[Paper Review] A theory of mass and gravity in 4-dimensional optics

José B. Almeida|ArXiv.org|Sep 12, 2001

Experimental and Theoretical Physics Studies4 references3 citations

TL;DR

This paper proposes that mass and gravity emerge from 4-dimensional waveguide modes in spacetime, where elementary particles are standing waves with Compton frequency, and inertial and gravitational mass arise from waveguide properties. It explains gravitational anomalies during solar eclipses via graviton exchange, offering a unified geometric explanation of mass and gravity through wave optics in 4D spacetime.

ABSTRACT

The paper deals with the concepts of mass and gravity in the formalism of 4-dimensional optics, previously introduced by the author. It is shown that elementary particles can be associated with 4-dimensional standing wave patterns with the Compton wavelength and both inertial and gravitational mass are derived from this concept and shown to be attributable to an waveguide laid along the particle's worldline; the same formalism is shown to accommodate also mass due to binding energy within compact bodies. Momentum exchange with accelerated bodies through gravitons is discussed and shown similar to mode exchange in optical fibers. Reported anomalies on the behaviour of the Foucault pendulum, both periodic and exceptional on the occasion of solar eclipses, are explained not only qualitatively but also on order of magnitude, resorting to graviton exchanges between Earth and the Sun or the Moon. It is argued that these effects provide experimental evidence of gravitons.

Motivation & Objective

• To derive inertial and gravitational mass from geometric wave properties in 4-dimensional spacetime.
• To explain the origin of mass as a standing wave pattern with Compton wavelength and frequency.
• To reconcile gravitational anomalies in Foucault pendulum experiments during solar eclipses with graviton exchange.
• To unify gravity with wave optics formalism by modeling particles as 4D waveguides and gravity as evanescent waves.
• To provide a foundation for extending the theory to include electromagnetism and strong/weak interactions via a unified wave mode framework.

Proposed method

• Uses 4-dimensional spacetime with metric $ g_{\alpha\beta} = m^2 n^2 \delta_{\alpha\beta} $, where $ m $ is mass and $ n $ is gravitational curvature.
• Applies the geodesic equation $ 2L = g_{\alpha\beta} \dot{x}^\alpha \dot{x}^\beta = 1 $ to describe particle worldlines.
• Reinterprets the particle worldline as a wave equation with Compton frequency $ \omega = m c^2 / \hbar $, equating mass to frequency in natural units.
• Models gravity as an evanescent wave solution in a 4D waveguide, with momentum exchange analogous to optical fiber mode exchange.
• Introduces graviton exchange between Earth and celestial bodies (Sun/Moon) to explain anomalous pendulum behavior during eclipses.
• Uses non-dimensional units where mass equals frequency, enabling wave-particle duality via $ m \leftrightarrow \omega $.

Experimental results

Research questions

• RQ1 Can inertial and gravitational mass be derived from the geometric properties of 4D spacetime and wave resonance?
• RQ2 How does the Compton wavelength and frequency of a particle relate to its mass and waveguide behavior in 4D spacetime?
• RQ3 What is the mechanism by which graviton exchange explains observed anomalies in Foucault pendulum experiments during solar eclipses?
• RQ4 Can gravity be described as an evanescent wave field arising from a 4D waveguide structure of massive particles?
• RQ5 Is there a unified wave-based description of all fundamental interactions, including gravity, electromagnetism, and strong/weak forces?

Key findings

• Inertial and gravitational mass are derived from the same 4D standing wave pattern with Compton frequency, showing mass as a manifestation of wave resonance.
• The theory explains the order of magnitude of anomalous Foucault pendulum behavior during solar eclipses through transient shielding of gravitons from the Sun and Moon.
• Graviton exchange with accelerated bodies is modeled as mode exchange in optical fibers, suggesting a physical mechanism for momentum transfer in gravity.
• Binding energy in compact bodies contributes negative mass via waveguide interference, consistent with mass-energy equivalence.
• Massless particles (photons, gravitons) are described as propagating 3D waves on an oscillatory 0th coordinate, distinct from standing waves of massive particles.
• The theory provides a geometric explanation for gravity shielding by free-falling or orbiting bodies, which absorb momentum and cast gravitational shadows.