Flat Particles
In 1884, Edwin A. Abbot published a short work of imaginative fiction called Flatland: a Romance of Many Dimensions. This book has become famous, and has been referenced in countless books and articles about physics, mathematics, philosophy, and other disciplines where multiple dimensions (or even just multiple perspectives) are discussed. Generally, it’s paraphrased, because the original language has a Victorian feel, and takes some getting used to.
I’d like to concentrate on one character in Flatland, a sphere that visits the two-dimensional world, where the main character, a square (A. Square) resides. The sphere does this several times, and, every time it does, the Flatlanders see a circle. The circle grows from a point, and then shrinks back to a point, as the sphere passes through. The sphere is able to see inside two-dimensional bodies and locked cupboards, and touch their contents.
The author decided to use the simplest possible shapes to populate his universes — squares, triangles, circles, lines, points, and a sphere. I don’t know his exact motivation, but my guess is that it was to avoid distraction — stretching the imagination is hard enough without having to picture what a human hand might look like in cross section. But it might have been interesting to have Flatland visited by a cylinder or a cone segment.
The thing about a sphere is that all its cross sections are circles. But a 
cylinder can appear to be a circle (just one size, though), or any number of flattened circles with the same radius, a rectangle, or a D-shaped morph of a semicirle. The cylinder could change shape dynamically, by rotating at various angles through Flatland’s plane. A cone segment could do the same, being a circle, ellipse, triangle, or its own semi-elliptical D-shape. The sphere already appears to be something that it’s not: it appears to be a point or a circle. But the cylinder adds variety to the paradox. It can appear to be very distinct and different things that it is not.
In 2-D space, a rectangle and a circle have very little in common. There is no way in two-dimensional space for a shape to be both a rectangle and a circle. Choose any intermediate shape between circle and rectangle (flatten out the circle, or round out a corner of the rectangle), and you no longer have either one. Yet a cylinder, without changing shape the slightest bit, can appear to be either one in Flatland. It can’t be both at once, mind you, but it can change freely between the two just by spinning around a bit.
Less than 30 years after Flatland was published, the world of science was reeling from the implications of quantum physics. People have different reactions to relativity and quantum mechanics, but the latter was always more difficult for me to assimilate. It depends on what your world view is all about. If you feel in your gut that time and space are constants, relativity is going to throw you for a loop. But, after bending my brain around the concepts for a while, I think I was able to accept it, even if I never fully understood it.
But quantum physics is another animal. Our smallest bits of matter act as either particles or waves — but never both at the same time. Some argue that a particle can’t have both position and momentum at the same time, but that comes mostly from the fact that we can’t observe both precisely. For me, learning about relativity was a radical change of view, but learning about quantum mechanics was like losing my religion. In my own, unscientific way, I tried with all my might to think of ways it might not be true — but, of course, the scientists who’d made the discoveries hadn’t missed anything that I was about to discover. They know their turf far better than I do.
Now, anyone who’s had discussions about quantum physics has probably encountered a smug, smirking individual who just loves the fact that intuition is assaulted so violently by the facts. I’ve encountered several. Sometimes this person has an agenda to interpret the physics to fit a particular philosophy, and sometimes not. But the smugness irritated me; I wanted to prove those smug scientists wrong!
But, of course, the scientists weren’t the smug ones. From all accounts I’ve read, quantum physics came as a shock. Nobody delighted in the discovery. Scientists fought it. Albert Einstein, himself, never stopped fighting certain aspects of it, despite having been instrumental in bringing its basic facts to light. The smug guys came along later, and latched onto it. I tend to think (without real justification) that most of them never really lost anything when they made their new discoveries. If you don’t have a paradigm to start with, you don’t have to shift anything to learn something new. So, I don’t have to prove anybody wrong. The smug guys aren’t that important.
I read a lot of books about quantum physics to try and get a handle on it. Each one, of course, felt the need to lay a foundation of classical physics to build from, so the opening chapters in these books grew tedious after a while. And a lot of them had very similar things to say, and I found no comfort for a long time. The book that finally did give me a mental framework was Quantum Reality: Beyond the New Physics by Nick Herbert. As you may guess from the title, this book is more philosophical than other titles I’ve read. What finally hit home is how much of physics, even classical physics, is mathematical modeling.
Magnetic fields aren’t real. They’re a mathematical construct that describes how physical objects act when they come together, especially if one or more of them is magnetic. The same is true of electrical fields, gravity, and even particles and waves. None of these mathematical models describes reality exactly. And I knew that much. But it’s easy to start thinking that a physical object is some kind of imperfect instance of the mathematical model that describes it, or that the mathematical model is some kind of ideal version of all applicible objects. But it’s not true. The model helps to serve intuition, and gives us enormous predictive power over the real world — but that doesn’t make them real, at all.
The main difference between these models and the quantum physics models is that the quantum physics models are not intuitive. They don’t parallel anything we can observe directly. You are familiar with a magnet picking up paper clips, and with an apple falling from a tree. But you have never seen an electron, and will never actually see what happens when it is measured as a wave, rather than as a particle. You may come up with a better guess at it than anyone else, but you’ll never know for sure.
