At the very heart of quantum mechanics lies a monster waiting to consume unwary minds. This monster goes by the name The Nature of Reality™. The greatest of physicists have taken one look into its mouth, saw the size of its teeth, and were consumed. Niels Bohr denied the existence of the monster after he nonchalantly (and very quietly) exited the monster's lair muttering "shut up and calculate." Einstein caught a glimpse of the teeth and fainted. He was reportedly rescued by Erwin Schrödinger at great personal risk, but neither really recovered from their encounter with the beast.

The upshot is that we had a group of physicists and philosophers who didn't believe that quantum mechanics represents reality but that it was all we could see of some deeper, more fundamental theory. A subclass of these scientists believed that the randomness of quantum mechanics would eventually be explained by some non-random, deterministic property that we simply couldn't directly observe (otherwise known as a hidden variable). Another group ended up believing that quantum mechanics did represent reality, and that, yes, reality was non-local, and possibly not very real either.

To one extent or another, these two groups are still around and still generate a fair amount of heat when they are in proximity to each other. Over the years, you would have to say that the scales have been slowly tipping in favor of the latter group. Experiments and theory have largely eliminated hidden variables. Bohm's pilot wave, a type of hidden variable, has to be pretty extraordinary to be real.

Quantum superposition Superposition is nothing more than addition for waves. Let's say we have two sets of waves that overlap in space and time. At any given point, a trough may line up with a peak, their peaks may line up, or anything in between. Superposition tells us how to add up these waves so that the result reconstructs the patterns that we observe in nature. Read more…

Waiving a function

This has left us with more refined arguments to settle. One of these is about whether the wave function represents reality or just an observer's view of reality.

For example, say I shoot a single photon at a single atom, which may or may not absorb the photon. According to quantum mechanics, the atom enters a superposition state where it's both in its ground state and its excited state. We describe this superposition state with a wave function. One view of quantum mechanics states that the wave function really represents the atom. But an alternative interpretation is that the wave function represents what I, the observer, know about the atom—reality may be something else entirely.

The difference is subtle, but we only need to return to an atom and a photon to see it. Imagine that a photon can excite the atom into one of two possible states, but I only know about one of them. When I make my measurement, I can't ask "what state are you in?" I can only ask "are you in state two?"—that's the nature of quantum measurements. In my previous example, where I only have two possibilities, this doesn't matter. If it's not in the excited state, I know the atom is in the ground state.

But now I have three possibilities: the atom is in its ground state or in one of the two excited states—one of which i don't know about. In a measurement of my atom, I am still limited to a yes or no answer. There is no way for me to use that to distinguish between a superposition of two states and a superposition of three states. That's because the wave functions that represent these two possibilities overlap; they both include the chance of being in the ground state and state two.

In the original example, the wave function that I know is the same as the wave function of the atom: it represents reality. In the second example, the wave function is only my knowledge of the atom, not the atom itself. This difference can be resolved by making multiple measurements. I'd see that my measured probability distribution differs from that predicted by the wave function. That is, given enough measurements, the two wave functions are distinguishable.

In this case, figuring out what's going on is trivial. But the question applies to other, more complicated cases. Can these two perspectives on the wave function always be distinguished from each other, even when the wave functions involved generate the same probability distribution function?

Are you for real?

Now, a group of researchers has extended previous work to show that, yes, under a wide range of conditions, these two points of view do differ. They show that the wave function must in some sense represent the observed system rather than what the observer knows about the system.

Their work essentially boils down to creating a measure of how much two probability distribution functions overlap. They use this latest research to argue that no matter what wave function is used and what it represents, the measurement results must remain the same. That is, over multiple measurements, we should obtain the same probability distribution function. So even if the wave functions are indistinguishable, do they all reproduce the measurement results?

The answer is not very simple. The proof that the answer is correct is only understandable to other theoretical physicists, and it only applies to wave functions with three or more dimensions (these are very common). Nevertheless, let me take a shot at explaining it anyway.

If you take the view that the wave function only produces a probability distribution and then take all the wave functions that produce the same probability distribution—in other words, the observer's possible choices of wave functions, based on his or her knowledge of the system—and try to reproduce measurement results, you'll fail. Consequently, there is a single wave function that must represent reality.

So which wave function represents reality? Many different wave functions could be right, because they produce the same probability distribution function, but we can't tell them apart. That's the consequence of this finding: one wave function represents reality, but our ability to tell which one is reduced.

This paper is one of a series that is starting to reveal that our world is actually a quantum mechanical world at its very heart. Some aspects of it are non-local, some aspects of it are not real, and some aspects of it allow you to perform counterfactual operations.

These have been our observations in a variety of experiments. But it seems that the observations are a close reflection of how the Universe operates.

I have a love-hate relationship with one of the comments my writing sometimes receives: "I have no idea what you just said, but I love it." That means that somewhere along the line, I obviously failed because you don't know what you just claimed to like. Well, now I find myself in the situation of saying to the new paper's authors, "I have no idea what you've just done, but I love it."

Physical Review Letters, 2014, DOI: 10.1103/PhysRevLett.112.250403