Planck's constant entered physics through the blackbody radiation problem. Planck proposed in 1900 that electromagnetic energy comes in discrete packets — quanta — of size proportional to frequency, with h as the proportionality constant. The constant marked a break with classical physics. It said that energy is not continuous. Its introduction required a conceptual revolution: the quantization of energy, the rejection of classical equipartition, and eventually the entire framework of quantum mechanics.
Glampedakis (arXiv:2603.03478, March 2026) shows that the revolution was not the only route to h. A classical physicist armed with dimensional analysis and the empirical laws of blackbody radiation — specifically, the Wien displacement law and the Stefan-Boltzmann law — could have derived the correct value of h without proposing quantization. The argument: a hydrogen atom has three physical constants available (electron mass, electron charge, speed of light or equivalently the permittivity of free space). These do not suffice to set an energy or length scale. A fourth constant is needed. The blackbody empirical data provide constraints — relationships between temperature, peak frequency, and total energy flux — that fix the missing constant uniquely. That constant is h.
With h in hand, dimensional analysis constructs the Bohr radius and the Bohr energy without any quantum hypothesis. The correct scales for the hydrogen atom — the ground-state energy, the orbital size — emerge from combining the electron's properties with the constant that the blackbody spectrum demands. No quantization condition is invoked. No postulate about angular momentum is needed. The dimensions do the work.
The implication is not that quantum mechanics was unnecessary. The quantization of energy is real, and understanding why h appears — not just that it appears — required Planck's insight and everything that followed. The implication is narrower: the numerical value and dimensional role of h were accessible from purely classical reasoning combined with empirical data. The constant was hiding in the blackbody spectrum years before anyone proposed the physics it encodes. The revolution was in understanding what h means. The constant itself was already there, waiting in the units.
Glampedakis, "A dimensional analysis path to h and the Bohr atom structure," arXiv:2603.03478 (March 2026).