A so-called pilot wave is key to David Bohm’s interpretation of quantum mechanics
Courtesy of Daniel Harris and John Bush, MIT
Sometime in the 1940s, US physicist David Bohm decided that the only way to understand quantum mechanics was to write a book about it. He wanted it to offer the reader something they could understand in the “customary imaginative sense”, including an interpretation of the equations of quantum mechanics that didn’t require tangling with advanced mathematics. This quest stayed with him for over a decade, through years of personal and professional tumult, until he ended it by developing his own interpretation of quantum theory.
A pair of papers announced this “Bohmian mechanics” in 1952, but, save a few ardent supporters, it never really took off. Bohm had become a politically controversial figure, and his work was weighed down by some of that baggage, on top of its already heterodox approach to quantum physics. In 2025, however, an experiment with particles of light brought it back into focus – and reignited the idea that Bohm may have been onto something after all.
Bohm’s political trouble lay in his affiliation with several communist organisations during his doctoral studies and his unwillingness to testify and provide evidence against his colleagues in front of the House Un-American Activities Committee at the height of the post-second world war Red Scare. What made him somewhat heretical among physicists, on the other hand, was that he thought that reality is, well, real.
One of the big open questions in quantum mechanics is what exactly happens when an experimenter interacts with a quantum object. The mathematics on which the forefathers of quantum mechanics – such as Niels Bohr and Werner Heisenberg – built up the theory seem to accommodate an odd situation: while it is unobserved, an object is an existentially fuzzy mix of all of its possible states, but when it is observed, that cloud becomes one concrete state. Light and electrons give us the most extreme example of this. They exhibit “wave-particle duality”, where light that typically seems to be a wave can be corralled into materialising as a particle in some experiments, while other experiments can nudge objects that ought to be particles, such as electrons, to assume a wave-like nature instead.
How exactly this happens, and whether there is a physical mechanism that literally changes the object, or if the effect stems from how we process information, remains frustratingly unclear. But back up a little and we end up in an even murkier situation: what does quantum mechanics have to say about the reality of the world before an observation or a measurement can be made?
Heisenberg held that “the idea of an objective real world whose smallest parts exist objectively in the same sense as stones or trees exist, independently of whether or not we observe them… is impossible”. This view became quantum orthodoxy; now called the Copenhagen interpretation, it is widely held among physicists. But that wasn’t enough for Bohm. In the 1990s, he told New Scientist he found Bohr’s idea that quantum mechanics could offer only formulae that make great predictions, but doesn’t engage with a description of reality deeply unsatisfying. “I said, that’s not enough. I don’t think I would be very interested in science if that were all there was,” he said.
Bohm’s major intervention into quantum mechanics concerned a mathematical object called the wave function, which physicists use to represent an object’s quantum state. When a mathematical operation that represents a measurement is used on a wave function, it changes. This is infamously known as wave function collapse, and it was the first thing that alerted physicists to the idea that quantum objects may congeal from a cloud of probability into something more tangible. As Bohm saw it, the trouble was that the wave function itself wasn’t physical, but rather an abstract object that lived in a purely mathematical space, at least according to the likes of Bohr and Heisenberg. Bohm’s wave function, on the other hand, was never fuzzy, never collapsed and stood a chance of being a lot more real.
For instance, there is no wave-particle duality in Bohmian mechanics because particles are always particles and don’t have to be observed in some special way to show up to us in their particle form. But they still behave like waves in some experiments, so what did Bohm make of that? He proposed that it is because their behaviour is guided by a “pilot wave”, which is caused by fields similar to electromagnetic fields but associated with some set of as-yet undiscovered, inherently quantum forces.
Physicist David Bohm held the controversial view that reality is real
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In Bohmian mechanics, the pilot wave is also to blame for everything odd that happens with quantum objects. If you can’t know something about a quantum object, for instance, it isn’t because that thing is fundamentally unknowable or because the world is probabilistic instead of deterministic, but because you disturbed the pilot wave. Details of the pilot wave are so-called hidden variables that we cannot access directly, but the pilot wave is physically there, a scaffolding for reality that exists even when absolutely no one is looking.
The price Bohm had to pay for going all in on pilot waves is that his idea by default allows for non-local effects – particles can stay inextricably connected across remarkable distances through “quantum entanglement”. Infamously, the idea of such non-locality was upsetting enough to Albert Einstein that he dismissed it entirely. There are many other so-called hidden variable theories that account for entanglement and other non-local effects, essentially trying to explain it away by invoking some unseen property or force. But Bohm was unbothered by the idea that incredibly distant parts of the cosmos could be sharing quantum states and affecting each other at all times.
His idea still relied on Erwin Schrödinger’s equation as the starting point of every quantum calculation, which is standard; he eliminated wave function collapse, which was bothersome to many; and some of his later philosophical ideas were even rather friendly to the notion that the whole cosmos may share some sort of implicit one-ness and connection.
Louis de Broglie, a pivotal figure in uncovering particles’ wave-like behaviour in the early days of quantum theory, formulated an idea similar to pilot waves in the 1920s, but was persuaded to abandon it by his peers. After Bohm independently came up with and further fleshed out this very similar framework, he was also met with resistance.
