Quantum Jumps and Schrodinger's Cat are predictable

[vanhees71]

Well, where is there a problem. They measure pretty many "quantum-jump events" in their given setup. You can do statistics using a single "artificial atom" ("quantum dot"). E.g., in the caption of Fig. 3 it's stated that it consists of about 7 Mio. "experimental realizations". If you check the theory in the supplemental material, there's nothing beyond standard QED used there to very accurately describe these findings. I see no contradiction whatsoever to the standard probabilistic interpretation, and I don't see any need of any assumption beyond this minimal interpretation to understand their findings.

 

[A. Neumaier]

Well, where is there a problem. They measure pretty many "quantum-jump events" in their given setup.

But on a single system. They can approximately tell from their measurements when this single system is in which energy eigenstate.

 

[vanhees71]

But on a single system. They can approximately tell from their measurements when this single system is in which energy eigenstate.

So, where is the problem with the standard minimal statistical interpretation? I've only glanced over the theoretical evaluation part (in the addons to the paper), but I don't see anything which is not in accordance with the standard interpretation, and this analysis explains the data.

Whether you do the repeated measurements on one and the same single electron or on always other new electrons, doesn't play a role at all. The only thing you have to do is to prepare it always in the same state and then do the same measurements under the same conditions. Instead of claiming that there's a conflict with the statistical interpretation, I'd say it's a paradigmatic example for its applicability to a real-world experiment. Also the dynamics is in accordance with modern QED rather than with some undynamical instantaneous quantum jumps. If consolidated, it's another experiment in very good accordance with standard QED/quantum optics.

 

[A. Neumaier]

Whether you do the repeated measurements on one and the same single electron or on always other new electrons, doesn't play a role at all. The only thing you have to do is to prepare it always in the same state and then do the same measurements under the same conditions.

But how is your condition realized in this experiment??

Prepared is only the initial state. It then changes through the in this case nearly continuous observation, which apparently (by the natural evidence gathered from the experimental results) collapses it to one of the energy eigenstates - different ones at different times. But your minimal interpretation has no collapse, so how do you find out about the state of this single system after each measurement? You seem to regard the state as a measure of knowledge of the observer - but the observer only knows the initial preparation and the measurement results, which show jumps between noisy observations of two energy levels. Without knowing the intermediate states, how can you assert that the system is ''prepared always in the same state''? When in fact it isn't, since one observes quantum jumps between the two possible energy eigenstates?

Thus you need to invoke much more than the minimal interpretation to interpret the result in the way it is done.

 

[vanhees71]

Where do I have to invoke more than the minimal interpretation? I don't think it makes sense to summarize the supplemental material, where everything is well explained, and of course they make very many observations on very many equally prepared systems to get the curves in Fig. 3 of the main text.

Always the "atom" is prepared in the same initial state and then they read out the population of the ground state as function of time. Everything discussed in the supplemental material is based on standard quantum mechanics. It's of course an open system, but in its description there's nothing used that's not derived beyond the usual minimal statistical interpretation. To see this, it is sufficient to read just Sect. I of the supplement, particularly the caption of Fig. S2.

 

[George Jones]

I'm always highly skeptical of sensational-sounding claims on phys.org. I'm doubly skeptical when there isn't even a link to a paper (not even an arxiv preprint) in the article, which tells me that the article writer doesn't want me to look up the actual paper and find out that, while their article says "man bites dog!", the actual paper is more like "dog bites man, and now we have a more detailed model of the tooth marks".

Today is the first time that I have looked at the article, and I see that "A study announcing the discovery appears in the June 3 online edition of the journal Nature" in the phys.org article, and that a link to the Nature article appears at the bottom of the phys.org article.

Also, the article was not written by a phys.org writer; the article was supplied to phys.org by Yale University ("by Yale University" at the top, and "Provide by Yale University" at the bottom). I do think that it is valid to criticize phys.org for uncritically accepting the Yale-supplied hyperbole. This highights what is becoming a major problem: too often, university PR departments put out over-ther-top bs versions of research performed.

 

[vanhees71]

What Einstein said concerning theorists is also valid for experimentalists: don't listen to their words (or in this case those of the popular press) but look at their deeds, i.e., read the Nature article (including the very valuable supplement). What has been observed are not "quantum jumps" (which do not exist according to modern QT since 1925/26) but the continuous spontaneous and induced transitions from one energy level of a system through coupling to external perturbations.

