I have been in love with quantum theory since before I started my Ph.D. in the subject over 30 years ago. Suddenly, however, I feel like we should maybe take a break.

The trigger for this quantum of doubt was a new paper. There’s nothing particularly special about it; it’s just a proposal for an experiment that might tell us something more about how the universe works. But, to me, it felt like the final straw. It has opened my eyes to the possibility that, without radical change, quantum physics may forever let me down.

Essentially, I just want to know what I am made of. One hundred years ago this year, the Danish physicist Niels Bohr received the Nobel prize “for his services in the investigation of the structure of atoms.” But I’m still waiting for a straight answer as to what the structure of the atoms that make up my body is. Quantum theory seems to promise an answer that it can’t deliver, at least not in any way that I can comprehend. As Bohr once put it, “When it comes to atoms, language can be used only as in poetry.”

We cover our ignorance with made-up stories known as “interpretations.”

Bohr is often fêted as the founding father of quantum theory and was one of the champions of its oddness. It’s true that quantum is both mysterious and attractive—as enigmatic as the Mona Lisa’s smile. However, there seems to be something troubling about the quantum grin. Whether probing it through theory or through experiment, we quickly arrive at an impasse: We can’t use any of the results to tell us what stuff actually is.

The trouble starts with the workhorse of quantum theory: Erwin Schrödinger’s famous wave equation. It assumes that all quantum stuff can be mathematically modeled as if it were a wave. Schrödinger’s equation is a huge success: It allows us to predict, for instance, exactly what colors of light an atom will emit when stimulated with electromagnetic energy.

However, the beautiful utility of this equation, which is put to work by physicists every day around the world, masks its enigmatic silence about the actual nature of the atoms whose behavior it so successfully describes. While Einstein won a Nobel Prize for proving that light is composed of particles that we call photons, Schrödinger’s equation characterizes light and indeed everything else as wave-like radiation. Can light and matter be both particle and wave? Or neither? We don’t know.

We cover our ignorance with made-up stories known as “interpretations.” There is one classic laboratory setup that inspires most of these stories. Known as the double-slit experiment, it involves a single quantum object being fired toward a pair of openings whose physical dimensions are tailored to the mass and velocity (combined as momentum) of the object. At the far end of the experiment is a detector that records the original object’s final location.

We tend to interpret this experiment through the lens of Schrödinger’s wave equation. To speak of an “object” that we “fire” is to picture it as a particle. But we ascribe it a wave-like character to explain the ensuing observations. So we say that a quantum object can pass through both slits simultaneously, just as a water wave would. The object then emerges from the slits as two separate waves. As these travel on toward the detector, they meet each other, creating a pattern that is characteristic of interacting waves.

This “interference pattern” is a comb-like pattern of alternating high and low density of electron impacts as you look from left to right across the detector. Waves—water waves, for example—produce interference patterns. And so, we reason, there is definitely something wave-like about the quantum object.

However, the interference pattern does not appear at the detector straight away. The single quantum object manifests in the detector as a single particle at a single location. We then repeat the process, and the next object manifests at a different location on the detector. After a million detections, say, we see a clear interference pattern.

**DOUBLE TALK:** Although the conventional story about the double-slit experiment is that the single electron goes through both slits at once in a wave-like “superposition” state, you don’t have to accept this, writes Michael Brooks. Illustration by magnetix / Shutterstock.

The Nobel Prize-winning physicist Richard Feynman once said that this experiment contains the only mystery of quantum physics. If the injected objects were just particles flying through slits like well-struck golf balls, there would be no interference pattern. How do these individual objects “know” that they are to be part of a building interference pattern? What causes a single particle to be detected in the high-density area, but never in the forbidden zones?

Although the conventional story about the double-slit experiment is that the single electron, say, goes through both slits at once in a wave-like “superposition” state, you don’t have to accept this.

