I use shell to refer to a place occupied by an electron that has a given energy level. It turns out that the two terms can be used interchangably, so I’ll switch to energy level.

As far as I’ve ever learned, this is incorrect. The state transition takes no time and the energy level never exists in an intermediate state.

I never stated that electrons are massless, because I know better. If I implied such, I was mistaken or misread.

Yes, de Broglie wavelenghts are precisely what I had in mind. I think that bringing the concept of wave-particle duality `up’ to the macroscopic realm and then explaining why we don’t notice it is a good first step in applying it to the quantum realm.

This is why I will renounce use of the term shell: It implies physical motion too strongly in the layman’s mind, and that leads to conclusions like the one above.

Enola, thinking of this as motion is not productive. Motion at infinite speed is nonsense: It would require an infinite amount of energy and break causality, to boot. Think of it as a state change, one that is constrained by the concept of energy levels. And don’t think of the electron as a particle. When it changes state, it behaving like a wave. It only behaves like a particle when it is traveling freely through space.

Batting 500. There is no in-between state, but it does take time. The closer the two energy levels, the longer it takes, and the math conspires to ensure that the “effective velocity” of such a transition (delta x over delta t) is always less than the speed of light.

As for how it gets from one place to another without ever being in between, the closest classical analogies are going to come from waves. Take a rope, tie one end to a doorknob, and wiggle the other end. If you wiggle at the right speed, you’ll get it to bend in a sort of S-shaped curve that’s growing, shrinking, and growing in the other direction, sort of like this

[sub][/sub]/[sup][/sup]

[sup]/[/sup][sub]/[/sub]

(it’s hard to draw, but if you play around with the rope a while, you should see what I mean)

What you have now is two regions where the rope is wiggling, but it’s not wiggling at all at the point right in between. Similarly (but not too similarly; this is only an analogy), the electron-wave in certain states can wiggle in two different regions, but it can’t wiggle in the exact center. Where the electron-wave is wiggling is where the electron can be, and where it’s wiggling the most is where it’s most likely to be.

The OP was asking not about transitions between states (which are not instantaneous) but about the distribution in one particular state. Yes, there are places where the wave function is zero, and the electron will never be found there. But remember, the wave function only tells you about the probability of finding the electron, given that it is in a particular state. Once you measure the position of the electron, you change its state. So, if you measure the electron to the left of the zero point, then later measure the same electron to the right of the zero point, you aren’t surprised - after the first measurement it was no longer in the state that had the zero point.

This is why there’s no way to talk about the path of an electron when the electron is in a particular energy state. If you know the energy state, you don’t know the path. If you decide to determine the path, it will no longer be in the energy state. So, we can’t worry about what the electron does when we’re not looking. We can only talk about specific sequences of measurement and their outcomes. QM tells what the outcomes will be, but doesn’t give us a “picture” of what the electron does in between measurements.

That’s the great thing about chemists: they are very pragmatic types; they accept experimental results and move on. Dr. Love’s prof doesn’t know the answer, and since he apparently doesn’t need to know for his chemistry research, he doesn’t care!

Now, theoretical physicists on the other hand are just the opposite. They are very prone to wax in all sorts of philosophia naturalis and navel-gazing (see “Tao of Physics”, “Godel Escher Bach”, “Dancing Wu Li Masters”, “The Quantum and the Lotus” *). They need to know why. It bothers them. A Lot.

I think Chronos’s analogy is the simplest answer to the OP so far. I will give you an alternate Zen-like view to the problem. Consider this: when you ask “how does an electron go between two points”, you are implicitly assuming it has a path, therefore for them to go “without crossing the space inbetween” becomes a paradox. Remove the assumption, and Paradox Lost:

“In quantum mechanics there is no such concept as the path of a particle” - Lev Landau, Quantum Mechanicsp. 2 (!).
(* Can anyone recommend books of this sort written by chemists? I’m curious about their POV.)

Exactly. And that’s why you shouldn’t learn physics from a chemist.

Feynman got it right. There is no macro scale analogy that is correct, so if you insist on imposing one, you will be wrong even if it makes you think you understand the situation better. You are thinking of an electon as a particle and asking how it gets from one place to another. But an electron isn’t a particle. It’s not a little moon orbitting a nucleus.

On of my physics proffessors said at one point: Nobody acutally understands this-- you just have to trust the math.

As had been said, electrons are “things” that exist in differnt energy states. What does that actually mean? Hell if anyone really knows… But we know how to predict certain behavior and force certain outcomes. And one of the behaviors we know is that it can’t be in an inbetween state. At least as far as we know now. Maybe some theory will come along in the future that changes all that.

I believe Doctor Gribbon is ignoring the energy time uncertainty relation just as I was. The position-momentum uncertainty decrees that a particle does not, in principle, have both a definite position and momentum. Whereas, the energy-time uncertainty relation deals more with limitations imposed by nature on the precision of measurements. Time is not a dynamical variable it’s a parameter.