When classical physics collapses

The challenge: explaining the curve

At the end of the 19th century, classical physics (thermodynamics + Maxwell's electromagnetism) was triumphant. Explaining the black-body curve should have been a formality. The opposite happened: it was a disaster.

The classical prediction

The classical reasoning treats the radiation in the cavity as a set of standing waves, sharing the energy equally among them (equipartition principle). It leads to the Rayleigh-Jeans law. The problem: this law predicts that the intensity increases without limit as the wavelength decreases.

   intensity
      ^
      |  CLASSICAL prediction (Rayleigh-Jeans)
      |  |
      |   \\                       it SHOOTS off to infinity
      |    \\                      at short wavelengths
      |     \\
      |      \\           .-''''---...    REAL curve (observed)
      |       \\      .-''            '''---...
      |        '..-''                          '''----...
      +----------------------------------------------------> λ
      UV                    visible           infrared

At long wavelengths (infrared), the classical law roughly matches the measurements. But on the short-wavelength side (the ultraviolet), it diverges: it predicts an infinite intensity.

The ultraviolet catastrophe

This prediction is absurd. Taken seriously, it would mean that a simple hot object — an oven, an ember — would emit an infinite amount of energy in the ultraviolet and beyond. Opening an oven door should release a deadly flood of UV and X-rays. Nothing of the sort happens, obviously.

This theoretical disaster was named the ultraviolet catastrophe: classical physics, applied flawlessly to the black body, leads to a physically impossible conclusion.

   What classical theory predicts  :  energy -> ∞ in the UV  (impossible)
   What experiment shows           :  the curve FALLS back to zero in the UV

A revealing failure

This is not a small numerical error: it is a fundamental contradiction. The real curve falls back toward zero at short wavelengths, exactly where the theory blows up. Something fundamental is missing from classical physics.

The crucial point is where it fails: everything is fine in the infrared (low frequency), everything fails in the ultraviolet (high frequency). The clue is there: the problem concerns high frequencies, that is, the most energetic photons. This is precisely what Planck will exploit.

In summary

Applied to the black body, classical physics (Rayleigh-Jeans law) predicts an intensity that diverges toward infinity at short wavelengths: this is the ultraviolet catastrophe, a total absurdity, whereas the real curve falls back to zero. This failure, localized at high frequencies, is the first sign that a revolution is needed — the one that Planck is going to trigger.