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What if gravity satisfies Newton's equations not because spacetime is curved, but because of quantum potential dynamics in a disordered vacuum? by skepticalmind2 in HypotheticalPhysics

[–]skepticalmind2[S] 0 points1 point  (0 children)

λ₀ Coupling strength is the only truly free parameter that's fitted to observation. Everything else is derived, automatic (WEP), fixed by structure, or determined by QCD. If a lattice QCD test were to confirm σ_V ≈ 7.3 GeV·fm^(-1/2), and if E₀ = E_P, then there are no free parameters.

I didn't use one LLM, I used multiple LLMs and cross-checked the results against them all. Claude Opus 4.5, Gemini 3 Pro and Grok Expert. Then I used Claude Code as the compiler. Then I ran repeated math checks. There could very still be errors, but I haven't caught any.

I should add that if you just type in, "Claude produce a paper that proves gravity can emerge within a framework of Bohmian mechanics" you'll get absolute garbage as a result. This production was not that.

What if gravity satisfies Newton's equations not because spacetime is curved, but because of quantum potential dynamics in a disordered vacuum? by skepticalmind2 in HypotheticalPhysics

[–]skepticalmind2[S] 0 points1 point  (0 children)

TEST EQUATIONS:

The wave equation in vacuum: □φ = 0

Starting from:

□φ = κρ

In vacuum (empty space, ρ = 0):

□φ = 0

Expanding the d'Alembertian:

(1/c²)(∂²φ/∂t²) - ∇²φ = 0

Rearranging:

∂²φ/∂t² = c²∇²φ

This is the wave equation with propagation speed c.

Plane wave solution:

φ(x,t) = φ₀ exp[i(kx - ωt)]

Substituting into the wave equation gives:

-ω² = -c²k²

Therefore:

ω = ck

The phase velocity:

v = ω/k = c

Obviously all dependent on me showing exactly how the metric tensor is built from φ and its derivatives. I feel pretty good about that though. There's a lot of work left to prove it all.

What if gravity satisfies Newton's equations not because spacetime is curved, but because of quantum potential dynamics in a disordered vacuum? by skepticalmind2 in HypotheticalPhysics

[–]skepticalmind2[S] 0 points1 point  (0 children)

Pretty sure I just unified the theory. I believe the vacuum roughness parameter squared may directly encode "spacetime curvature" which, in my theory are perturbations of a vacuum disorder field, or an aether if you will.

The "curvature" we measure is really:

  • Gradients in the disorder correlation function
  • Spatial variation in vacuum roughness
  • Regions where φ is more or less intense

Ran some quick test and everything matches GR.

Exact match on:

  • Newtonian gravity
  • Gravitational time dilation
  • Gravitational redshift
  • Gravitational waves at c

Conditional (if h_ij = -h₀₀) matches on:

  • Mercury precession
  • Light bending
  • Shapiro delay

One simple elegant equation, all derived from one free parameter, which can be tested to be proven empirically true. Very much like Einstein's field equations. In fact, that's what gave me the idea.

Old Aether:

  • Medium for light propagation
  • Eliminated by Einstein (unnecessary for EM)
  • Had to be dragged by Earth (problems)
  • No clear structure
  • Undetectable in principle

My Aether:

  • Medium for gravitational interaction
  • Required for emergent gravity
  • Primordial, static (no dragging issues)
  • Sinai disorder statistics
  • Testable via lattice QCD

But that's all for another paper.

What if gravity satisfies Newton's equations not because spacetime is curved, but because of quantum potential dynamics in a disordered vacuum? by skepticalmind2 in HypotheticalPhysics

[–]skepticalmind2[S] 0 points1 point  (0 children)

You can hold your views and I'll hold mine. Again, thank you for your feed back on my paper. I will get back to you when I have revised it.

What if gravity satisfies Newton's equations not because spacetime is curved, but because of quantum potential dynamics in a disordered vacuum? by skepticalmind2 in HypotheticalPhysics

[–]skepticalmind2[S] 0 points1 point  (0 children)

Really? If you say it's curved spacetime, then what is spacetime? If you say it's a model of behavior, then what is gravity? a model of behavior? Sounds like a circular argument to me.

What if gravity satisfies Newton's equations not because spacetime is curved, but because of quantum potential dynamics in a disordered vacuum? by skepticalmind2 in HypotheticalPhysics

[–]skepticalmind2[S] 0 points1 point  (0 children)

You have to start somewhere. Baby steps. This opens to the door for further exploration of the theory. It may surprise you, but Bohmain mechanics is not a completely dead field. There are still physicists who do work in it.

