Determinism in quantum mechanics

Since the beginning of the 20th century, quantum mechanics has revealed previously concealed aspects of events. Newtonian physics, taken in isolation rather than as an approximation to quantum mechanics, depicts a universe in which objects move in perfectly determinative ways. At human scale levels of interaction, Newtonian mechanics gives predictions that in many areas check out as completely perfectible, to the accuracy of measurement. Poorly designed and fabricated guns and ammunition scatter their shots rather widely around the center of a target, and better guns produce tighter patterns. Absolute knowledge of the forces accelerating a bullet should produce absolutely reliable predictions of its path, or so we thought. However, knowledge is never absolute in practice and the equations of Newtonian mechanics can exhibit sensitive dependence on initial conditions, meaning small errors in knowledge of initial conditions can result in arbitrarily large deviations from predicted behavior.

At atomic scales the paths of objects can only be predicted in a probabilistic way. The paths may not be exactly specified in a full quantum description of the particles. Actually, path is a classical concept which quantum particles do not have to possess. The probability arises from when we measure the path of the particle which actually it does not have precisely. However, in some cases quantum particles have exact path, and the probability of finding the particles in that path is one. The quantum development is at least as predictable as the classical motion, but it describes wave functions that cannot easily be expressed in ordinary language. In double-slit experiments, electrons fired singly through a double-slit apparatus at a distant screen do not arrive at a single point, nor do they arrive in a scattered pattern analogous to bullets fired by a fixed gun at a distant target. Instead, they arrive in varying concentrations at widely separated points, and the distribution of their hits can be calculated reliably. In that sense the behavior of the electrons in this apparatus is deterministic, but there is no way to predict where in the resulting interference pattern an individual electron will make its contribution (see Heisenberg Uncertainty Principle).

Some people have argued that in addition to the conditions humans can observe and the rules they can deduce there are hidden factors or hidden variables that determine absolutely in which order electrons reach the screen. They argue that the course of the universe is absolutely determined, but that humans are screened from knowledge of the determinative factors. So, they say, it only appears that things proceed in a merely probabilistically determinative way. Actually, they proceed in an absolutely determinative way. Although matters are still subject to some measure of dispute, quantum mechanics makes statistical predictions that would be violated if some local hidden variables existed. There have been a number of experiments to verify those predictions, and so far they do not appear to be violated although many physicists believe better experiments are needed to conclusively settle the question. (See Bell test experiments.) It is, however, possible to augment quantum mechanics with non-local hidden variables to achieve a deterministic theory that is in agreement with experiment. An example is the Bohm interpretation of quantum mechanics.

On the macro scale it can matter very much whether a bullet arrives at a certain point at a certain time, as snipers and their victims are well aware; there are analogous quantum events that have macro- as well as quantum-level consequences. It is easy to contrive situations in which the arrival of an electron at a screen at a certain point and time would trigger one event and its arrival at another point would trigger an entirely different event. (See Schrödinger's cat.)

Even before the laws of quantum mechanics were fully developed, the phenomenon of radioactivity posed a challenge to determinism. A gram of uranium-238, a commonly occurring radioactive substance, contains some 2.5 x 1021 atoms. By all tests known to science these atoms are identical and indistinguishable. Yet about 12600 times a second one of the atoms in that gram will decay, giving off an alpha particle. This decay does not depend on external stimulus and no extant theory of physics predicts when any given atom will decay, with realistically obtainable knowledge. The uranium found on earth is thought to have been synthesized during a supernova explosion that occurred roughly 5 billion years ago. For determinism to hold, every uranium atom must contain some internal "clock" that specifies the exact time it will decay. And somehow the laws of physics must specify exactly how those clocks were set as each uranium atom was formed during the supernova collapse.

Exposure to alpha radiation can cause cancer. For this to happen, at some point a specific alpha particle must alter some chemical reaction in a cell in a way that results in a mutation. Since molecules are in constant thermal motion, the exact timing of the radioactive decay that produced the fatal alpha particle matters. If probabilistically determined events do have an impact on the macro events, such as whether a person who could have been historically important dies in youth of a cancer caused by a random mutation, then the course of history is not determined from the dawn of time.

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 quantum mechanics is deterministic, provided that one accepts the wave function itself as reality (rather than as probability of classical coordinates). Since we have no practical way of knowing the exact magnitudes, and especially the phases, in a full quantum mechanical description of the causes of an observable event, this turns out to be philosophically similar to the "hidden variable" doctrine.

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. That is, the quantum mechanical problem can always be solved to a given accuracy with a large enough computer of predetermined precision, while the classical problem may require arbitrarily high precision, depending on the details of the motion. 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 big bang. 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 from the big bang. 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 and primordial fluctuations.) If so, the "wave function of everything" would carry the possibility that the region where our Milky Way galaxy is located could have been a void and the Earth never existed at all.