I Quantum Jumps and Schrodinger's Cat are predictable

[Cthugha]

There's nothing jumplike in the measurement problem. The only problem with some Copenhagen flavors of "interpretation" is the introduction of the collapse, which is neither needed nor physically consistent. That's why I follow the minimal statistical interpretation which, with a grain of salt, is just Copenhagen without collapse. Although I cannot be sure about this, because of Bohr's very murky style of writing intermingling always unsharp philosophy with science, this seems to be more or less Bohr's point of view.

Well, I do not disagree - at least I think so (and for the record: as an experimentalist I try to avoid discussing interpretations unless they advance to the point where they stop being mere interpretations and make predictions that can be tested experimentally or suggest a mathematical formalism that is easier to handle or results in computational speed-up).

In this field of physics people are usually interested in experiments involving conditional probabilities based on measurement outcomes of photon detection events, so there is some need to take measurements into account explicitly. If your take on this is that one should evaluate this using unitary evolution of the system, determine the probabilities for the outcomes of the first measurement, consider the unitary evolution of this system from the possible eigenstates again, determine the probabilities for the outcome of the second measurement again and so on and so forth: yes, this works. If you additionally assume that the measurement process (or decoherence or whatever you may call it) in this case is essentially a low-probability game - which means that you rather do not have a single photon interact with a single absorber in a manner that you drive the probability amplitude for absorption up to 1, but rather that you have this single photon interact with thousands of absorbers, where each of them is driven to absorption probabilities of, say, 0.03 and one of them finally "clicks": yes, this is still a fast but continuous process and you can still get the correct probabilities for this by following all the subensembles microscopically.

However, in terms of actual modeling, this approach is quite cumbersome. For open systems and a huge environment, I think it is only natural that people try to treat the environment in a more effective way and the quantum jump formalism is a natural one - treating the wavefunction instead of the density matrix saves a lot of time. Many people consider the "quantum jump" as a rather Bayesian update of our information about the system instead of being inherent. I always thought that within an open systems scenario, where one does not have access to the full information about the system, this is the closest thing to the bare minimal interpretation you can get.

 

[A. Neumaier]

I agree with the second statement, though I have still no clue, what the "universe as a whole" should be, let alone how to describe it adequately within QT.

Well, since it is only a single system, in is not covered by the statistical interpretation. This explain why you cannot describe it adequately within your interpretation framework.

With the thermal interpretation, there is no difficulty to describe it adequately, i.e., in a way matching all experiments known. For this, one doesn't have to solve all problems of quantum gravity.

 

[A. Neumaier]

"quantum jumps" (which do not exist according to modern QT since 1925/26)

From where did you get your account of history?

In his 1927 paper ''Das Adiabatenprinzip in der Quantenmechanik'', where Born derived the general rules for the scattering of a single particle that form until today the standard introduction to scattering, he writes (p.170 and p.172):

Datum scheint mir eine dringliche Aufgabe festzustellen, wie wir die mathematisch so glänzende Wellenmechanik mit der experimentell so fruchtbaren Vorstellungsweise der Quantensprünge vereinbar ist. Die Frage lautet also: In welchen Fällen lassen sich die Ergebnisse der Wellenmechanik in der Sprache der Quantensprünge interpretieren? [...]
Der Einzelprozeß, der ''Quantensprung'', ist also nicht kausal festgelegt, wohl aber die a-priori-Wahrscheinlichkeit für sein Auftreten; und zwar wird diese durch einen Integrationsprozeß der
Schrödingerschen Differentialgleichung bestimmt, der dem entsprechenden der klassischen Mechanik ganz analog ist und der zwei stationäre Zeitintervalle mit endlicher Zwischenzeit in gegenseitige Beziehung setzt. Der Sprung geht also über einen beträchtlichen Abgrund; was
während des Sprunges passiert, läßt sich schwerlich mit den Begriffen der Bohrschen Theorie beschreiben, ja vielleicht überhaupt nicht in elner Sprache, die unserem Anschanungsvermógen Bilder suggeriert.[...]
Das Quadrat $|b_{nm}|^2$ ist gemäß unserer Grundhypothese die Wahrscheinlichkeit dafür, daß das System sich nach Ablauf der Störung I am Zustand $m$ befindet.

