Could a hidden variable explain quantum weirdness?

This is the ninth in a series of articles exploring the birth of quantum physics.

Over the past few weeks, we’ve explored some of the fundamental concepts of quantum physics, from quantum leaps to superposition and beyond. Today we explore what may be the strangest of quantum effects, that of quantum entanglement, which Einstein called frightening action at a distance. The word says it all: to be entangled is to be connected – to have some sort of relationship with or dependence on something else.

The dictionary definition is more pragmatic: “to cause a twist or snag”, like a fish entangled in a net or a person entangled in a difficult situation. Well, pairs of quantum objects – such as pairs of photons, pairs of electrons, or electrons and detectors – get entangled. And this kind of quantum entanglement is actually a difficult situation, at least to understand. To grasp what entanglement is, it might be best to apply it to a practical circumstance. If you stick with me, you’ll understand the basics of entanglement and why it’s weird.

A polarizing explanation

When light is polarized (for example, passing through a polarizing filter), its associated wave goes up and down in the same direction of polarization, much like we go up and down when riding a horse. (This is the direction of the electric field characterizing the electromagnetic wave.) Photons, which we can understand as particles of light, share this polarization. The details of how it works are not important. What matters is that the photons have this property and that it can be measured.

Imagine that a light source creates a pair of polarized photons moving in opposite directions, as in the diagram below. Now imagine that two physicists, Alice and Bob, are each standing with a light detector one hundred meters from the source. Alice stands on the left and Bob on the right. Since photons travel at the speed of light, Alice and Bob would see photons arriving at their detectors at the same time.


The detectors can detect two directions of light polarization: vertical (⎮) and horizontal (—). The light source always produces pairs of photons with the same polarization. Alice and Bob don’t know what polarization the pair has until they measure their photons. Let’s say Alice is measuring vertically; Bob will also measure the vertical. If Alice measures horizontally, Bob will too. Even if there is a 50/50 chance that the photon is in one or the other polarization state (much like a coin toss, vertical or horizontal polarization appears randomly), Alice and Bob will still get the same result. The two photons leaving the source are entangled and seem to behave as one.

Alice decides to get a little closer to the source. This way her photon travels a shorter distance to her and arrives earlier than Bob’s photon. It measures a vertically polarized photon. Immediately, she knows that Bob’s photon will also have vertical polarization. She knows before the photon reaches Bob’s detector.

According to quantum mechanics, you can only know the state of something by looking. And since nothing can travel faster than the speed of light, Alice apparently instantly influenced Bob’s photon without interacting with it. Or at least that’s one way of thinking about it. (If not instantaneously, the influence is at least superluminal, faster than the speed of light.) This type of effect can be used in quantum teleportation, where information is transferred by reproducing the state of a remote quantum system. More directly, it can be used in future communication systems that will be faster and more secure than those we use today.

Surf the waves of the Universe

Surprisingly, the effect does not depend on the distance between Alice and Bob. They could have been 10 miles or 10 light years away, and the same thing would have happened. In the precision of current detectors, everything seems to happen instantaneously. Note however that no information was transferred between the two photons. They didn’t interact with each other in a (known) way. They behaved like a single entity completely insensitive to spatial separation.

In 2018, an experiment separated quantum entangled photons at distances of over 30 miles, and the same thing happened. More recently, a similar feat was achieved not with entangled photons, but with entangled rubidium atoms 33 kilometers apart. Quantum entanglement is an indisputable feature of quantum physics. It seems to defy space, as it is independent of distance between objects, and time, as if not instantaneous, it is at least faster than light.

Could physicists be missing something important and obvious? Have we just not reached the right understanding of what is going on? Are there what we might call hidden variables, not part of the traditional formulation of quantum mechanics, that could explain this? In the early 1950s, physicist David Bohm added an extra level of explanation to quantum theory, capable of describing the position of the electron with certainty. He called him the pilot wave function. While Schrödinger’s equation remained the same, another equation would function as its “driver”.

Just as a conductor controls how different sections of an orchestra play during a symphony, Bohm’s pilot would determine how the wave function branched into its different probable states. This conduct passes through one or more undetectable hidden variables, information that remains beyond the reach of the experiments. The pilot wave acted everywhere at once, like an omnipresent deity, exerting a property that physicists call non-locality. In the new de Broglie-Bohm mechanics, particles remained particles and their collective motion was deterministically guided by the nonlocal action of the pilot wave. The particles looked like a group of surfers gliding down a single wave, each pushed one way or the other as the ever-present wave moved forward.

The hidden variable would be the missing link between a classical conception of reality and the fuzzy world of quantum indeterminacy. The price to pay for making quantum mechanics deterministic was to impose an endless network of influence in the midst of all that exists. In principle, this means that the whole Universe participates in determining the outcome of each experience. For Einstein, abandoning locality was too high a price to pay for deterministic evolution.

It was still necessary to know whether Bohm’s idea was valid or not.

Quantum entanglement is really scary

In 1964, Irish physicist John Bell, working at the European Organization for Nuclear Research (CERN), came up with a brilliant way to test whether an alternative formulation of quantum mechanics including local hidden variables better described the results of experiments with entangled particles. The test involved an experiment similar to the one above involving Alice and Bob. Bell’s experiment, however, used another quantum property of particles called spin. It is a sort of intrinsic rotation, like a spinning top that never stops and can only spin at certain quantized speeds.

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The adoption is that over the past four decades Bell’s test has been implemented in real world experiments – which have been awarded the 2022 Nobel Prize in Physics – and the results have been truly shocking: there is no no theories of local hidden variables compatible with quantum mechanics.

In other words, nature seems to work through frightening actions at a distance. Non-local influences acting superluminally between members of spatially separated entangled quantum pairs – these are ghosts that appear to be real. The reality is not only stranger than we assume. It’s much stranger than us can assume.

What are the consequences of quantum entanglement and superposition on our conception of physical reality? How do we interpret all of this? Next week, we will conclude this series of articles with an overview of the different interpretations of quantum physics that are still the subject of heated debate among physicists. Behind the trenches, we see Einstein and Bohr, as inspiring today as they have been for more than a century of quantum perplexity and triumph.

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