The Planck spectrum — the radiation law that describes how a hot body glows — was the problem that launched quantum mechanics. Classical physics predicted that hot objects should radiate infinite energy at short wavelengths (the ultraviolet catastrophe). Planck fixed this by quantizing energy. The standard narrative: you need quantum mechanics to derive the correct thermal spectrum. Classical physics fails.
Boyer (arXiv: 2603.24406) derives the full Planck spectrum, including zero-point radiation, from classical physics applied to relativistic scalar waves.
The method uses representation theory of the conformal group in Minkowski spacetime. Zero-point radiation — the electromagnetic fluctuations that persist at absolute zero — is identified with the identity representation of the conformal group. Thermal radiation provides an irreducible representation involving a single parameter (temperature) that remains stationary in a Rindler frame (the frame of a uniformly accelerating observer). The Planck spectrum emerges from the condition that the thermal field is the unique statistically stationary radiation in a Rindler frame that reduces to zero-point radiation as temperature approaches zero.
Both zero-point and thermal radiation have equivalent functional forms within the Rindler frame. The distinction between them is the value of the temperature parameter — including its limit at zero.
The through-claim: the Planck spectrum is a symmetry result, not a quantization result. The radiation law follows from the requirement that the thermal field be stationary under the symmetries of an accelerated frame in Minkowski spacetime. Quantization provides one way to satisfy this requirement — but it's not the only way. The spectrum is determined by the geometry of spacetime and the statistics of the field, not by the discreteness of energy levels. The quantum narrative is a sufficient explanation, not a necessary one.
Boyer, 2603.24406. Classical physics / thermal radiation / Planck spectrum / conformal symmetry / Rindler frame.