I am not sure it is relevant but I guess you should have a look at

Article Measurement of the gravitational red shift with the M ssbauer effect

And also:

https://phys.org/news/2024-09-mssbauer-scheme-gravitation.html

Thanks Nikolay

Dario Delgado

According to electromagnetic theory, there is only phase shift between the electric and magnetic fields if the beam (wave packet) propagates in a conducting medium (wave equation in conducting media).

Thanks Hugo. The way I see it, a material sensible enough could in theory determine an insignificant dephasing in the em field. the working theory is that all the four forces are the same at certain energy scales. My point is that maybe a graviton interacts with a photon, extremely weakly.

Does that make sense?

Dario Delgado

I cannot give you a well-founded contribution on the subject.

Anyway, I do not believe that it is currently possible to detect changes (if they exist) of the phase shift between E and B in a conducting (or semi-conducting) medium, caused by an intense gravitational field. Nor is it possible today to have in a laboratory a gravitational field so intense that it can compete with EM actions.

I also add that we still do not know for sure what gravitational radiation is like. According to GR it should be quadripolar, but according to SR it could also be monopolar (longitudinal waves) or dipolar.

Regards

Dario Delgado

Maybe you can get more and better information using AI

Thanks Hugo, will do :-)

This is Not the Gravitational Redshift Measurement with the Mössbauer Effect

Dear colleagues,

I wanted to clarify that my recent proposal on gravitational gradients inducing measurable dephasing in the electromagnetic fields of a traveling beam is fundamentally different from the well-known Measurement of the Gravitational Redshift with the Mössbauer Effect or similar experiments.

While the Mössbauer effect focuses on extremely precise energy shifts in photons due to gravitational redshift, my work aims to explore phase shifts in the electromagnetic fields themselves as they traverse gravitational gradients. This focuses on the interaction between gravity and the electromagnetic fields—potentially shedding light on graviton-photon coupling and unifying perspectives in quantum gravity.

For broader visibility, I’ve recently reached out to Dr. Sabine Hossenfelder, known for her insightful work in theoretical physics and her popular YouTube channel, to share and possibly discuss this concept with a wider audience.

This helps: https://chatgpt.com/canvas/shared/67dcf2c5b79c8191b55863e31cc0a2e9

Interesting,

Section: Theoretical Basis for Electromagnetic-Gravitational Coupling

We propose a phenomenological interaction between the flow of electromagnetic (EM) energy and gravitational potential gradients, leading to a novel energy transfer term in the Hamiltonian. This coupling is intended to describe subtle interactions that may arise under weak-field conditions, such as those near Earth or in orbital environments.

1. Motivation Conventional physics describes electromagnetism and gravitation as distinct forces, governed respectively by Maxwell's equations and General Relativity. However, experimental sensitivity to small effects has increased to the point where weak couplings between these forces may become measurable. One such possibility is the coupling between EM energy flux (represented by the Poynting vector) and spatial gravitational gradients. This could manifest as a measurable dephasing effect of EM waves propagating across different gravitational potentials.

2. Hamiltonian Formulation We begin by proposing a semi-classical Hamiltonian interaction term:

HEM-G=α∫(∇ΦG)⋅(E×B) d3xH_{\text{EM-G}} = \alpha \int (\nabla \Phi_G) \cdot (\mathbf{E} \times \mathbf{B}) \, d^3x

Here, ΦG\Phi_G is the gravitational potential, E\mathbf{E} and B\mathbf{B} are the electric and magnetic fields respectively, and α\alpha is a phenomenological coupling constant representing the strength of the interaction. The vector quantity E×B\mathbf{E} \times \mathbf{B} is the Poynting vector, which describes the directional energy flux (the rate of energy transfer per unit area) of the EM field.

This Hamiltonian encapsulates an energy balance interpretation, where α\alpha acts analogously to an efficiency or transfer coefficient between gravitational and electromagnetic domains. However, it does not describe the microscopic mechanism for the interaction, such as graviton-photon scattering; instead, it provides an effective field-theoretic term that could model net energy exchange due to field alignment.

