*Margaret Wertheim is a science writer and author of “The Pearly Gates of Cyberspace: A History of Space from Dante to the Internet,” and “Physics on the Fringe.”*

‘I think I can safely say that nobody understands quantum mechanics,” wrote Richard Feynman in 1965, the year he was awarded the Nobel Prize for his work on quantum theory. Almost 100 years after the first quantum laws were discovered, physicists are still debating their meaning.

Does quantum mechanics mean there is no true reality at the subatomic level? Does it imply that the universe is constantly splitting off into billions of copies of itself ? Is it telling us that reality is inherently random? Or that consciousness brings the world into being? Or are there deeper laws we have yet to find from which quantum laws emerge? Two splendid new books, one from Adam Becker and another from Philip Ball — both trained as physicists — beckon us deep into science’s most enduring conundrum.

*[It’s inexplicable: A broken radio plays soothing music at just the right time]*

At the core of quantum mechanics is “wave-particle” dualism, a shorthand for the astounding fact that when we probe nature on subatomic and atomic scales, we find the objects of our study sometimes acting like waves and sometimes like particles, but not both at once. Niels Bohr, the Danish theorist whose philosophical ideas about the quantum world still dominate physics, called this phenomenon “complementarity” — though what precisely he meant by the term has been contested ever since.

In our direct experience we observe things acting as waves or particles — think of waves rippling across a pond vs. a baseball flying through the air. Particles are inherently localized, waves are inherently dispersed.

But light acts in both modalities. In the famous double-slit experiment, light passing through two slits creates an interference pattern of bright and dark bands that can be described only using wave equations. Yet Albert Einstein showed in 1905 that light travels as particles, called photons, each of which can knock an electron out of an atom like a miniature billiard ball.

And here’s the eerie part: If we do the double slit experiment and turn the light down so low that only one photon at a time passes through the slits, we still get the interference pattern — which means that the particle is interfering with *itself*. Somehow it manifests the presence of waves even though, as far as we can tell, there’s nothing doing any waving. Feynman said this experiment “has in it the heart of quantum mechanics.”

This waving-ness goes on across all phenomena at the quantum scale, so we can perform the double slit experiment with electrons or atoms, even molecules, and still get the wave-driven interference pattern. Atoms and molecules are quantum systems, and in addition to thinking about them as sets of particles, they also have wave descriptions. As befits the concept of complementarity, there are two completely different but ultimately equivalent mathematical formulations of quantum phenomena — Erwin Schrodinger’s wave equation and Werner Heisenberg’s matrix mechanics, the latter highlighting particle-like behavior.

How can we make sense of the waving-ness that quantum particles exhibit? And how does this quantum weirdness give rise to the human-scale world described by classical laws of physics?

In addressing these questions Becker takes a historical approach, leading us through responses starting with that of Bohr, the de facto leader of a group of early quantum theorists including Heisenberg (discoverer of the uncertainty principle), Max Born and Pascual Jordan, who collectively formulated the influential “Copenhagen interpretation” — though, strictly speaking, there isn’t a single unified view.

Despite their philosophical differences, Becker notes, Bohr, Heisenberg and the rest of the Copenhagen group “all agreed” that in the face of wave-particle duality “it was pointless to talk about what was ‘really’ happening in the quantum world.” According to Bohr, “Isolated material particles are abstractions, their properties on the quantum theory being definable and observable only through their interaction with other systems.” Heisenberg was equally blunt: “Elementary particles are not as real [as phenomena in daily life]: they form a world of potentialities or possibilities rather than one of things or facts.”

The idea that quantum waving-ness could be understood as a set of potentialities was pointed out by Born, who showed that the Schrodinger equation for a particle describes a set of probabilities for the values of its various properties, such as its position and momentum. Unlike a baseball, which can always be said to be here or there, a quantum particle seems to be in many places at once until we measure it, in which case it manifests in a particular spot. The range of places we can find it follows a statistical pattern defined by the wave equation, but until we do a measurement, we have no idea which place it will be. In quantum parlance, a measurement causes the wave function “to collapse.”

Jordan interpreted wave function collapse to mean that we, as observers, “produce the results of measurement.” In the 1930s, Eugene Wigner (a future Nobelist) took this a step further by suggesting that consciousness conjures reality into being. To put it mildly, this has been controversial, though it has inspired countless books of popular science, science fiction and New Age philosophy.

With deeply detailed research, accompanied by charming anecdotes about the scientists, Becker outlines attempts to understand wave-particle dualism, focusing on the work of three mid-century radicals: David Bohm, John Bell and Hugh Everett. The latter is responsible for the much-disputed “many-worlds interpretation,” which says that every time a quantum reaction takes place, the universe splits into many, nearly identical copies, in each of which one of the statistically available possibilities actually happens.

Becker’s intent is not to sway us to any one of the newer interpretations; rather he hopes to convince us that the Copenhagen interpretation has had too great an influence on physics for historically contingent reasons, including Bohr’s outsize charisma.

Bohr famously insisted that there could be no resolution to the cognitive dissonance of wave-particle duality: “It is wrong to think that the task of physics is to find out how nature is,” he declared. For Copenhagenists, we must be satisfied with equations as recipes for calculation and give up trying to understand the essence of reality.

Becker is having none of this: “There is something real, out in the world, that somehow resembles the quantum,” he insists. “We just don’t know what that means yet. And it’s the job of physics to find out.”

Ball also wants to know, and his gorgeously lucid text takes us to the edge of contemporary theorizing about the foundations of quantum mechanics. “Beyond Weird” is easily the best book I’ve read on the subject. Currently available in Britain, it will be published in the United States in October.

One of Ball’s achievements is to show how a bridge can be built between the quantum and classical domains via a process called decoherence, developed by a new generation of theorists including Dieter Zeh. As a particle intersects with the wider world, it gradually becomes quantum-mechanically entangled with ever more of its environment. The waving-ness doesn’t disappear; it spreads out further. Thus, says Ball, “the classical world is what the quantum world becomes.” For proponents of decoherence, all the universe is quantum-mechanical — it’s just that at the scale we live, quantum effects are too fuzzed-out to see.

Rather than asking why the quantum world isn’t like the macroscopic world, Ball turns the question on its head, asserting that we shouldn’t assume that human-scale effects and logic extend to the microscopic scale.

*[Thinking big thoughts about the boundaries of science]*

Which brings us to another aspect of complementarity: the dualism between our mathematical representations of quantum phenomena and our lived experience. We know that quantum math works — microchips, lasers and stunning new materials are proof of this — but the more sophisticated our equations become, the less they seem to make sense, literally and viscerally. As our symbolic power increases, our perceptual insights about the real become ever less valid in the miniscule realm, and we are pushed beyond the limits of natural language into a domain of abstract, apparently bizarre formalisms. As Ball puts it: “It’s not so much understanding or even intuition that quantum mechanics defies, but our sense of logic itself.”

Yet why should atoms conform to human-scale norms? “We have absolutely no reason to expect that it is ‘reality all the way down,’ ” Ball writes. By “reality” he means a clearly defined world where things have predetermined properties. Instead of a universe of “Isness,” Ball believes that quantum mechanics describes a world of “Ifness,” where a logic of probability reigns.

“Is there an Isness beyond the Ifness?” he finally asks. Possibly. If so, it won’t be anything like the Isness humans are used to. To echo Feynman: “I hope you can understand nature as she is — absurd.”