# I Quantum Jumps and Schrodinger's Cat are predictable

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#### Cthugha

Exactly, we just have to read the first paragraph of the introduction of the above cited PRA paper to set the records straight:
[...]

Indeed, for a textbook treatment of "quantum jumps" (neglecting however spontaneous emission) see the famous Wigner-Weisskopf treatment of decays, nicely covered in

O. Nachtman, Elementary Particle Physics, Springer
Well, you might want to become a politician. I have rarely seen a quote taken so out of context. ;)

The relevant part is of course:
Wiseman said:
However, it was the electron shelving experiments of Itano and co-workers [10] which refocused attention on the conditional dynamics of individual atoms. Subsequent work on waiting time distributions [11,12] led to a renewal of interest in quantum jump descriptions [13]. It was shown by Carmichael [14] that quantum jumps are an implicit part of standard photodetection theory. This link between continuous quantum measurement theory and stochastic quantum evolution for the pure state of the system was considered by many other workers around the same time and subsequently [15–24]. Independently, Dalibard, Castin, and Mölmer [25] derived the same stochastic Schro¨dinger equations, driven by the need for efficient methods for numerically simulating moderately large quantum systems. This technique, called Monte Carlo wave-function simulations, has been applied to great advantage in describing the optical cooling of a fluorescent atom [26–30]. Regardless of the motivation for their use, the evolution of systems undergoing quantum jumps and other stochastic quantum processes is known widely as quantum trajectories [14].
Of course you do not need quantum jumps (apart from the meaning that the energies of the states taken on are of course discrete) to describe basic introductory textbook physics, but also of course Wigner-Weisskopf is of absolutely no use beyond weak coupling. And strong coupling /dressed states are the topic of the cited paper and also of the major part of quantum optics within the last 30 years or so. As soon as you need to take the environment seriously, you need a more sophisticated description. And the number of real working physicists working on still reproducing basic textbook physics is somewhat small...

#### f95toli

Gold Member
I agree, the concept of "quantum jumps" is very much alive and is frequency used in quantum optics; specifically to describe open systems

see e.g.

for a review

#### Heikki Tuuri

If we isolate the system the atom & the electromagnetic field around it, it is a very ordinary quantum system whose wave function evolves in a smooth way. In that sense there are no "jumps". It is just like the double well thought experiment which I brought up, but there are more variables in the wave function.

However, you can probably find mathematical descriptions where the wave function is computed as an interference pattern of various "paths". That is, you compute a path integral in the Feynman style. Maybe in those descriptions something will come up which you could call "jumps".

In the case of the double well, the slow leak of the probability amplitude to the neighboring well might have a description as a process where a particle moves over the potential wall, and you might call that a "jump". If the wall is high, we call it "tunneling".

#### vanhees71

Gold Member
Well, you might want to become a politician. I have rarely seen a quote taken so out of context. ;)

The relevant part is of course:

Of course you do not need quantum jumps (apart from the meaning that the energies of the states taken on are of course discrete) to describe basic introductory textbook physics, but also of course Wigner-Weisskopf is of absolutely no use beyond weak coupling. And strong coupling /dressed states are the topic of the cited paper and also of the major part of quantum optics within the last 30 years or so. As soon as you need to take the environment seriously, you need a more sophisticated description. And the number of real working physicists working on still reproducing basic textbook physics is somewhat small...
My only point is that according to quantum mechanics there are no discontinous jumps for the occupation probabilities. These are smooth functions of time according to quantum dynamics, and that's made very clear in the introductory paragraph of the paper, explaining clearly what's meant by "quantum jumps" in the context of modern QT. The rest of the paper deals with precisely this dynamics for their case of an "open quantum system". Of course, that's not governed by Wigner-Weisskopf approximations, but that's where you first learn on hand of a simple example that there are no instantaneous jumps in QT.

#### Cthugha

If we isolate the system the atom & the electromagnetic field around it, it is a very ordinary quantum system whose wave function evolves in a smooth way.
Well, a lot of experimentalists would be very thankful if you told them how to do the isolation in practice. Coupling to an uncontrollable environment is an experimental reality. Just ignoring this by saying that one could do the isolation in practice is like optimizing a farm for point-like cows in vacuum or like saying that there is no need for thermodynamics because you can in principle perform a microscopic calculation of the behaviour of $10^{23}$ particles. Technically that is of course correct, but you do not get far with it.

My only point is that according to quantum mechanics there are no discontinous jumps for the occupation probabilities. These are smooth functions of time according to quantum dynamics, and that's made very clear in the introductory paragraph of the paper, explaining clearly what's meant by "quantum jumps" in the context of modern QT. The rest of the paper deals with precisely this dynamics for their case of an "open quantum system". Of course, that's not governed by Wigner-Weisskopf approximations, but that's where you first learn on hand of a simple example that there are no instantaneous jumps in QT.
Sure, I do not disagree with that. Unless you want to enforce a microscopic description of the measurement problem, there is nothing jump-like in QT. Here, I consider Carmichael's approach as quite nice because it allows one to avoid the measurement problem to some degree simply by taking the ensemble average and "picking" all the subensembles that are compatible with the measurement history.

#### romsofia

"The problem of quantum jumps is that quantum physicists are always jumping to conclusions."
-Matt Leifer

#### vanhees71

Gold Member
Well, a lot of experimentalists would be very thankful if you told them how to do the isolation in practice. Coupling to an uncontrollable environment is an experimental reality. Just ignoring this by saying that one could do the isolation in practice is like optimizing a farm for point-like cows in vacuum or like saying that there is no need for thermodynamics because you can in principle perform a microscopic calculation of the behaviour of $10^{23}$ particles. Technically that is of course correct, but you do not get far with it.

Sure, I do not disagree with that. Unless you want to enforce a microscopic description of the measurement problem, there is nothing jump-like in QT. Here, I consider Carmichael's approach as quite nice because it allows one to avoid the measurement problem to some degree simply by taking the ensemble average and "picking" all the subensembles that are compatible with the measurement history.
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.

#### A. Neumaier

the introduction of the collapse, which is neither needed nor physically consistent. That's why I follow the minimal statistical interpretation
Some form of collapse is necessary, for example to be able to say which state is prepared after passing a polarization filter. The minimal statistical interpretation has no rule for telling which state is prepared.

The collapse (in the general form of nonorthogonal projections related to POVMs) is also physically consistent as it correctly describes the net dynamics of an important class of open systems, including the system under discussion in this thread. There is no conflict with the unitary Schrödinger dynamics since the latter is claimed to be valid only for isolated systems, i.e., strictly speaking only for the universe as a whole. (There is no other truly isolated physical system.)

#### vanhees71

Gold Member
Which state is prepared after a polarization filter has nothing to do with collapse. It's through LOCAL interactions as described by relativistic QFT. That's utmost important in the context of entanglement and experiments at far-distant places on entangled systems (like the paradigmatic experiments with polarization-entangled photons in various setups).

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. This is the one pressing real physical problem of contemporary physics!

#### A. Neumaier

Which state is prepared after a polarization filter has nothing to do with collapse. It's through LOCAL interactions as described by relativistic QFT.
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!

#### 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):
Max Born said:
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 im 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

Gold Member
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

Gold Member
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

Gold Member
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?

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#### vanhees71

Gold Member
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

Gold Member
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

2018 Award
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

2018 Award
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

Gold Member
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

Gold Member
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.

"Quantum Jumps and Schrodinger's Cat are predictable"

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