In physics, do all particles have a particle-wave duality? And if so, what determines whether they behave as a wave, or become a one-dimensional point in space? I'm familiar with the electron double slit experiment, and it's my understanding that when it's not observed, an electron acts as a wave. But when it's looked at, it acts like a single particle. How about hadrons, like protons and neutrons, that are made of quarks. Even though the are composite objects, can they also behave as waves, while containing their constituents? If the act of being observed has no influence on particle-wave duality, then what causes this property? And how does it ultimately effect our perception of reality?

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There's no simple

There's no simple uncontroversial answer to your question, but perhaps a couple of points will be at least somewhat helpful.

"Wave-particle duality" is ultimately too narrow a way to think about what you're interested in. The things that get described as illustrating "wave-particle duality" are special cases of the phenomenon of quantum interference, and that, in turn, is a manifestation of the fact that quantum states obey a superposition principle. At the end of the day, there's no substitute for thinking of this mathematically, but I'll do my best to avoid that here.

You probably know at least a bit about polarization. If we hold a polarizing filter (e.g., a lens from good sunglasses) up to a light source, the light that gets past it is polarized along a common axis—let's say the vertical axis. In principle, with the right kind of light source, we can turn the intensity down so that only one photon is emitted at a time. If such a photon passes the filter, it will hit a screen in one spot—like a particle. But suppose that instead of simply letting photons that pass the filter head for a screen, we put a certain kind of crystal in between. Photons entering this crystal will exit along one of two paths. One path gives us photons polarized along one of the diagonals to the vertical direction, call it D1, and the other path gives us photons polarized along the other diagonal, at 90 degrees to the first diagonal, which we'll label D2.

Now suppose we have a second crystal, like this first one except that it's turned at a different angle. Photons exiting on one of its paths are polarized along the original vertical axis, which we'll label V. Photons that exit on the other beam are polarized horizontally, a 90 degrees to the vertical. Label that axis H. If we put this crystal downstream from the D1 path, half of the original collection of vertically polarized photons will exit on path V and the other half on path H. The same goes for path D2. This is a symptom of the fact that the quantum state for vertical polarization is an equal superposition of the two diagonal polarization states corresponding to D1 and D2. That is to say: the vertical polarization state is a certain kind of sum of the two diagonal polarization states. It's mathematically like adding two waves, but also like adding two abstract vectors. And in fact that's a better way to put it, because it gets us away from pictures that ultimately don't help.

States of classical particles don't add in this way. There's no such thing as a classical superposition of being on one side of a line and being on the other side, for example. For individual quanta, superposition expresses itself in probabilistic behavior. A vertically polarized photon has a 50% chance of showing up on D1, and a 50% chance of showing up on D2. Which it does, however, is not determined in advance.

Now back to our experiment. In principle, we can recombine the D1 and D2 beams, without recording which paths had photons on them when. And we can, in principle, take the recombined beam and pass it through the second crystal, whose exit paths are V and H. You might expect, given what we've described so far, that half the photons would exit on the V path and half on the H path. In fact, all of them will end up on path V. This is an example of interference, but there's nothing that especially point to waves here. We could have given similar examples with any kind of quantum particle. Superposition, and hence interference, is what makes quantum mechanics what it is.

In principle, superposition even applies to large composite objects. Conceptually, it's not a matter of being sometimes wave-like and sometimes particle-like. Rather, it's a matter of the possible quantum states that systems can occupy having the mathematical property that they are superpositions of other states, and that in principle we can detect such superpositions experimentally.

In practice, however, interference of states of macroscopic objects would be very, very hard to create/observe. The reason is that when a quantum system interacts with its environment, the coherence between the different parts of the superposition is destroyed. More correctly, the coherence is dissipated into the environment. The more entangled a system becomes with the environment—the more other systems it interacts with—the more horrendously difficult it would become to observe interference. Think how many air molecules, dust motes and other bits of stuff a typical object interacts with. We'd have to reassemble them all in just the right way to observe interference, and for most macro-level systems, this isn't even remotely possible

By the way, this means that if we think of observation in purely physical terms as a certain kind of interaction between "recording devices" and systems, then observation tends to destroy the coherence needed for interference. Suppose we checked to see which path a photon followed in the experiment described above before we recombined the beams. By doing this, we'd destroy the coherence between the states corresponding to the two paths. This has nothing to do with minds or consciousness. It has to do with the mathematics of quantum entanglement.

Asking about the "causes" of wave-particle duality is a question that tends to seem off kilter once we look at the structure of quantum theory. As we've said, so-called wave-particle duality is an expression of something absolutely basic to the math of quantum mechanics: quantum states (the mathematical objects we use to predict and describe the behavior of quantum systems) add together to form superpositions. This means that in the right carefully-arranged experimental conditions, we can detect interference effects. But the math of quantum theory also entails that we don't expect to see interference in systems that interact extensively with their environments—which in practice means just about every familiar object we encounter.

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