How is an “instantaneous” change in orbitals by an electron reconciled with the tenet that nothing travels faster than light?
There is (I think) a non-zero distance between orbitals. To go from one orbital to another, therefore, would seem to involve traveling, or traversing, that non-zero distance, yet the duration of said travel is zero. Again, why is this not considered a violation of the prohibition of superluminal travel?
Or is it, in fact, a legitimate example of faster-than-light travel but of no consequence because no laws of causality are violated and no information exchange is made possible by exploiting the phenomenon?
Or maybe the space between orbitals is like the two ends of a worm hole (picture the cliched diagram showing how two widely separated parts of the universe are actually connected by a short, maybe even zero-length, path) with the electron taking that path.
Or, less fancifully, is it allowed since the Heisenberg uncertainty principle guarantees an increasing uncertainty in the energy of the electron for shorter and shorter time intervals (in other words, at any “instant” we’d have zero idea what the electron’s energy is and thus which orbital it occupies).
Atomic orbitals aren’t like concentric rings or shells around the nucleus; they’re probability distributions whose shapes are determined by the quantum numbers. Specifically, they’re given by spherical harmonics, and it’s a straightforward but boring problem in representation theory to churn through the details. (The wikipedia page on the subject isn’t bad, if you’re interested in the details.) Changing the quantum numbers changes the probability distribution, but it doesn’t make sense to say that an electron instantaneously moves from definite position x to definite position y. Besides, the energy eigenvalues overlap in space.
It’s not that the change happens instantaneously, it’s that the electron goes from one state to the other without ever being in the space in between. This process does still take time, though, and that time is limited by (among other things) the speed of light.
A company has some workers that work M-W, and others that work M-F.
On Tuesday the boss decides that worker A will now work M-W instead of M-F. This worker is now on a totally different schedule, but didn’t have to leave his desk: the change in schedule did not cause a discontinuity in his presence.
There is a finite probability that an electron will be anywhere, regardless its valence state. A large change of energy state may result in it being momentarily in a position with a very low, but non-zero, probability for the new state…or not, regardless there is no discontinuity required.
If you look at the radial probabilities there are definite concentric rings where the probability of finding the electron is the highest. So it would seem that if you consider the electron to be a particle it would have to instantaneously traverse this distance at least some of the time.
If you consider the transition to be a probability wave changing frequency then you’ve got a problem with the emitted photon being a point particle.
Think about how short a time span it is at the speed of light to go between different points within the electron cloud of an atom. An atom’s diameter is around 10[sup]-10[/sup] meters. c = 3*10[sup]8[/sup] m/s, so that time is less than 10[sup]-18[/sup] seconds. For perspective, X-rays start at 3 x 10[sup]16[/sup] Hz.
To know that a transition took place “instantaneously”, you’d need to know the electron was in one orbital, then, in significantly less than 10[sup]-18[/sup] seconds, know it was in another orbital. I don’t know how you measure that small of a time scale (twice, for the initial and final states) without imparting so much energy that you’re completely disrupting what you’re trying to measure.
OK, maybe someone’s figured it out how to measure the transition time, or at least is trying to. But somebody here needs to cite that result before I believe “instantaneous” isn’t just shorthand for “really fast (and we’re not quite sure what’s going on in the mean time*)”.
ETA: *by this, I mean that what is “going on” isn’t a single, well defined transition/path/whatever, not that they can’t calculate the transition probability or energy level difference using QM.
The situation is not that the electron is in a definite position somewhere in that orbital cloud, but we can’t say where it is; instead the electron simply does not have a well-defined, single position. All the we can logically is that there’s some wavefunction (in the classical case, anyway) \psi for the electron such that if you do an experiment to determine whether it’s in a region X, the probability that you’ll find the electron there is equal to the integral of |\psi|^2 over U. Even then you can’t conclude that the electron was secretly in X all along; it just didn’t have a position beforehand. (Compare the simpler case of electron spin, where there are only two discrete possibilities for the outcome.) The wavefunction collapse does seem to be instantaneous, despite changing the position distribution.
I don’t follow what you mean by this. What do you mean by the frequency of the “probability wave”, and why are photons’ being point particles a problem?
It’s possible for a particle to travel faster than light - superluminal travel. It’s not possible for a particle (or anything) to accelerate from a subluminal speed to a superluminal speed. It just goes. It would be like waiting on a freeway onramp controlled by a light - rather than accelerating from 0 to 65 MPH, you would just be going 65 MPH when the light turned green, with no transition.
Unless it’s Thursday or Friday when the decision is made, in which case to preserve the energy distribution, worker A must travel instantaneously from the office to home.