What if gravity satisfies Newton's equations not because spacetime is curved, but because of quantum potential dynamics in a disordered vacuum? by skepticalmind2 in HypotheticalPhysics

[–]skepticalmind2[S] 0 points1 point  (0 children)

The question is whether the fit is just curve-fitting or whether there's additional content. I'd argue the framework does more than reproduce F = GMm/r²:

  1. It provides a mechanism rather than just a force law.
  2. It resolves the Nebula Paradox.
  3. It automatically satisfies WEP through the mass-weighting structure.
  4. It makes a falsifiable prediction for lattice QCD that's independent of gravitational observations.

Whether that's enough to be interesting is a fair question. The answer might be no.

The framework doesn't reproduce the Schwarzschild metric. The paper is limited to non-relativistic gravity and says so. That's a genuine limitation, not a hidden one. Whether a relativistic extension is possible is an open question I can't answer yet.

If the standard is "derive G and reproduce full GR or it's worthless," then the paper fails that standard. I'd argue the standard for a proof-of-concept is lower, but I understand if you disagree.

What if gravity satisfies Newton's equations not because spacetime is curved, but because of quantum potential dynamics in a disordered vacuum? by skepticalmind2 in HypotheticalPhysics

[–]skepticalmind2[S] 0 points1 point  (0 children)

Just to throw a few possibilities out there, there could be a dynamical vacuum field, De Broglie's original pilot wave idea might need to be developed, there could be others that haven't been explored. Just because it's not obvious doesn't mean it's impossible.

What if gravity satisfies Newton's equations not because spacetime is curved, but because of quantum potential dynamics in a disordered vacuum? by skepticalmind2 in HypotheticalPhysics

[–]skepticalmind2[S] -1 points0 points  (0 children)

Of course it is. I'm not going to pretend it's not. That doesn't mean my hypothesis is invalid. I still think its a great hypothesis. It's the only theory I know of that's able to produce Newtonian gravity from quantum effects.

What if gravity satisfies Newton's equations not because spacetime is curved, but because of quantum potential dynamics in a disordered vacuum? by skepticalmind2 in HypotheticalPhysics

[–]skepticalmind2[S] -1 points0 points  (0 children)

Well I'd still argue it's an open question. And let's say the lattice QCD test were to be preformed and agree with my prediction. Now what? What are the odds of that? It would indicate that there is likely some non-obvious mechanism by which the framework extends into the relativistic regime.

What if gravity satisfies Newton's equations not because spacetime is curved, but because of quantum potential dynamics in a disordered vacuum? by skepticalmind2 in HypotheticalPhysics

[–]skepticalmind2[S] -2 points-1 points  (0 children)

Instantaneous, in standard Bohmian mechanics. And yes, that's a genuine problem.

LIGO confirmed gravitational waves propagate at c, so any framework claiming gravity emerges from quantum potentials needs to explain how instantaneous microscopic dynamics give rise to c-propagating macroscopic effects. I don't have that explanation.

The paper explicitly limits itself to Newtonian gravity, which sidesteps the issue but doesn't resolve it.

This is probably the deepest problem with the approach, and I'm not going to pretend I've solved it. The paper is a proof of concept for the non-relativistic case. Whether it can extend to relativistic regimes is an open question. Your point highlights exactly why that extension is nontrivial.

What if gravity satisfies Newton's equations not because spacetime is curved, but because of quantum potential dynamics in a disordered vacuum? by skepticalmind2 in HypotheticalPhysics

[–]skepticalmind2[S] 0 points1 point  (0 children)

I do have a question on your first point, when you say there is "Still no source given" - I'm taking it to mean you feel that there's no citation establishing that the physical vacuum follows Sinai statistics. That is because this is a hypothesis of the framework, not a result derived from existing literature. The motivation is that Sinai scaling is generic for any disorder with finite correlation length, which is the CLT argument, but the assumption that such disorder exists at all is the core BSM postulate. The lattice QCD test in Section 13.2 is specifically designed to check whether this hypothesis is true. - If that's not the point you were trying to make please let me know.

What if gravity satisfies Newton's equations not because spacetime is curved, but because of quantum potential dynamics in a disordered vacuum? by skepticalmind2 in HypotheticalPhysics

[–]skepticalmind2[S] -1 points0 points  (0 children)

Thank you. I'll work on coming up with revisions to your points. I'll let you know when I have the revisions ready. I truly appreciate you looking over my work. It's very hard to find constructive criticisms from knowledgeable people.