Thus he identified - more than a year after your suggested fake history - the quantum jump with the
unpredictable outcome of a scattering experiment - a jump from being in one energy eigenstate to being in another energy eigenstate, thereby consolidating his probability interpretation!

It pays to read the originals to see what was really claimed when!

 

[vanhees71]

The effective collapse is needed for this on the level of ordinary quantum mechanics, as tested in foundational experiments. Thus it is a rule needed to be able to work with quantum mechanics in practice.

Moreover, if you give the argument from QFT in more detail, you'll see that you need a collapse argument along the way. Please justify how to do it without the collapse!

To the contrary, may I ask you to tell me, where you need a collapse? You cannot use standard QED and propose the collapse argument, because that's contradicting each other.

Formally the interaction of the electromagnetic fields with matter is given by the corresponding in-medium photon polarization (aka dielectric function). No need for any collapse ;-).

 

[vanhees71]

Well, I do not disagree - at least I think so (and for the record: as an experimentalist I try to avoid discussing interpretations unless they advance to the point where they stop being mere interpretations and make predictions that can be tested experimentally or suggest a mathematical formalism that is easier to handle or results in computational speed-up).

In this field of physics people are usually interested in experiments involving conditional probabilities based on measurement outcomes of photon detection events, so there is some need to take measurements into account explicitly. If your take on this is that one should evaluate this using unitary evolution of the system, determine the probabilities for the outcomes of the first measurement, consider the unitary evolution of this system from the possible eigenstates again, determine the probabilities for the outcome of the second measurement again and so on and so forth: yes, this works. If you additionally assume that the measurement process (or decoherence or whatever you may call it) in this case is essentially a low-probability game - which means that you rather do not have a single photon interact with a single absorber in a manner that you drive the probability amplitude for absorption up to 1, but rather that you have this single photon interact with thousands of absorbers, where each of them is driven to absorption probabilities of, say, 0.03 and one of them finally "clicks": yes, this is still a fast but continuous process and you can still get the correct probabilities for this by following all the subensembles microscopically.

However, in terms of actual modeling, this approach is quite cumbersome. For open systems and a huge environment, I think it is only natural that people try to treat the environment in a more effective way and the quantum jump formalism is a natural one - treating the wavefunction instead of the density matrix saves a lot of time. Many people consider the "quantum jump" as a rather Bayesian update of our information about the system instead of being inherent. I always thought that within an open systems scenario, where one does not have access to the full information about the system, this is the closest thing to the bare minimal interpretation you can get.

My very general point is precisely this: You don't have interpretational problems in the lab. Of course, the design of an experiment may be technically very challenging, but for this you use just quantum theory as it is used in practice, and there's no interpretational problem, which is obvious for the simple reason that the so designed experiments work as predicted. For me a physical theory has only a problem, if reproducible experiments contradict unanimously its predictions.

Of course you are right in saying that it's impossible to treat these interactions in full microscopic detail. That's where the methods of quantum statistics and corresponding coarse-graining procedures come into the game. I'm not an expert in quantum optics, but reading in some textbooks and also the one or the other research paper, I've the impression that many things simply boil down to use effective (linear or non-linear) constitutive relations to describe the electromagnetic response of the "matter" to describe lenses, beam splitters and all that and then apply it to single-photon states. Obviously this works very well, and I don't see any fundamental problem in it.

Also theoretical condensed-matter physics is a "whole industry" to find models to derive such effective phenomenological "constitutive relations", and also this is quite successful.

So from a physicist's point of view there's no fundamental problem with quantum theory, when applied to macroscopic systems and to the interaction of microscopic systems with macroscopic systems, and measurement devices are nothing else than macroscopic systems.

 

[vanhees71]

From where did you get your account of history?

In his 1927 paper ''Das Adiabatenprinzip in der Quantenmechanik'', where Born derived the general rules for the scattering of a single particle that form until today the standard introduction to scattering, he writes (p.170 and p.172):

Thus he identified - more than a year after your suggested fake history - the quantum jump with the
unpredictable outcome of a scattering experiment - a jump from being in one energy eigenstate to being in another energy eigenstate, thereby consolidating his probability interpretation!

