Interpretations of Quantum Mechanics

I have emphasized that quantum mechanics is merely a set of rules for predicting experiments. It does not try to explain why those rules happen to work. It does not tell us “what is really going on”. Given that, it is natural to seek a deeper theory that can answer these questions. Indeed, many people have spent years searching for that deeper theory. Depending on how you look at it, they have either been very successful, or not successful at all. You see, they have identified dozens of candidates for that deeper theory, and we do not know which one is correct!

These candidate theories are called “interpretations of quantum mechanics”. That is an unfortunate piece of terminology. It seems to imply that quantum mechanics is still the fundamental theory, and an interpretation is just a way of thinking about it. The truth is the other way around. When we speak of an “interpretation” of quantum mechanics, we are actually referring to a candidate for the deeper theory from which quantum mechanics can be derived and which explains why its rules work.

I cannot give a full account of all the interpretations that have been proposed. That could easily make up an entire book in itself. But I will try to give brief summaries of a few of the more prominent, historically important, or (in my personal opinion) noteworthy examples.

When quantum mechanics was first introduced, the community mostly coalesced around two interpretations. One was the Copenhagen Interpretation, developed by Bohr and Heisenberg. The name refers to their time working together in Copenhagen during the 1920s. According to this interpretation, the wavefunction is a complete and accurate description of a physical system. The wavefunction contains everything that could possibly be known about it. However, the wavefunction is still not sufficient to make definite predictions about the results of experiments. You can only derive probabilities. According to the Copenhagen Interpretation, this means the universe is fundamentally random and non-deterministic. If the wavefunction does not uniquely determine the result of an experiment, that means the result truly is undetermined until you perform the measurement. If two measurable quantities (such as the position and momentum of a particle) do not commute, such that no wavefunction can uniquely determine both at once, that means they are inherently incompatible. It is meaningless to talk about both having well defined values at the same time.

The alternative viewpoint, argued most prominently by Schrödinger and Einstein, is the Stochastic Interpretation. According to this interpretation, the wavefunction is merely a statistical description of our knowledge of a system. It is not itself a physical object. If the wavefunction does not uniquely define the position of a particle, that just reflects our limited knowledge. The particle still has a well defined (but unknown) position. The impossibility of exactly measuring its position and momentum at the same time is due to the limitations of the measurement process, not to inherent properties of the particle being measured.

A central aspect of the Stochastic Interpretation is the idea of “hidden variables”. These are aspects of the physical system that are omitted by the wavefunction. They are unknown, but in principle still knowable. For example, when a particle is in a momentum eigenstate, its position is a hidden variable. The particle has a well defined position, but the wavefunction does not contain enough information to determine it. If you could somehow determine the values of all hidden variables at the same moment, you could exactly predict the result of any measurement.

The field has come a long way since those early days. For many years, the Copenhagen Interpretation was widely accepted as the “conventional wisdom”, but more recently it has fallen out of favor. For one thing, it was never rigorously defined. Even Bohr and Heisenberg could not entirely agree on what it said. It also was not really a theory, since it predicted nothing and could hardly even be said to explain anything.

Although fewer people take the Copenhagen Interpretation seriously today, there are modern interpretations that share aspects of it and can perhaps be viewed as its spiritual successors. Probably the most prominent of these is the Many Worlds Interpretation, first proposed by Hugh Everett in 1957. 1 It begins by assuming the wavefunction is a real physical object. It further assumes the wavefunction to be the only physical object. There are no hidden variables in this interpretation.

It breaks with the Copenhagen Interpretation by rejecting the idea of fundamental randomness. Instead it assumes that the wavefunction never collapses. Entanglement just grows without limit. If a particle is in a superposition of spin up and spin down states, and you measure it to have spin up, that means you are now entangled with the particle, and are yourself in a superposition of states. Along with the “you” observing the particle to have spin up, there is a second “you” observing it to have spin down.

Another class of “Copenhagen-like” interpretations are the objective-collapse theories. These theories again start by assuming the wavefunction to be a real physical object, and also assume there are no hidden variables. They then add terms to the Schrödinger equation. The terms are chosen to be negligible for microscopic systems but non-negligible for macroscopic ones, and to directly cause the wavefunction to collapse. By doing this, they provide a single equation which leads to correct results for both microscopic and macroscopic systems.

The Stochastic Interpretation, as originally proposed, was also not really a theory, just a vague idea. One of the first serious efforts at a complete theory based on it was pilot wave theory, developed in 1952 by David Bohm based on an earlier idea by Louis de Broglie. 2 This theory starts by treating particles as classical point-like objects obeying classical mechanics. It then adds in the quantum mechanical wavefunction, but interprets it in a completely new way. According to pilot wave theory, the wavefunction generates a potential function called the “quantum potential”, which exerts forces on the particles; that is, it acts as a pilot to steer the particles. The positions and momenta of the classical particles are hidden variables. They are influenced by the wavefunction but cannot be exactly determined.

Another influential theory was Stochastic Mechanics, proposed by Edward Nelson in 1966. 3 Like Bohm, Nelson began with classical particles obeying Newtonian mechanics. In place of the complicated and seemingly arbitrary “quantum potential”, Nelson made a much simpler assumption: that all particles are subject to rapidly fluctuating stochastic forces that he modeled as uncorrelated white noise. Remarkably, this simple classical model leads directly to the Schrödinger equation and the Born rule, and thus to all the quantum phenomena that follow from them: tunneling, the uncertainty principle, entanglement, the collapse of the wavefunction, etc.

Stochastic Mechanics does not try to explain the origin of the stochastic forces. It simply postulates that they exist, then explores the consequences that follow from them. It has largely been superseded by a more complete theory, Stochastic Electrodynamics, which does offer an explanation for them. According to Stochastic Electrodynamics, the stochastic forces are due to electromagnetic radiation that pervades all of space. I will have much more to say about this theory in a later chapter.

This is only a very brief sampling of some of the theories that have been proposed to explain quantum mechanics. We do not know which one is correct. It could be any one of them, or some other theory that has not even been suggested yet. Ultimately, this question can only be answered by experimental evidence.

Many people become quite emotionally attached to their preferred interpretations. When someone spends much time studying a particular interpretation, they start to see all of quantum mechanics through the lens of that interpretation, and it becomes obvious to them that it “must” be right. After all, it explains everything so perfectly! This tendency is understandable but not productive. Let me say it again: we do not know which interpretation is correct. Anyone who claims otherwise is mistaken. There are dozens of known interpretations that are consistent with the available evidence.

You may have heard that all hidden variable theories have been experimentally disproven. This claim is often repeated in the popular press, and more unfortunately, in the scientific literature as well. It is false. Sometimes it is stated in a more nuanced way: that local, realistic hidden variable theories have been disproven. This version of the claim fixes some of the problems in the original version, but it is also false. The truth behind this common misunderstanding is the subject of the next chapter.

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1

Everett, H. “Relative State Formulation of Quantum Mechanics.” Reviews of Modern Physics 29(3): 454-462 (1957).

2

Bohm, D. “A Suggested Interpretation of the Quantum Theory in Terms of Hidden Variables. I.” Physical Review 85(2): 166-179 (1952).

3

Nelson, E. “Derivation of the Schrödinger Equation from Newtonian Mechanics.” Physical Review 150(4): 1079-1085 (1966).