Problem — Science fiction, h multiplied by ten

Problem

Imagine Planck’s constant is multiplied by ten. Discuss at least three visible consequences on ordinary matter (de Broglie wavelengths, atomic levels, uncertainty).

Solution

With $h' = 10\,h$ the quantum character of nature is amplified by an enormous factor. Three main consequences.

1 — De Broglie wavelengths ($\lambda = h/p$). They would become $10$ times larger. Increasingly massive objects would show wave effects: diffraction and interference effects, today confined to electrons and atoms, would become noticeable on a much larger scale. The boundary between the “classical” and “quantum” world would shift towards macroscopic objects.

2 — Atomic levels and sizes. The Bohr radius scales as $r_1 \propto h^2$, so it would become $100$ times larger: atoms would be huge. Binding energies scale as $E_n \propto 1/h^2$, so $100$ times smaller: chemical bonds would be extremely weak and solid matter unstable against ordinary thermal agitation. Spectral lines would change completely.

3 — Uncertainty ($\Delta x\,\Delta p \gtrsim \hbar/2$). Heisenberg’s limit would grow by $10$ times: a particle could no longer be well localised without giving it a huge momentum uncertainty. Even mesoscopic objects would have “blurred” positions, making the deterministic classical physics we use every day impossible.

Summary. Increasing $h$ does not “tweak” a detail: it rescales the entire architecture of matter. Chemistry, the stability of solids and even the distinction between micro and macro depend on the small value of $h$ in our universe.

Collegamenti

Argomenti: Quantum physics Concetti: De Broglie wavelength · Bohr model · Uncertainty principle Competenze: Limiting-case and science-fiction analysis