Thoughts on “Wave Particle Duality” and Other Sources of Quantum Confusion

1 Introduction

Science in general, and physics in particular, is often seen by both the layperson and the practitioner through a strange lens, where odd mystical or dogmatic aspects become mixed with the mathematical truths of theories and associated actual observed evidence. Quantum physics seems to be particularly prone to this, probably best embodied by the term "wave-particle duality". A lot of nonsense has been built up around this idea, and frankly, no small part of it has been promoted by people who really ought to know better. The foundations of quantum physics are far from being a settled issue, but there’s a big difference between telling people "we don’t completely understand things" and "nature is weird and spooky and you’ll never get it". The purpose of science is to further understanding, and part of that is admitting when our knowledge is incomplete (as it pretty much always is). And science education should share this honesty.
Enough editorializing. "Wave-particle" duality actually can refer to a couple of different things. One has to do with the formalism of quantum field theory, i.e. why are there any particles at all? That’s a more technical issue. The more popular notion has to do with basic quantum mechanics, the idea that something might appear as a wave or a particle depending on how you observe it. We’ll focus on that, with the caveat that this is a more conceptual than technical discussion, and further that the "solution" I will describe is in no way set in stone from a scientific perspective. But I think we can at least clear up some confusion around the point, and give a better conceptual framework than "weird and spooky". The explanation here is intentionally simplified, both because I want it to be accessible to a broad audience, and because quite frankly I don’t understand the details myself. But hopefully by the end of this article you’ll at least have some understanding that goes deeper than hocus pocus.
If you’re not familiar with wave-particle duality, watch this video, starting at about 40 minutes (and when you’re done reading this, watch the whole thing - great stuff). The video demonstrates the interference of electrons when scattering from a crystal. Interference is obviously a wave phenomenon, yet electrons are "particles", right? It’s not obvious from the video, but the interference pattern is the effect of many electrons hitting the detector (in this case, phosphor-coated glass). The device is sending a stream with large numbers of electrons to scatter off the crystal. Suppose we turned down the intensity of this stream, so it sent only one electron at a time. What would you see? Would it be the interference pattern, just much dimmer?
Actually, you’d see individual dots of light flash as each electron hit the phosphor. Suppose we replaced the phosphor with a detector that had some memory, like that of a digital camera. As each electron hit the camera, we’d see a dot appear, and if we waited long enough, eventually those dots would fill in and form the interference pattern.
So far this is all empirical. The attempt to explain this phenomenon is where things usually go off the rails. The usual explanation involves “wave-function collapse”, the notion that before the electron hits the phosphor it is a “wave”, spread out across space. Somehow the act of observation collapses this wave to a single point, i.e. a particle. It is crucial to understand that nothing in the equations of quantum mechanics describes this wave-function collapse. The wave equation is a rather boring differential equation, linear in time and space, while collapse as usually described is definitely non-linear, and for that matter not even differentiable. One of my favorite science cartoons sums it up nicely. In other words, collapse as usually described is essentially metaphysical, i.e. something which occurs outside of the known laws of physics. So it’s no wonder so much nonsense about the “quantum consciousness” is born from this idea.
Now, it’s understandable how one might get into this mess. Consider a simplified version of the electron scattering experiment. Instead of scattering electrons from the surface of a crystal, we send them toward a barrier with two narrow slits. You can do this experiment in a shallow pool with water waves, and observe the interference pattern. Similarly, as we build up enough electron detections we’ll see the interference pattern emerge for the electrons as well. Clearly the waves in water go through both slits. But do the electrons? Since there’s an interference pattern it seems they must. But if electrons are particles, how can this be? Let’s augment the experiment, and set up a detector which can tell us through which slit the electron passes, without significantly altering its path. Doing so will cause the interference pattern to disappear, and be replaced by two spots, as if the electrons now behaved like particles! Take away the detector at the slits, and the interference pattern is restored. Wave-particle duality, born of wave-function collapse, right? But as we’ll see, these observations can be explained without resorting to metaphysics, using the boring old wave equation. We just need to understand two key aspects of quantum systems: entanglement and decoherence.

