simpler theory, than the alternatives.

1. It can reproduce the flat rotation curves and Tully-Fisher relationship for spiral galaxies recovered in other theories with dark matter and/or modified gravity.

2. More generally, essentially all arguments for modified gravity theories relative to dark matter theories are also arguments in favor of this theory (e.g. the close relationship between luminous matter distributions and dark matter distributions and the low scatter of this relationship, the contrived assumptions necessary to make N-body dark matter simulations work, etc.).

3. It explains why satellite galaxies tend to arrange themselves in a plane of rotation around a galaxy.

4. It explains the variation in the proportion of dark matter amongst elliptical galaxies, which almost all other modified gravity and dark matter particle theories fail to do.

5. Unlike MOND which ceases to be predictive beyond the galactic scale, it correctly predicts the approximate proportion of dark matter in galactic clusters.

6. It can explain the bullet cluster entirely without resort to supplemental dark matter.

7. It naturally explains why the proportions of ordinary matter, dark matter and dark energy in the universe at this moment are of the same order of magnitude in the lamdaCDM model of cosmology (the "coincidence problem").

8. It likewise explains why the apparent cosmological constant is so small (i.e. there actually isn't any dark energy or cosmological constant and the observational evidence is a function of gravitational fields between non-elliptical galaxies being weaker than one would expect because gravitons tend to stay within gravitationally bound galaxies more often than they would if gravitons did not interact with each other).

9. It explains all dark matter phenomena and much if not all dark energy phenomena with a single, widely assumed hypothetical particle beyond the Standard Model, the graviton, without having to hypothesize additional new physics particles or additional fields or extra dimensions that are not observed.

10. It has just one experimentally determined constant (the gravitational coupling constant) rather than the three experimentally determined constants (G, the cosmological constant lambda and one constant related to dark matter such as the dark matter particle mass) of General Relativity with a cosmological constant and cold dark matter. Relativistic MOND theories such as TeVeS also need three (the MOND acceleration constant, G and the cosmological constant).

11. Its mathematical conclusions are well motivated by experimentally confirmed consequences of QCD in circumstances where the gravitational equations and the quantum gravitational equations are similar.

12. The respects in which Deur's approach differs from conventional general relativity (e.g. it localizes gravitational energy, it effectively includes gravitational fields in the stress-energy tensor, it conserves mass-energy, it considers higher order terms that are natural in a graviton formulation) involve issues that have been the subject of considerable scholarly discussion over the last century, while it does realize the Einstein equations as its classical limit for a sufficient set of simplifying assumptions.

13. Unlike other modified gravity and dark matter theories which are generally purely phenomenological, Deur's approach is well motivated theoretically from a fundamental physics perspective.

14. It would not lead to significantly different predictions around time of the Big Bang because the Big Bang is widely assumed to have been spherically symmetric.

15. It would not lead to very different predictions about the properties of black holes which are also widely assumed to be spherically symmetric. In general, in the spherically symmetric limit, which is a good approximation of most situations involving strong gravitational fields, it reduces to General Relativity in a domain where the predictions of General Relativity have been rigorously confirmed.

16. It would not lead to very different predictions at the solar system scale where mass distributions around the Sun are very spherically symmetric and the mass of the total system is very small compared to galaxies.

17. This is the basis of two peer reviewed published articles in respectable journals by a professional physicist. Whether or not it is correct, it is not a crackpot theory. Indeed the author's primary background in QCD, rather than general relativity, may explain why he was able to see mathematical possibilities that others in the seemingly unrelated fields might not, and to appreciate what simplifications of the naively intractable equations could make them workable without sacrificing their accuracy greatly.

18. In this theory it is natural that space-time is extremely close to being topologically flat as is observed.

19. There are serious problems with most dark matter theories and the few that remain viable are close to being overconstrained by the observational evidence.

20. The apparent shortcomings of this approach (failure to explain inflation - although it might if a cosmology on this basis were developed, and failure to explain baryogenesis and leptogenesis) are shared by almost all of its competitors, but unlike those theories it doesn't also have to explain where dark matter comes from as the emission and absorption of gravitons on an ongoing basis over the life of the universe is well explained.

In short, the Standard Model and a Deur type quantum gravity theory involving just one additional tensor boson beyond the Standard Model, suffice to explain all observed phenomena in the Universe, delivering us to the "end of physics" at the fundamental level, except for the very early parts of Big Bang cosmology and the deeper relationships between the component parts of the core theory in some kind of unification of the forces and particles.

## 2 comments:

I always thought Deur's idea was a bit arbitrary, but that slideshow from 2014 (which I had not seen before) has impressed me with its list of analogies!

The biggest insight in terms of making this mathematically tractable bears noting even though it is buried: "For static case, we can approximate ψ as scalar".

A scalar graviton without self-interaction in the static case is Newtonian gravity. Essentially what he is really modeling is a scalar graviton with self-interaction, which in the static case isn't materially different from a tensor graviton with self-interaction since in most astrophysical applications relevant to dark matter, the contribution to the stress-energy tensor from EM flux, angular momentum, linear kinetic energy and pressure are zero or negligible relative to the rest mass term. (Indeed, most DM N-body simulations are actually done using Newtonian gravity.)

The terms of the self-interacting graviton converge much more rapidly than either QCD loops or a tensor graviton, but at pretty modest sacrifices in terms of predictive power.

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