Scientists are like prospectors, excavating the natural world seeking gems of knowledge about physical reality. And in the century just past, scientists have dug deep enough to discover that reality’s foundations do not mirror the world of everyday appearances. At its roots, reality is described by the mysterious set of mathematical rules known as quantum mechanics.

Conceived at the turn of the 20th century and then emerging in its full form in the mid-1920s, quantum mechanics is the math that explains matter. It’s the theory for describing the physics of the microworld, where atoms and molecules interact to generate the world of human experience. And it’s at the heart of everything that made the century just past so dramatically unlike the century preceding it. From cell phones to supercomputers, DVDs to pdfs, quantum physics fueled the present-day electronics-based economy, transforming commerce, communication and entertainment.

But quantum theory taught scientists much more than how to make computer chips. It taught that reality isn’t what it seems.

“The fundamental nature of reality could be radically different from our familiar world of objects moving around in space and interacting with each other,” physicist Sean Carroll suggested in a recent tweet. “We shouldn’t fool ourselves into mistaking the world as we experience it for the world as it really is.”

In a technical paper backing up his tweet, Carroll notes that quantum theory consists of equations that describe mathematical entities roaming through an abstract realm of possible natural events. It’s plausible, Carroll argues, that this quantum realm of mathematical possibilities represents the true, fundamental nature of reality. If so, all the physical phenomena we perceive are just a “higher-level emergent description” of what’s really going on.

“Emergent” events in ordinary space are real in their own way, just not fundamental, Carroll allows. Belief that the “spatial arena” is fundamental “is more a matter of convenience and convention than one of principle,” he says.

Carroll’s perspective is not the only way of viewing the meaning of quantum math, he acknowledges, and it is not fully shared by most physicists. But everybody does agree that quantum physics has drastically remodeled humankind’s understanding of nature. In fact, a fair reading of history suggests that quantum theory is the most dramatic shift in science’s conception of reality since the ancient Greeks deposed mythological explanations of natural phenomena in favor of logic and reason. After all, quantum physics itself seems to defy logic and reason.

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It doesn’t, of course. Quantum theory represents the ultimate outcome of superior logical reasoning, arriving at truths that could never be discovered merely by observing the visible world.

It turns out that in the microworld — beyond the reach of the senses — phenomena play a game with fantastical rules. Matter’s basic particles are not tiny rocks, but more like ghostly waves that maintain multiple possible futures until forced to assume the subatomic equivalent of substance. As a result, quantum math does not describe a relentless cause-and-effect sequence of events as Newtonian science had insisted. Instead science morphs from dictator to oddsmaker; quantum math tells only probabilities for different possible outcomes. Some uncertainty always remains.

“Since it concerns itself with the relations between matter and radiation,” Harkins wrote, quantum theory “is of fundamental significance in connection with almost all processes which we know.” Electricity, chemical reactions and how matter responds to heat all require quantum-theoretic explanations.

As for atoms, traditional physics asserts that atoms and their parts can move about “in a large number of different ways,” Harkins stated. But quantum theory maintains that “of all the states of motion (or ways of moving) prescribed by the older theory, only a certain number actually do occur.” Therefore, events previously believed “to occur as continuous processes, actually do occur in steps.”

But in 1921 quantum physics remained embryonic. Some of its implications had been discerned, but its full form remained undeveloped in detail. It was Heisenberg, in 1925, who first transformed the puzzling jumble of clues into a coherent mathematical picture. His decisive advance was developing a way to represent the energies of electrons in atoms using matrix algebra. With aid from German physicists Max Born and Pascual Jordan, Heisenberg’s math became known as matrix mechanics. Shortly thereafter, Austrian physicist Erwin Schrödinger developed a competing equation for electron energies, viewing the supposed particles as waves described by a mathematical wave function. Schrödinger’s “wave mechanics” turned out to be mathematically equivalent to Heisenberg’s particle-based approach, and “quantum mechanics” became the general term for the math describing all subatomic systems.

Still, some confusion remained. It wasn’t clear how an approach picturing electrons as particles could be equivalent to one supposing electrons to be waves. Bohr, by then regarded as the foremost of the world’s atomic physicists, pondered the question deeply and by 1927 arrived at a novel viewpoint he called complementarity.

Bohr argued that the particle and wave views were complementary; both were necessary for a full description of subatomic phenomena. Whether a “particle” — say, an electron — exhibited its wave or particle nature depended on the experimental setup observing it. An apparatus designed to find a particle would find a particle; an apparatus geared to detect wave behavior would find a wave.

At about the same time, Heisenberg derived his uncertainty principle. Just as wave and particle could not be observed in the same experiment, position and velocity could not both be precisely measured at the same time. As physicist Wolfgang Pauli commented, “Now it becomes day in quantum theory.”

But the quantum adventure was really just beginning.