It pays to read the originals to see what was really claimed when!

I didn't claim this in a science historical sense. Of course in the early time of modern quantum theory the probabilistic interpretation had to be formulated first. That at such early stages the full understanding was not reached is natural. The same is true for the theory of relativity. In some cases it took more than 50 years to gain the correct understanding (e.g., for thermodynamics and the transformation properties of the thermodynamical quantities).

Nevertheless I've also read some of these old papers, and there already the full theory is present, and there's simply nothing like quantum jumps. It's all described by partial differential equations, where nothing jumps. Already writing down a differential equation for the time evolution implies that there are no jumps. I have to read the specific paper you quote from, but of course born talks about "quantum jumps", because that was the common Bohr theory, and of course the successes of the Bohr theory had to be also consolidated in the new theory.

 

[A. Neumaier]

To the contrary, may I ask you to tell me, where you need a collapse? You cannot use standard QED and propose the collapse argument, because that's contradicting each other.

Formally the interaction of the electromagnetic fields with matter is given by the corresponding in-medium photon polarization (aka dielectric function). No need for any collapse ;-).

In-medium photon polarization does not tell what happens to a single photon. It gives a finite-time description of fields only.

 

[A. Neumaier]

Already writing down a differential equation for the time evolution implies that there are no jumps.

Well, the jump of a person over an obstacle is also described by a differential equation. Nevertheless it is a jump. That a jump takes time is obvious.

Born talks about "quantum jumps", because that was the common Bohr theory

And why does Herzberg 20 years later (see #46) still talk about quantum jumps as synonymous with electronic transitions?

 

[vanhees71]

In-medium photon polarization does not tell what happens to a single photon. It gives a finite-time description of fields only.

It gives an accurate description of what happens to the single photons used all the time in the quantum opticians' labs. As far as I can see, all the phantastic results can be understood by an effective theory describing the single-photon matter interaction by (even quite standard) constitutive laws like indices of refraction etc. Of course you also need some "non-linear optics" due to strong laser fields and to understand parametric fluorescence (parametric downconversion), which is the most important technique to provide stable and efficient sources of polarization (as well as momentum) entangled photon pairs.

 

[vanhees71]

Well, the jump of a person over an obstacle is also described by a differential equation. Nevertheless it is a jump. That a jump takes time is obvious.

And why does Herzberg 20 years later (see #46) still talk about quantum jumps as synonymous with electronic transitions?

It's, because physicists just use their jargon. It's very clear what they mean, but only among physicists. One has to read the papers to understand what's really meant, when physicists write about "quantum jumps", "wave particle dualism", and all that jargon from the short era of "old quantum mechanics", which was obsolete only 25 years after its discovery by Planck and Einstein.

Given, how long Aristotelian physics survived, that's however not that bad a record to getting the facts straight. Nevertheless the use of these outdated notions by physicists even in scientific papers and (even worse) introductory textbooks is indeed a bad habit, but what can you do...

Another example is the claim by almost all HEP physicists that the Higgs mechanism is some spontaneous symmetry breaking. I'm pretty sure that a majority of these people know that this is self-contradicting due to Elitzur's theorem, but it seems very hard to convince people just to call it "Higgsing a local gauge symmetry" than to call it "spontaneous breaking of local gauge symmetry". As I said, it's a bad habit...

 

[Demystifier]

Well, this is often the case with Nature papers. I find this disturbing too! The only point is that if you read the text, it becomes clear that the abstract and introduction is just "popular-science gibberish", and in the rest of the paper the science usually gets correctly stated. That's the difference to many popular-science articles, where often you don't even understand the science, if you are an expert in the field ;-)).

I think Nature has policy that all their readers (biologists etc.) can understand abstracts and introductions of all their papers. That, I believe, is where the pop-science gibberish comes from.

 

[Demystifier]

To the contrary, may I ask you to tell me, where you need a collapse? You cannot use standard QED and propose the collapse argument, because that's contradicting each other.

