I’ve been talking to Jerome Cardano for years now. What’s more, he talks back to me—in a voice that often drips with gentle mockery. He clearly thinks my sanity is as precarious as his always was.

Jerome was Europe’s pre-eminent inventor, physician, astrologer, and mathematician in the 16th century. He created the first theory of probability, and discovered the square root of a negative number, something we now call the imaginary number and an essential part of our understanding of how the universe holds together. He invented the mechanical gimbal that was to make the printing press possible. His idea led to the “Cardan joint” that takes the rotary power in the driveshaft of your car’s engine and allows it to be transmitted to the front and rear axles. He pioneered the experimental method of research in areas as diverse as medical cures for deafness and hernia, cryptography, and speaking with the dead (forgive him, his were not strictly scientific times).

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My obsession with Jerome has taken me over. I’ve been schooled in quantum physics and trained to think rationally, dissecting facts and ideas dispassionately. And here I am constantly carrying on imaginary conversations with a 16th-century astrologer. Perhaps the most amusing aspect of this is that Jerome is not remotely humbled by talking to someone from the future. On the contrary, he feels he has earned such visitations through his earnest attempts to discern the truth about how the universe works.



He’s not altogether wrong about this. I was first drawn to Jerome by a simple statement in his autobiography: He told his academic colleagues that many of his best ideas came from a spirit that visited him at night. He knows this is an odd claim, but he also sees himself as a pioneering visionary who would be worth the attention of celestial beings. He even writes in one of his books that, on his death, “The earth will not cover me over, but I will be snatched up to high heaven and live in distinction in the learned mouths of men.” This is precisely why he is willing to take so many intellectual risks: He doesn’t worry about being taken seriously on Earth when he already feels he is taken seriously in the heavens.

There is a neat payoff to this hubris. Jerome’s belief that a visiting spirit holds secrets that are yet to be revealed to humans means he also appreciates there is a lot that is still hidden from him. Jerome is aware that he doesn’t have all the information required to understand the universe, and I find his acknowledged ignorance engaging. As an observer of science, I’m fascinated by the gaps—known and unknown—in our understanding of the universe. There are plenty of gaps in Jerome’s understanding too, but he seems more aware of his evidential gaps than do many of the scientists I meet.

Whenever the powerful are threatened by progress, they will suppress debate. Science has not escaped this phenomenon.

If only more of Jerome’s contemporaries—particularly those running the Catholic Inquisition—had shown a similar humility, we might know more about him. In 1570, Jerome was arrested by the Inquisition. We don’t know exactly why, because one of the many conditions of his eventual release under house arrest was that he could never discuss the reason for his initial detention. The charge could have been that he once presented the Pope with a horoscope of Christ. It might have been Jerome’s pronouncement that a loving God couldn’t possibly condemn devout Jews or Muslims. Or maybe it was his writings considering “whether there is one universe, or more, or an infinity of them.” After all, that was among the questions that pushed the Inquisition to burn Giordano Bruno at the stake two decades later.



Other conditions of Jerome’s release included that he could no longer teach or publish—which may explain why he fell into obscurity and you are only just learning about him now. But despite Jerome’s life story being relatively unfamiliar today, his experiences of what happens when people reject orthodoxy are not. The spirit of the Inquisition has never been fully extinguished; wherever the powerful are threatened by progress, they will suppress debate. Science has not escaped this phenomenon. Even something as fundamental as quantum mechanics, built on the twin pillars of probability and imaginary numbers that Jerome erected, has been stunted by censure. There are a number of examples even within this small area of physics, but perhaps none is more resonant of Jerome’s experience than the story of David Bohm.





During the latter part of World War II, when Bohm was a graduate student at the University of California, Berkeley, J. Robert Oppenheimer recruited him into the newly formed effort to build an atomic bomb. Bohm’s contributions to the Manhattan Project were so valuable that they were immediately classified and Bohm was shut out. Even though Oppenheimer was his Ph.D. supervisor, Bohm was not allowed to write his own Ph.D. thesis. He only got his Ph.D. after insisting that Oppenheimer vouch for the quality of his work.

By 1950, Bohm was working with Einstein at Princeton, where his past came back to haunt him. Early in his Ph.D. studies he had joined a trade union and, briefly, a couple of communist groups. Those communist associations, coupled with the national security implications of his Ph.D. work, made him a target for Senator Joe McCarthy’s crusade against un-American activities.

