Geodesics in quantum gravity: Missing Link

[kodama]

TL;DR

a quantum mechanical reason

​

what do you think of the relationship between the cosmology constant and MOND ao, coincidence that they are close or a quantum mechanical reason​

Sabine Hossenfelder, think that

Physicists Find Missing Link Between Quantum Mechanics and Gravity​

reference

Physical Review D​

Geodesics in quantum gravity​

Benjamin Koch1,2,3,*, Ali Riahinia1,2,†, and Angel Rincon4,‡
Phys. Rev. D 112, 084056 – Published 22 October, 2025

DOI:https://doi.org/10.1103/w1sd-v69d

could explain why

comment ?

 

[PeterDonis]

what do you think of the relationship between the cosmology constant and MOND ao, coincidence that they are close or a quantum mechanical reason

It's one of many quantum gravity speculations that are open areas of research. It's much too early to be able to give any definite opinion on how any such speculations will turn out.

 

[ChrisF]

● The closeness of a₀ and Λ-derived quantities isn't coincidence — it's been noted explicitly in the literature. Milgrom himself pointed out that a₀ ~ cH₀, which connects MOND's critical acceleration directly to the cosmological
expansion rate. Since in ΛCDM the cosmological constant satisfies Λ ~ 3H₀²/c², both a₀ and Λ trace back to the same cosmological scale H₀. The "coincidence" is really two phenomena sharing a common origin in whatever sets H₀.

The interesting question is whether that shared origin is dynamical or fundamental. If H₀ is just a boundary condition of this particular universe, then the Λ-a₀ relationship is environmental. If H₀ is set by something deeper — vacuum
properties, quantum geometry — then both Λ and a₀ are expressions of that deeper thing and their ratio should be derivable rather than tuned.

The Koch et al. geodesic paper is relevant here. If quantum corrections to geodesic motion generate effective acceleration terms at scales ~ c²√Λ, that would naturally produce a₀-scale physics from Λ without any separate MOND
postulate. That's a genuine structural connection, not a numerical coincidence.

Whether it's quantum mechanical in origin is the real question and the answer depends entirely on what sets Λ. That's unsolved.

 

[PeterDonis]

which connects MOND's critical acceleration directly to the cosmological
expansion rate.

By $H_0$ do you mean the present expansion rate? Or the "expansion rate" derived from the estimated value of $\Lambda$? In the literature $H_0$ usually means the former, but you seem to be using it as though it referred to the latter.

 

[ChrisF]

By $H_0$ do you mean the present expansion rate? Or the "expansion rate" derived from the estimated value of $\Lambda$? In the literature $H_0$ usually means the former, but you seem to be using it as though it referred to the latter.

The measured present value — Milgrom's original observation is a₀ ~ cH₀ using the observed expansion rate. The connection to Λ is then one step indirect: in flat ΛCDM, Λ = 3H_Λ²/c² where H_Λ = H₀√Ω_Λ ≈ 0.84 H₀. So a₀ ~ cH₀ implies a₀
~ c√(Λ/3) to within that same factor. The coincidence holds either way but you're right that they're not the same quantity — H₀ is the cleaner statement since it's directly observed rather than derived from a model-dependent Λ estimate.

 

[PeterDonis]

The measured present value

Then the connections you are talking about are only valid now; they're not generally true.

The connection to Λ is then one step indirect

If you want to look at it that way. But the more important point is that it's only valid now; it's not generally true. $H$ changes with time, but $H_\Lambda$ does not.

 

[ChrisF]

Then the connections you are talking about are only valid now; they're not generally true.


If you want to look at it that way. But the more important point is that it's only valid now; it's not generally true. $H$ changes with time, but $H_\Lambda$ does not.

That's a fair and important distinction. You're right — within ΛCDM, H(t) is time-varying and Λ is not, so any relationship built on H₀ specifically is epoch-dependent, not fundamental. Milgrom noted the numerical coincidence but the problem you're identifying — why now? — is real and known in the literature as the MOND coincidence problem.

The cleaner version of the connection, if one exists, would have to be a₀ ~ c√(Λ/3), which IS constant since Λ doesn't evolve. That's numerically similar to cH₀ right now — since H_Λ = H₀√Ω_Λ ≈ 0.84H₀ today — but the two diverge over cosmic time. Whether a₀ is actually tied to Λ directly rather than to the present H is an empirical question: if a₀ tracks H(t) as the universe evolves, it's dynamical. If it stays fixed while H changes, it points to Λ or something equally constant as the underlying quantity.

 

[kodama]

The Koch et al. geodesic paper is relevant here. If quantum corrections to geodesic motion generate effective acceleration terms at scales ~ c²√Λ, that would naturally produce a₀-scale physics from Λ without any separate MOND
postulate. That's a genuine structural connection, not a numerical coincidence.

