Planck's hypothesis

What the Planck constant changed

A constant that sets the scale of the quantum world

The Planck constant h is not a mere technical coefficient: it is the signature of the quantum world. Its value, tiny, tells at what scale quantum effects become visible.

   h ≈ 6,63 × 10^-34 J·s

This number recurs in all the great relations of quantum physics — we have already come across it everywhere:

   E = h f              (energy of a photon)
   p = h / λ            (de Broglie : matter wave)
   ΔE = h f             (atomic transitions)
   Δx Δp ≥ ħ/2          (Heisenberg, with ħ = h/2π)
   E_n = -13,6/n^2 eV   (hydrogen levels, where h is hidden)

Wherever h appears, we leave classical physics. It is the constant that "switches on" quantization.

Why we do not see the quanta in daily life

If h were large, the macroscopic world would be openly quantum. But h ≈ 10^-34 is so small that, for ordinary objects, the energy quanta are of an imperceptible fineness:

   A bulb (visible f) : each photon is worth hf ≈ 3×10^-19 J
   It emits ~10^20 photons per second
   -> the "grain" is drowned in an apparently continuous flow

It is like a jet of water: made of molecules, it nonetheless appears continuous. Quantization always exists, but its grain is too fine to be noticed at our scale. The classical limit is the world where h can be neglected.

The classical / quantum boundary

The logic of this whole course can be summed up in one sentence:

   action of the system >> h   ->  CLASSICAL world (invisible quanta)
   action of the system ~ h    ->  QUANTUM world (decisive quanta)

An electron in an atom has an "action" of the order of h: it is fully quantum. A rolling marble has a gigantic action compared to h: it is classical. h is the cursor that separates the two worlds.

The legacy

In 1900, Planck opens a door he did not dare to walk through. In twenty-five years, this "computational" hypothesis becomes an entire physics: photons (Einstein), energy levels (Bohr), matter waves (de Broglie), uncertainty (Heisenberg), wave function (Schrödinger). The black body, an apparently technical problem, will have been the first crack in the classical edifice — and the starting point of the greatest scientific revolution of the 20th century.

In summary