# Physicists debate whether quantum math is as real as atoms

## Words like ‘ontic’ and ‘epistemic’ are hurled as weapons in war over meaning of subatomic equations

*Second of two parts (read Part 1)*

Ernst Mach found atoms useful. But he didn’t believe they were real.

The 19th century physicist-philosopher gained his greatest fame as an atom denier. He believed that reality consisted of sounds and colors and pressures, features of nature susceptible to “sensuous contemplation.” Reality was what the senses perceived; things like atoms were mere “mental artifices” designed to represent nature for practical purposes.

Hypothesizing atoms permitted successful predictions about chemical reactions or properties of heat, for instance. It’s much like how hypotheses about circles and epicycles allowed ancient astronomers to plot the paths of planets and predict eclipses. Epicycles weren’t real, and Mach saw no reason that atoms should be, either.

“Atoms cannot be perceived by the senses,” he declared. “Like all substances, they are things of thought.”

No scientist today denies the reality of atoms. Mach did not foresee the technology that allows them to be imaged, split and smashed. But Mach’s conception of atoms and the question of their reality echoes today in a different debate on the physics frontier: the nature of the mathematical expression at the heart of quantum mechanics.

Quantum math describes how atoms behave, in much the way atomic theory helped explain the behavior of the observable world. But atoms, Mach insisted, would forever remain “a tool for representing phenomena, like the functions of mathematics,” and you shouldn’t mistake mathematical equations for the real phenomena they describe. Yet today some experts believe that the quantum formula describing atomic phenomena is not simply a mathematical tool, but is just as real as atoms are.

That formula is known as the state vector or (a bit loosely) the wave function. Atoms, or any physical system, can be considered to be in a “quantum state”; the wave function describing it permits predictions of the system’s future. But to the despair of many fans of traditional, or classical, physics, those predictions are not definite. In a classical state, the math describes the locations and motion of all the particles in the system, enabling a precise forecast of future states. Quantum math offers up only the odds for various possible futures.

Nature obeys those odds — in the long run, quantum probabilities accurately forecast the distribution of experimental results. But the explicit cause-and-effect certainty of classical Newtonian physics is rendered fuzzy. Hopes of restoring such certainty with “hidden variables” have been dashed by experiments based on work by John Bell a half a century ago.

Such experiments have persuaded many physicists to live comfortably with the wave function’s probabilities, happy to comply with an often-repeated quantum theorist creed: “Shut up and calculate.” But others insist that the wave function or quantum state has real physical existence. Whether it’s real or merely a tool for calculating probabilities is today “perhaps the most hotly debated issue in all of quantum foundations,” quantum physicist Matthew Leifer writes in a recent paper in the journal *Quanta*.

Dressing this debate in philosophical jargon, Leifer and others in the field label the two possibilities as “ontic” and “epistemic.” These are not words you should try to use at home. But when eavesdropping on quantum debates, you should know that “ontic” refers to something physically real; “epistemic” alludes to mere knowledge about something.

An ontic state exists independently of anybody’s knowledge or awareness. “Ontic states are the things that would still exist if all intelligent beings were suddenly wiped out from the universe,” writes Leifer, of the Perimeter Institute for Theoretical Physics in Waterloo, Canada. “An epistemic state is … a description of what an observer currently knows about a physical system. It is something that exists in the mind of the observer rather than in the external physical world.”

Historically, quantum states have usually been regarded as epistemic. As the Danish quantum pioneer Niels Bohr famously said, “It is wrong to think that the task of physics is to find out how nature *is*. Physics concerns what we can *say* about nature.”

Bohr’s attitude was incorporated into the view of quantum physics known as the Copenhagen interpretation, once the predominant approach but now widely challenged. Modern adherents of the Copenhagen view tend to favor the epistemic side of the ontic-epistemic debate.

“If asked what quantum states represent knowledge about, neo-Copenhagenists are likely to answer that they represent knowledge about the outcomes of future measurements, rather than knowledge of some underlying observer-independent reality,” Leifer writes.

Others think the quantum world makes more sense if the quantum state wave function actually does exist in a physically real sense. In fact, in 2012 physicists Matthew Pusey, Jonathan Barrett and Terry Rudolph published a theorem in *Nature Physics* positing that the wave function must be ontic. Other theorems seem to demonstrate the opposite, though, and all such mathematical arguments rely on assumptions that may not be valid.

And so the debate goes on — for instance, during a workshop a few months ago at the IBM Watson Research Center north of New York City. There a group of quantum experts, plus one impartial observer, explored various perspectives on the foundations of quantum physics and its relationship to the classical appearance of the ordinary world.

