I support the idea of ​​quantum gravity.

But what is its physical and mathematical model?

What laws of physics are its foundations?

I want to delve deeper and compare with all the studies shown on the channel:

https://www.youtube.com/@energyscientist777

Perhaps we will do a joint lecture on the channel!

Vasiliy Karpenko Thank you for your interest in quantum gravity and for taking the time to respond.

The technical details you're asking about are covered comprehensively in my manuscript, which includes the complete mathematical derivation, foundational physics principles, and detailed comparisons with existing approaches. I'd encourage you to review the full paper for the specific technical content.

At this stage, I'm focused on obtaining detailed technical feedback from experts in the field before considering broader outreach opportunities. I appreciate your interest in collaboration, but I think it would be premature until the work has undergone proper peer review.

Thank you again for your engagement, and best of luck with your channel.

Best regards, Aswathy

Your preparation in manuscript is well deserved appreciation even noted as highly speculative according physics community.

I suggest more physical new predictions of unsolved physics problems base on computational simulation such as Lattice to get more recognized is peer reviewed process.

Aswathy Prakash Thekkepurakkal Prakashan

What is the space-time geometry that emerges?

We have shown own multiple occasions that material points do not move in geodetic lines, that the rule of gravitation is that the energy lost by the wave in an energy wave sphere becomes the Newtonian energy of motion of the energy wave sphere, and the rate of a unit clock, the multiplicative inverse of Einstein's unit clock rate, is (1-(alpha)/r)1/2. This is a classical quantum hidden variable gravitation.

Article Classical Quantum Hidden Variable Gravitation

Article The Dying of a Principle: The Bending of Light, the Oppenhei...

Here are my concerns:

The core mechanism, specifically the conversion of vibrational standing waves into spacetime curvature, lacks a clearly defined derivation. It leans on metaphor without grounding in gauge-invariant field theory or well-formulated Lagrangians.

The idea of “quantum foam interacting with vibrations” is speculative and lacks a tensorial or operator formulation within a known framework (GR, QFT, etc.).

No full field equations (Einstein-like or Schrödinger-like) are laid out.

The suppression dynamics are mentioned, but there is no derived Lagrangian, variational principle, or stress-energy tensor.

The “Quantum Equivalence Principle” is asserted but not demonstrated through formalism. There are no covariance arguments or geodesic equivalence paths.

No specific experiments or bounds are proposed.

No connection to existing interferometry, decoherence, or gravitational wave detection experiments.

Stefan-Alexandru Gheorghe Thank you for this excellent technical feedback - these are exactly the right questions to ask about any quantum gravity framework.

Let me address your concerns point by point:

These predictions are testable with current/near-future gravitational wave detectors and cosmic ray observatories.

Which aspects would you like me to clarify further? Your technical questions help identify where the presentation needs strengthening.

Stefan-Alexandru Gheorghe To address the points about lagrangian formulation-

You're right that a more complete Lagrangian treatment would strengthen the framework. The current action (Eq. 13, Section 3.3) does provide the field dynamics through proper variational principles, yielding both the Prakash Wave Equation and modified Einstein equations, but the quantum foam interaction terms require fuller development.

The framework does include:

• Complete action-to-field-equation derivation (Section 3.3.2)
• Stress-energy tensor derived from metric variation T^(φ)_μν (Section 3.8.2, Eq. 39-40)
• Conservation laws verified through covariant derivatives (Appendix C)
• Curvature-coupled kinetic terms: R_μν ∇^μ φ ∇^ν φ and scalar terms R ∇_μ φ ∇^μ φ

However, I acknowledge that the quantum foam interactions and suppression dynamics need more rigorous operator formulation, which I'm addressing in my follow up papers.

Gauge Invariance and Covariance

The framework preserves diffeomorphism invariance (general covariance) as demonstrated in Section 3.4. All tensorial components transform properly under coordinate changes x^μ → x'^μ(x):

• The d'Alembertian □φ transforms as a scalar
• Ricci tensor R_μν and scalar R are intrinsic geometric objects
• The suppression function S(R) maintains scalar character

Additionally, the theory exhibits local scaling symmetry φ(x) → f(x)φ(x) under specific coupling constraints, though this geometric scaling invariance requires further development beyond the current presentation.

I’ve reviewed your response carefully, and I’d like to follow up on a few areas that I believe merit further discussion or clarification:

1. Prakash Wave Equation (Eq. 17):

The formalization here is appreciated. Does this equation reduce to a known wave equation (e.g., Klein-Gordon or Dirac) under a limiting condition, or is it novel in all regimes? Understanding the symmetry properties of your solutions—particularly Lorentz covariance—would help position it within known field theoretic structures.

2. Suppression Function :

The coupling to the stress-energy tensor via is intriguing. Is this function derived from a symmetry-breaking mechanism or an effective field treatment? If it’s phenomenological, how is it protected from large loop corrections? Some renormalization discussion would be helpful here.

3. Modified Einstein Equation (Eq. 44):

The inclusion of quantum correction terms raises interesting questions about classical limits. Have you checked its consistency with solar system constraints or binary pulsar timing data? Or are such tests outside the current scope?

4. Quantum Equivalence Principle:

I completely agree this is a conceptually rich idea that could benefit from a more rigorous formulation. A path-integral sketch or a toy model showing reparameterization invariance under proper time would go a long way in strengthening this pillar of the framework.

5. Experimental Predictions:

The echo delay scaling is compelling. Could you clarify whether this emerges from horizon structure quantization, causal set discretization, or some other mechanism?

The UHECR cutoff alignment with GZK observations is impressive. Is this derived assuming standard dispersion relations, or do your high-energy corrections modify particle kinematics directly?

