Why doesn’t the world make sense? At the fundamental level of atoms and subatomic particles, the familiar “classical” physics that accounts for how objects move around gives way to quantum physics, with new rules that defy intuition. Traditionally these are expressed as paradoxes: particles that can be in two places at once, cats that are simultaneously alive and dead, apparently impossible faster-than-light signaling between distant particles. But quantum rules are perfectly logical and consistent—the “paradoxes” are the result of our trying to impose on them the everyday reasoning of classical physics.

What’s more, over the past several decades we’ve come to understand that the classical and quantum worlds don’t exactly operate by “different” rules. Rather, the classical world emerges from the quantum in a comprehensible way: you might say that classical physics is simply what quantum physics looks like at the human scale.

All the same, we’re confronted with the question: why is the quantum world the way it is? Why do fundamental particles dictate this set of rules and not some other? Normally that question carries an implication that quantum particles are being a bit perverse by not behaving like billiard balls, reassuringly solid and definite and thing-like. But that might be the wrong way to think about it. Last December, I spoke with Romanian-British physicist Sandu Popescu of Bristol University in England, who told me that things could have been even stranger than quantum.

In fact, Sandu said, we’re not even completely sure that things aren’t even stranger. Maybe we just haven’t detected this extra strangeness yet.

Scribbling on his whiteboard with infectious enthusiasm, Sandu explained that this hypothetical “super-quantum” world comes into view by thinking about what now seems to be the defining characteristic of quantum theory: nonlocality.

Increasingly, it looks as though we have come at quantum mechanics from the wrong direction. At first it seemed to be about how energy is not continuous but is divided up into discrete chunks (quanta). Then it seemed to be about how quantum objects have to be described by smeared-out, wavelike mathematical entities called wave functions. Then, the question became how all the possible states of an object encapsulated by a wave function get crystallized into just one state when we measure it using classical apparatus. But in 1935, Einstein and two younger colleagues unwittingly stumbled upon what looks like the strangest quantum property of all, by showing that, according to quantum mechanics, two particles can be placed in a state in which making an observation on one of them immediately affects the state of the other—even if they’re allowed to travel light years apart before measuring one of them. Two such particles are said to be entangled, and this apparent instantaneous “action at a distance” is an example of quantum nonlocality.

Erwin Schrödinger, who invented the quantum wave function, discerned at once that what later became known as nonlocality is the central feature of quantum mechanics, the thing that makes it so different from classical physics. Yet it didn’t seem to make sense, which is why it vexed Einstein, who had shown conclusively in the theory of special relativity that no signal can travel faster than light. How, then, were entangled particles apparently able to do it?

We now know that entanglement and nonlocality don’t violate relativity. Although a measurement here does seem to instantly affect what happens there, you can’t actually send any faster-than-light signal or information this way—because you can only verify the effect of the measurement elsewhere by exchanging information classically. Arguably it’s better to forget this picture of cause-and-effect: you could say that two entangled particles aren’t really two particles at all, but have actually become one single, nonlocalized quantum entity. Alternatively, nonlocality can be regarded as an indication that the properties of a quantum object needn’t all be located on the object itself. There’s no classical analogue: it doesn’t really mean anything to say that the speed or color of a tennis ball aren’t entirely situated on the ball itself. But that’s what the quantum world is like.

Quantum nonlocality seems almost ingeniously designed, then, to allow an event at one place to have instant consequences elsewhere without violating relativity. But in the late 1990s Sandu asked a curious question: are the rules of quantum the only way to do that? When he and physicist Daniel Rohrlich looked closely at that question, they found that it isn’t. It’s possible that nature could have been even more nonlocal while still respecting relativity. If so, understanding why the strength of quantum nonlocality is limited could give some clues about where quantum mechanics comes from in the first place.

What do we mean by “more nonlocal”? Picture two observers, called Alice and Bob, each of whom has a black box that dispenses a cuddly toy dog or cat when fed with a coin. The boxes will accept only dimes or quarters, and let’s say Alice’s box is designed so that a dime always elicits a cat. (Techie readers will see that these are just binary inputs and outputs: you could write them more prosaically as 1’s and 0’s.)

So here’s a challenge. Is it possible for these black boxes to achieve the following: if Alice and Bob both put in quarters, then the boxes will yield one cat and one dog, but any other combination of coins will yield either two cats or two dogs? If you work through the options, given also the constraint that a dime in Alice’s box must produce a cat, you find it can’t be done. Three times out of four, the boxes will fail to satisfy that requirement. The best you can get, then, is a success rate of 75%.

What, though, if Alice’s and Bob’s boxes can communicate using quantum nonlocality? Now Bob’s box can instantaneously use some information about what Alice’s box has done to switch its output. It’s possible to show that these quantum rules raise the possible success rate to about 85%—not perfect, but better.

Can we get 100% success? Yes, Popescu and Rohrlich showed, we can—if we allow the boxes even more nonlocal exchange of information than the rules of quantum mechanics permit. That’s possible, they say, still without violating relativity. These super-quantum boxes have become known as Popescu-Rohrlich (PR) boxes.

This improved performance, they say, comes down to the efficiency of sharing information between PR boxes. In general, communications are very inefficient because they involve exchanging lots of information that doesn’t actually feature in the final answer. Suppose, Sandu said, that he and I want to arrange a meeting. We’re both very busy, but we compare diaries by phone. We might hit on a suitable date by fairly randomly asking “Are you free on 6th June?” and so on. But it could take a while if our diaries are very full. So let’s say we look for an answer to what sounds like a simpler question: whether the number of possible days they’re both free to meet is even or odd. (OK, that doesn’t exactly help – but just suppose we’d like to know anyway.) The answer is just one bit of information: say, 0 for “even”, 1 for “odd.” But the only way we can deduce this bit is for me to get a list of every day in the year that Sandu is free, to compare against my own calendar.

Quantum nonlocality can reduce some of this redundancy of information, but not all. But if we have PR boxes, they can remove it all. The question can then be answered by feeding each of our PR boxes with the details in our respective diaries and having them exchange just one bit of information. For certain types of information processing like this, there is a sharp boundary between what can be done in quantum mechanics and what can be done with super-quantum PR boxes.

So PR boxes tell us that quantum nonlocality is actually a measure of the efficiency with which different systems can communicate and share information. In other words, quantum mechanics is a set of rules with which some outcomes of information sharing and processing are possible, while some are not (like Alice and Bob achieving 100% success).

Given their super-efficiency, PR boxes could do computation even faster than quantum computers. Could they ever exist, though? Sure, the world looks quantum-mechanical, not super-quantum; but it also looked classical for a long time, until we figured out how to spot quantum nonlocality. Could it be that we've just failed so far to uncover a stronger PR-box nonlocality that exists in the real world?

But even if quantum nonlocality is the best we can hope for, PR boxes may offer clues about why that is. The question becomes not so much why nature isn’t completely classical, but why it’s not “more” quantum. We should then seek answers not by wondering why, say, objects are described by wave functions (or what a wave function is anyway), but by looking at a more fundamental matter of how information can be shunted about—of how efficient communication in nature can possibly be. What is it that apparently limits quantum nonlocality’s ability to make information exchange more efficient?

All this fits with a growing conviction among many physicists that quantum mechanics is at root a theory not of tiny particles, but of information. It’s about how much we can deduce about the world by looking at it, and how that depends on intimate, invisible connections between here and there.