# Jürg Fröhlich on the deeper meaning of Quantum Mechanics

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DarMM
Gold Member
DarMM
Gold Member
What do others think of Fröhlich's argument about the inequivalence of the Schrödinger and Heisenberg pictures?

Lord Jestocost
Gold Member
Different people have different criteria for ''well-defined''and' 'clear' '. Those with loose criteria are easily satisfied, only those with strict ones see the problems.
Come on, why this undertone? Maybe, those who are “satisfied” with quantum theory have already gained deep insights and clarity.

2019 Award
Maybe, those who are “satisfied” with quantum theory have already gained deep insights and clarity.
Not only maybe, but surely.

However, only according to their own criteria for insight and clarity. Certainly not to mine.

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eloheim and Auto-Didact
stevendaryl
Staff Emeritus
Come on, why this undertone? Maybe, those who are “satisfied” with quantum theory have already gained deep insights and clarity.
No, it's obvious that that is not the case.

Auto-Didact
ftr
Although it's an interesting popular account, it doesn't really have much to do with the issue being discussed here.
It is not black and white

https://arxiv.org/pdf/1604.02589.pdf
"Quantum gravity may have as much to tell us about the foundations and interpretation of quantum mechanics as it does about gravity. The Copenhagen interpretation of quantum mechanics and Everett’s Relative State Formulation are complementary descriptions which in a sense are dual to one another. My purpose here is to discuss this duality in the light of the of ER=EPR conjecture."

2019 Award
However I do think that some research come very close to explaining it.
https://www.nature.com/articles/d41586-018-05095-z
It is not black and white
https://arxiv.org/pdf/1604.02589.pdf"Quantum gravity may have as much to tell us about the foundations and interpretation of quantum mechanics as it does about gravity. The Copenhagen interpretation of quantum mechanics and Everett’s Relative State Formulation are complementary descriptions which in a sense are dual to one another. My purpose here is to discuss this duality in the light of the of ER=EPR conjecture."
It doesn't make sense to inject into a dedicated thread random papers about foundations. If you want these to be discussed, create a new thread about them, or wait until one of them really fits an existing discussion topic.

Auto-Didact, mattt and dextercioby
dextercioby
Homework Helper
What do others think of Fröhlich's argument about the inequivalence of the Schrödinger and Heisenberg pictures?
I have always perceived that the equivalence of Schroedinger and Heisenberg pictures is nothing but a disguised form of the Born's rule: for a single Hilbert space, there is a unique unitary time evolution operator conserving probabilities or densities of probability. Does this inequivalence set forth by this paper mean there is a nonunitary time evolution?

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DarMM
DarMM
Gold Member
I have always perceived that the equivalence of Schriedinger and Heisenberg pictures is nothing but a disguised form of the Born's rule: for a single Hilbert space, there is a unique unitary time evolution operator conserving probabilities or densities of probability. Does this inequivalence set forth by this paper mean there is a nonunitary time evolution?
Still digesting his paper and looking at other papers. I'll throw up a summary soon once I'm sure I understand it.

bob012345
Gold Member
Feynman said nobody understands Quantum Mechanics. I think that's even more true today. I think it was Dirac who famously said something paraphrased as "shut up and calculate".

Lord Jestocost
2019 Award
What do others think of Fröhlich's argument about the inequivalence of the Schrödinger and Heisenberg pictures?
I haven't yet understood what Fröhlich means with his nonequivalence claim.
I have always perceived that the equivalence of Schroedinger and Heisenberg pictures is nothing but a disguised form of the Born's rule
But it has nothing to do with Born's rule, unless you identify Born's rule with the existence of the expectation mapping (which, however, would empty Born's rule from all its empirical content).
Surely it is not equivalent to Born's rule, for it says nothing about measurement.

The equivalence just says that the time dependence of ##Tr~A(t)\rho(t)## can be distributed in different ways to that of ##A## and ##\rho##.

vanhees71
DarMM
Gold Member
I haven't yet understood what Fröhlich means with his nonequivalence claim
He's basically referring to the fact that his interpretation has "constant collapse" for lack of a better word.

