This question may reveal a lot more about my ignorance of modern physics than is comfortable, but here goes. And good luck figuring out what I’m getting at, as it’s a bit hard to put into words.

Subatomic particles have a dual identity. Use an apparatus that detects particle-like characteristics, and it says, “Mmmm, particles!” (Homer Simpson voice.) Use an apparatus that detects wave-like characteristics, and it says, “Mmmm, waves!” And it’s the “same entity” going into the detector–in this case, what we call electrons.

Now think of the atoms that join together to form molecules. The atoms interlock and, I believe I recall from my ancient physics class, do this by sharing outer electrons.

Does the formation of a molecule amount to a sort of “detector” that causes the electrons to “be” particles? Or is there a co-equal mechanism of intra-molecular bonding that is based on the electons being “wave-orbits”?

If electrons are regarded as waves, what’s the diff between an orbit holding one electron, and several? Stronger waves? Higher frequency?

If moving electrons produce a magnetic field–what is the complementary picture of how propagating wavelike electons produce such a field?

Hmm. Difficult question. Personally I think that the wave-particle duality is not a useful concept in thinking about quantum mechanics. Fundamental particles are point particles which propagate according to the rules of quantum mechanics, which means that their position and momenta are described by wave functions rather than precise numbers.

In an isolated atom, electrons are located in orbitals, which are the quantum states in which they can legally exist. When two atoms come together to form a molecule, new molecular orbitals come into being between the two atoms. Electrons occupy the molecular orbitals, and if these new orbitals have a lower energy than the previous atomic orbitals the molecule will be stable because it would require energy to pull the atoms apart. You can find more information about this by searching for “molecular orbitals.”

As for how propagating electrons produce a magnetic field in quantum mechanics, I can’t answer that. A magnetic field is really just a mathematical way of expressing the consequences of relativistic effects applied to electrostatic forces, so it may be modeled that way. I don’t know enough about quantum electrodynamics. I do know that even stationary electrons have a magnetic moment that produces a magnetic field ? an effect that is not present in classical physics.

The simplest possible answer, if not particularly satisfying, is “They’re Electrons”. Doesn’t help much eh?
The thing is, they’re NOT really particles, they’re NOT really waves… but, in certain circumstances, in certain ways, they act kinda like either one… the duality thing.
The important thing is that they’re not ANYTHING else… quantum mechanical principles only work on QM levels. You can’t have something else like an electron… if you did, you would call it an electron.

If you take two very powerful magnets and bring them near one another, you can play with electromagnetic waves and develop a mental picture of their forces… in fact I highly reccomend it.

When you do, you’ll realize that there’s nothing else in the universe exactly like the property of magnetism.

Not quite. If you took a classical charged sphere and spun it, it would, indeed, have a magnetic field. If the charge of the sphere is distributed in the same way as its mass, the magnetic field would be directly proportional to its angular momentum. The weird thing with electrons, is that the magnetic field of an electron is twice as strong as classical theory predicts that an object with that angular momentum should have (actually, it’s a little more than 2 times: Something like (2 + [symbol]a[/symbol][sup]2[/sup]) times).

Fortunately, however, this is exactly the result, to over 20 decimal places, predicted by Quantum Electrodynamics. And we knew we shouldn’t trust classical physics at that level, anyway, didn’t we?

But about 2/3 of what I’m asking isn’t coming thru to me (unless I’m just not grasping it).

We describe a situation as “here’s an electron shooting off through the vacuum at [pick a convenient velocity value].”

If it’s an itty-bitty ball carrying a charge, the old rule about moving charges being associated with magnetic fields seems to describe something visualizable (if no less strange).

Now somebody says, “look, there’s a wave of such-and-such frequency propagating along thru space–an electron wave!” (I assume it’s one of those “orbitals,” but linear rather than circular, yes?) So…if a “line” in space is occupied by an electron-wave, a “cylinder” of magnetic force will surround it (actually, many such cylinders inside one another)? What is the relationship between each individual wave-front (ie, one cycle) and a, er, “bit” of magnetic force?

By the way–side issue, though relevant–isn’t the “probability-distribution” interpretation of wave-particle duality considered somewhat outmoded, or in some sense an oversimplification? From a number of contemporary books that I’ve read on the general subject, I have the impression that (pace Feynman’s QED) you can’t really boil it all down to “they really are particles after all.” (But I’d rather have an answer to my main question…)

Not to cut you short, here, but it looks like what you’re asking for here is the entirety of QED, summed up into a few-paragraph post. I know that I sure as heck can’t do that.

But as for probability distributions: No, that’s really not adequate. If you want to go that route, you need to start with the wavefunction, which is related to the probability distribution, but carries more information. The probability distribution is the square of the wavefunction, so while the probability distribution is always positive, the wavefunction can be positive or negative. Actually, it’s even more involved than that: The wavefunction can even be imaginary or complex (in that case, instead of just squaring, you multiply by the complex conjugate). You can never directly observe the wavefunction by itself, but you cann observe consequences of it. If you tried to “interfere” two probability distributions, you could never get cancellation, since probability is always positive. But with wavefunctions, you can get cancellation, and this is, in fact, observed.