Bohm refused to answer questions, and refused to name anyone that the McCarthyists should investigate. He was arrested. By the time he was acquitted, he had been suspended from Princeton. In 1951, unemployable in the United States, Bohm took a job in Brazil. The United States authorities then confiscated his passport and he was forced to apply for Brazilian citizenship. It was as a Brazilian that he traveled to England and began a long career as a professor of theoretical physics at Birkbeck College in London. There, he successfully applied for a British passport. Then, in 1986, he won back his American citizenship in a legal battle with the U.S. government.

I’ve been schooled in quantum physics and trained to think rationally. So why am I carrying on imaginary conversations with a 16th-century astrologer?

Nothing in that long and painful saga distracted David Bohm from physics. He made significant contributions in a variety of areas, but it is for his interpretation of quantum physics that he is best known. In 1952, Bohm published a seminal paper that is now seen as a complementary, but independently derived, version of work begun decades before—and then abandoned—by the French aristocrat and physicist Louis de Broglie.



De Broglie first mentioned it in his 1924 dissertation. He brought it up again when he gave a talk in October 1927, at the same meeting where Albert Einstein and Niels Bohr had their famous debates over quantum theory. In his talk, he spoke about the théorie de l’onde pilote—pilot wave theory.

It deals with the “double slit experiment,” where quantum objects such as photons seem to have two different locations at once before this anomaly is resolved at the photon detector. Bohr’s view (now central to the “Copenhagen” interpretation of quantum theory) was that the objects have no definite position or momentum until they hit the detector. According to de Broglie, though, each photon fired at the double slit exists as a real object. He suggested it has a definite position and momentum at all times. What you can’t know is the initial position.

And since the initial position would be what you combine with the momentum to give you the final position, you can’t know the final position in advance, explaining the apparently random outcomes of each measurement.

Because it is a real object, with a well-defined position, the photon can pass through only one of the slits. However, its trajectory is guided by a “pilot wave,” in much the same way that a ferry entering a treacherous harbor is guided by a pilot boat. This pilot wave is also real and has properties that are a reflection of the “wave function” in the theory described by the Schrödinger equation.

Alexandre Gondran

Because of this link to the Schrödinger equation’s wave function, although the particle will only pass through one of the slits, there is still a final distribution of particles determined by an interfering wave. That means the major consequence of interference—the strange clumping at certain points on the target and absence at others—will occur.



Eventually, de Broglie abandoned his idea and fell in with Bohr, becoming what we would now call a Copenhagenist. It wasn’t that the pilot wave theory was particularly flawed; it was just that Bohr was probably too powerful and charismatic a figure to resist. So the pilot wave theory sank.

In 1952, however, it resurfaced in the hands of David Bohm. Bohm’s idea of an invisible, undetectable pilot wave was roundly criticized, but a man who had survived the McCarthy witch hunts was not easily put off. Having overcome the most heinous character assassination of the era, he could take a little heat. And so he stuck to his guns, suggesting we needed to look at quantum experiments in a different way. In a 1952 paper, published in Physical Review, he said, “the history of scientific research is full of examples in which it was very fruitful indeed to assume that certain objects or elements might be real, long before any procedures were known which would permit them to be observed directly.” In other words, why shouldn’t there be an as-yet-undiscovered pilot wave?

“Of course, we must avoid postulating a new element for each new phenomenon,” Bohm continued. “But an equally serious mistake is to admit into the theory only those elements which can now be observed ... In fact, the better a theory is able to suggest the need for new kinds of observations and to predict their results correctly, the more confidence we have that this theory is likely to be good representation of the actual properties of matter and not simply an empirical system especially chosen in such a way as to correlate a group of already known facts.”

Fortunately, the brainwashed generation is passing: The Copenhagen intepretation doesn’t dominate like it used to.

So far, so good, perhaps. But there are two problems. The first is that, in order to get the predictions right about the interference effect and the ultimate distribution of the photons at the detector, you have to work backward from the final result.

The second problem is that Bohm’s pilot wave is odd—in a way that physicists call “nonlocal.” This means that the properties and future state of our photon are not determined solely by the conditions and actions in its immediate vicinity. The photon’s pilot wave and the photon’s wave function are linked to the wave function of the much, much larger system in which they sit—the wave function of the whole universe, effectively. So our photon can be instantaneously affected by something that happens half a universe away.

