Do electrons really perform instantaneous quantum leaps?

Question

This is not a duplicate, non of the answers gives a clear answer and most of the answers contradict.

There are so many questions about this and so many answers, but none of them says clearly if the electron's change of orbitals as per QM can be expressed at a time component or is measurable (takes time or not), or is instantaneous, or if it is limited by the speed of light or not, so or even say there is no jump at all.

I have read this question:

Quantum jump of an electron

How do electrons jump orbitals?

where Kyle Oman says:

So the answer to how an electron "jumps" between orbitals is actually the same as how it moves around within a single orbital; it just "does". The difference is that to change orbitals, some property of the electron (one of the ones described by (n,l,m,s)) has to change. This is always accompanied by emission or absorption of a photon (even a spin flip involves a (very low energy) photon).

and where DarenW says:

A long time before the absorption, which for an atom is a few femtoseconds or so, this mix is 100% of the 2s state, and a few femtoseconds or so after the absorption, it's 100% the 3p state. Between, during the absorption process, it's a mix of many orbitals with wildly changing coefficients.

Does an electron move from one excitation state to another, or jump?

where annav says:

A probability density distribution can be a function of time, depending on the boundary conditions of the problem. There is no "instantaneous" physically, as everything is bounded by the velocity of light. It is the specific example that is missing in your question. If there is time involved in the measurement the probability density may have a time dependence.

and where akhmeteli says:

I would say an electron moves from one state to another over some time period, which is not less than the so called natural line width.

the type of movement in electron jump between levels?

where John Forkosh says:

Note that the the electron is never measured in some intermediate-energy state. It's always measured either low-energy or high-energy, nothing in-between. But the probability of measuring low-or-high slowly and continuously varies from one to the other. So you can't say there's some particular time at which a "jump" occurs. There is no "jump".

How fast does an electron jump between orbitals?

where annav says:

If you look at the spectral lines emitted by transiting electrons from one energy level to another, you will see that the lines have a width . This width in principle should be intrinsic and calculable if all the possible potentials that would influence it can be included in the solution of the quantum mechanical state. Experimentally the energy width can be transformed to a time interval using the Heisneberg Uncertainty of ΔEΔt>h/2π So an order of magnitude for the time taken for the transition can be estimated.

H atom's excited state lasts on average $10^{-8}$ secs, is there a time gap (of max 2*$10^{-8}$ secs) betwn. two consec. photon absorpt.-emiss. pairs?

So it is very confusing because some of them are saying it is instantaneous, and there is no jump at all. Some are saying it is calculable. Some say it has to do with probabilities, and the electron is in a mixed state (superposition), but when measured it is in a single stable state. Some say it has to do with the speed of light since no information can travel faster, so electrons cannot change orbitals faster then c.

Now I would like to clarify this.

Question:

1. Do electrons change orbitals as per QM instantaneously?

2. Is this change limited by the speed of light or not?

Answer 1

Do electrons change orbitals as per QM instantaneously?

In every reasonable interpretation of this question, the answer is no. But there are historical and sociological reasons why a lot of people say the answer is yes.

Consider an electron in a hydrogen atom which falls from the $2p$ state to the $1s$ state. The quantum state of the electron over time will be (assuming one can just trace out the environment without issue) $$|\psi(t) \rangle = c_1(t) |2p \rangle + c_2(t) | 1s \rangle.$$ Over time, $c_1(t)$ smoothly decreases from one to zero, while $c_2(t)$ smoothly increases from zero to one. So everything happens continuously, and there are no jumps. (Meanwhile, the expected number of photons in the electromagnetic field also smoothly increases from zero to one, via continuous superpositions of zero-photon and one-photon states.)

The reason some people might call this an instantaneous jump goes back to the very origins of quantum mechanics. In these archaic times, ancient physicists thought of the $|2 p \rangle$ and $|1 s \rangle$ states as classical orbits of different radii, rather than the atomic orbitals we know of today. If you take this naive view, then the electron really has to teleport from one radius to the other.

It should be emphasized that, even though people won't stop passing on this misinformation, this view is completely wrong. It has been known to be wrong since the advent of the Schrodinger equation almost $100$ years ago. The wavefunction $\psi(\mathbf{r}, t)$ evolves perfectly continuously in time during this process, and there is no point when one can say a jump has "instantly" occurred.

One reason one might think that jumps occur even while systems aren't being measured, if you have an experimental apparatus that can only answer the question "is the state $|2p \rangle$ or $|1s \rangle$", then you can obviously only get one or the other. But this doesn't mean that the system must teleport from one to the other, any more than only saying yes or no to a kid constantly asking "are we there yet?" means your car teleports.

