In all the quantum theory books I’ve read, describing the wave function of an electron is said to be very difficult because proper analogies don’t exist in reality. I have a hard time accepting that. I’ve been pondering this for months and I wonder if I’ve come up with a few that are at least close.
Plasma Ball
I’m sure everyone’s seen a plasma ball. It’s a glass orb with this thing in the center that looks like it came out of a mad scientist’s lab, probably called a plasma generator [duh!], and when plugged in it creates a plasma cloud inside the orb. But when the outside of the orb is touched, the plasma will concentrate itself to the point on the orb where contact is being made. (These things have a potentiometer of sorts that allows the user to change the plasma cloud from cloud-like to appearing like a bunch of little lightning bolts. The former setting is used for this analogy.)
Isn’t this an analogy for an atom, in that the plasma cloud is kind of like the wave function of the electron? It’s all over the atom all at the same time, but when we apply a measuring device (or in the case of a plasma ball: a finger) to the “atom”, the wave function collapses on that point. Furthermore, if multiple fingers (measuring devices) were to be applied, we’d see the electron at each finger (or in the case of the plasma ball, the plasma concentrates itself on each finger) and thus the one electron is “visible” at each measuring device at the same time. Cyberspace
It is a ubiquitous entity, not at any one point at any time, but at the same time everywhere. If you attach a measuring device (a computer), there it is, the wave function has collapsed. But at the same time, it’s still all over the place. Point to the Internet, and you’ll fail, but you can still see it. It’s right here in front of you…sort of.
I think those are interesting analogies. To me, they are not descriptions of the atom so much as descriptions of the effects of measurement on it’s physical state.
Also, consdering how many people actually understand how cyberspace or a plasma ball works, you might not be that much better off!
The failure of the plasma sphere analogy is that when you touch the glass dome, the plasma is always concentrated at where your finger is. But when you ask “Is an electron right here”, the answer can be either “yes” or “no”.
There are actually some good classical analogies for quantum-mechanical behaviour, but most of those good analogies come from the study of classical waves. There’s a version of the Heisenberg Uncertainty Principle for every sort of wave, for instance, not just for quantum-mechanical ones. But most people don’t become really familiar with classical waves until around the same time they’re really becoming familiar with quantum mechanics anyway, so most such analogies aren’t very useful.
Part of the problem is just this; every explaination for what goes on at the quantum level involves some kind of analogy to an everyday experience, like basketballs, planets, or ocean waves. While these analogies are valid in describing the mathematical model used to represent certain aspects of a the behavior of a sub-atomic particle, the reality is that fundamental particles (such as the electron, quark, photon, et cetera) behave in ways that cannot be fully understood as either a particle or a wave; hence, the “particle-wave duality” notion which serves to discombobulate everyone. The truth is that whatever an electron is–a “string” vibration, a distortion in the underlying plenum, a little green charged elf, whatever–it is something that is not part of our common experience; to think of or describe an electron or quark as being made of “stuff” gives an ultimately incomplete or misleading impression.
I was just trying to explain this to someone last night, and unfortunately I think I made a fairly incoherent job of it, in no small part because I was simultaneously trying to explain special relativity, gravity and general relativity, and the invarience of the speed light. (Note to self: when discussing modern physics with a layperson, stick to one insanely convoluted and poorly understood topic at a time.) This is hard stuff for physics students to truely wrap their heads around, especially when the math starts offering up nonintuitive answers. For someone without that theoretical basis, quantum mechanics just seems like so much arbitrary voodoo, and indeed, at some point it does indeed become strictly arbitrary; what does like move at and only at c? “Uhdunoo,” says the typical Nobel Laurate in physics. (Well, actually they’ll dress it up in all sorts of fancy clothes, but in the end, there is no answer.)
Regardless analogies hold up only so far, and then they fall apart by the nature of comparing two unlike things. The “plasma ball” analogy is a good visual comparison of a probability distribution but, as Chronos points out, doesn’t really represent what happens when you attempt to interact or measure the position of the particle.
[thread=299054]Here[/thread] and [thread=262525]here[/thread] are some old threads which delve into the topic of trying to explain how objects on the quantum scale can be described.
Thanks for the responses…especially Stranger, you tend to explain things pretty well.
The Chaos theory concept of Self-Similarity is ubiquitous to a profound level, and it seems to me that the atomic world should be included. There must be something that can be compared to the wierdness of the atomic world, and I don’t just mean plasma balls and the internet (which are at best, just analogies for small portions of atomic theory). Perhaps we’re trying too hard to find a physical analogy, but what we should be looking for is something conceptual.
Has the concept of “truth” ever been used as an analogy for Quantum theory? For example, if two people, one on each side of a road, see a car drive by, they each see different things. Their version of the “truth” is different, but at the same time, both are accurate. It seems that quantum theory has many of the same “inconsistencies”. Truth is hard to pin down in some cases, and depending on the circumstances, it can be downright impossible.
I dunno, maybe it’s just my twisted sense of pattern recognition. I’m not a physicist but whenever I read about the weird shit that happens down at that level, I’m often reminded of “truth”.
'Cept for Wave - Particle Duality, which to me has similarities to Mind and Body…but that’s a different thread.
Well, that’s essentially what physicists do – the concept we use is that of self-adjoint and unitary operators on complex Hilbert spaces, i.e., mathematics. Ninety-nine percent of all physicists are perfectly willing, after seeing the mathematical formalism succeed again and again and again, to trust that these concepts are correct; only a small minority concern themselves about what it really means in some deeper sense (if such a sense indeed exists.)
Exactly. What’s analogous to the behavior of quantum “weirdness” is the behavior of an operator algebra as opposed to the classical (commutative) algebra of real-valued functions on a base space.
The problem is that this analogy really works more for relativity than for quantum theory. When you move into the quantum world you actually have to replace the boolean algebra of propositions to a non-boolean structure. Quantum logic behaves fundamentally differently than classical logic does.