2 Tangled!

The source of this confusion is our intuition about the physical behavior of objects, learned through constant interaction with the “classical” world. Even this notion of “classical” is somewhat slippery, often being confused with “macroscopic”. The key difference between quantum and classical physics is that quantum systems exhibit entanglement, the hand-waving definition of which is that systems one initial considered physically distinct become intertwined, effectively becoming a single physical entity. The implication of entanglement is that the observer and system under observation must always be considered together, in a much deeper way than explained in the video. We’re used to the idea that what we observe is largely independent of the observer. Baseballs do not change their trajectory just because you look at them, nor does the act of observation change your physical state (beyond adding some information to your brain - hold that thought for later). This notion is ultimately fundamental to the mathematical structure of classical physics. And it goes deeper than just “observation”. Suppose the baseball actually hit you in the head, causing it (and you) to change trajectory. After this event, any observer could measure the current position and momentum of the baseball and predict it’s subsequent path with no regard to what’s happening to your head. Physics is cold, but precise.
Quantum mechanics does not afford us this luxury. Consider an atom of positronium, an electron and it’s anti-particle the positron orbiting each other. At some point the electron and positron annihilate into a pair of photons moving in opposite directions (oversimplifying here for the purposes of illustration). Those photons now exist in an entangled quantum state. Suppose we measure some physical property of the photons, like the polarization. Lather, rinse, repeat. The distribution of results for the entangled photons will not be the same as for two photons prepared independently. This phenomenon is mathematically reflected in the Bell Inequalities, and led to Einstein’s famous statement about “spooky action at a distance”. But as we’ll see, there is no “action at a distance” if we find an alternative to wave-function collapse to explain the transition from the quantum to the classical world. The confusing bit is our preconception that photons, like baseballs, are independent physical entities. They’re not. And rigorously speaking, neither are baseballs.

3 What is a “Classical” System?

We need to make a brief digression, and have some idea what is meant when we talk about a “classical” system vs. a quantum system. The distinction is often couched in terms of size: quantum mechanics describes the physics of very small things, while classical physics is that of the very large, the world of our everyday experience. Apart from being completely unhelpful, it’s just wrong. Lasers are decidedly “macroscopic”, and definitely not describable by classical physics. Or take a look at this video about superfluids, or this one on superconductivity. While not exactly something you can do in your kitchen, the behaviors seen here only arise as a result of quantum mechanics operating at the visible scale.
So size is not the thing which divides the quantum and classical worlds. And we probably should not expect any sort of hard division anyway, but instead a continuum, with examples like lasers and superconductivity at one extreme and baseballs hitting you in the head at the other. The distinguishing feature is coherence. In lasers or superconductors/fluids, the wave functions of the quanta line up “just right”, producing behavior which can only be explained by the constructive interference of these waves. The quantum waves in a classical system, by contrast, are completely scrambled, i.e. they are decoherent.
The macroscopic classical and quantum systems are also the same in one very important aspect. Let’s consider our traditional microscopic quantum system again, the electron two-slit experiment. We can easily destroy the quantum interference pattern by (quite literally) “looking at it the wrong way”. But the quantum effects seen in superfluids etc. do not vanish when we observe them. A similar effect is seen for classical systems: baseballs don’t behave differently depending on how or if we observe them. This notion of robustness will be important in understanding what follows.

4 Decoherence

Let’s go back to our two slit experiment done with water waves. Apart from just removing the slits, how might we destroy the interference pattern? It’s not quite so simple as with the electron, clearly just observing one slit or the other isn’t going to do the trick (there’s that robustness again). What if we just put a bunch of rocks of varying sizes and shapes in the pool? That clearly is going to break up the fun. The interference we saw in the first place was caused by the coherence of the ripples across the pool, and the random placement and size of the rocks will cause decoherence of the waves. And this decoherence has its own sort of robustness. It is entirely possible that the precise placement and size of the rocks conspires to actually reconstruct the original interference pattern. Possible, but extremely unlikely. There’s a vastly larger number of ways to arrange the rocks that cause decoherence than those that maintain coherence. While it’s not obvious yet, this kind of “strength in numbers” is likely to underlie the robustness seen both in superfluids and baseballs.
But what about the electron version? We’ve already seen how observing the slits will cause decoherence of the electron wave function, though at this point how or why may seem mysterious. But we can also achieve decoherence roughly analogous to throwing rocks in the wave pool. Remember the cathode ray tube James Burke used to demonstrate electron interference? A key aspect is that the tube itself contains a vacuum. Let some air in, and the interference pattern goes away, as the electrons interact with the various quanta comprising the air molecules. And the quantum flavor of decoherence is much more robust than the classical, because of entanglement. Every time the electron interacts with another particle, the two become entangled. For that matter, all of the air molecules are interacting with each other, the walls of the vessel, and so forth. The number of possible entangled states is much larger than in our classical version of decoherence, where we could basically assume that once a wave passed a rock we could again consider them as having independent states (or more rigorously, the states are correlated, but separable).
So now we come to the heart of the matter. How is that letting air into the two-slit experiment gives essentially the same decoherence effect as observing through which slit the electron passes? To our classically trained minds these are two very different situations. But from a quantum perspective they are quite similar. Both the air in the tube and our measurement apparatus are decoherent “classical” systems, in the sense that we do not see quantum interference effects. Similarly the quantum components of both the air and measurement device will be entangled. To observe the electron passing through a slit, our measurement device must interact with it, which means that now the electron becomes entangled with that whole decoherent mess, and thus decoherent itself. Bye bye interference pattern.
We now have at least part of the answer. As we are macroscopic and decoherent, any attempt we make to observe a quantum system is likely to cause it to decohere (with the important exceptions of macroscopic quantum phenomena, which we’ll discuss below). But that doesn’t explain why observing the electron makes it behave more like a baseball than a wave in a water tank. In fact, it seems we’ve made the problem much worse, because now the number of possible outcomes for the entangled and decoherent combination of the electron and measurement apparatus is vastly larger than what we had to consider before. How is it that we only observe one of these states, and why is it always particle-like?