3. Effective Lagrangian FormIn a semi-classical (non-covariant) approximation, the corresponding Lagrangian density can be written as:

LEM-G=α (∂iΦG) ϵijkEjBk\mathcal{L}_{\text{EM-G}} = \alpha\, (\partial_i \Phi_G)\, \epsilon^{ijk} E_j B_k

This expression couples the spatial gradient of the gravitational potential to the Poynting vector via the Levi-Civita tensor, capturing the directional nature of the interaction.

For more rigorous, Lorentz-invariant treatment, an effective Lagrangian in curved spacetime could be written as:

LEM-Gcov=αMRμνρσFμνFρσ\mathcal{L}_{\text{EM-G}}^{\text{cov}} = \frac{\alpha}{M} R^{\mu\nu\rho\sigma} F_{\mu\nu} F_{\rho\sigma}

where RμνρσR^{\mu\nu\rho\sigma} is the Riemann curvature tensor, FμνF_{\mu\nu} is the electromagnetic field strength tensor, and MM is an energy scale (e.g., the Planck mass). This form appears in various extensions of General Relativity and quantum gravity models but is typically suppressed in Earth-scale gravitational fields.

4. Interpretation and Implications The proposed coupling leads to the possibility of detecting gravitational effects on EM propagation without invoking large spacetime curvature. For example, satellites in different orbits may experience measurable phase shifts in EM wave propagation due to variations in gravitational potential. This effect could also contribute to new technologies for gravitational sensing or, in speculative extensions, mechanisms for energy transfer and propulsion.

Importantly, this macroscopic approach circumvents the limitations of direct graviton-photon scattering processes, which are known to have extremely suppressed cross-sections ( 10−60 cm2~10^{-60}\,\text{cm}^2). Instead, it relies on cumulative effects integrated over large distances and time, making phase shift detection between satellites or spacecraft not only feasible, but potentially insightful for probing weak EM–gravity couplings.

5. Microscopic Perspective and Speculative Quantum Interactions From a quantum field theoretical point of view, photons and gravitons can interact via loop-level processes involving virtual charged particles (such as electron–positron pairs). These interactions are described using Feynman diagrams in which a photon fluctuates into a virtual fermion loop, which then couples to a graviton. Such processes are extremely rare due to the gravitational coupling being suppressed by the Planck scale, resulting in effective cross-sections on the order of 10−60 cm210^{-60}\,\text{cm}^2.

Speculative theories such as string theory and extra-dimensional models propose the existence of exotic mediators like dilatons, axion-like particles, Kaluza–Klein gravitons, or torsion fields that could enhance graviton–photon coupling. These frameworks offer mechanisms for observable coupling effects under extreme conditions or engineered configurations, though they remain unconfirmed.

While these mechanisms lie beyond current experimental capability, they provide theoretical justification for phenomenological models like the one presented here. If cumulative EM–gravity coupling effects are observed in satellite-based experiments, they could indicate underlying quantum-gravitational interactions not yet captured by classical theories.

6. Analogy to Atomic Spectroscopy and Cesium Clocks An instructive comparison can be made between the challenge of triggering EM–gravity coupling and the historical difficulty in identifying atomic transition frequencies, such as the famous 9.192 GHz hyperfine transition in cesium used to define the second. Although this transition could, in principle, be calculated from quantum mechanics, the full Hamiltonian for cesium includes many complex corrections—electron-electron interactions, relativistic effects, spin-orbit coupling, hyperfine splitting, and QED contributions. These make the exact prediction extremely challenging without experimental guidance.

Likewise, in the EM–gravity case, we do not yet know the “resonant configuration” that would maximize the coupling coefficient α\alpha. Just as the right frequency had to be discovered experimentally for atomic clocks, the optimal materials, field structures, and geometries for coupling EM fields to gravitational gradients may need to be uncovered through iterative exploration. This analogy reinforces the approach of using semi-empirical models and sensitive phase shift experiments as the most viable path to discovery.

7. Speculative Extension: Toward Metric Manipulation and Time Engineering If the EM–G interaction is confirmed and shown to be tunable through material structuring or field configuration, it could, in principle, open new routes to spacetime manipulation. Gravitational time dilation and closed timelike curves (CTCs) are allowed solutions within general relativity under exotic conditions, such as intense energy-momentum curvature or negative energy densities. If structured EM fields can induce cumulative spacetime distortions, this may form the basis for precision gravitational time control, propulsion through metric engineering, or even hypothetical temporal displacement.

