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New Measurements Show that the Unrealest Part of Quantum Physics Is Very Real

Weird times for Schrödinger's cat.

Physicists at the University of Queensland in Australia are offering new evidence in support of quantum physics' most understated yet fully unreal reality: the fundamental indeterminateness of the quantum wave function, the mythic math that would seem to imply the possibility of overlapping realities and superimposed truths.

Subatomic particle-points in the quantum world like to behave as clouds of possibilities (waves) rather than points, a feature of "wave-particle duality," and the interpretation of this is an open question and a source of great discomfort among physicists. The new research suggests it may just turn out that weirdest part of it is really as strange and counterintuitive as it looks.

Some background:

Quantum physics and all of its apparent oddities and quirks boil down to waves. Reality, when left to its own devices, is indeterminate. Here and there are really probably here and probably there; is or isn't is really probably is and probably isn't. Schrödinger's cat is probably alive and probably dead. Nothing itself is, again, only probably nothing, which means that it's probably something. Probably something means not nothing.

Image: uoregon.edu

All of this probability is given by wave functions, which are really, truly the most important thing. And we can look at wave functions just as statements of how likely something is to be true, like where an electron is located or if a quantum bit of information (represented by particle spin or however else) is going to be a 1 or a 0 (as a wave, it can in a sense be both). But a wave function can be ruined if, say, we decide to perform a measurement with enough precision to say where a particle actually is at a given time. Such a measurement "collapses" the wave function—wiping away its probabilistic information, leaving us with just the particle in this one place at one time, no longer in many places at many times. That's a lot less information than was contained in the original wave.

Matt Liefer, a researcher at the Perimeter Institute for Theoretical Physics in Ontario, has a good explanation of the whole wave function/reality mess on his website. He puts the phenomenon in more precise terms as such: " When we acquire new information about a classical epistemic state (probability distribution) say by measuring the position of a particle, it also undergoes an instantaneous change. All the weight we assigned to phase space points that have positions that differ from the measured value is rescaled to zero and the rest of the probability distribution is renormalized." (Here renormalization can be thought of as the sudden reduction from indeterminateness to an actual value.)

If particles exist as real, determinate entities when we measure them, we have to ask what the wave was in the first place. It supplied real information about a real probabilistic system, but what were we seeing? Is fine-grained reality just like that? A bunch of clouds of possibilities where things can be many things? 

That's one interpretation, but not the only one. The alternative is to say that the wave function is just a statement about what we're able to know above a given particle system or, rather, what the limits of our knowledge about the system are. So, we might look at a probabilistic description of some particle and say that the particle IRL has not chosen to be in an exact location at an exact time and is really existing in a bunch of possible realities at once, or we could say that the particle is obviously in one place or another place at every time, for sure, and it's just that we don't have access to that information until we make our measurement.

In terms of Schrodinger's cat, the question above would be as to whether the cat unobserved in the box with equal probabilities of being alive or dead is both alive and dead or if the cat is really just alive or dead and we describe the situation probabilistically as a fudge, because we don't have access to the information until we open the box.

The cat example makes the question seem pretty goofy, because of course it's alive or dead. How can a cat be both alive and dead? It can't, but particles aren't cats, nor are they moons. Which is how Einstein expressed his frustration with the wave function question: "Do you really believe the moon exists only when you look at it?"

"One popular interpretation that gets rid of this zombie cat is that the wave function is just a mathematical tool with only a loose correspondence to this underlying reality," Alessandro Fedrizzi, lead author of a new study in Nature Physics, told me. "If the wave function merely represents our ignorance, or limited knowledge, of the cat's actual state—presumably: definitely dead, or definitely alive)—there is no problem."

Image: Wikimedia Commons

"Looking in the box reveals that state, end of story, the previous superposition only existed because we didn't know any better," Fedrizzi explained. "Our results, however, rule out this particular interpretation of the wave function. We show that if there is an underlying reality, the wave function is in direct correspondence to it."

Think about what that means. If the wave function isn't just some mathematical fudge, but a description of actual IRL reality, the cat is IRL both dead and alive. Cats of course are giant, classical collections of matter (as are moons) and as such don't quite play by same rules as particles, but as a fundamental statement about the nature of reality, it'd be hard to find something better than reality at its most indivisible.

So, how does one go about proving that the lack of knowledge implied by a wave function is in fact a statement about reality—where a lack of knowledge means that there is an actual lack of properties to have knowledge about—rather than a statement about our limitations as observers?

The answer starts with what's known as orthogonality, which in the most generic sense means that two things are at right angles to each other, but in the sense of particles means two properties that don't overlap.

Welcome to a world of part-dead, part-alive cats

"One of the features that defines quantum mechanics is that we cannot perfectly distinguish quantum states unless they are orthogonal to each other," Fedrizzi said. "To stick with the cat example, 'alive' and 'dead' are orthogonal, so those two we can distinguish. But if the states aren't orthogonal, e.g. 'alive' versus 'alive+dead,' we can not perfectly distinguish them. A more sensible example for non-orthogonal states would be polarised light. Light can be vertically or horizontally polarised, and those two states are orthogonal. But it could also be diagonally polarised."

The interpretation of this limitation varies depending on how we look at wave functions. If we assume that the wave function is just a representation of our limited knowledge of some system, then we could say that the diagonal polarization and the horizontal polarization are really just representations of some deeper, yet unobservable reality in which the two properties overlap. So, the question in these terms is whether or not the indistinguishability of two non-orthogonal properties means that they really, truly are not indistinguishable or whether we just can't distinguish them as limited observers.

"Consider a deck of cards," Fedrizzi offered. "Now, there is a probability distribution of 'red cards,' and another for 'kings.' If I asked you to draw a card from the deck and tell me which probability distribution that card belonged to, you will usually be able to determine that. However, if you happen to draw a red king, you can't. Because the red king belongs to both distributions: that's where they overlap."

"Long story short, in the experiment we measure what these probability distribution overlaps are, and we find that they aren't sufficiently large to fully explain why we cannot distinguish certain quantum states," Fedrizzi said.

So, there is something deeper that is real and is not just some statement about what we're capable of observing. "We show that if there is an underlying reality, the wave function is in direct correspondence to it," Fedrizzi said. Welcome to a world of part-dead, part-alive cats. Interpret that how you willl.