5 Robustness Through Redundancy

The final step requires that we again think about robustness, by which we mean that small perturbations (i.e. you looking at it) to a system do not change its behavior. Another way to think about it is that the system is predictably observable. You see a baseball flying toward the fence, look away for a moment, then look back, and have no trouble finding it in the air and following it as it leaves the park for a home run. The robustness of macroscopic quantum systems is the result of quantum mechanics itself. A superfluid is an example of a Bose-Einstein condensate, and it’s robustness essentially follows from the quantum nature of bosons, particles with integer spin values. Roughly speaking, because the wave-functions of bosons are symmetric, particles in the same state tend to reinforce the wave function (i.e. become more coherent) rather than cancel it out (as occurs with half-spin particles called fermions). If you get enough bosons in the same state, it becomes highly unlikely that any of them will leave that state, which is another way of saying they don’t interact with anything. Far and away the most likely state is for superfluids to flow with zero viscosity, the electrons in a superconductor to move effectively without resistance, and so forth. Once again, strength in numbers, but in this case that strength is a consequence of strong quantum coherence.
What is the source of robustness in a classical decoherent system? Since we can’t rely on coherence, you might guess we have to look to entanglement, and you’d be right. Decoherence is the suppression of interference between quantum states. We saw how decoherence results from entanglement between the system under observation and the environment. But while our classical states result from entanglement, the defining characteristic of the classical state is that it is not further entangled on subsequent interaction. And it turns out that starting from nothing but the basic wave equation of quantum mechanics, you can show that the states for which interference is suppressed are precisely those having this characteristic. Now, in the case of the superfluid, the robustness resulted because the information about the quantum state was encoded in the system itself in a highly redundant way (which is a fancy way of saying most of the quanta were in the same state). But when a system decoheres, what we find is that the information about the state is redundantly encoded in the environment itself through entanglement, and by the same token, that redundancy leads to robustness. The strength of the numbers vastly favors those states which behave classically. In other words, with no extra “weirdness” like ad hoc wave-function collapse, one can show that classical physics is by far the most likely outcome when you consider decoherence and entanglement of a quantum system with the environment.

6 Final Thoughts

Well, that’s probably quite a bit to swallow, and I’ve glossed over the details, many of which I don’t understand myself. If you’re interested in diving in further I recommend starting with this article, and following the references therein. Returning to our original topic: does an electron exhibit some sort of split personality? Is it sometimes a wave, and sometimes a particle? The answer provided by decoherence is that it’s always a “wave”, in the sense of always being modeled as a solution of the quantum wave equation. When we account for the effects of decoherence and entanglement with the environment, we find that that an initial “wave” state can transition to one that looks more like a particle. It’s really a wave-packet with a very narrow width. The more important point is that the entire process can be described by quantum mechanics, with no extra metaphysics required. Decoherence is neither instantaneous nor absolute. It can happen very fast, but the “non-classical” states are not completely excluded, they just become very improbable. But this transition is a prediction of standard quantum mechanics.
None of what I’ve described here is “proven” in any scientific sense, though the evidence is building. And the approach at least has Occam’s Razor going for it. But the “measurement problem” still remains. The astute reader may have noted that while we claim that classical states are overwhelmingly the most likely, we said nothing about which of those classical states is actually observed. If we watch the slits for the electron, we’ll see it pass through one or the other, but can say nothing about which we’ll actually see. So in some sense we’ve just moved the problem from the experimental apparatus to the mind of the observer. This then leads to ideas like “many worlds” or “many minds”, which are basically ideas about parallel universes branching out for each possible classical outcome. While this sounds like science fiction, and has exactly zero evidence to support it, it also has none against it. And like the decoherence approach, it has the advantage that it ascribes no extra metaphysical properties to the human mind (albeit at the cost of positing an infinity of unobservable parallel universes; pick your poison).
But here’s some food for thought. Consider what we said earlier about predictability in classical systems, e.g. you can see the baseball flying, look away, and find it again. Now you can turn this notion around by reversing time. We can say that the most likely decoherent entangled systems are those that have the best “memory”, that is, the greatest correlation as we look back through their history. Could one take this so far as to say that the most likely states of the universe are those which maximize their memory, their correlation with the past? Because that describes life, starting with DNA being copied through time, and culminating with the human mind and it’s ability to remember the past and transmit that information to others. Completely speculative, but certainly fun to think about.