While a full “time machine” remains speculative, the controlled deformation of spacetime through EM–gravity interaction could serve as a foundation for future time-engineering frameworks—similar to how early EM theory preceded the development of lasers, radar, and GPS. Experimental steps focused on dephasing, gravitational lensing of modulated light, and interferometric delays under dynamic gravitational gradients may reveal the first measurable steps toward this bold frontier.

8. Outlook While the interaction term does not derive from a complete quantum theory of gravity, it serves as a testable bridge between EM and gravitational phenomena. Experimental validation of the effects described by this Hamiltonian would represent a significant step toward unifying classical field theories and potentially opening pathways to new physical understanding.

Further work is recommended to develop the full variational formalism, derive the modified Maxwell equations from this interaction, and propose realistic experimental tests involving phase-sensitive interferometry in variable gravitational fields.

Aligned with this, actually it could prove my idea is on the right track.

Title: Gravitationally Induced Electromagnetic Dephasing as a Potential Explanation for the Proton Radius Puzzle in Muonic Hydrogen

Abstract

Recent measurements of the proton radius derived from muonic hydrogen Lamb shift experiments reveal significant discrepancies compared to traditional hydrogen spectroscopy, known as the proton radius puzzle. This paper proposes a novel theoretical explanation based on gravitationally induced electromagnetic (EM) dephasing. Working backwards from the magnitude of the observed Lamb shift discrepancy (~4.4 µeV), we infer the required EM phase shift to be on the order of ~10⁻⁵ rad for typical atomic timescales, suggesting that gravitational effects on EM fields could play a measurable role at atomic scales. Furthermore, the implications of this model suggest a strong correlation with gravitational wavefunction collapse mechanisms as proposed by Penrose, and with localized energy density contributions to spacetime curvature via the Einstein field equations, providing a unified perspective of quantum-gravity interactions observable at the atomic scale.

Introduction

Precision spectroscopy of hydrogenic atoms provides fundamental tests of quantum electrodynamics (QED) and nuclear structure theories. The so-called proton radius puzzle emerged following precise Lamb shift measurements in muonic hydrogen (µH), which yielded a proton charge radius significantly smaller (~4%) than electron-based hydrogen spectroscopy. Conventional explanations involving systematic errors, QED corrections, or nuclear structure uncertainties have not fully resolved this anomaly.

Here, we present a novel hypothesis linking gravitational EM dephasing and gravitationally induced quantum wavefunction collapse. Motivated by Penrose's objective collapse theory and recent considerations of gravitationally induced EM phase shifts, this paper explores whether a gravitationally mediated correction may reconcile observed discrepancies. We also propose that local energy density—entering the Einstein stress-energy tensor—may play a more critical role than previously assumed in shaping quantum behavior through gravitational backreaction.

Theoretical Background

Penrose proposed gravitational self-energy as a mechanism inducing quantum wavefunction collapse, characterized by the collapse timescale:

τ_collapse ≈ ħ / E_G

where E_G represents gravitational self-energy between superposed quantum states. Considering gravitational fields as influencing electromagnetic wave propagation, we posit an EM dephasing proportional to gravitational potentials encountered by photons.

Rather than assume a fixed dephasing value, we reverse the logic: based on the energy discrepancy observed in muonic hydrogen Lamb shift measurements (~4.4 µeV), and using ΔE ≈ ħ δφ / Δt with Δt ≈ 10⁻¹⁵ s, we infer the phase shift needed to be approximately:

δφ ≈ ΔE × Δt / ħ ≈ (4.4 × 10⁻⁶ eV)(10⁻¹⁵ s) / (6.6 × 10⁻¹⁶ eV·s) ≈ 6.7 × 10⁻⁵ rad

This inferred value (~10⁻⁵ rad) aligns with earlier EM dephasing estimates proposed in large-scale gravitational scenarios, suggesting that even atomic systems with extremely high local energy density—such as muonic hydrogen—may exhibit such effects. This alignment becomes more plausible when considering that the Einstein field equations relate spacetime curvature to energy and momentum density, implying that extreme EM field energy densities could induce measurable spacetime effects.

