The fork in the road

One of the most bizarre (and misunderstood) features of quantum physics is indeterminacy.

This is because we live in a macroscopic universe that -- most of the time, at least -- behaves in a determinate fashion.  Now, that doesn't mean we necessarily know everything about it.  For example, if we drop balls into a Galton board -- a device with a grid of pegs to deflect the ball's path -- eventually we'll get a normal distribution:

[Image licensed under the Creative Commons Matemateca (IME USP), Galton box, CC BY-SA 4.0]

With a device like a Galton board, we can accurately predict the probability of any given ball landing in a particular slot, but the actual path of the ball can't be predicted ahead of time.

Here's where the difficulty starts, though.  When people talk about quantum phenomena and describe them as probabilities, there's a way in which the analogy to macroscopic probability breaks down.  With a Galton board, the problem with predicting a ball's path doesn't mean it's not completely deterministic; it has to do with our (very) incomplete knowledge about the ball's initial state.  If you knew every last detail about the game -- each ball's mass, spin, air resistance, elasticity, the angle and speed of release, the angle at which it strikes the first peg, as well as the position, shape, and composition of every peg -- at least in theory, you could predict with one hundred percent accuracy which slot it would land in.  The ball's path is completely controlled by deterministic Newtonian physics; it's only the complexity of the system and our lack of knowledge that makes it impossible to parse.

This is not the situation with quantum systems.

When a particle travels from its source to a detector -- such as in the famous double-slit experiment -- it's not that the particle really and truly went through either slit A or slit B, and we simply don't happen to know which.  The particle, or more accurately, the wave function of the particle, took both paths at the same time, and how the detector is set up determines what we end up seeing.  Prior to being observed at the detector, the particle literally existed in all possible paths simultaneously, including ones passing through Bolivia and the Andromeda Galaxy.

To summarize the difference -- in a determinate system, we may not be able to predict an outcome, but that's only because we have incomplete information about it.  In an indeterminate system, the probability field itself is the reality.  However tempting it is to say that a particle, prior to being observed, took a specific fork in the road, and we just don't know which, completely misses the truth -- and misses how utterly bizarre the quantum world actually is.

People who object to this admittedly weird model of the world usually fall back on a single question, which is surprisingly hard to answer.  Okay, so on the one hand we have deterministic but complex systems, whose outcome is sensitively dependent on initial conditions (like the Galton board).  On the other, we have quantum systems which are probabilistic by nature.  How could we tell the difference?  Maybe in a quantum system there are hidden variables -- information about the system we don't have access to -- that make it appear indeterminate.  (This was Einstein's opinion, which he summed up in his famous statement that "God does not play dice with the universe.")

Unfortunately for Einstein, and for anyone else who is uncomfortable with the fact that the microscopic basis of reality is fundamentally at odds with our desire for a mechanistic, predictable universe, research at the Vienna University of Technology, which was described in a paper this week in Physical Review Letters, has shown conclusively that there are no hidden variables.  Our reality is indeterminate.  The idea of particles having definite positions and velocities, independent of observation and measurement, is simply wrong.

The experiment hinges on something called the Leggett-Garg Inequality -- described in a 1985 paper by physicists Anthony James Leggett and Anupam Garg -- which clearly distinguishes between how classical (determinate) and quantum (indeterminate) systems evolve over time.  Correlations between three different time measurements of the same system would show a different magnitude depending on whether it was behaving in a classical or quantum fashion.

The problem is, no one was able to figure out how to create a real-world test of it -- until now.  The team developed a neutron interferometer, which splits a neutron beam into two parts and then recombines it at a detector.  And the results of the experiment showed conclusively that contrary to our mental image of neutrons as hard little b-bs, that of course have to take either the left or the right hand path, every single neutron took both paths at the same time.  This violates the Leggett-Garg Inequality and is a crystal-clear hallmark of an inherently indeterminate system.

"Our experiment shows that nature really is as strange as quantum theory claims," said study co-author Stephan Sponar.  "No matter which classical, macroscopically realistic theory you come up with, it will never be able to explain reality.  It doesn't work without quantum physics."

Now, mind you, I'm not saying I completely understand this.  As Richard Feynman himself put it, "I think we can safely say that no one understands quantum physics."  (And if the great Feynman could say this, it doesn't leave much room for a rank amateur like me to pontificate about it.)  But perhaps the most fitting way to end is with a quote by the brilliant biologist J. B. S. Haldane: "The world is not only queerer than we suppose, it is queerer than we can suppose."

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