Determinism - Modern Perspectives - Quantum Mechanics and Classical Physics - Other Matters of Quantum Determinism

Other Matters of Quantum Determinism

All uranium found on earth is thought to have been synthesized during a supernova explosion that occurred roughly 5 billion years ago. Even before the laws of quantum mechanics were developed to their present level, the radioactivity of such elements has posed a challenge to determinism due to its unpredictability. One gram of uranium-238, a commonly occurring radioactive substance, contains some 2.5 x 1021 atoms. Each of these atoms are identical and indistinguishable according to all tests known to modern science. Yet about 12600 times a second, one of the atoms in that gram will decay, giving off an alpha particle. The challenge for determinism is to explain why and when decay occurs, since it does not seem to depend on external stimulus. Indeed, no extant theory of physics makes testable predictions of exactly when any given atom will decay. At best scientists can discover determined probabilities in the form of the element's half life.

The time dependent Schrödinger equation gives the first time derivative of the quantum state. That is, it explicitly and uniquely predicts the development of the wave function with time.

So if the wave function itself is reality (rather than probability of classical coordinates), quantum mechanics can be said to be deterministic.

According to some, quantum mechanics is more strongly ordered than Classical Mechanics, because while Classical Mechanics is chaotic, quantum mechanics is not. For example, the classical problem of three bodies under a force such as gravity is not integrable, while the quantum mechanical three body problem is tractable and integrable, using the Faddeev Equations. This does not mean that quantum mechanics describes the world as more deterministic, unless one already considers the wave function to be the true reality. Even so, this does not get rid of the probabilities, because we can't do anything without using classical descriptions, but it assigns the probabilities to the classical approximation, rather than to the quantum reality.

Asserting that quantum mechanics is deterministic by treating the wave function itself as reality implies a single wave function for the entire universe, starting at the origin of the universe. Such a "wave function of everything" would carry the probabilities of not just the world we know, but every other possible world that could have evolved. For example, large voids in the distributions of galaxies are believed by many cosmologists to have originated in quantum fluctuations during the big bang. (See cosmic inflation, primordial fluctuations and large-scale structure of the cosmos.)

Read more about this topic:  Determinism, Modern Perspectives, Quantum Mechanics and Classical Physics

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