Hidden Variable Theories Failed to Replace the Copenhagen Interpretation

FROM THE LECTURE SERIES: What Einstein Got Wrong

By Dan Hooper, Ph.D., University of Chicago

The EPR paradox and the Schrödinger’s Cat thought experiments raised objections to the Copenhagen interpretation of quantum mechanics, but didn’t really offer a solution. However, around the same time, some alternatives to the Copenhagen interpretation were also proposed. The hidden variable theories were one of the alternatives.

Schrödinger's Cat thought experiment from the perspective of the many-worlds interpretation.
The many-worlds interpretation of the Schrödinger’s Cat thought experiment. (Image: Christian Schirm/CC0 1.0/Public domain)

According to the hidden variable theories of quantum mechanics, the wave function is typically incomplete, and it provides only a partial description of a given particle or system. The missing information, if it were known, would allow one to calculate the state of a system at any given point in time, without any indeterminism or any uncertainty.

In addition, there would be no superposition of states. In a hidden variable theory, there is no situation in which a cat is both alive and dead. With the full and complete body of information, you could work out whether any given cat is alive or dead at each moment in time.

Bell’s Theorem Failed to Offer an Alternative

A number of physicists tried to develop theories that would provide this missing information and ultimately replace the Copenhagen interpretation, but no progress was made until 1964. In that year, physicist John Bell from Northern Ireland wrote a paper in which he proposed a way all possible hidden variable theories could be put to the test, or at least all such theories that don’t involve faster-than-light travel.

This became known as Bell’s theorem, or sometimes as Bell’s inequality, and pertains to experiments involving quantum entanglement.

A two-channel Bell test.
Illustration of a two-channel Bell test, which is used to test the theory of quantum mechanics in regard to local realism – a concept created by Albert Einstein. (Image: Maksim/CC BY-SA 3.0/Public domain)

In his paper, Bell showed that if there really were a more complete form of quantum mechanics that underlies reality, then certain combinations of observable quantities would have to be correlated with each other. If you make a large enough number of measurements, you could measure this kind of correlation. You could also test the kinds of hidden variable theories that Albert Einstein had long imagined might restore scientific realism and determinism to quantum mechanics.

The first experiments to apply Bell’s theorem were performed in the early 1970s, and many variations of these experiments have been conducted since. The results of these experiments have been clear. Bell’s theorem is strongly violated, which means that no combination of hidden variables can even possibly restore determinism or scientific realism to quantum mechanics. Despite Einstein’s objections and hopes to the contrary, particles do often exist in superposed states.

Learn more about Einstein’s devotion to the principle of determinism.

Hugh Everett’s Many-Worlds Interpretation of Quantum Mechanics

Almost a decade earlier, in 1957, another alternative to the Copenhagen interpretation was proposed by a young physics graduate student named Hugh Everett III.

Everett was something of a polymath. He studied chemical engineering in college and went on to study graduate-level mathematics at Princeton, where he focused on the new field of game theory. While still at Princeton, Everett gradually shifted his focus away from math and toward physics, where he became immersed in quantum theory. After he graduated from Princeton, Everett left theoretical physics, and instead worked for the Defense Department, where he had a notable career in nuclear weapons research.

This is a transcript from the video series What Einstein Got Wrong. Watch it now, on The Great Courses Plus.

Everett’s work in quantum theory culminated in a paper that was originally entitled, Wave Mechanics without Probability. At some level, Everett’s proposal was remarkably simple.

Recall that according to the Copenhagen interpretation, a wave function evolves until the thing that it describes is measured, and at that moment the wave function collapses to a single value. This raises the difficult question of why an observation or measurement causes such a change. Why does it cause the wave function to collapse?

What Everett suggested in his paper was that perhaps wave functions don’t collapse at all.

To better understand the implications of Everett’s proposal, let’s consider it within the context of the Schrodinger’s Cat thought experiment. According to the Copenhagen interpretation of this hypothetical experiment, the apparatus creates a wave function that describes a cat that is in a superposition of both dead and alive states. Everett’s proposal agrees with the Copenhagen interpretation on this point.

