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arXiv:0902.1008

La Probabilidad de la Mecanica Cuantica: Una Introduccion en noventa minutos

Stephen Bruce Sontz

Published Feb 6, 2009• 0 citations
arXivHTMLPDF

Abstract

Referring to quantum mechanics, Einstein used to say "The old one does not play dice." And this is true since the probability of quantum mechanics is not the classical probability of games such as dice. Historically this was the first example of a non-classical probability theory, which we introduce in this expository article using undergraduate linear algebra. There is a short appendix on qubits. Knowledge of quantum mechanics is not required.

DOI
10.48550/arxiv.0902.1008

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Referring to quantum mechanics, Einstein used to say "The old one does not play dice." And this is true since the probability of quantum mechanics is not the classical probability of games such as dice. Historically this was the first example of a non-classical probability theory, which we introduce in this expository article using undergraduate linear algebra. There is a short appendix on qubits. Knowledge of quantum mechanics is not required.
Einstein wrote his famous sentence "God does not play dice with the universe" in a letter to Max Born in 1920. All experiments have confirmed that quantum mechanics is neither wrong nor “incomplete”. One can says that God does play dice with the universe. Let quantum mechanics be granted as the rules generalizing all results of playing some imaginary God’s dice. If that is the case, one can ask how God’s dice should look like. God’s dice turns out to be a qubit and thus having the shape of a unit ball. Any item in the universe as well the universe itself is both infinitely many rolls and a single roll of that dice for it has infinitely many “sides”. Thus both the smooth motion of classical physics and the discrete motion introduced in addition by quantum mechanics can be described uniformly correspondingly as an infinite series converges to some limit and as a quantum jump directly into that limit. The second, imaginary dimension of God’s dice corresponds to energy, i.e. to the velocity of information change between two probabilities in both series and jump.
Einstein wrote his famous sentence "God does not play dice with the universe" in a letter to Max Born in 1920. All experiments have confirmed that quantum mechanics is neither wrong nor “incomplete”. One can says that God does play dice with the universe. Let quantum mechanics be granted as the rules generalizing all results of playing some imaginary God’s dice. If that is the case, one can ask how God’s dice should look like. God’s dice turns out to be a qubit and thus having the shape of a unit ball. Any item in the universe as well the universe itself is both infinitely many rolls and a single roll of that dice for it has infinitely many “sides”. Thus both the smooth motion of classical physics and the discrete motion introduced in addition by quantum mechanics can be described uniformly correspondingly as an infinite series converges to some limit and as a quantum jump directly into that limit. The second, imaginary dimension of God’s dice corresponds to energy, i.e. to the velocity of information change between two probabilities in both series and jump.
El electrón introduce en la mecánica subatómica el nuevo concepto de probabilidad cuántica. Este artículo estudia el proceso de esta introducción, de 1916 a 1927. Einstein lo ocasionó, al elaborar un formalismo de emisión y absorción de radiación, que Bohr incluyó en su principio de correspondencia, como «probabilidades a priori». Heisenberg las recogió en su mecánica matricial, mientras Schrodinger introducía en su mecánica ondulatoria una función de onda, que Born convirtió en amplitud de probabilidad. Dirac fundamentó esos conceptos de probabilidad con su teoría de transformaciones, y Heisenberg, inspirado en ella, formuló las relaciones de indeterminación de la nueva física subatómica.
Albert Einstein once said that he does not believe in a God who plays dice. He was referring to the fundamental principle that quantum theory permits only statistical assertions concerning the values of physical quantities. This issue, namely, whether the description of Nature in statistical terms is complete or even consistent, was the subject of a very lively debate-dialogue between Einstein and Niels Bohr in the years 1920-1930. Nowadays there is no debate as the principles of quantum theory have been verified countless times in experiments. In this lecture (which requires no previous background) I shall discuss both classical and quantum probabilities. Although the meaning of probability remains the same in both contexts, the method of calculating them is different. I shall explain the strange but beautiful manner in which quantum probabilities are calculated, explaining the mathematical foundations in an elementary manner. The meaning of probability
Este artículo presenta y discute la Interpretación de la Mecánica Cuántica de Ithaca (IIQM). La sección 1 expone el formalismo estándar de la mecánica cuántica y el problema de la medición. La sección 2 bosqueja la interpretación de Everett como preámbulo a la IIQM. La sección 3 plantea la tesis central de la IIQM: es posible dar sentido a la mecánica cuántica tomando como sujeto propio (y único) de la física las correlaciones entre subsistemas. La sección 4 expone el teorema SSC de la mecánica cuántica que sustenta esta tesis. En la sección 5 se sostiene que existen al menos dos problemas con la IIQM, y una seria objeción en su contra. Para sortear esta objeción, la sección 6 discute una estrategia basada en probabilidades relacionales.
Albert Einstein made fundamental contributions to the development of quantum mechanics. However, he was never satisfied with the quantum worldview. In fact, during most of his life he attempted to find inconsistencies and paradoxes within quantum mechanics. His famous quote "God does not play dice" shows how disturbing was to Einstein one of the most important aspects of quantum mechanics: non-determinism. In this paper we will present the basic concepts of quantum mechanics, we will describe Einstein's attempts to destroy it and we will discuss why we can nowadays state that, in this regard, Albert Einstein was not right.