Another, less defensible reason, is that people are just passing it on because it's a well-known example of "quantum spookiness" and a totem of how unintuitive quantum mechanics is. Which it would be, if it were actually true. I think needlessly mysterious explanations like this hurt the public understanding of quantum mechanics more than they help.

Is this change limited by the speed of light or not?

In the context of nonrelativistic quantum mechanics, nothing is limited by the speed of light because the theory doesn't know about relativity. It's easy to take the Schrodinger equation and set up a solution with a particle moving faster than light. However, the results will not be trustworthy.

Within nonrelativistic quantum mechanics, there's nothing that prevents $c_1(t)$ from going from one to zero arbitrarily fast. In practice, this will be hard to realize because of the energy-time uncertainty principle: if you would like to force the system to settle into the $|1 s \rangle$ state within time $\Delta t$, the overall energy has an uncertainty $\hbar/\Delta t$, which becomes large. I don't think speed-of-light limitations are relevant for common atomic emission processes.

Answer 2

1. No. Instantaneous state transfer violates causality, which is a premise of all rational deterministic theories in natural philosophy. Like two magnets clicking together once they are in close proximity, the state transfer can occur very quickly relative to our perception and so can be considered "approximately" instantaneous, but this approximation only applies to systems that do not take time periods of this finer granularity into account. The term "instant" is often hyperbole, as it depends on your measurement interval--all that it conveys is that the event occurs within a lapse of time too small to be measured using the present apparatus.
2. I don't see why the speed of the transfer would be limited by the perceived speed of light.

Answer 3

an electron mostly acts like a wave. An atomic electron spreads out into cloud-like wave shapes called "orbitals". If you look closely at the various orbitals of an atom (for instance, the hydrogen atom), you see that they all overlap in space. Therefore, when an electron transitions from one atomic energy level to another energy level, it does not really go anywhere. It just changes shape. The orbital shapes with more fluctuations (with more highs, lows, and bends to its shape) contain more energy. In other words, when an electron transitions to a lower atomic energy level, its wave shape changes to have less kinks in it. But the electron does not "leap" anywhere. I got this answer from here and I was convinced by it.

Answer 4

(An edit for all you editors out there: I know the 'How to edit' says 'fix grammatical and spelling errors'; but before you start correcting '-sing' to '-zing', please check with a dictionary whether this is in fact British English spelling. We ain't all from the States;-)

This is a good question, certainly in the sense that it asks something we are not yet equipped to answer with much certainty; thus it provokes us to think harder. I can't give you a better answer than what knzhou has already done.

However, I think it bears repeating, that QM is very hard to understand, not least because it tries to explain observations that are made by, in a sense, throwing a lot of particles rather forcefully at something very small, from very far away, and then seeing what happens. We have no way of observing an electron moving around a nucleus, even if it does; our methods of observation force us to think in purely statistical terms about what really amounts to 'steady states': electrons smeared out over an orbital.

QM does a marvellous job, without a doubt, but I think it is reasonable to ask whether this is because it offers genuine insight into what individual particles do or are; or whether this is instead due to the use of clever statistics. In analogy, think of how we can't predict what any individual person will do over the course of a day, but we can make very good predictions of what a population is likely to do.

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Edit on 2 July 2019

The whole subject of quantum mechanics continues to be an area of contention, which to me is a sign of good health; science is at its heart about scrutinising and challenging theory. That, however, also means that we can never pronounce with absolute certainty, that we know the truth - it lies in the logical nature of the empirical method: experiments, however sophisticated, can, even in the ideal situation of perfect measurement, only ever disprove a theoretical prediction with absolute certainty. "Past Performance Is No Guarantee of Future Results" is even more true in science than in the world of investment.

So, about downvoting; I don't mind it, but please leave a comment to explain why, don't be an anonymous coward. I think those of us who take the time and make the effort to answer the sometimes very difficult questions that people ask, deserve better, for one thing. And of course, if you have an insight, why not share it?

@TCooper: I fully agree with your sentiment - people who are interested in science, are attracted exactly to the unanswered questions; they are curious and feel excited about the things that are yet to be discovered.

"thermomagnetic condensed boson": kzhou's answer is very much the orthodox, correct QM answer, but there is a lot of uncertainty about why it makes logical sense to talk about wavefunctions in the first place. It is in fact important to understand this part, not least because on the one hand, we know that QM and General Relativity aren't compatible, and on the other hand, wavefunctions as simply complex valued functions do not make good sense when space is not flat; they will at least have to be sections of the complex bundle over the space-time manifold.

Answer 5

It seems to me that the quantum state function evolve continuously as per the Schrödinger equation, but that reflects only the probability of the measurement in a state or the other. The transition itself must be as instantaneous as it can be because a photon is produced, and energy levels in quantum fields being discontinuous, it can only be instantaneous.