Experiments and the Concepts They Introduced

Different experiments test different claims. A line spectrum suggests discrete energy differences; an interference pattern reveals phase-sensitive propagation; a Bell test constrains a specified class of correlation models. This map connects each observation to the explanation you can calculate today. No individual experiment derives the entire quantum formalism.

From an observation to a calculation

Observation	What the result teaches	Continue with
Blackbody spectrum	Classical equipartition predicts too much radiation at high frequency. Planck’s law introduces the scale $h\nu/k_BT$.	Planck’s radiation law
Photoemission	In the one-photon regime, the maximum kinetic energy follows $K_{\max}=h\nu-\Phi$; intensity mainly changes the emission rate.	Light-quantum hypothesis
Compton scattering	The wavelength shift follows energy–momentum conservation for a photon scattering from an initially resting free electron. Classical light already carries momentum; the new result is the recoil-dependent frequency shift.	Photon momentum
Atomic spectra	Sharp frequencies correspond to differences between allowed atomic energies, not to classical orbital frequencies.	Hydrogen atom
Franck–Hertz collisions	Repeated excitation thresholds reveal an atomic energy gap. Apparatus effects matter when converting voltage intervals into excitation energies.	Energy eigenstates
Electron diffraction	Massive particles produce phase-sensitive angular patterns consistent with $\lambda=h/p$.	Matter-wave interference
Stern–Gerlach splitting	A magnetic atomic beam separates into discrete components. The modern spin explanation came after the original experiment.	Spin and angular momentum
Bell tests	Suitable correlations violate inequalities obeyed by local hidden-variable models with measurement-setting independence.	Bell’s theorem

A new atomic model need not already be quantum

Rutherford scattering is an important example. Large-angle alpha scattering supported a compact, positively charged nucleus. The elementary Coulomb-scattering calculation is classical. The observation changed the model of atomic structure; it did not by itself establish quantized energy levels or a probability rule.

The Bohr model then added special rules for stationary orbits and transitions. Matrix mechanics and wave mechanics supplied a more general dynamics. These are theoretical developments, so they should be distinguished from experimental rows in the table.

What amplitudes add

For two coherent alternatives with amplitudes $a$ and $b$, the detection probability contains

$$|a+b|^2=|a|^2+|b|^2+2\operatorname{Re}(a^*b).$$

The last term depends on relative phase. Adding the probabilities of mutually exclusive classical paths would omit it. This motivates learning amplitudes and interference, but interference alone does not rule out every possible hidden-variable theory. Bell and contextuality results require additional, explicitly stated assumptions.

Exercise

A metal surface is illuminated in the weak, one-photon photoelectric regime. The frequency is held fixed above threshold while the intensity is doubled. Which change is expected: a doubled maximum electron kinetic energy, or a larger electron emission rate?

Solution

The rate generally increases; the maximum kinetic energy remains $h\nu-\Phi$ for the same surface. Doubling intensity increases the incident photon flux without changing each photon’s energy. The qualification excludes strong-field and multiphoton processes, where the simple relation need not describe the measurement.

References

• J. S. Bell, “On the Einstein Podolsky Rosen paradox,” Physics Physique Fizika 1, 195–200, 1964, doi:10.1103/PhysicsPhysiqueFizika.1.195.
• A. H. Compton, “A Quantum Theory of the Scattering of X-rays by Light Elements,” Physical Review 21, 483–502, 1923, doi:10.1103/PhysRev.21.483.
• A. Einstein, “Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt,” Annalen der Physik 322, 132–148, 1905, doi:10.1002/andp.19053220607.
• M. Jammer, The Conceptual Development of Quantum Mechanics, 2nd ed., American Institute of Physics, 1989.
• M. Planck, “Ueber das Gesetz der Energieverteilung im Normalspectrum,” Annalen der Physik 309, 553–563, 1901, doi:10.1002/andp.19013090310.