Bohr said you can be entirely agnostic about it and accept that there’s nothing we can say about the electron after we’ve fired it at the slits and before the detector has told us its final position. This is one form of what has come to be known as the Copenhagen interpretation of quantum mechanics.

But you also don’t have to accept that the electron goes through the slits you provided—not exactly, anyway. Some adherents of the Many-Worlds interpretation would claim that the electron goes through both the left and right slits, but in different versions of reality. The interference pattern is the result of interference between these different realities. However strange this seems, it can be a useful way of thinking. This is how Oxford physicist David Deutsch was able to conceptualize the blueprint for quantum computation, for instance.

Another alternative is to suppose there are hidden factors that we can’t quite access. David Bohm influentially suggested that a particle is accompanied by a “pilot wave” that guides its trajectory through the double-slit experiment and creates the interference pattern. Most physicists will tell you that this kind of “hidden variable” interpretation of quantum theory has been ruled out by a combination of experimental results and mathematical proofs.

Physicists choose which quantum theory they subscribe to largely by taste.

Or what if we live in a universe where the person doing the experiments doesn’t realize that they are actually limited in the choices they can make about how the experiment will run? This is “superdeterminism,” which is not quite an interpretation of quantum theory—more a framing of how the universe works from which experimental quantum observations might emerge. In this scheme, there are unappreciated connections between the quantum states of the experimental apparatus, including the mechanism for injecting the electron and the mechanism for detecting it.

These hidden connections are akin to a set of hidden strings that connect all the equipment, making it impossible for the experimenter to know whether the detector settings have affected the electron’s properties, and thus altered the experimental scenario. With superdeterminism, it becomes impossible for the experimenter to determine exactly how the experiment is done.

All of these scenarios have another implicit assumption: that cause always precedes effect. Our experience of time is that it runs in only one direction, but that is not a constraint that quantum objects experience. That means we can interpret the double-slit experiment via “retrocausality,” whereby counterintuitive flows of action mean that what seem like later effects actually create earlier conditions.

Some suggest that an electron’s state might be affected by both its past state and its future state. This would provide a way for each electron to create a sliver of the detector’s interference pattern, despite ostensibly not having a way to “know” where it should end up.

The wide range of interpretations proposed by physicists and philosophers—there are many more than I have mentioned here—demonstrates that there is no right answer. Interested physicists choose which one they subscribe to largely by taste.

It would be reassuring to think that further experiments will allow us to choose between them. However, there is little reason to think that will ever be the case. Some experiments by Aephraim Steinberg of the University of Toronto seem to support the idea of pilot waves, for example. Steinberg is often cited as having revealed so-called Bohmian trajectories that quantum objects follow through the double-slit experiment. But he demurs. “I don’t wish to think of our experiments as measuring Bohmian trajectories,” he has said. Instead, he concedes, “they ‘naïvely’ measure properties of quantum systems which I expect any underlying explanation to reproduce.”

In other words, this experimental evidence remains open to interpretation. For some interpretations, there is no experimental evidence. The many-worlds idea, for instance, allows no meaningful interaction between the worlds, which means there will never be any way of telling empirically whether it is a reasonable point of view.

New experiments come along every now and then, but they rarely make any difference. And that includes the idea that broke me. In late 2021, Colm Bracken of Maynooth University in Ireland, Jonte Hance of the University of Bristol, and Sabine Hossenfelder of the Frankfurt Institute for Advanced Studies proposed an experimental setup that, to their minds, could distinguish between superdeterminism and retrocausality. It involves the double-slit experiment with some added bells and whistles that attempt to engineer a logical paradox in the concept of backward-in-time influences.

But the researchers concede that the result will make no difference to anyone who believes in Many-Worlds, Copenhagen, or Pilot-Wave Theory. It only reduces the range of options by one, at most. And retrocausality proponents doubt that it does even that. In short, it doesn’t get us anywhere. Like all of the other experiments. Have I been chasing rainbows?

We know nothing more than Bohr, Einstein, Schrödinger, and Heisenberg.

