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GUEST BLOG: Philosophical Implications of Wave-Particle Duality: Part 1

Hello world!

For those of you who missed the announcement, I am Lauren, Kenny's fiance, and now a guest blogger here. As Kenny mentioned, I'm majoring in physics, math, and philosophy, so one thing that I'm hoping to discuss on this blog is philosophical issues related to physics. As you can probably guess from the title, the first thing I've decided to try is wave-particle duality, an aspect of quantum mechanics. In particularly, wave-particle duality raises interesting questions about the relationship between properties and objects, whether there is one "thing" with wave properties and particle properties, or whether there is a particle and a wave that are related somehow.

However, before I begin, I'd like to take a moment to discuss methodology. Before one can talk about the meaning of different ideas of physics, it's important to have a firm grasp on the experiments that led to these ideas. The experiments place boundaries on what interpretations of the results are valid; if an interpretation conflicts with an experiment, we must reject it in favor one that doesn't. (However, the interpretation of those experiments is dependent on some earlier ideas, so we have to beware of circular reasoning...but that is another post for another day.) Therefore, before getting to the philosophical meat of the issue, I'll be taking a brief detour through the physics. I'm going to try to keep the physics discussions on a not very technical level (which is helped by the fact that Kenny doesn't have this set up to handle math equations well). However, please feel free to tell me if you want more or less detail in the physics explanations; I'll be happy to adjust.

To this end, here are the parts I foresee for this series:
1) What are particles and waves
2) Experimental evidence for wave-particle duality for light (massless particles)
3) Experimental evidence for wave-particle duality of matter (has mass)
4) What can this mean? (Philosophical part)
I apologize for two whole sections of mostly physics before the philosophy; I'll try to incorporate philosophical questions into those as I write them.

Part 1: Classical assumptions: What are waves and particles anyway?

Before discussing wave-particle duality, however, it’s important to understand what waves and particles are. To interpret whether an experiment shows a wave property or a particle property, we have to determine what those properties are first. Physical definitions are abstracted, through a long process, from basically everyday experiences. For example, there seem to be two ways of transporting energy- for example, one could throw a rock at something and knock it down, or one could drop the rock in water and watch the waves spread out and move things like leaves sitting on the water, even a far way away. The first corresponds roughly to "particle" and the second corresponds roughly to "wave".

Let’s look at dropping the rock in the pond. We notice:
1) The waves spread out in all directions, and gradually dies out instead of ending abruptly.
2) The waves seem to have a regularly, curvy-like shape that repeats (sinusoidal). If we’re really good at throwing rocks and throw several in at the just right times, we see that we can get interesting combinations of these shapes that don’t look very much like the shape from just one rock, but if we throw any one rock in, we basically get this shape.
3) If we put a leaf on the top of the water and drop a rock in, at the end of the wave passing by, the leaf is in more-or-less the same place, implying that at the end of everything, the water hadn’t had a net motion.

Now let’s look at throwing the rock. We notice:
1) Unlike waves, the rock doesn’t seem to spread out much as we throw it. It has a definite stopping point, the edges of the rock.
2) The path of the rock in our example does seem to be regular, but it’s not periodic like the waves.
3) The rock definitely ends up in a different place than when it began.

Over time, these definitions became slightly more refined.
Classically, the definition of a wave became:
W1) Energy is spread continuously in time and space
W2) Its propagation obeys, or it is made out of components that obey, the wave equation (a second order differential equation.)
W3) Propagation occurs within a medium
And for the particle-
P1) A particle is localized in space
P2) A particle exchanges energy at a point

Letting x be a phenomena, and Wx = x is a wave and P = x is a particle, the classical assumptions about waves and particles can be summarized as:
1) Wx if and only if (W1 & W2 & W3)
2) Px if and only if (P1 & P2)
3) For all x, (Wx or Px)
Everything is either a wave or a particle.
4) For all x, not (Wx & Px)
Nothing is both a wave or a particle.

Finally, let’s take a look at what tests can be used to determine if something is a particle or a wave. We’ll discuss 2:
O1) Interference and/or diffraction
The continuous spread of energy means that if we block most of a wave, but let part of it through, it’s going to have to “spread” out after it’s let through, because otherwise it would have a discontinuous drop to zero. This phenomena is called diffraction. Similarly, if you let two parts of a wave through, they’ll both spread out, and then start overlapping with each other to make bigger peaks and deeper troughs than just one of them had, which is interference. (W1->O1). However, a single particle only exchanges energy at a point, so one particle cannot display interference and diffraction, which are patterns of the exchange of energy observed over space. Additionally, a stream of particles wouldn’t create interference or diffraction patterns. If one shoots a bunch of particles at a gap in the wall, one will get a pile of particles behind the gap; they’re not going to spread out immediately beyond the gap. (P2-> ~O1). Thus, the observation of interference and/or diffraction proves something is a wave.

O2) Faster in matter of difference densities
Consider if a phenomena was made of a bunch of particles. For a phenomena to be observed a long distance away, at least some of those particles would have to move over there, because the particles are localized. Now, if there’s a lot of other particles in the way, it’s going to take them longer to get there, because they keep getting bumped around (like it takes longer to get anywhere in a crowd). It takes longer for a single particle, or a stream of them, to travel the same distance in a denser medium. Hence, O2 -> ~P, or consequently, that something is a wave. To double check, we can experiment with waves. If we take our experiment with dropping a rock in water, and repeat it with oil and other liquids, we’ll find that waves go faster in denser mediums. So far, everything is consistent.

O3) Interaction in only discrete amounts of energy
Waves have a continuous distribution of energy in space and time. So, a wave can transfer any amount of energy in its range. However, particles can have distinct values of energy. Now, for something like throwing a rock, you can throw a rock with a lot of different energies, so observations on a series of rocks could mimic observations on a wave. However, if we observe something that can only have distinct values, classically it cannot be a wave, and so must be a type of particle that has distinct energy values.

O4) Localized interaction
Waves spread out continuously through space and time. A wave, therefore, should interact everywhere along its' front; there's a wide spatial range of where energy is to cause interactions. However, particles must have localized transfer of energy. So one test is to look at the interaction pattern of a phenomena when it encounters a wide strip of possible interaction points- whether it strikes them all, or whether it hits some and misses some. In the first case it would provide evidence for a wave (although not conclusive proof, since it could be a really dense uniform spray of particles). However, in the second case (ignore apparatus error) would be conclusive evidence for particles.

That's probably more than enough for this post, although it's been mostly definition. Next I'll talk about what the experiments show for light.