Many physicists—most physicists—are not happy about allowing this nonlocal action. After all, such action is prohibited by Einstein’s special theory of relativity, which says an influence can’t travel faster than the speed of light.

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On the plus side, it does give us an explanation for the relativity-breaking entanglement-based phenomena that Einstein derided as “spooky action at a distance.” And it’s not clear that accepting Bohmian mechanics is any worse than shoehorning entanglement into a relativity-friendly physics. Many fine physicists are certainly happy to talk in terms of Bohmian mechanics. I attended a conference in Vienna where an experimenter called Aephraim Steinberg explained his experimental results from a Bohm-eyed view; this, he says, is the easiest way to think about it. What Steinberg presented was a picture showing the trajectories of photons as they pass through the double slit apparatus. In the Copenhagen interpretation, remember, this is impossible because the photons have no meaningful existence before they are detected. Without an existence, they can’t logically have a trajectory.

The de Broglie-Bohm interpretation of quantum physics, as it is now known, is not popular. Only one venerated physicist has ever really championed it: John Bell, the Irishman who came up with the first definitive test for the existence of entanglement. Here’s what Bell had to say:



While the founding fathers agonized over the question ‘particle’ or ‘wave’, de Broglie in 1925 proposed the obvious answer ‘particle’ and ‘wave.’ Is it not clear from the smallness of the scintillation on the screen that we have to do with a particle? And is it not clear, from the diffraction and interference patterns, that the motion of the particle is directed by a wave? De Broglie showed in detail how the motion of a particle, passing through just one of two holes in screen, could be influenced by waves propagating through both holes. And so influenced that the particle does not go where the waves cancel out, but is attracted to where they cooperate. This idea seems to me so natural and simple, to resolve the wave-particle dilemma in such a clear and ordinary way, that it is a great mystery to me that it was so generally ignored.

Bell felt de Broglie-Bohm was a better bet than anything the Copenhagenists had to offer. They had elevated the issue of measurement to the status where it was fundamental to the subject without ever making clear what it actually entailed. “The concept of ‘measurement’ becomes so fuzzy on reflection,” Bell said, “that it is quite surprising to have it appearing in physical theory at the most fundamental level ... does not any analysis of measurement require concepts more fundamental than measurement? And should not the fundamental theory be about these more fundamental concepts?”

Bell is widely venerated. Go to quantum physics conferences and his name comes up again and again, with some people quoting from his writings as if from scripture. He has the advantage, from the fame perspective, of having died suddenly and relatively young. A cerebral hemorrhage took him out of the blue in 1990, aged just 62. But even his influence is not enough. When it comes to quantum interpretations, the Copenhagenists appear to have won the day. For now, at least.





As I have said to Jerome many times as we discuss this deplorable situation, the Copenhagen interpretation can’t last. It doesn’t give us an answer to the question “why” when we see the results from the double-slit experiment; it refuses to explain anything about what reality looks like. Steven Weinberg has called it “clearly unsatisfactory.” Murray Gell-Mann, who died in May, said the Copenhagen interpretation has survived for so long only because “Niels Bohr brainwashed a whole generation of theorists.” The phrase made Jerome chuckle. “That’s a nice way of putting it,” he said. “All doubts and questions rinsed away in a flow of appealing nonsense.” He shook his head and laughed again. “I suspect my entire life has been a struggle against having my brain washed.”

Fortunately, the brainwashed generation is passing: Copenhagen doesn’t dominate like it used to. Just as Jerome’s inventions and creations ultimately survived the strictures of the Inquisition, Bohm’s ideas are also still alive, despite some of the “killer blows” they are reputed to have suffered. There are other options, too. The many-worlds interpretation, where quantum events occur in separate realities, is growing in popularity. This is more appealing to Jerome; he always liked the dangerous idea of a plurality of worlds.

In the end, we can be reasonably confident that none of our current interpretations of quantum theory are right. The most likely scenario is we, like Jerome, don’t have all the information necessary to make a correct inference about the nature of reality. The point, though, is to keep trying. Why wouldn’t we? As Jerome said, “There is nothing better than a mind that understands everything.”





Michael Brooks is an author and journalist based in the United Kingdom.

Adapted from The Quantum Astrologer’s Handbook by Michael Brooks. Copyright © 2019. Forthcoming in September from Scribe U.S.

Lead image: painting by Christiano Banti (1824-1904).