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Coincidenze significative (Majorana-Heisenberg-Ehrenfest)

Il neutrone venne scoperto nel 1932 per opera di James Chadwick. Poco più di un anno prima, il fisico teorico Werner Heisenberg aveva elaborato un modello di nucleo atomico in cui protoni e neutroni non sono altro che due differenti stati di carica di una sola particella: il nucleone. Un pò prima della pubblicazione di questa teoria, Ettore Majorana congetturò l'esistenza del neutrone attraverso un modello più elegante di quello proposto da Heisenberg. Tuttavia non pubblicò tale brillante e rivoluzonario risultato.

A gennaio del 1933, Majorana si recò a Lipsia da Heisenberg. Grazie alle insistenze del fisico tedesco, finalmente Majorana pubblicò il suo articolo.
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[Video] I limiti dell'interpretazione di Copenaghen

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Today's article is a summary of topics covered in the past. Specifically, we refer to the Copenhagen Interpretation of Quantum Mechanics.

According to the aforementioned ontology, the collapse of the wave function ? of a quantum mechanical system Sq is determined by the interaction of the measuring apparatus Am with Sq. Indeed, Am is a macroscopic system which "perturbs" the quantum system in such a way not controllable. And this determines the collapse of ? in one of the eigenstates of the observable subjected to measurement.

However, assuming that quantum mechanics is a logically closed theory, we are forced to schematize Am in the quantum paradigm and not in the classical one. In the latter case, we end up with a quantum theory which actually makes use of classical mechanics as regards the behavior of the measuring apparatus. On the contrary, Quantum Mechanics must contain Classical Mechanics as a limiting case, exactly as happens in Relativistic Mechanics with regard to Newtonian Mechanics. Incidentally, Special Relativity was developed by Albert Einstein independently of Newtonian theory, and in the non-relativistic limit (speeds far below that of light in a vacuum), it reproduces Newtonian results.

The schematization of the measuring apparatus in the quantum paradigm was performed by Von Neumann around 1930. The eminent mathematician demonstrated that the superposition of the eigenstates of the observable subjected to measurement is transferred to the measuring apparatus, as a consequence of the linearity of the Schrödinger equation. It follows that it is necessary to insert a new measuring apparatus which unfortunately (or rather, inevitably) will go into linear superposition. By iterating the procedure, we arrive at a so-called Von Neumann chain. The only way to "break" such an entity consists in the introduction of a measuring apparatus endowed with an introspective capacity (that is able to read its own state). The aforementioned ability is identified with what is commonly classified as "consciousness" (human, artificial, other).
Playfully but effectively, we devised a concept experiment in which a Von Neumann chain is implemented by infinitely many Schrödinger cats

The Copenhagen interpretation is actually a consequence of the positivist attitude of Bohr and Heisenberg. Above all of Heisenberg (who paradoxically was very interested in philosophy): think, for example, of the Mechanics of matrices equivalent to the wave mechanics formulated by Schrödinger. While equivalent, these schemes are nonetheless complementary. Incidentally, a matrix is a table of numbers, and this recalls experimental data. In other words, for Heisenberg it was essential to refer to the raw data. It is no coincidence that the term "observable" used in quantum mechanics refers to the circumstance of having to define a physical quantity solely and exclusively for measurement operations.

Traduzione in italiano

L'articolo di oggi è una sintesi di argomenti trattati in passato. Nello specifico, ci riferiamo all'Interpretazione di Copenhagen della Meccanica quantistica.

Secondo la predetta ontologia, il collasso della funzione d'onda ψ di un sistema quanto-meccanico S_q è determinato dall'interazione dell'apparato di misura A_m con S_q. Infatti, A_m è un sistema macroscopico che "perturba" il sistema quantistico in modo non controllabile. E ciò determina il collasso di ψ in uno degli autostati dell'osservabile sottoposta a misura.
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