So Fröhlich says that at time ##t## we have the algebra of observables located times ##\geq t##. This is denoted ##\mathcal{E}_{\geq t}##. An event is a particular set of projectors, ##\{\pi_{E,t}\}##, summing to unity. An event is then said to occur at ##t## if its projectors commute with all other observables in ##\mathcal{E}_{\geq t}## under the state ##\omega##:
$$\omega\left(\left[\pi_{E},A\right]\right) = 0$$

This is meant to be a purely mathematical condition with no need for observation as a primitive. In a given state ##\omega## and given a particular time ##t## and its associated observables ##\mathcal{E}_{\geq t}## there will be such a set of projectors. Thus there is always some event that occurs. After that event has occurred one should use the state ##\omega_{E,t}## given by the conventional state reduction rule.

However imagine I am an experimenter in a lab. I have performed a measurement and updated to ##\omega_{E,t}##. Fröhlich's point is that there will then be, under a proper mathematical analysis, some event ##\{\pi_{E^\prime,t^\prime}\}## that via his condition will occur. This will then cause an update to the state ##\omega_{E^\prime,t^\prime}##. However under conventional QM the experimenter, since he has not made a measurement, continues to use ##\omega_{E,t}##. In the ETH-interpretation he has made an error by restricting the events that occur to be solely his measurement events. Thus his state is incorrect.

Fröhlich discusses why usually it is almost completely accurate. Essentially because the event that follows at ##t^\prime## (under certain assumptions about the Hamiltonian) has projectors that almost overlap with those of the event that occurred at ##t##.

This results in the ETH-interpretation having slightly different predictions from standard QM.

Operators evolve under the Heisenberg equations of motion, but states between measurements do not exactly follow Schrödinger evolution. Thus the inequivalence.

Auto-Didact
2019 Award
Operators evolve under the Heisenberg equations of motion, but states between measurements do not exactly follow Schrödinger evolution. Thus the inequivalence.
But traditionally, if operators evolve under the Heisenberg equations of motion, states remain constant.

Thus Fröhlich changes the meaning of the Heisenberg picture!?

it seems to me that, when viewed in the Schrödinger picture, Fröhlich is proposing something like the piecewise deterministic procesess (PDP) of Breuer & Petruccione referred to in my Part III. There is also old work by Jadczyk on PDP and event-enhanced quantum mechanics: https://arxiv.org/pdf/hep-th/9409189, https://arxiv.org/pdf/quant-ph/9506017, and a few more. But so far I didn't have the time to check out the precise relations to Fröhlich's setting.

DarMM
Gold Member
But traditionally, if operators evolve under the Heisenberg equations of motion, states remain constant.

Thus Fröhlich changes the meaning of the Heisenberg picture!?
Yes I would say. Operators follow the Heisenberg equations of motion, but states do not remain constant. In standard QM they remain constant except upon "collapse", so constant except at measurements. Fröhlich however has "constant collapse" so states are truly always evolving even in the Heisenberg picture.

DarMM
Gold Member
it seems to me that, when viewed in the Schrödinger picture, Fröhlich is proposing something like the piecewise deterministic procesess (PDP) of Breuer & Petruccione referred to in my Part III
There is a relation I suspect, but for Fröhlich the evolution is fundamentally stochastic/random. The state update rule is not an "effective" proscription, but literally true.

2019 Award
Fröhlich however has "constant collapse" so states are truly always evolving even in the Heisenberg picture.
Do you mean continuous collapse - at every moment in time, as in continuous measurement theory?
There is a relation I suspect, but for Fröhlich the evolution is fundamentally stochastic/random. The state update rule is not an "effective" proscription, but literally true.
The same holds in PDP, except that the times of collapse are random, not continuous (else one has a quantum diffusion process - relevant for measuring operators with continuous spectra).

DarMM
Gold Member
Do you mean continuous collapse - at every moment in time, as in continuous measurement theory?
I believe so. He discusses only the case where time is discrete. There he has collapse at each discrete moment of time. The natural extension to continuous time is continuous collapse.

