Quantum Jumps: Do they really exist?

[fzero]

There is no reason to distinguish between cases 1 and 2, since the fundamental physics is the same. I already explained that the description of a first-order process, like spontaneous emission from a single atom, via QED leads to the conclusion that the process occurs instantaneously.

Whatever QM interpretation that one wants to apply to the actual measurement problem is not really something that I'm interested in. The way that I would think of the process is as before. If at time t_1 we measure an H-atom in the state 2p and at time t_2 we find it in the 1s state, we know that the decay happened at some time in between and it was instantaneous. The theory does not allow for any other description of the first-order process.

Now if you want to take into account higher-order processes, which would also include the microscopic description of the effects of the environment, things get a little bit more complicated, both technically and otherwise. For example, there will be processes where the 2p state absorbs a photon from the environment to move to an even higher excited state, say 3s. This is another process that occurs instantaneously, but the 3s state might exist for a finite amount of time before it emits another photon.

So higher-order processes can include new states that live for an indeterminate amount of time, but since there are no intermediate states between 2p and 1s, the first-order process must be a jump.

Now, the comments you make about the interpretation of half-life seem confusing. For example, "Individual atoms of U-238 should always decay with the same mean rate, whether (passively) measured/observed or not." Individual atoms or nuclei do not "decay with the mean rate," rather, the mean rate is directly related to the probability to measure that the state has decayed, as I used in https://www.physicsforums.com/showpost.php?p=3828463&postcount=27. Perhaps the linear combination of states is what you were referring to? That linear combination is what we choose to explain our ignorance of the actual state of the system between measurements. Experimentally, the mean rate is not obvious from a single measurement, but must be determined from studying a large sample. Theoretically, we can compute the mean rate by computing quantum amplitudes.

 

[Jano L.]

There is no reason to distinguish between cases 1 and 2, since the fundamental physics is the same.

The times of both processes are very different.

The first process: the atom is slowly decaying, it can take billions of years, but will decay eventually. Individual atoms have different times of decay and we cannot predict it now.

The second process begins when the atom has decayed into some other particles and these enter the detector and trigger the detection process in it. This is very fast, <milliseconds or so.

It is most natural to think that these are two different processes. If the Copenhagen explanation of the formalism does not distinguish them, I think so much worse for the tenability of that explanation.

The way that I would think of the process is as before. If at time t1 we measure an H-atom in the state 2p and at time t2 we find it in the 1s state, we know that the decay happened at some time in between and it was instantaneous.

I do not think one can measure which electronic state the atom is in. The 1s, 2p symbols only refer to terms of optical spectra, or eigenfunctions of Schroedinger's equation, but not to results of measurement of the state. Such measurement could be done by measuring X-rays scattered by the electron in the atom, but this would necessarily perturb the atom so much that its state would be far away from what it is in natural conditions (it would ionize).

I may be mistaken; do you have some reference to a paper which deals with direct measurement of electronic states?

What we can do is to resolve light radiated/scattered by the atoms. If one measure this, many features of the spectra (splitting in el./mag. field, sharpness of lines) is well explained by Schroedinger's wave mechanics, with no need to introduce instantaneous Copenhagen jumps.
There are transitions, but there is solid evidence that they are gradual - coherence time of 1s-2p line is 1 ns, interference and dispersion phenomena, ...

But let us suppose the electron really have jumped instantaneously from 2p to 1s state and radiated photon of frequency f = \frac{E_{2p} - E_{1s}}{h}.

Now what the frequency of the photon means if the process was instantaneous ?!

The frequency of radiation can only be defined within 1 ns coherence time if the wave has at least this extent. So the radiation has to be produced at least for 1 ns.

How can you explain the coherence of the radiated wave and preserve instantaneity of the transition? This was and is a serious problem for theory with instantaneous jumps.

 

[Demystifier]

But the length of this second process (of measuring and "realizing" whether the atom has decayed or survived in its initial state), seems irrelevant for the actual physical process going on with the atom.

This is very very deeply wrong. The best counterexample is the quantum Zeno effect, due to which a frequent observation of decay may significantly slow down the decay process, or even completely stop. I think THIS is the crucial thing to concentrate on. See e.g. the literature on decoherence I have already mentioned in one of the previous posts.

The measurement deeply influences quantum processes and properties, which is the fact known also as quantum contextuality, with dramatic consequences e.g. in spin measurements and Bell-inequality violations. E.g., measurement of spin in x-direction drastically influences spin in z-direction.

Even if you never heard about things such as quantum Zeno, contextuality, spin measurements in different directions and Bell-inequality violations (which you should inform yourself about if you didn't already), you must have heard about wave-particle duality. The quantum system behaves very differently when you measure its wave properties from the behavior when you measure its particle properties. For example, if you measure the particle position there is no interference, and vice versa.

In short, the behavior of quantum systems depends very much on the measurement you perform, which is probably the main conceptual difference between quantum and classical mechanics and the source of most (if not all) quantum weirdness.