In 1989, philosopher Renée Weber, speaking to John Stewart Bell, a visionary physicist whose work on quantum entanglement also challenged our view of reality, asked why Bohmian mechanics had seemingly been so easy to ignore. Bell, who was a champion of Bohm’s work, demurred: “Let’s not go into that. That’s another question. That’s the psychology and history of physicists.” Bohm’s work always carried with it the shadow of his unfair political persecution. Yet there are also two major scientific problems with Bohmian mechanics.
The first gets to the core of how physics ought to work – can Bohmian mechanics suggest an experiment whose results would differentiate it from more orthodox interpretations of quantum mechanics? The word “interpretation” itself suggests that the answer should be no, because it is only distinct theories rather than interpretations of the same theory that can typically be told apart through experiments. But in July 2025, a study in the journal Nature suggested otherwise. Its title read “Energy-speed relationship of quantum particles challenges Bohmian mechanics”, offering a counterpoint to Bohm’s work more concrete than matters of philosophy or politics.
It didn’t start out that way, says Jan Klaers at the University of Twente in the Netherlands, who worked on the experiment. He and his colleagues set out to study the quantum phenomenon of tunnelling, where a particle manages to enter a space that ought to be forbidden to it, when they realised that they could actually infer something about Bohm’s work, too. They think they have identified a detail of his idea that could be experimentally tested after all.
Putting Bohm to the test
Their experiment was similar to a ball rolling down a hill and colliding with a wall. Outside of the quantum world, this is a straightforward situation, but in the quantum realm, the ball can “tunnel” into the wall. This process is distinct from the ball having enough energy to physically break a hole in the wall. With quantum tunnelling, there is simply some probability of the ball showing up inside the wall even if it isn’t very energetic at all. (In the mathematical world, the wave function of the ball “spills” into the wall.)
Klaers and his team made their own “ball” by shining a laser into a thin layer of a liquid filled with fluorescent dye molecules and sandwiched between two mirrors. The mirrors, the liquid and the molecules had to be there to make the massless photons behave as if they had mass, like a ball does, and the bottom mirror was also adorned with special nano-sized patterns that made the photons move along two pre-set parallel paths or “waveguides”. One was designed so that a photon would experience it as a downward ramp that ended in a bump – the wall at the bottom of a hill.
The researchers created photon after photon at the top of the hill and tracked what happened to them. Some jumped from one waveguide into another, and some tunnelled into the wall. Klaers says counting how many were hopping between the waveguides could serve as an internal clock for the system, with each hop like a tick – which let them determine the speed of the photons that were tunnelling through the barrier. The speeds they measured were rather high – thousands of kilometres per second – but when Klaers and his colleagues used Bohm’s approach to calculate what they ought to be, the answer was nearly zero. The discrepancy was large enough to put Bohmian mechanics into peril.
Not everyone agrees. Hui Wang at the University of Science and Technology of China says the velocity of tunnelling photons that could be calculated from the team’s setup cannot be directly compared to predictions of Bohm’s theory. Other quantities the researchers calculated from their measurements are, in his view, correct, and present no challenge to Bohmian mechanics, but their definition of speed is too close to its classical, rather than quantum, definition.
“I think Bohmian mechanics is still a promising interpretation of quantum mechanics,” says Wang. “Copenhagen interpretation is just a very powerful tool to correctly predict the experimental measurement results, but it provides very limited ‘physical reality’ of nature itself. Yet the core of science is to discover more of that reality in order to better understand nature. Bohmian mechanics is on this path.”
In fact, Wang says his own team is preparing a paper that will also offer a resolution to the second big problem with Bohmian mechanics, namely that it has historically not been applicable for objects that move close to the speed of light and therefore have to obey Einstein’s theory of special relativity – a pillar of physics that has withstood decades of testing. While their work has yet to be reviewed by other physicists, if successful, it could give Bohmian mechanics a real boost in the race to become the next best theory of physical reality. In that decades-old interview, Bell told Weber that he, essentially, felt similarly. Were it not for discrepancies with the mathematics of relativity, he would have simply adapted Bohm’s view as correct instead of seeing “a big, deep mystery in quantum mechanics”, he said.
While Klaers disagrees with Wang on the interpretation of his team’s data and how they used it to calculate photons’ speeds, he doesn’t think it’s fully lights out for all ideas like Bohm’s. There are two equations that are crucial for Bohmian mechanics, and they are the unavoidable: Schrödinger’s equation and the “guiding equation”, which is more specific to Bohm’s work. This second equation determines the velocity of any one particle from the configuration made by all particles. The experiment with tunnelling photons specifically points to issues with this guiding equation, says Klaers.
“There are many guiding equations possible, and you can come up with additional models that actually produce the same particle density and are in agreement with our speed measurements. So, it’s not really a distinction between Bohm mechanics and standard quantum mechanics. It’s really a question of, OK, this guiding equation that the standard Bohmian mechanics choose, is that actually the physically correct one?” he says. In a follow-up study, he and his colleagues have shown that tweaks to the guiding equation can push Bohm’s mathematics to match their experiment.
Is this actually good news for realists and Bohmians in the ranks of modern-day physicists? There is no straightforward answer. Finding a way to match a Bohmian theory to experimental evidence should add more credence to it, but a theory that must be repeatedly tweaked to catch up with experiments is at risk of not being sufficiently well-defined or fully complete. It is more likely that it is a stepping stone on the way to a theory that would have fewer ambiguities and more predictive power. In this way, Bohmian mechanics has been handed a new challenge – but at least it is staying in the ring.
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