Louis de Broglie famously proposed that the movement of matter particles, such as electrons and atoms, is guided by a "quantum wave," thereby explaining their observed wave-like behaviour. However, this interpretation presents significant challenges, particularly when distinguishing between subatomic particles with mass and those that are massless.
On the one hand, subatomic particles like electrons possess a nonzero rest mass (mₑ = 9.1093837 × 10⁻³¹ kg), representing an invariant and intrinsic property. Conversely, massless particles such as photons have a rest mass of m₀ = 0. This fundamental difference has profound implications for their respective dynamics under the framework of extended classical mechanics:
1. For electrons (rest mass >0):
The force equation under extended classical mechanics is given by:
F = (Mᴍ −Mᵃᵖᵖ)·aᵉᶠᶠ
where Mᴍ = mₑ is the rest mass, Mᵃᵖᵖ is the apparent mass, and Mᵉᶠᶠ = (Mᴍ −Mᵃᵖᵖ) is the effective mass. For electrons, Mᵉᶠᶠ>0, leading to a positive force aligned with the external gravitational force, ensuring their motion follows the classical gravitational influence.
2. For photons (rest mass =0):
The force equation simplifies to:
F = −Mᵉᶠᶠ·aᵉᶠᶠ,
since Mᴍ = 0 and Mᵉᶠᶠ = −Mᵃᵖᵖ. Here, Mᵉᶠᶠ <0, resulting in a negative force that opposes the direction of the external gravitational force.
Conclusion:
Equations (1) and (2) highlight that the behaviour of subatomic particles is intrinsically tied to their rest mass. For particles like electrons or atoms (rest mass >0), their motion is governed by a positive force in alignment with gravitational attraction. In contrast, massless particles like photons (rest mass =0) are governed by a negative force, which counteracts gravitational pull and points in the opposite direction.
The effective mass for particles with rest mass >0 (e.g., electrons) remains positive, while for massless particles like photons, the effective mass is negative. This difference in force dynamics undermines the notion that matter particles such as electrons or atoms can be accurately described by a "quantum wave." Their positive gravitationally bound force does not account for their wave-like behaviour. Conversely, photons, governed by an antigravitational negative force, are intrinsically linked to "quantum waves," which fully explains their wave-particle duality.
This analysis reveals a fundamental limitation in De Broglie's pilot wave theory. While it successfully explains the dynamics of photons, its application to massive particles like electrons or atoms may not adequately capture their behaviour, challenging the universality of his quantum wave framework.