If confirmed, it's a great step forward, i.e., away from old-fashioned instantaneous "quantum jumps" of the old Bohr-Sommerfeld model to the empirical verification of the predictions of modern quantum theory.

 

[Heikki Tuuri]

Bohr conceived of quantum jumps in 1913, and while Einstein elevated their hypothesis to the level of a quantitative rule with his AB coefficient theory, Schrödinger strongly objected to their existence. The nature and existence of quantum jumps remained a subject of controversy for seven decades until they were directly observed in a single system. Since then, quantum jumps have been observed in a variety of atomic and solid-state systems. Recently, quantum jumps have been recognized as an essential phenomenon in quantum feedback control, and in particular, for detecting and correcting decoherence-induced errors in
quantum information systems .

https://arxiv.org/abs/1803.00545

The authors definitely claim in the introduction that they have observed "quantum leaps" of popular science. As we have several times noted in this thread, quantum leaps do not exist in standard quantum mechanics. Erwin Schrödinger was right.

A. Neumaier brought up that quantum jumps and trajectories are a numerical method of quantum optics. But the authors seem to claim that the numerical method would prove the existence of quantum leaps.

I have to repeat my opinion that Nature has published a paper which is confusing terms of quantum mechanics. Nature made a mistake. The confused philosophical part of the paper should be removed and the authors should just report the experiment.

 

[vanhees71]

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 ;-)).

 

[A. Neumaier]

What Einstein said concerning theorists is also valid for experimentalists: don't listen to their words (or in this case those of the popular press) but look at their deeds

I wonder if anyone knows the source of this saying.

If you want to find out anything from the theoretical physicists about the methods they use, I advise you to stick closely to one principle: don't listen to their words, fix your attention on their deeds.

I found in several places the precise wording quoted above, but nowhere an attribution to the precise source.

By the way, adhering to Einstein's advice, I was lead to my thermal interpretation of quantum physics!

 

[A. Neumaier]

I found in several places the precise wording quoted above, but nowhere an attribution to the precise source.

Actually, a more thorough search lead me to a https://www.jstor.org/stable/pdf/184387.pdf, but it had another formulation, though with essentially the same meaning:

If you wish to learn from the theoretical physicist anything about the methods which he uses, I would give you the following piece of advice: Don't listen to his words, examine his achievements. For to the discoverer in that field, the constructions of his imagination appear so necessary and so natural that he is apt to treat them not as the creations of his thoughts but as given realities.

Maybe he said similar things at multiple occasions...

 

[Cthugha]

If confirmed, it's a great step forward, i.e., away from old-fashioned instantaneous "quantum jumps" of the old Bohr-Sommerfeld model to the empirical verification of the predictions of modern quantum theory.

I kind of disagree and this is the thing, which disappoints me a bit about this paper. If you have a look at the derivation of the dynamics of the "quantum jump", especially equations 11 and 14 in the SOM, you will find that the timescale of this continuous evolution is given by the effective transition time scale t_{mid}, which is given by t_{mid}=(\frac{\Omega_{BG}^2}{2\gamma_B})^{-1} \ln{(1+\frac{\Omega_{BG}^2}{\gamma_B \Omega_{DG}})},
where \Omega_{BG} and \Omega_{DG} are the Rabi frequencies of the drives for the bright and dark state transitions, respectively and \gamma_B is the loss rate of the bright state, which is proportional to its spectral width.
Now the interesting thing is that the dominant time scale for the "quantum jump" to the dark state is not given by the Rabi frequency for the driving field that couples the ground and the dark state, but the one that couples the ground and the bright state. This is explained quite easily by the authors by pointing out that this is the quantity that determines the mean time between clicks for the weak measurement in the bright channel. This mean time between clicks is given by:
t_{click}=(\frac{\Omega_{BG}^2}{\gamma_B})^{-1}.
So in fact, the time scale of the transition is given by:
t_{mid}=\frac{t_{click}}{2} \ln{(1+\frac{1}{t_{click} \Omega_{DG}})}.
Now, \Omega_{DG} is of course just the inverse of the time t_{dark} a dark state Rabi cycle takes (up to some prefactors of 2 pi or 2 - I did not follow the normalization), so the whole time scale of the "quantum jump" is something like:
t_{mid}=\frac{t_{click}}{2} \ln{(1+\frac{t_{dark}}{t_{click}})}.
In other words: You can and will change this time scale just by driving the bright transition more strongly because you expect more counts in this case. Basically, this just gives you the probability to be in the dark state after so-and-so-many non-counting events on the bright state transition, which is just a function of how many absent counts you need to get some level of certainty and how long it takes to get to this absent count level. It is not directly related to anything concerning the dark state transition. If you just ramp up the driving field of the bright state transition, so that t_{click} becomes short, you can get arbitrarily close to an instantaneous jump again.

