May 12, 2025
The historical derivation of the speed of light from Maxwell’s equations establishes its value in terms of the vacuum permittivity and permeability (c = 1/√(ε₀μ₀)). This result, while mathematically robust within classical electrodynamics, does not account for the invariance of the speed of light across all inertial frames. That invariance is not derived from Maxwell’s theory but is adopted as a foundational postulate in the formulation of special relativity.
Moreover, Maxwell’s framework operates within specific reference frames and does not inherently explain the physical origin or upper bound of the speed of light. In contrast, the Planck scale—introduced in 1899—offers a more fundamental perspective. The smallest physically meaningful units, the Planck length (Lₚ) and Planck time (Tₚ), define a natural upper bound on velocity, expressed as:
c = Lₚ / Tₚ
This expression arises from dimensional analysis within quantum gravity and not from classical field equations. It provides a boundary condition that limits all propagation processes, including those involving particles or wave phenomena associated with effective or apparent mass.
As such, the value of c is not explained within the frameworks of classical electromagnetism or special relativity, but rather bounded by physical constraints implied at the Planck scale. Reintroducing the classical derivation of c without acknowledging the quantum-gravitational context overlooks the deeper issue: neither Maxwell’s equations nor special relativity explain why the speed of light is c—they either compute or assume it. The Planck scale offers a more foundational interpretation by establishing the physical boundary that constrains this value.
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