Mark Srednicki, of the University of California, Santa Barbara, argued strongly for the superiority of the ontic wave function over the epistemic approach.

“There are people who are trying to come up with a fully epistemic theory of quantum probability,” Srednicki pointed out. “It’s really hard. Those guys have been working a long time in trying to get this to work, and I think they have basically not been able to do it.”

Another theoretical physicist at the workshop, Sean Carroll of Caltech, also views the quantum state as ontic. “It represents reality,” he says. “It’s what the universe is.”

Probabilities come into play, as he sees it, because of “self-locating uncertainty.” You can know what the quantum state is without knowing which branch you occupy on the tree of quantum possibilities described by the wave function.

“The point of self-locating uncertainty is that you can know what the state is, and know what your environment looks like, and yet not know where you are in the state, because there is more than one place that looks like your environment, including you,” Carroll says.

But another leading quantum theorist, Wojciech Zurek of the Los Alamos National Laboratory in New Mexico, isn’t ready to jump on the ontic bandwagon.

“I don’t think the [quantum] state is either epistemic or ontic,” he said at the IBM workshop. “For the record, the state is definitely epi-ontic.”

Zurek pointed out that quantum states do not exist in the same sense that ordinary classical states exist. For classical states, information about the state can be recorded, copied and shared. A quantum system can be prepared in a known state, but an unknown quantum state can’t be examined or copied without destroying it.

“I can confirm a quantum state exists if I know it,” Zurek said. “If I don’t know it, I cannot find it out.… So I can have a situation where, for example, the state exists for me because I know what it is, but I haven’t told you.”

Perhaps, Zurek suggested, it doesn’t really matter whether you regard a quantum state as ontic, epistemic or epi-ontic. As Leifer notes in his review, the issue doesn’t even arise if you don’t believe in any underlying reality to begin with — in that case, there is no ontic. And even if some mysterious reality does underlie quantum knowledge, that doesn’t mean the quantum state captures that reality uniquely.

But Carroll believes such issues really do make a difference for cosmologists in their efforts to understand the universe. Building a comprehensive model of the universe that faithfully represents its origin and evolution requires a solid quantum foundation.

For instance, much of the discussion at the IBM conference focused on Boltzmann brains, hypothetical transient configurations of matter possessing consciousness and memories (if for just an instant). In some scenarios, quantum fluctuations could produce such an arrangement of matter and energy that exactly duplicates the state of your brain at this moment. So how do you know that you’re not just an ephemeral flux of randomness that popped into existence a moment ago and will go poof a moment later?

You’d think that wouldn’t be likely. But in fact, if the universe spends most of eternity in a quantum vacuum state, as some cosmological theories suggest, it becomes overwhelmingly probable that you *are* a Boltzmann brain, since Boltzmann brains would vastly outnumber real ones (if certain views of quantum physics are correct).

Carroll would rather not be a Boltzmann brain. And he and collaborators Kim Boddy and Jason Pollack have proposed a view of quantum physics that avoids them.

“Boltzmann brains are supposed to be things that arise through quantum fluctuations,” Carroll explained to me during a break in the action at IBM. “But what a quantum fluctuation is depends upon one’s views about the foundations of quantum mechanics.”

For instance, a quantum state that doesn’t change over time should imply that nothing happens, and so there should be no fluctuations (and no Boltzmann brains). But in quantum physics, multiple possibilities can exist at the same time. So a nonchanging quantum state could be expressed as the sum of two other states that *are* evolving in time.

“Then the quantum foundation question is, are those evolving states real in some sense, or is it just a math trick and we shouldn’t treat them as real?” Carroll said.

If his approach rules out Boltzmann brains, then various approaches to modeling the cosmos become more feasible. Models with multiple universes, for instance, that might be tossed in the trash because they imply too many Boltzmann brains, could be reconsidered.

“So we’re saying you can relax a little bit,” Carroll said. “It is an example … where your opinion about certain issues in quantum foundations affects whether you think a certain cosmological model is legitimate or not. So I think that’s great, because it’s really saying that you can’t just shut up and calculate.”

Perhaps Mach would say the quantum state is just a mathematical tool for representing phenomena, just as he believed atoms to be. Or maybe he’d see in it progress toward his view that physicists would someday give up playing with atoms as though they were stones and forge a more vivid picture of reality.

“As the intellect … grows in discipline,” Mach predicted, “physical science will give up its mosaic play with stones and will seek out the boundaries and forms of the bed in which the living stream of phenomena flows.”

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