Standard QED can be expressed as a claim that the state $|\psi(t)\rangle$ evolves as $e^{-iH_{QED}t}|\psi(0)\rangle$ where $H_{QED}$ is the local QED Hamiltonian, except when a measurement is performed in which case $|\psi(t)\rangle$ collapses. In this form there is no logical contradiction between collapse and locality of $H_{QED}$. The problem is that such a formulation is ambiguous because it is not clear what exactly is a measurement and what isn't, but you would probably agree that it is only a philosophical problem because in practice one always knows what is a measurement and what isn't.

Of course, it doesn't mean that collapse is necessary. But if you want quantum theory without the collapse, you need either many worlds or additional variables. In particular, the minimal statistical ensemble interpretation is a theory in which the additional variables are implicit but one refuses to talk about them explicitly. (One refuses to talk about the additional variables because one cannot say much about them with certainty without introducing some philosophy in the form of additional hypotheses that cannot be directly tested in experiments). Bohmian mechanics can be thought of as an extension of the minimal statistical ensemble interpretation, in which one risks his reputation of a serious scientist by deciding to talk about the additional variables explicitly.

 

[A. Neumaier]

the use of these outdated notions by physicists even in scientific papers and (even worse) introductory textbooks is indeed a bad habit, but what can you do...

The term ''quantum jump'' is used as a standard, well-defined in quantum optics in a very appropriate way, even in very highly cited technical work. The usage of the term has steadily grown a lot since Herzberg 1944: A google scholar search for ''quantum jump" in quotation marks give 173 papers up to 1960, growing in the following decades 1961-1970 to 547, 1971-1980 to 1880, then to 2320, 3240, 5950, and 2011-2019 to 6730.

But though not working in the field you feel qualified to decree what is outdated. When did the notion become outdated, and according to which criteria?

 

[vanhees71]

Standard QED can be expressed as a claim that the state $|\psi(t)\rangle$ evolves as $e^{-iH_{QED}t}|\psi(0)\rangle$ where $H_{QED}$ is the local QED Hamiltonian, except when a measurement is performed in which case $|\psi(t)\rangle$ collapses. In this form there is no logical contradiction between collapse and locality of $H_{QED}$. The problem is that such a formulation is ambiguous because it is not clear what exactly is a measurement and what isn't, but you would probably agree that it is only a philosophical problem because in practice one always knows what is a measurement and what isn't.

Of course, it doesn't mean that collapse is necessary. But if you want quantum theory without the collapse, you need either many worlds or additional variables. In particular, the minimal statistical ensemble interpretation is a theory in which the additional variables are implicit but one refuses to talk about them explicitly. (One refuses to talk about the additional variables because one cannot say much about them with certainty without introducing some philosophy in the form of additional hypotheses that cannot be directly tested in experiments). Bohmian mechanics can be thought of as an extension of the minimal statistical ensemble interpretation, in which one risks his reputation of a serious scientist by deciding to talk about the additional variables explicitly.

That's my very point! Collapse proponents claim that you need to envoke some mysterious event when a measurement is made which is outside the dynamics of the very theory you try to interpret. That makes no sense since after all measurement apparati are made of usual matter and thus function according to the general physical laws as any other piece of matter. It doesn't make sense to claim that only because something is measured the interaction between the measurement apparatus and the measured object must be described by some esoteric law outside the general physical laws.

In practice, however, measurement apparati are constructed by using the general physical laws, and the observational fact that they function as predicted is proof enough that the general physical laws are applicable to measuremente devices as to any other piece of matter.

 

[vanhees71]

The term ''quantum jump'' is used as a standard, well-defined in quantum optics in a very appropriate way, even in very highly cited technical work. The usage of the term has steadily grown a lot since Herzberg 1944: A google scholar search for ''quantum jump" in quotation marks give 173 papers up to 1960, growing in the following decades 1961-1970 to 547, 1971-1980 to 1880, then to 2320, 3240, 5950, and 2011-2019 to 6730.

But though not working in the field you feel qualified to decree what is outdated. When did the notion become outdated, and according to which criteria?