People writing about quantum physics will talk about waves of probability, as if that’s something real — as if the probability that a particle will show up in one place or another can propogate itself through space as a physical wave. A common pattern in observation is that, if a particle’s position is measured, it acts like a particle from then on, at least until we lose track of it. If its position is not measured, it continues to act like a wave. That is, the mathematical model for a wave fits until we observe it — then the mathematical model for a particle works. But, as we noted before, waves and particles aren’t real, even in classical physics.
So, an electon doesn’t change from a wave to a particle, any more than the cylinder in my Flatland-inspired scenario changes from a circle to a rectangle. Sometimes you’ll hear the phrase “wave/particle duality” thrown about, but this does not mean that an electron is a particle and a wave. What it really means is that an electron sometimes seems to fit the mathematical model of a wave, and, at other times, seems to fit the mathematical model of a particle. The way I deal with this mystery now is to believe that:
- An electron is not a particle.
- Further, an electron is not like what we think of as a particle, even when it’s acting like one.
- An electron is not a wave.
- Further, an electron is not like what we think of as a wave, even when it’s acting like one.
There are other quantum mysteries, but they can all be dispensed with, to my satisfaction, by similar methods.
When I say “to my satisfaction”, I do not mean I’m actually satisfied. I’d still like to know what an electron really is. But I feel at least like the mystery is no longer in the realm of the paradoxical, but in the realm of the unknown. So, I think an electron is not only something different from anything we see in the macroscopic world; it’s also something we have absolutely no intuitive feel for. It’s not simply like a bacterium, different from any life form we know in the naked-eye-visible world, but still understandable on many levels using just classical physics. This is like an object from a different universe, obeying totally different laws. The mathematics of how electrons behave is well understood and predictable. But we simply have no good idea what’s behind the mathematics.
So, what we find when we look at a quantum entity depends a lot on what we’re looking for. If we look for a particle, we’ll find a particle. If we look for a wave, we’ll find a wave. If we look for a particle after observing the wave, we’ll find it. If we look for a wave after observing a particle — well, too bad. They’re only so flexible. So, once a particle, always a particle? Not really. If we pin down the position of an electron at any point in time, we automatically lose its momentum, so we have no idea where it goes after that point. We’ve lost track of it, and it can be like a wave again, for all we know.
Our methods of tracking single electrons or photons generally end with recording them on a sensitive plate, which is able to record where it hit the plate. After that, you can’t get hold of the same particle again. At least I’ve never heard of anybody doing that, and I think Heisenburg’s Uncertainty Principle pretty much forbids that. Record its position, and you don’t know where it went. Record its momentum, and you don’t know where it was when you recorded the momentum — so you STILL don’t know where it went.
When you hear someone trying to give special meaning to the act of observation, you have to understand that it doesn’t matter whether the observation is recorded or not. It’s not as if the entrance of data into the human mind is what changes the behavior of a quantum particle. It’s the mechnanics of taking the observation that changes wave behavior to particle behavior. A computer can take the observation, and never record or report the observation. But the particle will still act like a particle after that point — until we record its final position. Then it’s gone again. I believe Schrödinger’s Cat is either alive or dead. There’s nothing magical about opening the box.
So, observation itself does not necessarily affect reality. The mechanics of observation — that you have to send a photon to intercept or leave a sensitive plate to stop and record the particle is enough. You find what you set out to measure, but that, again, can be due to the mechanics of the situation. Like an enzyme can find one protein in a huge, chaotic mess of other chemicals, just by waiting for it to come along, and “fitting” it when it does, perhaps a measurement method will “rotate” the quantum particle into the “position” it needs to be in to act like the intuitive entity being measured. Whether this is a physical transformation of some kind, a re-arrangement of tiny, tiny component parts, a rotation through other dimensions, or something even further outside our imaginations, I cannot say. Nobody can say for sure. There are theories, like string therory, where other dimensions are actually involved.
The point I’m trying to distill from all this is that, when you’re dealing with the unknown and unobservable, even the most precise predictors are analogies at best. Whatever you think an electron is, you know that it’s certainly something else, something totally outside the realm of your experience.
So my thinking is that the mysteries of quantum physics are no more paradoxical than what a cylinder in Flatland can do. Wave/particle duality, in my thinking, is akin to circle/rectangle duality. A cylinder is neither a circle nor a rectangle, but it can have the properties of either (but not both) at any one time, while visiting Flatland. It can do that because it is actually something far outside the understanding of any Flatlander.
An electron is neither a particle nor a wave, but it can take the properties of either (but not both) at any time, while manifested in our universe. It can do that because it is actually something far outside the understanding of any human. But, as A. Square (the main character in Flatland) eventually attains an understanding of the third dimension, maybe we’ll someday have a better idea what electrons and photons are. In the meantime, the unknown feels better to me than a paradox.
