[Paper Review] Modern Michelson-Morley experiments and gravitationally-induced anisotropy of c

M. Consoli|ArXiv.org|Jun 23, 2003

Noncommutative and Quantum Gravity Theories6 references4 citations

TL;DR

This paper proposes that the tiny anisotropy in the speed of light observed in modern Michelson-Morley experiments arises from gravitational effects on a Higgs condensate vacuum, which acts as a medium with a refractive index ${\cal N}_{\rm vacuum} \sim 1 - 2\varphi$, where $\varphi$ is a scalar field identified with the Newtonian potential. The theoretical prediction $B^{\rm th} \sim -4.2 \cdot 10^{-9}$ matches the experimental value $B^{\rm exp} = (-3.1 \pm 1.6) \cdot 10^{-9}$, suggesting a breakdown of exact Lorentz covariance due to long-wavelength vacuum fluctuations.

ABSTRACT

The recent, precise Michelson-Morley experiment performed by Muller et al. suggests a tiny anisotropy of the speed of light. I propose a quantitative explanation of the observed effect based on the interpretation of gravity as a density fluctuation of the Higgs condensate.

Motivation & Objective

• To explain the tiny anisotropy in the speed of light reported in high-precision Michelson-Morley experiments.
• To reconcile vacuum condensation in quantum field theory with potential Lorentz symmetry breaking at long wavelengths.
• To link the refractive index of the vacuum to the Newtonian gravitational potential via a scalar field $\varphi$.
• To provide a quantitative explanation for the experimental value $B^{\rm exp} \sim -3.1 \cdot 10^{-9}$ using a Higgs condensate model.

Proposed method

• Models the vacuum as a Bose-condensed Higgs field with a non-zero vacuum expectation value, leading to long-wavelength density fluctuations.
• Introduces a scalar field $\varphi(x) \equiv h(x)/v_R$ to describe low-energy excitations of the Higgs condensate, with $\varphi$ identified as the Newton potential $U_N$ up to a constant.
• Derives an effective refractive index for light in the vacuum as ${\cal N}_{\rm vacuum} \sim 1 - 2\varphi$, based on wave-particle duality and metric deformation.
• Uses the weak-field approximation of general relativity to compute $\varphi_{\rm earth} \sim -0.7 \cdot 10^{-9}$ at Earth's surface.
• Applies the Robertson-Mansouri-Sexl parametrization to relate the refractive index to the anisotropy parameter $B$, yielding $B = -\frac{3}{2}(\mathcal{N}^2_{\rm vacuum} - 1)$.
• Performs a perturbative expansion in $v/c$ to derive the two-way speed of light anisotropy in a moving frame, linking it to the experimental observable $B$.

Experimental results

Research questions

• RQ1 Can the observed anisotropy in the speed of light from modern Michelson-Morley experiments be explained by vacuum condensation effects?
• RQ2 Does the Higgs condensate in the Standard Model give rise to a refractive index for light that breaks Lorentz invariance at low energies?
• RQ3 Is the long-wavelength scalar fluctuation field $\varphi(x)$ naturally identified with the Newtonian gravitational potential in the weak-field limit?
• RQ4 What is the predicted value of the anisotropy parameter $B$ in the Robertson-Mansouri-Sexl framework based on a Higgs vacuum model?

Key findings

• The theoretical prediction for the anisotropy parameter is $B^{\rm th} \sim -4.2 \cdot 10^{-9}$, which is in good agreement with the experimental value $B^{\rm exp} = (-3.1 \pm 1.6) \cdot 10^{-9}$.
• The vacuum refractive index is estimated as ${\cal N}_{\rm vacuum} \sim 1 - 2\varphi$, with $\varphi_{\rm earth} \sim -0.7 \cdot 10^{-9}$, derived from the Newtonian potential at Earth's surface.
• The scalar field $\varphi(x)$, representing long-wavelength Higgs condensate fluctuations, is identified with the Newton potential $U_N(x)$ when $\delta = \sqrt{G_N M_H^2 / G_F}$.
• The effective metric structure $ds^2 = (1+2\varphi)dt^2 - (1-2\varphi)(dx^2+dy^2+dz^2)$ reproduces the first-order weak-field limit of general relativity.
• The model predicts that Lorentz symmetry is not exact at low energies due to ultraviolet cutoff effects, leading to observable anisotropies in light speed.
• The refractive index correction $\mathcal{N}^2_{\rm vacuum} - 1 \sim -1.4 \cdot 10^{-9}$ leads to $B \sim -4.2 \cdot 10^{-9}$, matching the experiment within error bounds.