Sigh. As I said, it's very clear in which sense the notion of "quantum jump" is meant. It's NOT the outdated view a la Bohr within "old quantum mechanics". It's the transition between energy eigenstates of some Hamiltonian due to perturbation. E.g., the usual energy eigenstates of the hydrogen atom are calculated leaving out terms of the full QED Lagrangian. As soon as you take the corresponding radiative corrections into account, you get spontaneous emission and thus quantum jumps from excited states to lower states. This is, because the approximate energy eigenstates are not energy eigenstates of the full Hamiltonian, and the spontaneous emission of a photon in that case is not a quantum jump of "old quantum mechanics" but a dynamical process as any other in QED, and for sure it's not instantaneous.

Aside from this, only that some wording is frequently used is not necessarily a hint that this might be good practice didactics wise.

 

[A. Neumaier]

Sigh. As I said, it's very clear in which sense the notion of "quantum jump" is meant. It's NOT the outdated view a la Bohr within "old quantum mechanics". It's the transition between energy eigenstates of some Hamiltonian due to perturbation.

Yes, and everybody in this thread except you understood it in this way. You alone ranted against the name. You want to reserve the name quantum jump for Bohr's old understanding, but others find the term far too descriptive to put it permanently to rest.

the spontaneous emission of a photon in that case is not a quantum jump of "old quantum mechanics" but a dynamical process as any other in QED, and for sure it's not instantaneous.

This non-instantaneous dynamical process is called in modern quantum optics (and already long ago) a quantum jump. (As any jump in real life it takes time, but can often be idealized as being instantaneous.)

In quantum mechanics (which can be used without invoking QED), the quantum jump is represented by a collapse of the state (another very common term that you decree to be taboo) when a small quantum system passes a filter where it undergoes scattering, or when a single atom is manipulated in an ion trap.

If you would stop fighting for your ideosyncratic restriction of this common terminology in the scientific literature on quantum mechanics, some of the repetitive overhead in the foundational discussions would go away.

 

[vanhees71]

This socalled "collapse" is also a dynamical process, not a quantum jump and nothing that's outside of the dynamics of QT.

Of course, in non-relativistic QM you can enwoke instantaneous processes as an "explanation" without being in conflict with causality, but you cannot do so within relativistic local microcausal QT, because that would be a contraction.

I think it's very important to emphasize this point, and if it comes to debates on the foundations, the use of clear and unambiguous language is utmost important. That's why in my opinion one should not use some of the (in my opinion unfortunate) standard notions in the scientific literature (among them "quantum jumps", "collapse"). Even worse are philosophical notions like "realism"...

 

[A. Neumaier]

This socalled "collapse" is also a dynamical process, not a quantum jump and nothing that's outside of the dynamics of QT.

Of course. But it is a dynamical process of QED, and must therefore be postulated explicitly in simple quantum mechanics for nonexperts.

That the collapse cannot be instantaneous follows already from the fact that performing a measurement or passing a filter takes time, and was well-known very early in the discussion of foundations. For example, in his 1932 book, von Neumann writes:

we have repeatedly shown that a measurement [...] must be instantaneous, i.e., must be carried through in so short a time that the change [...] is not yet noticeable

He makes clear that instantaneous is just an idealization for ''very short time''.

Of course, in non-relativistic QM you can invoke instantaneous processes as an "explanation" without being in conflict with causality, but you cannot do so within relativistic local microcausal QT, because that would be a contradiction.

So what? In relativistic local microcausal QT you can not even invoke Born's rule - since it implies positive probabilities of a system prepared locally for being observed one second later light years away. See Hegerfeldt's paper
Instantaneous spreading and Einstein causality in quantum theory,
Annalen der Physik 7 (1998), 716--725.

 

[vanhees71]

Indeed, spontaneous emission is one of the (amazingly few) things you cannot make plausible in the semiclassical interpretation. Everything else you can, e.g., putting the hydrogen atom in a weak classical em. radiation field (e.g., a plane wave solution) and discuss the corresponding absorption and induced-emission "quantum jumps" via (first-order) time-dependent perturbation theory (usually in the dipole approximation, leading to the usual well-known selection rules for em. transitions). From this calculation you see very well that you get the literal quantum jump only in an idealizing approximation. Otherwise the occupation probabilities for the hydrogen eigenstates turn out to be smooth functions of time (oscillatory in this case).

 

[Demystifier]

That's my very point!

So do you agree, as I argued in the post, that the minimal statistical ensemble interpretation is a theory in which additional variables are implicit?