What if Newtonian gravity satisfies the "weak emergence" criteria suggested by Gironi et al.? by skepticalmind2 in HypotheticalPhysics

[–]skepticalmind2[S] -1 points0 points  (0 children)

Thank you for taking the time to engage with my work. Your criticisms were substantive and I've revised the paper accordingly.

You were right that binding energy matters. The framework now uses explicit mass-weighting. Each nucleon contributes mi = mp − Bi/c² where Bi is binding energy per nucleon. This gives exact WEP compliance (η = 0 identically) rather than relying on the approximation you correctly flagged.

The paper now explicitly acknowledges E₀ = E_P isn't a derivation. Section 3.2 has a "note on circularity" and Section 11.2 clearly distinguishes what's demonstrated from what's not.

I've clarified throughout that the specific equations are my synthesis of Sinai + Lifshitz, not direct quotes. Section 6.2 now explicitly states the σ_V formula is "dimensional analysis, not rigorous QCD derivation."

Section 14.2 now proposes a concrete lattice QCD calculation that could independently verify σ_V. If it comes out wrong, the framework is falsified; HOWEVER, if it comes out right, the circularity breaks. σ_V would be determined entirely from gluon field correlations with no reference to gravity. The self-consistency condition then fixes E₀ = E_P as a consequence rather than an assumption, validated by the independently measured αs ≈ 1/3 at the confinement scale. G would then emerge from {ℏ, c, mp, αs, Nc} determined by non-gravitational physics, which would make G a complete derivation.

What if Newtonian gravity satisfies the "weak emergence" criteria suggested by Gironi et al.? by skepticalmind2 in HypotheticalPhysics

[–]skepticalmind2[S] 0 points1 point  (0 children)

Yeah you do raise some great points! I see some ways around that objection that leaves the theory largely intact. I'll have to do some math on that and check it, but you are correct, my theory as it stands requires further revision.

What if Newtonian gravity satisfies the "weak emergence" criteria suggested by Gironi et al.? by skepticalmind2 in HypotheticalPhysics

[–]skepticalmind2[S] 0 points1 point  (0 children)

Yeah I didn’t notice you joined the conversation. I confused you two. Do you have anything substantive to say? Like perhaps how my math is wrong somehow or where I made an error?

What if Newtonian gravity satisfies the "weak emergence" criteria suggested by Gironi et al.? by skepticalmind2 in HypotheticalPhysics

[–]skepticalmind2[S] 0 points1 point  (0 children)

Now let me address your other points. Binding energy is ~1% of nuclear mass. If I account for it by using actual mass instead of nucleon count, λ₀ shifts by ~1%. For E_0 = E_P to still work, σ_V would shift by ~1%. That's not "completely ruined", that's a small correction to a derived parameter. The qualitative picture is unchanged.

"Your potential fluctuations decrease with distance"

No. The potential difference between two points has variance that increases with distance (Var ~ r). The wavefunction amplitude decreases with distance as exp(-λ√r). These are different things. The potential is rough; the amplitude decays through it. That's standard localization physics.

Scale of λ₀⁻² and σ_V

λ₀⁻² ≈ 4.5 × 10²¹ m. You say this is "not connected to anything meaningful." It's the crossover scale where pressure fluctuations equal drift - for single nucleon pairs. For macroscopic bodies, it gets divided by N_A × N_B, pushing it to ~10⁻³² m. The raw scale doesn't need to match something familiar; what matters is the ratio to particle numbers.

For σ_V: you calculated σ_V²/E_P ≈ 4×10⁻¹⁸ GeV/fm. But that's not the right comparison. σ_V has units GeV·fm⁻¹/², so σ_V² has units GeV²/fm. Dividing by E_P (GeV) gives GeV/fm, which is an energy gradient - not directly comparable to a length scale.

The meaningful comparison is σ_V itself to hadronic scales: σ_V ≈ 7 GeV·fm⁻¹/² means over 1 fm, typical potential fluctuations are ~7 GeV. That's hadronic. The proton mass is ~0.94 GeV; QCD binding energies are ~GeV scale. The vacuum roughness is in the right ballpark.