To reflect this in the atomic model, we propose a corrected Hamiltonian of the hydrogen atom in weak gravitational fields:

H = H₀ + H_QED + H_FS + H_grav-dephase

Where:

• H₀: Standard non-relativistic Coulomb Hamiltonian
• H_QED: QED corrections including Lamb shift
• H_FS: Fine structure corrections
• H_grav-dephase: New proposed gravitational EM dephasing correction

With: H_grav-dephase ≈ ħ × δφ / Δt ≈ 4.4 µeV (targeting the observed anomaly)

Application to Muonic Hydrogen

Muonic hydrogen, with a muon orbiting significantly closer to the proton, experiences dramatically increased gravitational self-energy (approximately 10⁷ times greater than electronic hydrogen). Consequently, gravitationally induced collapse rates would be significantly enhanced. Incorporating this increased gravitational interaction, our model predicts distinct corrections in the measured Lamb shift in muonic hydrogen compared to electronic hydrogen.

This effect is also mass-dependent, since heavier leptons like the muon are more localized and have tighter wavefunctions, which increases their gravitational self-energy in a superposition. The increased mass (muon mass m_μ ≈ 207 m_e) leads to stronger gravitational interaction with its own quantum state, accelerating gravitationally induced collapse and amplifying energy level shifts.

Moreover, the extremely high local electromagnetic energy density near the muon's orbit significantly contributes to the stress-energy tensor TμνT_{\mu\nu}, the source term in Einstein’s field equations. This means that even in the absence of large-scale gravitational fields, localized spacetime curvature arising from EM field energy density may lead to observable dephasing effects, strengthening the plausibility of this mechanism in atomic systems.

Experimental Implications and Predictions

Our hypothesis predicts distinct, mass-dependent deviations observable in precision spectroscopy experiments:

• Muonic hydrogen Lamb shift experiments will systematically differ from electronic hydrogen measurements.
• Isotope-dependent variations will reflect gravitational coupling strength, enhancing the detectability of this gravitational EM dephasing.
• Altitude- or location-dependent measurements: A variation in gravitational potential (e.g. mountaintop labs vs underground labs) could reveal differences in energy levels or spectral line positions, offering a direct experimental probe of gravitationally sensitive quantum effects.

Future experiments designed to systematically vary gravitational potentials, either through altitude-dependent spectroscopy or controlled gravitational environments, could test the predictions made here and provide empirical evidence of quantum-gravity interactions at atomic scales.

Conclusion

We propose gravitationally induced electromagnetic dephasing as a plausible explanation for the proton radius puzzle observed in muonic hydrogen spectroscopy. Our model does not rely on fixed assumptions but derives the necessary EM phase shift from known experimental discrepancies, showing that a value on the order of ~10⁻⁵ rad is consistent with the energy shift observed. Moreover, by framing the origin of this dephasing in terms of local contributions to the Einstein stress-energy tensor, we introduce a novel mechanism by which localized energy density may curve spacetime at quantum-relevant scales. Experimental validation of these predictions would not only resolve current puzzles in precision atomic physics but also open new frontiers in quantum-gravity research.

🔭 Outlook: Extension to Propulsion Applications

The gravitationally induced electromagnetic (EM) dephasing mechanism described in this work—emerging from phase instability due to energy density in gravitational gradients—may extend beyond quantum-scale systems to engineered macroscopic configurations.

In particular, asymmetric resonant cavities and high-field Casimir-type structures may generate directional energy gradients sufficient to produce net momentum transfer without propellant. This effect would emerge from the same fundamental EM–gravity interaction responsible for the quantum-level phase distortions analyzed in this proposal.

Such a mechanism may offer a unified theoretical framework for interpreting recent experimental claims of propellantless propulsion, and potentially inform future field-based propulsion designs based on spacetime energy flow engineering.

(PDF) Gravitationally Induced Electromagnetic Dephasing as a Potential Explanation for the Proton Radius Puzzle in Muonic Hydrogen

Research Proposal Gravitationally Induced Electromagnetic Dephasing as a Poten...

Brief: Parallel between Darwin Term and Gravitationally Induced EM Dephasing

Dr. Dario Delgado proposes a novel theoretical framework in which gravitationally induced electromagnetic (EM) dephasing may account for observed anomalies in atomic spectroscopy, particularly the proton radius discrepancy in muonic hydrogen. A key insight reinforcing this hypothesis is the structural similarity between:

• the Darwin term in relativistic quantum mechanics, and
• the gravitational EM dephasing correction proposed in Dr. Delgado’s model.

