The statistical interpretation of the wavefunction, ψ, is due to Max Born who, in his 1954 Nobel prize acceptance speech, ascribed his inspiration for the statistical interpretation to an idea of Einstein’s. Here is the relevant quote from Born’s speech: “He had tried to make the duality of particles — light quanta or photons — and waves comprehensible by interpreting the square of the optical wave amplitudes as probability density for the occurrence of photons. This concept could at once be carried over to the ψ-function: |ψ|2 ought to represent the probability density for electrons (or other particles).”
Einstein, in a December 1926 letter to Max Born, speaking of the “secret of the Old One,” said that he was “convinced that He does not throw dice.” And when Philipp Franck pointed out to Einstein, around 1932, that he was responsible for the idea because of papers he published during his annus mirabilis in 1905, Einstein responded that “Yes, I may have started it, but I regarded these ideas as temporary. I never thought that others would take them so much more seriously than I did.” Later, Einstein put it this way to James Franck: “I can, if the worse comes to the worst, still realize that the Good Lord may have created a world in which there are no natural laws. In short, a chaos. But that there should be statistical laws with definite solutions, i.e. laws which compel the Good Lord to throw the dice in each individual case, I find highly disagreeable.”
Einstein was not alone in being uncomfortable with the statistical nature of quantum mechanics and since then the vast literature that has appeared on the foundations of quantum mechanics was driven at least in part by an attempt to come to terms with the unusual and counterintuitive features inherent in the subject.
There were many attempts in the past to find hidden variables to avoid the statistical interpretation of the wavefunction, and there was even an informal monthly set of briefs called the Epistemological Letters put out by the Association F. Gonset or Institut de la Methode, which was distributed to, and contained theoretical correspondence from, some 100 prominent people in the field. In particular there was much discussion of Bell’s theorem,1 which ruled out the possibility of hidden variables, by Bell and others. I mention this in particular since those studying this period may not be aware of the past existence of this “Symposium”, and it would be a very valuable resource for those working in the history of this area. Those who nonetheless choose to pursue the issue of hidden variables will sooner or later come across a poem written on the subject by Abner Shimony for a conference in the early 1970s (a Google translation for the poem is included below):2
| Tout le monde cherche les variables cachées | Everyone is looking for the hidden variables |
| Hélas, avec quel insuccès! | Alas, with what failure! |
| Elles sont timides, elles sont petites, | They are shy, they are small, |
| De courte durée, toujours en fuite. | Short lived, always on the run. |
| Elles sont partout en déguisement, | They are everywhere in disguise, |
| Empruntant bien des vêtements | Borrowing many clothes |
| Aux particules élémentaires. | Elementary particles. |
| Pour décider ce qu'on doit faire, | To decide what to do |
| Une assemblée de quarante mille | An assembly of forty thousand |
| Savants se tient à Célesteville. | Savants is held in Célesteville. |
| «Haute énergie!» Rataxès crie, | “High energy!” Rataxès cries out, |
| «Pour pénétrer le dernier nid | “To penetrate the last nest |
| De créatures si décevantes.» | Such disappointing creatures.” |
| «Hourrah! les rhinoceros chantent, | “Hurray! the rhinoceros are singing, |
| «Agrandissons les cyclotrons!» | “Let’s make the cyclotrons bigger!” |
| Babar pourtant conseille: «Non, | Babar, however, advises: “No, |
| La nature ouvre sa richesse | Nature opens up its wealth |
| Non par force, mais par finesse. | Not by force, but by finesse. |
| On verra les variables cachées | We will see the hidden variables |
| Aux rayonnements polarisés.» | Polarized radiation.” |
| «Il a raison», dit Gregory, | “He’s right,” says Gregory, |
| Et la vieille dame fièrement sourit. | And the old lady proudly smiles. |
| Toute l'assemblée acclame son plan | The whole assembly applauds his plan |
| Et autorise avec élan | And emphatically authorizes |
| Un projet international, | An international project, |
| Créant le centre mondial | Creating the world center |
| Des appareils ingénieux. | Ingenious devices. |
| Les techniciens méticuleux | Meticulous technicians |
| Olur et Hatchibombotar | Olur and Hatchibombotar |
| Sous la conduite de Babar, | Under the leadership of Babar, |
| Commencent la grande expérience. | Begin the great experiment. |
| Pour en connaître les conséquences | To know the consequences |
| Variables cachées, oui ou non | Hidden variables, yes or no |
| Lisez la prochaine livraison. | Read the next issue. |
There was no next issue and hidden variables were soon ruled out as a possibility. Babar the elephant first appeared in a French children’s book written in 1931 by Jean de Brunhoff. The tale was made up and told to their children by Brunhoff ’s wife Cécile. Célesteville was the capital of Babar’s kingdom where Olur was a mechanic and Hatchibombotar a street cleaner. Lord Rataxès, a rhinoceros, is the monarch of Rhinoland in Babar’s kingdom.
While fully consistent with the usual quantum mechanics, a different interpretation of the wavefunction will be offered here. The classical conception of a point particle is replaced with one consonant with the quantum world.
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1 J.S. Bell, “On the Einstein Podolsky Rosen Paradox,” Physics 1 (1964), 195–200; for a review of the subject, see: J.S. Bell, “On the problem of hidden variables in quantum mechanics,” Rev. Mod. Phys. 18 (1966), 447.
2 B. d’Espagnat (ed.), Foundations of Quantum Mechanics (Proceedings of the International School of Physics “Enrico Fermi”, course 49), Academic Press, New York, 1971, pp. 56–76.