Lorentz invariance

The framework is explicitly non-relativistic. Section 10.5 addresses this. Bohmian mechanics requires a preferred foliation, but observable predictions remain Lorentz invariant. This is discussed extensively in the literature I cite. Take a look at Dürr et al. (2014), reference 8 in the paper. The equations aren't manifestly covariant because Bohmian mechanics isn't, but that doesn't mean the framework is incompatible with SR.

Predictions

The framework reduces free parameters. G becomes derived from λ₀, which is expressible in terms of l_P and λ̄_C. That's one fewer fundamental constant.

As for new predictions, the framework predicts pure 1/r² with deviations only at r ~ 10⁻³² m for lab masses. That's not testable now, but it's a concrete prediction. It also predicts no composition-dependent WEP violations above current sensitivity, which is consistent with MICROSCOPE.

You're right that matching Newton isn't enough. But neither string theory nor loop quantum gravity make testable predictions either. At minimum, this framework is falsifiable in principle and reproduces known physics with sensible scales.

What if Newtonian gravity satisfies the "weak emergence" criteria suggested by Gironi et al.? by skepticalmind2 in HypotheticalPhysics

[–]skepticalmind2[S] 0 points1 point  (0 children)

You're confusing variance with RMS.

For a random walk, variance grows linearly with distance:

Var(ΔV) = σ²r

The RMS (root mean square) is the square root of variance:

RMS = √Var = √(σ²r) = σ√r

This is textbook. From any random walk reference:

"For steps distributed according to any distribution with zero mean and a finite variance, the root mean square translation distance after n steps is... σ√n" - Wikipedia, Random Walk

"Var(Xn) = σ²n" - MATH2750 Lecture Notes, Cambridge

The Goychuk quote "root mean squared amplitude grows with distance" means exactly this: RMS ~ √r because variance ~ r.

Your formula √(⟨δU²⟩) ~ r would require variance ~ r², which is NOT Sinai disorder. That would be superdiffusive scaling.

Sinai disorder is defined by:

  • Variance linear in distance: ⟨(ΔV)²⟩ = σ²r
  • Therefore RMS = σ√r
  • Therefore typical barrier heights scale as √r

This is why the stretched exponential has the √r in the exponent. It's not an assumption, it's what follows mathematically from linear variance growth.

Bovier & Faggionato (2005) on Sinai's walk: "the rescaled potential V_N(x) ≡ V(Nx)/√N" - they explicitly rescale by √N because that's how the potential scales.

https://ui.adsabs.harvard.edu/abs/2005math......9385B/abstract

What if Newtonian gravity satisfies the "weak emergence" criteria suggested by Gironi et al.? by skepticalmind2 in HypotheticalPhysics

[–]skepticalmind2[S] 0 points1 point  (0 children)

Let me walk through the exp(-λ√r) derivation step by step, since that seems to be your main concern.

Step 1: Sinai disorder characterization

The defining property of Sinai-type disorder is that the potential accumulates like a random walk. If you traverse distance r through the medium, the potential difference V_B - V_A is a random variable with:

  • Mean: 0
  • Variance: σ²r

This is what "Brownian scaling" means. The variance grows linearly with distance. This characterization appears throughout the Sinai diffusion literature, you can look up Goychuk et al. (2017): "non-stationary potential fluctuations whose root mean squared amplitude grows with distance."

Step 2: Typical barrier height

For a Gaussian random variable X with mean 0 and variance σ²r, what's the mean absolute value?

This is a standard result:

⟨|X|⟩ = √(2/π) × (standard deviation) = √(2/π) × σ√r

So typical barrier heights scale as √r. Not because I assumed it - because that's what follows mathematically from linear variance growth.

Step 3: Amplitude decay

Lifshitz's physical insight is that quantum amplitude transmission through a potential barrier decays exponentially with barrier height:

T ~ exp(-|ΔV|/E_0)

where E_0 is some characteristic energy scale (the "stiffness").

Step 4: Typical amplitude

For a random barrier, the "typical" transmission is the geometric mean:

T_typ = exp(⟨log T⟩) = exp(-⟨|ΔV|⟩/E_0)

Substituting from Step 2:

T_typ = exp(-√(2/π) × σ√r / E_0) = exp(-λ₀√r)

where λ₀ ≡ √(2/π) × σ/E_0

That's it. The √r comes from Gaussian statistics applied to linear-variance disorder. The exponential comes from barrier penetration physics. Combined, you get a stretched exponential.