 

[Demystifier]

Also, there is no reason to think that it is influenced by the presence of the detector. Individual atoms of U-238 should always decay with the same mean rate, whether (passively) measured/observed or not.

Quantum Zeno effect is not only a reason, but a proof that detector may influence decay a lot.

2) The second process is the change of our knowledge on the state of _one_ particular radioactive atom (decayed or not decayed) when trapped inside of a detector.

This second process also takes some time t', mainly due to the time our brain takes to process the readout from the apparatus, say, 1 millisecond or so.

Before this brain-process there is a much more important process caused by the measuring apparatus (or more precisely, the first thing that interacts strongly with the observed object) that determines how the observed object will behave.

 

[Jano L.]

This is very very deeply wrong. The best counterexample is the quantum Zeno effect, due to which a frequent observation of decay may significantly slow down the decay process, or even completely stop. I think THIS is the crucial thing to concentrate on. See e.g. the literature on decoherence I have already mentioned in one of the previous posts.

Letting atoms traverse a strong inhomogeneous magentic field surely changes their magnetic moments. It is natural that the magnet influences spins significantly.

In experimental examples of "quantum Zeno effect" Wikipedia mentions, strong perturbation of atoms by external radiation was used. No surprise the atoms changed their natural behaviour.

In case the measurement perturbs atoms significantly, I agree that the process of measurement has strong influence on the behaviour of atoms.

However, the situation with radioactive atom I was thinking about is very different. The atom sits inside the cavity, whose walls are able to detect fission products. The detector clicks when the products arrive at the wall.

There is no reason to believe that passive wall has any influence on the atom whatsoever. As far as I know, no passive observation/measurement has been reported in which the decay rate was altered. Temperature, chemical status of the atoms does not matter, the decay rate is always the same. Why should the detector, which is far away, make any difference? There is no evidence for any such effect.

Of course, if we irradiate the atom with gamma radiation, this can perturb the nucleus significantly. But this is not necessary. The detector can just wait for products to arrive.

In short, the behavior of quantum systems depends very much on the measurement you perform, which is probably the main conceptual difference between quantum and classical mechanics and the source of most (if not all) quantum weirdness.

I would say the behaviour of atoms depends on the way the measurement disturbs them. This is conceptually no different from classical mechanics.

But we can choose to not disturb the atom at all and just look how the natural process works.

There is no need to repeat the projection postulate of quantum theory whenever something is observed. Nature is far more rich than that, and physics can be too, we just have to think out of the box.

 

[lugita15]

In short, the behavior of quantum systems depends very much on the measurement you perform, which is probably the main conceptual difference between quantum and classical mechanics and the source of most (if not all) quantum weirdness.

But as a Bohmian, don't you view the contextuality of QM as nothing special or weird, just a consequence of the fact that measurement, like any other interaction, can have an effect on a system? Isn't that equally true of classical mechanics?

 

[Demystifier]

But as a Bohmian, don't you view the contextuality of QM as nothing special or weird, just a consequence of the fact that measurement, like any other interaction, can have an effect on a system? Isn't that equally true of classical mechanics?

Of course, it is natural to adopt that interpretation in which weird things do not longer look weird. But I wanted to present the known facts about QM which do not depend on interpretation. Part of the reason why people are not interested in foundations and interpretations of QM is because they are not aware how QM looks weird without better understanding of foundations and interpretations. That's why I want to increase the awareness of that weirdness.

 

[Demystifier]

In case the measurement perturbs atoms significantly, I agree that the process of measurement has strong influence on the behaviour of atoms.

That is true. But the right question is: Can we perform a measurement of atom WITHOUT strongly influencing it? The answer is that we cannot, except in a special case when the system is already in an eigenstate of the observable we want to measure.

As far as I know, no passive observation/measurement has been reported in which the decay rate was altered.

Of course it hasn't, but that is because passive measurements of microscopic isolated systems DO NOT EXIST (except in the the special case I mentioned in the sentence above).

Temperature, chemical status of the atoms does not matter, the decay rate is always the same.

It is APPROXIMATELY the same, and there is a good reason why is that so. This is because the probability of decay as a function of time is well approximated by the EXPONENTIAL law
p(t)=exp(- gamma t)
Namely, the exponential function has a special property
p(t/N)^N = p(t)
not shared by any other function. Let me explain what that means physically. If without measurement the probability of survival is given by some free-evolution function p(t), then one is interested to calculate what is the survival probability when the free evolution is disturbed N times at equal time intervals during the time t. Whenever you do the measurement to see whether the atom has decayed or not, the quantum state collapses into the either initial state or fully decayed state. Therefore, the probability of survival after N measurements during time t is p(t/N)^N. In general this is not p(t), except for the exponential law. For times much smaller than 1/gamma the exponential law is actually not a good approximation for free evolution, which is why quantum Zeno effect is effective only for such early times of decay.