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Foundational issues of Chaos and Randomness: "God or Devil, do we have a Choice?"

Prabhakar G. Vaidya, Nithin Nagaraj, B. V. Sreekantan

Published Jan 1, 2006• 1 citation
OpenAlex

Abstract

This article is about two competing paradigms to explain the nature of our physical world. The prevalent paradigm is ‘Randomness’, which is intrinsic in Quantum Mechanics (QM) and regarded as essential to our universe, an attribute that led to the famous remark by Einstein – “God does not play dice

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Abstract Quantum mechanics, like other enormously successful physical theories, accurately describes how the natural world behaves. Its explanatory powers regarding the indeterminate behavior of the smallest constituents of nature have proven to be both profound and practical. Many technological devices from lasers to computer chips are based on quantum mechanics. Not surprisingly, the universe filled with microscopic random events revealed by quantum mechanics has generated wonder and interpretive bewilderment. Reactions to the unsettling revelations of quantum unpredictability have included appeals to unknown variables to preserve classical physics, and even wholesale theoretical dismissals. Far from proof of mathematical trickery or theoretical incompletion however, the now well-established and irreducible quantum randomness suggests a physical universe that is open to a future not determined by the past, and perhaps to a God that really does play dice.
Einstein initially objected to the probabilistic aspect of quantum mechanics— the idea that God is playing at dice. Later he changed his ground, and focussed instead on the point that the Copenhagen Interpretation leads to what Einstein saw as the abandonment of physical realism. We argue here that Einstein’s initial intuition was perfectly sound, and that it is precisely the fact that quantum mechanics is a fundamentally probabilistic theory which is at the root of all the controversies regarding its interpretation. Probability is an intrinsically logical concept. This means that the quantum state has an essentially logical significance. It is extremely difficult to reconcile that fact with Einstein’s belief, that it is the task of physics to give us a vision of the world apprehended sub specie aeternitatis. Quantum mechanics thus presents us with a simple choice: either to follow Einstein in looking for a theory which is not probabilistic at the fundamental level, or else to accept that physics does not in fact put us in the position of God looking down on things from above. There is a widespread fear that the latter alternative must inevitably lead to a greatly impoverished,
Now that we have defined, described, and tested random numbers, the question arises: do random numbers exist? Can true randomness occur in nature? Albert Einstein’s famous dictum “God does not play dice” – uttered about the then new-fangled theory of quantum mechanics and its inherent random nature – expressed his belief that everything is deterministic, that there is no true randomness in nature. Did the great physicist turn full circle to the early religious doctrines which claims that it is God’s finger that determines everything?
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.
The idea of determinism has had a powerful grip on the imagination of physicists ever since Pierre Simon Laplace evoked the idea of the clockwork universe. When Einstein uttered his famous phrase God doesn't play dice, he was expressing his unhappiness with the probabilistic nature of quantum mechanics, believing that beneath quantum theory must lie a deeper, deterministic theory of nature. But such has been the huge success of quantum theory that most physicists now believe that the ultimate physical theory will be quantum mechanical and that nature is fundamentally random.
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