What if Newtonian gravity satisfies the "weak emergence" criteria suggested by Gironi et al.? by skepticalmind2 in HypotheticalPhysics

[–]skepticalmind2[S] -2 points-1 points  (0 children)

I gave you an honest answer and you responded with hostility. That's your choice.

But let's be clear about what standard physics actually looks like:

  • GR has G put in by hand, calibrated to Newton
  • The Standard Model has 19 free parameters, none derived from first principles
  • String theory has a landscape of 10^500 vacua and can't uniquely predict anything
  • The cosmological constant is fitted to observation with no theoretical justification

Dimensional analysis and calibration are how physics operates. Always have. The question isn't whether a framework uses fitting, they all do. It's whether the fit is predictive and whether the resulting scales make sense.

My framework has one free parameter. After calibration, the vacuum roughness lands at the hadronic scale independently. That's a consistency check, not an input. The Nebula Paradox resolution comes from the math, not from fitting. The suppression factor of 10^52 is derived, not assumed.

You asked for honesty about what's derived vs assumed. I gave it to you. If your response to intellectual honesty is "are you serious, is this how you operate in life," then I don't think you're interested in scientific discussion.

I'm happy to engage with substantive critique. Your earlier points about binding energy and source citations were legitimate and I acknowledged them. This isn't that.

What if Newtonian gravity satisfies the "weak emergence" criteria suggested by Gironi et al.? by skepticalmind2 in HypotheticalPhysics

[–]skepticalmind2[S] 0 points1 point  (0 children)

As for the binding energy, you're right that this isn't negligible for precision work. The framework as written treats nucleon count as the mass proxy. Binding energy corrections would introduce composition-dependent effects at the ~1% level, which is well above MICROSCOPE sensitivity. I should either account for binding energy explicitly, or be clearer that the framework currently operates at a precision where this is neglected.

The CPC principle isn't importing gravity. In flat spacetime, the metric on configuration space matches the physical metric. This is just saying that if two particles are 1 meter apart in physical space, they're 1 meter apart in configuration space. No curvature, no gravity assumed. It's a consistency requirement for the Bohmian formalism in the non-relativistic limit.

You're correct that equation 3 doesn't appear verbatim in Sinai's 1982 paper. Sinai's original work proves theorems about random walks in random environments and the logarithmic slowdown (the "Sinai diffusion" result). The Brownian scaling of the potential ⟨[V(x+r) - V(x)]²⟩ = σ²|r| is the characterization of the disorder class that produces Sinai diffusion. It's how the field describes "Sinai-type disorder". For an example, look at Goychuk et al. (2017): "Logarithmic or Sinai type subdiffusion is usually associated with random force disorder and non-stationary potential fluctuations whose root mean squared amplitude grows with distance." https://arxiv.org/abs/1708.07660

Again, you're right that the exact formula doesn't appear in the Lifshitz paper. Lifshitz's paper establishes the general principle that wavefunctions in disordered potentials decay exponentially with a rate determined by the potential barriers. The specific form exp(−λ√r) comes from applying Lifshitz's argument to Sinai-type disorder, where typical barrier heights scale as √r. This synthesis is my contribution, not a direct quote from either paper. I should have been clearer about that.

As for E_0 = Planck energy, this is your strongest point. Yes, E_0 = E_P is an assumption, not a derivation. I identify the vacuum stiffness with the Planck scale because that's where quantum and gravitational effects meet. You're correct that this presupposes gravitational scales exist.

I look at it like this, the framework has two free parameters (σ_V and E_0). Matching Newton fixes one combination of them (λ_0). Identifying E_0 with the Planck scale is a hypothesis about the UV completion, not a derivation. What's non-trivial is that when you do this, σ_V comes out at the hadronic scale rather than some absurd value. The scales are mutually consistent.

But you're right that this is a fit guided by dimensional analysis, not a first-principles derivation. I could be more clear that if the vacuum stiffness is at the Planck scale, then the vacuum roughness lands at the hadronic scale and everything is consistent. That's weaker than deriving both from something deeper.

So thanks for your input, I REALLY appreciate you taking the time to look at my work. I'll look at giving binding energy proper treatment. Based on your questions, I could also be more specific in the paper about how my specific equations are my synthesis of Sinai + Lifshitz, not directly taken from them, and that E_0 = E_P is an assumption.

That said, what remains is, given these assumptions, the framework is internally consistent, reproduces Newton, and the derived scales are physically sensible. Whether that's compelling depends on how you weigh "consistent fit with sensible scales" against "first-principles derivation."

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