ECM-Based Rebuttal on the Gravitational Nature and Weight of Massless Waves:

Soumendra Nath Thakur

April 14, 2025

The assertion that “some waves with no mass undergo a kind of gravity” is more meaningfully addressed within the framework of Extended Classical Mechanics (ECM). In ECM, a positive massless particle—such as the photon, a gauge boson and carrier of the electromagnetic force—does not possess a positive matter mass (in fact, Mᴍ < 0), but instead carries a dynamic negative apparent mass (−Mᵃᵖᵖ). This combination results in a negative effective mass (Mᵉᶠᶠ < 0).

Therefore, the claim that “some waves with no mass” is accurate by conventional standards is actually incomplete. ECM refines this understanding: photons, while traditionally labelled as massless, are not devoid of gravitational character. Instead, they exhibit antigravitational behaviour precisely due to their negative apparent mass (−Mᵃᵖᵖ) corresponding to negative effective mass (Mᵉᶠᶠ < 0). In this model, positive massless particles like photons actively interact with gravity, but in a repulsive manner—due to their own inherent antigravitational nature.

Additionally, the further assertion regarding the “existence of weight of waves”— termed as the “gravity of wave”—is inconsistent within conventional physics. The classical formula for weight is (W = mg), where (m) is mass and (g) is the gravitational acceleration. Weight is defined as a force and is measured in Newtons (N). Therefore, any entity with zero mass cannot possess weight, by definition.

However, ECM provides a more nuanced insight. Since photons possess a dynamic negative apparent mass (−Mᵃᵖᵖ) and a negative matter mass (Mᴍ < 0), they do not follow the conventional gravitational attraction model. Instead, they exhibit repulsive antigravitational effects, leading to negative weight.

The gravitational mass in ECM is represented by the effective mass:

Mᵉᶠᶠ = Mᴍ + (−Mᵃᵖᵖ)

For positive massless particles (like photons), within a gravitational influence, this becomes:

Mᵉᶠᶠ = (−Mᵃᵖᵖ) + (−Mᵃᵖᵖ)

Outside gravitational influence, it simplifies to:

Mᵉᶠᶠ = −Mᵃᵖᵖ

Given that ECM defines gravitational force (or weight) as:

W = Mᵉᶠᶠ × g

then for a photon within a gravitational field:

W = (−Mᵃᵖᵖ −Mᵃᵖᵖ) × g = −2Mᵃᵖᵖ × g < 0

This clearly represents negative weight, which cannot be accommodated in classical physics but is a natural outcome in ECM.

In conclusion, your statement regarding the gravitational behaviour of massless waves lacks precision in light of ECM. ECM not only explains how such particles can have gravitational interactions but also demonstrates that these interactions are antigravitational in nature, with corresponding negative effective mass and negative gravitational weight.

References: 

(1) Thakur,  S. N. (2024). Extended Classical Mechanics: Vol-1 - Equivalence Principle, Mass and Gravitational Dynamics. Preprints. https://doi.org/10.20944/preprints202409.1190.v2

(2) Thakur,  S. N. (2024). Photon Dynamics in Extended Classical Mechanics: Effective Mass, Negative Inertia, Momentum Exchange and Analogies with Dark Energy. Preprints. https://doi.org/10.20944/preprints202411.1797.v1

(3)Thakur,  S. N. (2024). A Nuanced Perspective on Dark Energy: Extended Classical Mechanics. Preprints. https://doi.org/10.20944/preprints202411.2325.v1

(4) Thakur,  S. N. (2024). A Symmetry and Conservation Framework for Photon Energy Interactions in Gravitational Fields. Preprints. https://doi.org/10.20944/preprints202411.0956.v1

(5) Thakur,  Soumendra Nath (2025). Mass-Energy Transformations in Extended Classical Mechanics (ECM): Reframing Kinetic Energy, Analysis of −Mᵃᵖᵖ, Gravitational Interaction, and the Role of Frequency in Mass-Energy Dynamics. ResearchGate. http://dx.doi.org/10.13140/RG.2.2.24863.27040

(6) Thakur,  Soumendra Nath (2025). Mathematical Derivation of Frequency Shift and Phase Transition in Extended Classical Mechanics (ECM). ResearchGate. http://dx.doi.org/10.13140/RG.2.2.36663.02721