 

[vanhees71]

I don't think that you can come to an instantaneous jump again. There's nothing instantaneous in QT's time evolution.

 

[Cthugha]

In practice: Yes, I agree.
The bare time evolution of the probability amplitude for dark state occupation happens on a slower time scale, anyway. So there should be some point at which a finite time scale of the "quantum jump" (or coupling to the environment or decoherence or whatever you want to call it) emerges. In fact, I would have loved to see a measurement series that just investigates this "mid-time" for several Rabi frequencies of the bright transition. I wonder why the authors did not do that. Either it would have spoiled the mass appeal slightly (because the fact that the timescale is actually not that meaningful physically is a bit downplayed in the manuscript), or non-linearities become non-negligible at high pump powers or at some point the electronics would become too slow to follow the experiment adequately. Still, it would be interesting to perform such an experiment.

 

[vanhees71]

I guess it's also technically pretty difficult to cover all the possible time scales you discuss. I find it remarkable that one can nowadays start to resolve such quantum dynamics at all.

In some cases "timing" is even difficult to grasp theoretically. One example is the "tunnel time", i.e., the time it takes for a particle to tunnel through a potential barrier. I'm not sure whether this has been defined convincingly yet. At least it's a decade-long problem. Today, there's however some progress with the advent of "attosecond laser pules" to make it possible to measure such processes with the necessary time resolution. Of course the measured "tunnel times" also have to be analyzed taking into account the full experimental setup, then also providing the "correct" definition of "tunnel times", as measured by the specific experiment.

 

[A. Neumaier]

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

Why then did Schrödinger write in 1952 a paper with the title ''https://www.jstor.org/stable/pdf/685552.pdf" ?
Why then did accomplished quantum physicists again and again refer to quantum jumps?

the reaction shall not involve a jump in the quantum state of the electrons [Footnote 2: The possibility of chemical reactions without quantum jumps in the state of the electronic system has been first realized by F. London]

(Wigner, Calculation of the Rate of Elementary Association Reactions, 1937)

according to quantum mechanics we need, for a complete description of the universe, not only the laws of motion and the initial conditions, but also information about which quantum jump occurs in each case when a quantum jump does occur. The latter information must be included, together with the initial conditions, in that part of the description of the universe outside mathematical theory. [...] Quantum mechanics provides an escape from the difficulty. It enables us to ascribe the complexity to the quantum jumps, lying outside the scheme of equations of motion. The quantum jumps now form the uncalculable part of natural phenomena, to replace the initial conditions of the old mechanistic view.

(Dirac, The relation between mathematics and physics, 1940)

Radiation is emitted or absorbed by a transition of the electron from one quantum state to another - by a quantum jump - the energy difference between the two states being
emitted or absorbed as a light quantum of energy $h\nu'$ [...] Radiation results only through a quantum jump from such a state of positive energy to a lower state of positive or negative energy. [...] In addition, there is the rule that, so long as the interaction of the electrons is not very large, only those quantum transitions take place for which only one of the emission electrons makes a jump—that is, only one alters its $l$ value, the alteration being in accordance with the selection rule (I, 29):
$\Delta l = \pm 1$. [...] Transitions in which teo or more electrons jump at the same time are considerably weaker but are not forbidden by any strict selection rule. [...] one electron making the quantum jump (transition between even and odd terms) . [...] Such a radiationless quantum jump was first discovered by Auger, and is called after him the Auger effect

(Herzberg, Atomic spectra and atomic structure, 1944; then the bible for spectroscopy)

That the term ''quantum jump'' does not figure everywhere in the literature is simply because a ''transition'' between energy levels - an ubiquitous term in spectroscopy and photochemistry - is just a quantum jump called by a different name. It even occurs in the modern definition of the second:

The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the Cesium 133 atom.