Where Everett’s proposal disagrees pertains to the question of what happens when you open the door to the chamber. When the chamber is opened and you observe the cat, according to the Copenhagen interpretation, the wave function collapses, and afterward the cat exists in either an entirely alive, or an entirely dead state.

This, of course, doesn’t match our human experience. There are no half-alive and half-dead cats. Most importantly, we don’t witness things that are in a state of quantum superposition.

Everett interpreted this differently. According to his interpretation of quantum mechanics, when you open the door to the chamber, the wave function does not collapse.

What happens is that the world at that point in time is in a superposition of you, the observer, observing an alive cat, and of you, the observer, observing a cat that is dead. So according to Everett’s interpretation of quantum mechanics, the world is in a permanent state of quantum superposition, with all possible outcomes fully realized and moving forward through time.

For this reason, Everett’s interpretation is often called the many-worlds interpretation of quantum mechanics.

Learn more about what Einstein got right.

Strengths of the Many-Worlds Interpretation

One of the primary points of difference between the many-worlds interpretation and the Copenhagen interpretation is the fact that there’s a special role for the observer in the many-worlds interpretation. This is also one of the strengths of Everett’s interpretation.

You don’t have to wonder why the act of observation causes a wave function to collapse, and you don’t have to wonder what exactly does or doesn’t constitute an observer.

The other strength of the many-worlds interpretation is that there is no longer any role for chance or probability in the many-worlds version of quantum mechanics.

After the chamber containing the cat is opened, there is a 100% chance that the world will be in a superposition of alive and dead states. It’s totally predictable. Sure, a given observer can’t predict whether they will find the cat to be dead or alive, and the outcome that you personally observe still comes down to chance. However, from a global perspective, there is no uncertainty in this determination at all, as both outcomes necessarily occur.

The role that chance plays in the many-worlds interpretation is not in determining how the universe evolves, but in determining which world within the larger universe you will witness and experience.

We will never know for sure what Einstein would have thought about the many-worlds interpretation, but it does restore both determinism, and a sense of scientific realism to the quantum world. At least initially, Everett’s proposal was not received well. Of the minority of physicists that even heard about Everett’s work, most tended to dismiss it harshly. With the passage of time, Everett’s interpretation became increasingly popular, and now it’s a rather mainstream view.

However, even now, more than half a century later, there is no consensus about whether one should adopt the many-worlds interpretation or the Copenhagen interpretation of quantum mechanics.

The fact is, there is no experiment that could even hypothetically distinguish between these two very different views of quantum mechanics. Both interpretations predict exactly the same outcome for all possible experiments. No test in the laboratory and no measurement or observation will ever be able to distinguish between these two very different interpretations of quantum theory.

Common Questions About the Hidden Variable Theories and Many-Worlds Interpretation

Q: What does Bell’s theorem prove?

Bell’s theorem proves that quantum particles do often exist in superposed states and that this makes hidden variables theories fundamentally incompatible with quantum theory.

Q: Is the many-worlds interpretation deterministic?

Yes, Hugh Everett’s many-worlds interpretation indeed is a deterministic theory. This interpretation also provides an explanation for why the quantum world appears to be indeterministic to human observers.

Q: Is the Copenhagen interpretation correct?

In recent years, the many-worlds interpretation has become a mainstream view. However, it hasn’t replaced the Copenhagen interpretation and is unlikely to ever replace it. The fact is, there is no experiment that could even hypothetically distinguish between these two very different views of quantum mechanics. Both interpretations predict exactly the same outcome for all possible experiments. So, the Copenhagen interpretation is as correct as the many-worlds interpretation.

Q: What causes entanglement?

Quantum entanglement takes place when a pair of quantum particles physically interact with each other. It results in the particles becoming entangled with each other. In the entangled state, even though the particles are separated by a large distance, a specific action on one particle is experienced by the other particle as well.

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