[Paper Review] The speed of light need not be constant

Asher Peres|ArXiv.org|Oct 19, 2002

Cosmology and Gravitation Theories3 references3 citations

TL;DR

This paper argues that the speed of light need not be constant, challenging the conventional assumption of its invariance. Using the invariance of Maxwell's equations under arbitrary nonlinear coordinate transformations and dimensional analysis of tensor fields, it proves that electric charge $e$ and Planck's constant $\hbar$ are absolute constants, while $c$—though defined as 299,792,458 m/s—can vary in curved spacetime or early-universe conditions due to the absence of a fundamental metric in the equations.

ABSTRACT

Recent observations of the fine structure of spectral lines in the early universe have been interpreted as a variation of the fine structure constant. From the assumed validity of Maxwell equations in general relativity and well known experimental facts, it is proved that $e$ and $\hbar$ are absolute constants. On the other hand, the speed of light need not be constant.

Motivation & Objective

• To challenge the assumption that the speed of light is universally constant, especially in cosmological or strong gravitational contexts.
• To resolve the controversy over whether observed variations in the fine structure constant stem from changes in $e$, $\hbar$, or $c$.
• To establish the absolute constancy of $e$ and $\hbar$ using dimensional analysis and fundamental field equations.
• To demonstrate that $c$ is not a fundamental constant but a derived quantity dependent on the metric, which may vary in spacetime.
• To explore the implications of variable $c$ for early-universe physics and the interpretation of spectral line shifts.

Proposed method

• Uses the form of Maxwell's equations in arbitrary coordinates: $F_{\mu\nu,\rho} + F_{\nu\rho,\mu} + F_{\rho\mu,\nu} = 0$ and $\mathcal{F}^{\mu\nu}{}_{,\nu} = \mathcal{J}^\mu$, without assuming a metric.
• Applies dimensional analysis to tensor fields, defining absolute dimensions via invariance under coordinate transformations.
• Shows that the electric charge $e$ is invariant because its flux integral $Q = \int \mathcal{J}^\mu dS_\mu$ is a scalar under arbitrary coordinate changes.
• Establishes that $\hbar$ is an absolute constant by linking it to the quantum of magnetic flux $h/2e$, observed in superconductors.
• Argues that $c$ is not fundamental because it emerges from the metric via $\mathcal{F}^{\mu\nu} = \sqrt{-g}\,g^{\mu\rho}g^{\nu\sigma}F_{\rho\sigma}$, which is not fixed in the fundamental equations.
• Uses the lack of Lorentz invariance in the early universe and the presence of a preferred frame to suggest that vacuum may behave as a dielectric medium, allowing $c$ to differ from its standard value.

Experimental results

Research questions

• RQ1 Can the speed of light vary in spacetime, especially in non-inertial or strong gravitational fields?
• RQ2 Why are the electric charge $e$ and Planck's constant $\hbar$ considered absolute constants, while $c$ is not?
• RQ3 What is the role of the metric in determining the value of $c$, and can it be derived from more fundamental principles?
• RQ4 How does the constancy of $e$ and $\hbar$ follow from the invariance of Maxwell's equations under arbitrary coordinate transformations?
• RQ5 Could the observed variation in the fine structure constant be due to a varying speed of light in the early universe?

Key findings

• The electric charge $e$ is an absolute constant because its flux integral is invariant under arbitrary coordinate transformations, establishing its absolute dimension [Q].
• Planck's constant $\hbar$ is an absolute constant, as evidenced by the quantization of magnetic flux in superconductors in units of $h/2e$, which is experimentally verified.
• The speed of light $c$ is not a fundamental constant but a derived quantity dependent on the spacetime metric, which can vary in general relativity.
• Maxwell's equations in the form $F_{\mu\nu,\rho} + F_{\nu\rho,\mu} + F_{\rho\mu,\nu} = 0$ and $\mathcal{F}^{\mu\nu}{}_{,\nu} = \mathcal{J}^\mu$ are invariant under arbitrary nonlinear coordinate transformations, allowing $c$ to vary without breaking fundamental laws.
• In the early universe, where Lorentz invariance fails and a preferred frame exists, the vacuum may behave as a dielectric medium, leading to a different effective speed of light than $c = 299,792,458$ m/s.
• The 1983 definition of the meter via $c$ creates a circular dependency in time synchronization, as it relies on light signals to define distance and time, undermining the universality of $c$.