In the case of the Darwin term, derived either from the Dirac equation or via Taylor expansion of the electric potential V(r+u)V(r + u)V(r+u), the electron is modeled as a spatially extended charge distribution rather than a strict point particle. This leads to a correction proportional to the Laplacian of the electric potential:

Delta V_Darwin(r) ≈ (1/6) × ⟨u²⟩ × ∇²V(r)

This reflects the idea that the electron "samples" the surrounding electric field over a small region due to zitterbewegung (quantum jitter).

In parallel, Dr. Delgado's model argues that electromagnetic waves — or virtual photons mediating atomic transitions — undergo phase shifts while propagating through gravitational energy density gradients (not simply gravitational acceleration or mass-based potential). In systems like muonic hydrogen, where the muon orbits much closer to the proton, the local gravitational energy density is significantly higher. This causes measurable EM dephasing that leads to an energy-level correction.

The resulting correction resembles the Darwin term structurally — except that the gravitational energy density gradient replaces the electric potential. The proposed final form of the gravitational correction may therefore involve a second-order Laplacian, expressed as:

Delta E_gravity ∝ ⟨L²⟩ × ∇²(∇φ) (or more precisely, ∇² of the gravitational energy density gradient)

where:

• ⟨L²⟩ is the squared orbital length scale (e.g., the muonic hydrogen radius),
• ∇φ is the gravitational field,
• and the Laplacian of this gradient captures the spatial non-uniformity in gravitational energy density.

This leads to a compelling proposal: the gravitational EM dephasing acts as a nonlocal correction to the energy levels, structurally mirroring the Darwin term — but driven by variations in gravitational energy density rather than electromagnetic potential alone.

Correction: In the earlier expression, I referred to the gravitational correction term as proportional to “∇²(∇φ),” which is mathematically ambiguous. The correct form, consistent with the structure of the Darwin term in quantum mechanics, should be:

ΔE_gravity ∝ ⟨L²⟩ × ∇²ρ_G

Here, ρ_G represents the local gravitational energy density. This correction reflects second-order spatial variation in gravitational energy, much like the Darwin term reflects second-order variation (∇²V) in electric potential. It highlights how nonlocal sampling of gravitational fields at quantum scales — particularly in muonic hydrogen — could lead to observable energy shifts analogous to relativistic quantum corrections.

🧠 Could Our Understanding of Dark Matter Be a Measurement Illusion? 🌌

Recent discussions around gravitationally induced electromagnetic (EM) dephasing raise a fascinating possibility: could our spectroscopic measurements — the very methods we use to infer dark matter — be subtly biased by this effect? If gravitational energy density gradients cause tiny phase shifts in our EM probes, it could lead to systematic errors in how we estimate mass distributions in the universe.

This raises a provocative question: are we overestimating the amount of dark matter because of this subtle measurement bias? Or could it even hint that what we perceive as dark matter is partly an illusion created by our measurement tools?

While dark matter has robust evidence from multiple observations, considering the possibility of a systematic bias in our methods could refine our understanding of the universe’s true mass distribution — or even reshape the dark matter paradigm.

What do you think? Could gravitationally induced EM dephasing be the missing piece in our cosmic puzzle? 🤔

🧠 Spectroscopic Biases from Muonic Hydrogen Discrepancies: Implications for Cosmology

Recent analysis of the ~6.6 μeV energy shift in the Lamb shift of muonic hydrogen suggests a possible curvature-coupled correction to electromagnetic field behavior. If this discrepancy arises from a fundamental interaction — such as a term of the Ricci Scalar–Electromagnetic Field Coupling — it may indicate that high-precision spectroscopy is subtly affected by gravitational curvature.

As many cosmological parameters (e.g. dark matter density, dark energy, and the Hubble constant) rely on spectroscopic inference, such a coupling could introduce systematic biases. This raises the possibility that our current understanding of the universe’s composition and expansion may be slightly miscalibrated due to overlooked curvature-induced electromagnetic dephasing effects.

🔗 Follow-up work explores how this framework could refine or reinterpret cosmological observations. Feedback welcome.

On Alcubierre's warp drive: https://chatgpt.com/canvas/shared/687311cd8ba881919450a3fe37590437