(http://physics.nist.gov/cuu/Units/second.html)

Thus without quantum jumps no modern high precision measurement of time!

 

[Heikki Tuuri]

A. Neumaier, I think that in an earlier message I already wrote that the probability amplitudes (complex values) of a wave function develop smoothly in time.

A simple example is a single particle in a double potential well. We prepare the particle to be in the well A. Slowly, the probability amplitude leaks to the well B beside A. We measure the system and find the particle in B.

Should we say that the particle "jumped" from A to B? That language is not used in quantum mechanics. There is no definite path of the particle. It may "tunnel" to B if the wall between A and B is high, but that word is misleading, too.

 

[vanhees71]

Well, I don't know, why Schrödinger at all wrote against the clear evidence of their own theory.

I'd also be very interested to learn, where in the measurement of time, using atomic clocks like the "cesium fontain" or even more accurate measurements with more modern quantum-optical equipment (e.g., "frequency combs") you need to invoke "quantum jumps". I've no clue!

 

[Cthugha]

A. Neumaier, I think that in an earlier message I already wrote that the probability amplitudes (complex values) of a wave function develop smoothly in time.

A simple example is a single particle in a double potential well. We prepare the particle to be in the well A. Slowly, the probability amplitude leaks to the well B beside A. We measure the system and find the particle in B.

Should we say that the particle "jumped" from A to B? That language is not used in quantum mechanics. There is no definite path of the particle. It may "tunnel" to B if the wall between A and B is high, but that word is misleading, too.

How is this even related to the topic at hand? This has absolutely nothing to do with quantum jumps or quantum trajectories (or more formal: Monte Carlo wave function methods). The scenario is a totally different one. Consider for example simple emission from a two-level system. We all know that in non-qed quantum mechanics the excited state should be stable in the absence of external fields. Now one may perturb the system, which puts it into a superposition state of the excited state and the ground state, where the probability amplitudes for occupation of these states oscillate in time. One can either do this via external fields, which yields stimulated emission or one can consider QED and the properties of the vacuum state, which yields spontaneous emission. Anyway, you recover a picture similar to the classical one. In classical physics, you get electromagnetic radiation from accelerating charges. Here you get a state with time-dependent probability amplitudes for different charge configurations which in turn couple to probability amplitudes for photon emission.
So in a nutshell, a correct description of the system will more or less be similar to a dressed state picture, where the state of the atom is necessarily entangled with the state of the light field. This also means that you do not have to do a measurement on the atom to get it into an eigenstate. Performing a measurement on the photon is sufficient. For a local experimentalist sitting next to the atom, information about the light field is usually unavailable. So he has an open system and an environment perturbing his atom, which frequently "resets" his system to one of the eigenstates. This would be an example of a quantum jump. And at more than 1000 citations (https://www.osapublishing.org/josab/abstract.cfm?uri=josab-10-3-524), this is also far from being non-mainstream. The are also some good explanations demonstrating what is not meant by quantum jumps. The introduction of this paper by Wiseman ( https://journals.aps.org/pra/abstract/10.1103/PhysRevA.60.2474 ) for example is a good read.

 

[vanhees71]

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

Wiseman et al, PRA 60, 2474 (1999)
The quantum jump, the effectively instantaneous transi-
tion of an atom from one state to another, was the first form
of nontrivial quantum dynamics to be postulated [1]. Of
course Bohr’s theory did not survive the quantum revolution
of the 1920s. In particular, the idea of jumps appeared to be
in sharp conflict with the continuity of Schro¨dinger’s wave
mechanics [2]. In the aftermath of the revolution, quantum
jumps were revived [3] with a new interpretation as state
reduction caused by measurement. But Wigner and Weis-
skopf [4] had already derived the exponential decay of spon-
taneous emission from the coupling of the atomic dipole to
the continuum of electromagnetic field modes. That is, they
did not require the hypothesis of quantum jumps. Later, more
sophisticated theoretical techniques, such as the master equa-
tion, were developed for dealing with the irreversible dynam-
ics of such open quantum systems [5-7]. In the master equa-
tion description, the atom’s state evolves smoothly and
deterministically. Perhaps as a consequence, interest in quan-
tum jumps as a way of describing of atomic dynamics faded.

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

 

[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:

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]

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.
https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.70.101
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]

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]

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]

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!