It’s hard to imagine a more mercurial pairing of minds in physics than that of John Archibald Wheeler and Richard Feynman. The latter went to Princeton University in 1939, expecting to work on his PhD under Eugene Wigner, but found that he had been assigned to Wheeler instead, less than seven years his senior. Both wildly inventive thinkers, they clicked, and each helped the other to reach the top of their game. Physicist and science writer Paul Halpern describes the duo’s work and relationship in The Quantum Labyrinth: How Richard Feynman and John Wheeler Revolutionized Time and Reality.

From Feynman came the approach to quantum electrodynamics that Wheeler christened a “sum over histories” – a way of dealing with the bothersome infinities that appeared when one tried to quantize Maxwell’s theory of electromagnetic fields, and which featured the famous Feynman diagrams. From Wheeler and his other collaborators came black holes and wormholes (terms he popularized), quantum “many worlds” and the foundations of quantum information theory encapsulated in the mantra “It From Bit”. Between them, the two physicists built a bridge between the physics of Einstein, Bohr and Pauli, and that which laid the foundations of so much of the discipline today: quantum field theory, quarks, the Standard Model, quantum and relativistic cosmology.

Whether this amounts to “revolutionizing time and reality”, as Halpern’s subtitle has it, is a matter of debate. But by documenting the relationship between the two men, his book provides a portrait of a rather neglected era in physics. Following the twin revolutions of quantum theory and relativity in the early 1900s, the 1940s to the late 1960s can appear like a time when already challenging ideas became all but incomprehensible beyond the academy. But Halpern shows that it was every bit as significant as the pre-war period that looks now to be an age almost of gods and legends.

Wheeler was astonished by Feynman, who as a student at the Massachusetts Institute of Technology had achieved the highest score by far in the daunting national Putnam Mathematics competition. “Nobody else who’s applying here at Princeton comes anywhere near so close to the absolute peak,” he said, adding, however, that “We’ve never let in anyone with scores so low in history and English.” He must be, Wheeler concluded, “a diamond in the rough”.

A working-class kid from Queens in New York, Feynman certainly was rough around the edges by the standards of the day. Wheeler’s wife Janette once scolded him for not standing up when approached by a lady, but Wheeler enjoyed the young man’s candour and humour. After Feynman’s first meeting with his new supervisor when Wheeler laid out a pocket watch on the desk to stick to time, Feynman went out and bought a cheap one that he set out in their next interview “like a countering move in a chess game”. Both young men burst out laughing; there was plenty more where that came from.

Wheeler quickly realized that he could treat Feynman as an equal in discussing physics, and that he could rely on his student to find mathematical solutions to the most challenging problems. What’s more, both of them were open to ideas as crazy as you like, provided that they didn’t obviously contravene physical laws. Some of their earliest work was on the “absorber theory” of how accelerating charged objects emitted radiation, which entailed signals travelling backwards in time. It was a fertile notion, but ultimately wrong.

As Halpern points out, the calm and elegant Wheeler was generally more wildly speculative than the flamboyant, excitable Feynman. It was Wheeler who called Feynman up one day to exclaim that he knew why all electrons are identical: they are all the same one electron, zigzagging all over time and space. That idea too came to nothing. Wheeler delighted in coining paradoxical turns of phrase – “law without law”, “charge without charge” – that set you thinking. When the Wheeler–Feynman absorber theory was resurrected, and adapted by steady-state cosmologists, it was dubbed Wheeler Without Wheeler.

For developing ideas that led to a theory of quantum electrodynamics without infinite singularities – the key problem was how to tame a point-charge electron’s interaction with its own field – Feynman won the 1965 Nobel Prize for Physics, shared with Julian Schwinger and Sin-Itiro Tomonaga. (Freeman Dyson, who showed how to weave the theories of the three men together, would surely have shared it too, says Halpern, but for the three-person limit.) Wheeler never attained that height, but his influence on modern physics was wide and deep: as well as Feyn­man, his students included Hugh Everett, who concocted what is now known as the “many worlds” interpretation of quantum mechanics, as well as several of the protagonists of the renaissance of general relativity, such as Jacob Bekenstein, Charlie Misner and Kip Thorne.

It’s hard to tell this story without delving into some recondite physics. Halpern makes ample and generally effective use of analogies, but there are limits to what they can do, and once you’re trying to picture rocking chairs coupled by a clothesline draped with blankets, it’s not easy to keep sight of the phenomenon it is meant to explain. Halpern occasionally ducks the deeper issues. It’s all very well to invoke the common notion that Feynman’s path-integral method in quantum electrodynamics implies that “everything that can happen does”, but what does that mean in ontological terms? To say that “reality proceeds by an awareness of all the possibilities before you arrive at an actuality” is to seek refuge in ambiguous words. It’s far from clear that Feynman himself would have been happy with an “everything happens” interpretation; pragmatic and disdainful of philosophy, he took Bohr’s view (so says Dyson) that the purpose of quantum theory is “to describe nature, not to explain nature”. It works, and that’s enough.

That no-nonsense attitude is part of Feynman’s enduring appeal. But Halpern hints that it was at least partly an intentionally constructed persona. Feynman liked to play the Everyman, but one capable of magical feats: his legendary safe-cracking at Los Alamos during the Manhattan Project was the result of much concealed study and practice. His celebrated “ask me anything” lectures at Caltech also reveal a desire to be seen as an insouciant wizard.

Those exploits make for great stories, but they suggest there was more ego and artifice in Feynman than he wanted us to see. Here too the contrast with Wheeler is illuminating. Feynman was, I suspect, the more brilliant, but despite Feynman’s bongo-playing and (slightly voyeuristic) life drawing, Wheeler was the more rounded – prepared, like his mentor Bohr, to entertain the idea that questions science can’t answer can still be worth asking.

• Paul Halpern The Quantum Labyrinth: How Richard Feynman and John Wheeler Revolutionized Time and Reality 2017 Basic Books £25/$30hb 320pp
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