Probing quantum physics is really, really difficult. It is, by necessity, an experimental science far removed from the scale of human experience. But it is also instructive to note that a century of technological progress has not helped answer my question. We essentially know nothing more than Bohr, Einstein, Schrödinger, and Heisenberg did about the actual nature of reality. We have created interesting technologies and philosophical conundrums, but little else. Is it actually possible to find out what the universe is made of?

My hope is that it is. But I suspect that it might require a radical pivot. Maybe the only way forward is to go back: to revisit the mathematics behind quantum theory.

It has worked before. When science has been stuck, people have opened up hidden paths by inventing new ways of manipulating numbers or by borrowing mathematical techniques from other fields. Newton and Leibniz’s calculus, Babylonian algebra, and the Chinese and Indian invention of negative numbers provide good examples. As does general relativity: Einstein solved his roadblock over describing curved spacetime by borrowing tensor calculus, which had been developed by pure mathematicians with no application in mind. So, is novel mathematics the solution that quantum physics didn’t know it needed?

“It is quite possibly the case that we need new mathematics to crack this problem,” Hossenfelder said. She thinks the solutions might come from getting a better handle on the mathematics of chaos theory. Her collaborator in investigating superdeterminism, Oxford’s Tim Palmer, thinks that quantum mechanics arises from a deeper theory that involves chaotic attractors. Or, she suggests, it might come from new approaches to escaping, as quantum stuff does, the tyranny of time’s arrow. “All our current theories work with differential equations, where you have an initial state and then an evolution law,” Hossenfelder explained. “I don’t think this is going to work for whatever the theory is that underlies quantum mechanics.”

To this end, Hossenfelder has been eschewing Schrödinger’s wave equation and working with a mathematical approach called path integrals, which are more flexible about time’s flow. “I don’t know if this will work out in the end though,” she admits. “Maybe we indeed need something else entirely.”

University of Western Ontario physicist Emily Adlam is also open to the need for new math. She thinks that the best path forward might be to ditch the reductionist approach of positing ever-smaller components. Instead, she suggests that we should try to understand the quantum world in a more holistic way. “The mathematical methods we currently use in physics do not seem adequate for this kind of holistic description, so it’s likely that something new will be needed,” she told me.

But, she points out, it doesn’t have to be brand new. “There is a lot of mathematics that has been developed by the pure mathematicians that hasn’t yet found any application in physics,” she said. “So I think it’s actually very likely that the mathematics we need does already exist in the pure mathematics world, and we just haven’t seen how to apply it to physics yet.” In other words, if it worked for relativity, maybe it can work for quantum theory.

Full disclosure: Plenty of scientists disagree with me on this. Oxford’s Vlatko Vedral, for instance, is skeptical. “It seems to me that the mathematics needed for quantum physics—linear algebra—works perfectly well,” he told me. He thinks, like Bohr, that any problem comes from the limitations of language. “Neither the connective ‘or’ nor ‘and’ describe what we mean by a quantum superposition,” he pointed out. “Perhaps, rather than our mathematics, it is our language that needs to evolve to properly reflect the quantum world.”

Deutsch, too, seemed impatient with my dissatisfaction over our understanding of the nature of reality. “Someone might equally well say: We may know what dogs look like and how they behave, but we don’t know what a dog ‘actually is’,” he said. Dogs, he says, are collections of atoms, and an atom is a collection of quarks and leptons, and those can be described by quantum fields. What more does anyone want?

Even Hossenfelder is not fully convinced. “I don’t think it’s the task of science to answer the question what something ‘is’,” she told me. She thinks science has only to do with describing what we observe.

What am I? I’m a cluster of tiny indescribable quantum objects waiting for my new crush, mathematics, to reveal the truth.

Michael Brooks is a United Kingdom-based science writer. His most recent book is The Art of More: How Mathematics Created Civilization.

Lead image: watchara / Shutterstock

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