Whether it's quantum mechanical in origin is the real question and the answer depends entirely on what sets Λ. That's unsolved.

how difficult for Koch to derive
quantum corrections to geodesic motion generate effective acceleration terms at scales ~ c²√Λ, that would naturally produce a₀-scale physics from Λ without any separate MOND
postulate

 

[ChrisF]

how difficult for Koch to derive
quantum corrections to geodesic motion generate effective acceleration terms at scales ~ c²√Λ, that would naturally produce a₀-scale physics from Λ without any separate MOND
postulate

kodama,

The dimensional scaling is the easy part — any quantum gravity approach that introduces corrections at the cosmological scale will naturally produce terms of order c²√(Λ/3). That's just dimensional analysis with the constants available. The hard part is getting the right numerical prefactor.

The naive estimate c²√(Λ/3) gives roughly 6-7 × 10⁻¹⁰ m/s², depending on which Λ value you use. But the observed MOND acceleration is a₀ ≈ 1.2 × 10⁻¹⁰ m/s² — about a factor of 5-6 smaller. So the quantum corrections can't just produce "something at the Λ scale." They need to produce a specific dimensionless coefficient of order ~1/6 that brings the magnitude down to match observations.

In Koch et al.'s asymptotic safety framework, this prefactor would emerge from the specific form of the quantum-corrected geodesic equation — essentially from how the running gravitational coupling G(k) modifies geodesic motion at large distances. Whether that gives exactly the right number depends on the details of the renormalization group flow, which is where the real technical difficulty lies.

The conceptual ingredients they have:
- Asymptotically safe gravity gives a running G(k) that becomes scale-dependent
- At cosmological scales, k ~ √Λ, so modifications appear at the right energy scale
- The geodesic equation picks up effective acceleration terms from the scale-dependent coupling

What they'd need to show:
- That the effective acceleration from running G is attractive (not repulsive) at galactic scales
- That the magnitude matches a₀ without tuning — the prefactor has to come OUT of the calculation, not be put in
- That it reproduces the specific phenomenology of MOND (the interpolation function, the Tully-Fisher relation), not just the characteristic acceleration scale

That last point is the real challenge. Getting the right scale is necessary but not sufficient. MOND isn't just "extra acceleration below a₀" — it's a specific functional form (Milgrom's μ function) that transitions between Newtonian and deep-MOND regimes. Deriving that transition from quantum corrections to geodesics would be genuinely new.

So to answer your question directly: the dimensional analysis is straightforward, the prefactor is hard, and the full interpolation function is very hard. But if it works, it would establish that MOND phenomenology is a low-energy manifestation of quantum gravity rather than a separate postulate — which would be a significant result.

 

[kodama]

ChrisF

btw are you familiar with Deur approach to MOND phenomenology?

 

[kodama]

kodama,

The dimensional scaling is the easy part — any quantum gravity approach that introduces corrections at the cosmological scale will naturally produce terms of order c²√(Λ/3). That's just dimensional analysis with the constants available. The hard part is getting the right numerical prefactor.

The naive estimate c²√(Λ/3) gives roughly 6-7 × 10⁻¹⁰ m/s², depending on which Λ value you use. But the observed MOND acceleration is a₀ ≈ 1.2 × 10⁻¹⁰ m/s² — about a factor of 5-6 smaller. So the quantum corrections can't just produce "something at the Λ scale." They need to produce a specific dimensionless coefficient of order ~1/6 that brings the magnitude down to match observations.

In Koch et al.'s asymptotic safety framework, this prefactor would emerge from the specific form of the quantum-corrected geodesic equation — essentially from how the running gravitational coupling G(k) modifies geodesic motion at large distances. Whether that gives exactly the right number depends on the details of the renormalization group flow, which is where the real technical difficulty lies.

The conceptual ingredients they have:
- Asymptotically safe gravity gives a running G(k) that becomes scale-dependent
- At cosmological scales, k ~ √Λ, so modifications appear at the right energy scale
- The geodesic equation picks up effective acceleration terms from the scale-dependent coupling

What they'd need to show:
- That the effective acceleration from running G is attractive (not repulsive) at galactic scales
- That the magnitude matches a₀ without tuning — the prefactor has to come OUT of the calculation, not be put in
- That it reproduces the specific phenomenology of MOND (the interpolation function, the Tully-Fisher relation), not just the characteristic acceleration scale

That last point is the real challenge. Getting the right scale is necessary but not sufficient. MOND isn't just "extra acceleration below a₀" — it's a specific functional form (Milgrom's μ function) that transitions between Newtonian and deep-MOND regimes. Deriving that transition from quantum corrections to geodesics would be genuinely new.

So to answer your question directly: the dimensional analysis is straightforward, the prefactor is hard, and the full interpolation function is very hard. But if it works, it would establish that MOND phenomenology is a low-energy manifestation of quantum gravity rather than a separate postulate — which would be a significant result.

what are the prospect of actual work on all - the prefactor is hard, and the full interpolation function is very hard- being a success ?

could the cc play a role ?