When the electron appears as a particle it has an electric charge. What happens to the charge and where does it appear in the elctron’s wave aspect?
Er, charge is a fundamental, inseperable, and invariable property of an electron and proton. (Quarks, which make up hadronic particles like protons and neutrons, have e/3 fractional charges, but they never appear independently except under the extreme pressures that existed shortly after the Wicked Wallop.) Charge isn’t related to the probability density of an electron, which I think you know, so I’m a little confused at your question about “wave aspect”. Are you asking about the superstring formulation of an electron?
Stranger
Stranger, I didn’t quite understand your answer. Dosen’t an electron “switch” from a particle to a wave? And does this switch effect the charge of the electron?
Yes, I know that charge is conserved which is why I asked the question. Until it is detected or interacts in some fashion an electron is described by a probablity function and doesn’t exist as a particle. So during that time when the electron is not really any particular place what is the charge attached to?
The electron’s “wave aspect” is just a construction scientist make to explain certain behavior. An electron isn’t a wave and it isn’t a particle. It’s an electron.
The charge is associated with the electron regardless of how we choose to describe it’s behavior.
Does that make sense?
Further…
If you take the square of the wave function, that can be treated as a probability density for the location of the electron. Think of the charge as being “smeared out” with that same probability density.
Yes it does and I should have worked it out myself. Sort of like circuit theory. Electricity really travels by EM waves which affect electrical charges. It just so happens that the vast majority of the charges in the vicinity of the EM waves are in the metal conductors and so circuit theory works even though that isn’t exactly the way electricity works.
This is the problem with people walking around and talking about “wave/particle duality”. There is no duality; an electron isn’t a particle at all, in the sense of being made of “stuff”. It’s not a scaled down baseball, and it doesn’t spin around the nucleus of an atom in an orbit; we just sometimes treat it as a point (centered at its locus) because, like assuming that a horse is a sphere, it makes the math easier. An electron is best thought of as a three (or more, perhaps) area of effect centered about a locus (which itself is a big smear of probability density, ψ[sup]2/sup), i.e. mathematically described as a field, albeit one that behaves discretely (i.e. only occuring at incremental steps rather than continuously).
An electron (and every other particle, be they leptons or quarks) are, AFAWK, formed from perturbutions in the vacuum of space, or, to borrow a phrase from Douglas Adams, disturbances in the wash. (It’s not that this makes it any more meaningful of an explaination; I just like the laundry metaphor.) If you listen to the string theorists, they’re made of 1-D “strings” of twisted vacuum that are shorter than a Planck length and vibrate in 10, 11, or 26 dimensions, or do other weird things that honest, hardworking, decent people don’t even want to think about, but we don’t have any evidence, direct or indirect that this is actually the case–the math just works out (as far as it is worked out) to make this a viable model. Anyway, fundamental properties, like mass, spin, and charge don’t change, and the characteristics that arise from them, like gravity and electromagnetic attraction, are just functions of how the particles interact (in string theory, how the vibrating patterns distort adjacent strings).
And that should make it all as clear as a massive planetary nebula for you. No, please, it was my pleasure.
Stranger
As one of my Physics professors was fond of saying about QM: “No one understands this stuff. You just get more comfortable with it over time.”
“EM waves” is just another way of saying photons. Photons, of course, have no charge (and Maxwell’s Equations in a vacuum reflect this), but can cause atoms to become charged by interacting with electrons in the atoms. Moving charges result in magnetic fields owing (simply stated) to the change in the vector between two charged particles.
Much of the jargon we use to describe electricity, like the term electromotive force predates Maxwell’s discover and offer up a confusing picture of how electromagnetism actually works; although charge can be likened to mass (and hence static electricity to gravity) and magnetism to inertia (sort of), the fact that there is no repulsive gravity akin to a negative charge makes that comparison fall apart rather quickly.
And if you want to get into the quantum theory of electromagnetism you need to review Quantum Electrodynamics…which is not exactly a trivial undertaking, even when reduced to layman’s terms. But, if you’re up for it, look up Richard Feynman’s QED for starters.
Stranger
Comfortable? No. Inured? Perhaps.
Stranger
In terms of quantum field theory, I believe you can say the charge of the electron is simply the strength of the coupling between the electron field and the photon field.
(These are the fields of which electrons and photons are the respective excitations. The photon field is the ordinary electromagnetic field, but because the electron has mass its field acts distinctly nonclassical.)
As such, this charge is manifested wherever electrons are in exactly the degree and fashion in which they are there.
One can only be aware of an electron’s charge when an observation is made. However this is true for everything. When a property is ascribed to a system that is not being measured (observed) this is an act of faith not a scientific fact.
And with respect to the OP: when an observation is made an electron always presents itself as a charged particle.
An electron doesn’t switch anything. There are some properties of an electron that are nicely captured by an analogy with waves, and others which are captured by an analogy with particles. It’s really neither of the two, but it’s similar to both.
Read the old fable about the five blind men and the elephant.
I think it’s more accurately stated that e is the coupling strength of the electromagnetic interaction, and 1 is the representation of U(1) according to which the electron field transforms.