Stefan-Alexandru Gheorghe Thank you for these incisive and technically rigorous questions. I'll address your points systematically:

1. Prakash Wave Equation: Limiting Behavior and Lorentz Covariance

The Prakash Wave Equation is novel in its full structure but exhibits clean reductions in the appropriate limits:

• Flat spacetime: As R_μν → 0 and S(R) → 1, the equation reduces to: □φ ≈ 0, recovering the massless Klein–Gordon equation.
• Lorentz covariance is explicitly preserved. All terms — □φ, R_μν, and S(R) — are scalars or covariant tensors, and the action is constructed to remain invariant under diffeomorphisms. The interaction term R_μν ∇^μ φ ∇^ν φ acts as a geometry-dependent kinetic modifier without introducing local Lorentz violation.
• The novelty lies in its feedback structure: the field's energy density sources curvature, which in turn modulates coherence, forming a closed, curvature-coupled vibrational system.

2. Suppression Function S(R): Origin and Loop Protection

• While currently introduced phenomenologically, S(R) = 1/log(1 + 1/(RL_p²)) is not arbitrary:
  • Several candidate forms (exponential, power-law, rational-log) were tested.
  • Only this specific structure both produces a self-consistent vacuum energy density and satisfies echo delay predictions and GZK scaling, and show a stabilised standing wave model which is crucial for my theory.
• loop protection arises from geometry, not counter-terms. As curvature increases, S(R) saturates rather than diverging, naturally suppressing high-energy contributions and rendering external cutoffs unnecessary (Quantum coherence boundary)
• The suppression function S(R) provides intrinsic geometric regulation. Unlike traditional QFT approaches requiring external renormalisation, the logarithmic form emerges from the vibrational structure of spacetime itself, naturally preventing UV divergences through curvature-dependent modulation.

3. Modified Einstein Equation: Classical Limit and Observational Consistency

• In the low-curvature limit, S(R) → 1, and the standard Einstein field equations are recovered. Quantum corrections scale with α_v ξ ~ L_p² ρ_Planck, ensuring they are undetectable in classical regimes.
• Observational constraints:
  • Solar system: Vibrational corrections are utterly negligible.
  • Binary pulsar systems: Preliminary results in Section 5.8 show that vibrational effects introduce a small but potentially observable orbital-phase-dependent modulation in systems like PSR J0737-3039A/B.
  • I am also using LIGO GW data to constrain the theory's dispersion relation empirically.

4. Quantum Equivalence Principle (QEP): Toward Rigorous Formulation

You're absolutely right — this principle deserves deeper formalism. I'm currently developing:

• A coherence-weighted path integral: ∫ D[φ] e^(i ∫ d⁴x √(-g) L[φ] · S(R)), where classical paths dominate in high-coherence (low-curvature) regions, and quantum delocalisation re-emerges as curvature increases.
• A 1+1D toy model where the coherence function C(x) modulates transition amplitudes between localised (classical-like) and delocalised (quantum-like) vibrational states. The QEP then becomes a symmetry between classical and quantum configurations under local curvature constraints.
• The QEP is also central to my singularity resolution mechanism: at a critical curvature R_q ~ 0.582/L_p², coherence breakdown reverses, geodesics converge, and the system dynamically stabilizes — forming a nonsingular vibrational core.

5. Experimental Predictions: Echoes and High-Energy Cutoff

• Echo delay scaling: Δt = 6.43 · GM/c³ arises from the vibrational core boundary, not from horizon quantisation or causal sets. The inner coherence limit acts as a semi-reflective surface, and the delay emerges from classical geometric integration — vibrational in origin, but testable through gravitational wave interferometry.
• UHECR cutoff: ω² = k² [1 - (kL_p)² + α_v ξ (kL_p)⁴] This modified dispersion relation suppresses superluminal propagation and naturally yields a cutoff at ~5.7 × 10¹⁹ eV, in agreement with the GZK limit — derived blindly, not fitted. (As I was not aware such a cosmological phenomenon existed before I researched about this blind prediction of mine against observables).

Overall, the framework is ambitious and creative; however I would be trying to clarify the following technical points that will allow the traditional community to engage with its ideas on more solid footing:

Meanwhile, I would like to invite you and have a look at this, maybe you can draw some inspiration for your further work:

Preprint Event-Dependent T₀ and the Quantum → Classical Crossover

All the best,

Stefan

Stefan-Alexandru Gheorghe Thank you so much for this incredibly thoughtful and encouraging discussion. Your thorough technical review has been invaluable, and I'm genuinely grateful for the time and expertise you've invested in examining this work.

You're absolutely right that the modified dispersion relation:

ω² = k²[1 - (kLₚ)² + αᵥξ(kLₚ)⁴]

leads to a group velocity deviation of Δvₓ ~ O((kLₚ)²) ~ 10⁻³⁶ for 100 Hz gravitational waves—which is trivially consistent with the GW170817 constraint |Δvₓ| < 10⁻¹⁵.

You've identified a significant calculation error in Section 3.15. The correct dispersion-induced delay using:

Δt ~ (Δvₓ × D)/c²

with D = 100 Mpc gives:

Δt ~ 10⁻²⁸ s

which is completely negligible and poses no contradiction with GW170817.

I will definitely correct this error in the revised version. The 10⁻⁸ s delay initially quoted was indeed incorrect—I'm truly grateful you caught this.

I cannot express enough how much I appreciate your careful reading, technical rigor, and constructive engagement with the framework. Your insightful questions have not only identified important corrections but have genuinely enhanced the theoretical clarity and robustness of the work. I'm deeply thankful for your contributions to improving this research. I’m also glad to check out the paper. :)