The same holds in PDP, except that the times of collapse are random, not continuous (else one has a quantum diffusion process - relevant for measuring operators with continuous spectra).
You're right of course. I had in mind your Thermal version view of such cases when contrasting it with Fröhlich. PDP is very similar to Fröhlich as you said.

DarMM
Gold Member
I should say as far as I can tell Fröhlich doesn't consider the quantum state to be physically real, just a method of keeping track of which events might occur. So the collapse processes above are physical in the sense of specifying the occurrence of an event, but not the reduction of a physical state vector.

So in ETH the world is composed of a sequence of randomly realized events. Events from non-commuting projector sets are not comparable. A history only involves a subset of possible quantities. This is the typical counterfactual indefiniteness that distinguishes QM from a classical stochastic process, e.g. there will be an event where a value for ##S_x## is realized, not the whole spin vector ##\left(S_x, S_y, S_z\right)##.

In an Bell-Aspect experiment one cannot compare different measurement pair choices for Alice and Bob since they occur in different histories.

So a Copenhagen variant very similar to Decoherent histories and the "Event"-interpretation of Haag @bhobba . Again I'm not really sure there is a true difference between Fröhlich, Haag and Bub here or just a difference of formulation.

vanhees71
Gold Member
2019 Award
I've not read all the recent postings, but some of the proponents of the claim that there's a measurement problem, raised two issues:

(a) how do measurement outcomes occur?
(b) the need to prove Born's rule.

I don't see any issues with both points since a measurement result comes about through interactions of the measured system with the measurement device. QT gives an adaquate and accurate description about all so far reproducibly observations.

Concerning (b), I consider the Born rule as one of the fundamental postulates of QT, that can not be derived from the other postulates. I think Englert is right!

bhobba
DarMM
Gold Member
I don't see any issues with both points since a measurement result comes about through interactions of the measured system with the measurement device. QT gives an adaquate and accurate description about all so far reproducibly observations.
I think people's issues is that it doesn't tell you which result will occur. There's also the unusual feature that only the observable you look at "occurs", e.g. for Spin in the x-direction only a ##S_x## outcome occurs, so quantum observables are as much a property of the device as the quantum system itself.

I think you are fine with this because you think there isn't anything but the statistics, i.e. you can't know which occurs because that's what the world is like.

stevendaryl
Staff Emeritus
I consider the rules of the minimal interpretation to be outright contradictory. If something is a contradiction, it can't be correct. On the one hand, one of the rules of the minimal interpretation says that a measurement always results in an eigenvalue of the operator corresponding to the observable being measured. That means that after a measurement, the device is in a definite "pointer state". On the other hand, if you treat the measuring device (plus observer plus the environment plus whatever else is involved) as a quantum mechanical system that evolves under unitary evolution, then unless the observable being measured initially has a definite value, then after the measurement, the measuring device (plus observer, etc) will NOT be in a definite pointer state.

This is just a contradiction. Of course, you can make the use of the quantum formalism consistent by just imposing an ad hoc distinction between measurement devices (or more generally, macroscopic systems) and microscopic systems. But that's not a physical theory, that's a rule of thumb.

eloheim, Auto-Didact, dextercioby and 1 other person
I've not read all the recent postings, but some of the proponents of the claim that there's a measurement problem, raised two issues:

(a) how do measurement outcomes occur?
(b) the need to prove Born's rule.

I don't see any issues with both points since a measurement result comes about through interactions of the measured system with the measurement device. QT gives an adaquate and accurate description about all so far reproducibly observations.

Concerning (b), I consider the Born rule as one of the fundamental postulates of QT, that can not be derived from the other postulates. I think Englert is right!
I agree except perhaps one should say "... a measurement result comes about through non-unitary interactions..." . It is non-unitary-ness that seems to give people a problem.

DarMM
Gold Member
That has never been demonstrated.

Your contradiction equally applies to Spekkens model where the device is measuring a system and obtains an outcome ##a## from a set ##\{a,b\}##, but an observer isolated from the device models it as being in a superposition. However one can explicitly see that there isn't a contradiction in Spekkens model.

dextercioby and vanhees71
vanhees71
Gold Member
2019 Award
I consider the rules of the minimal interpretation to be outright contradictory. If something is a contradiction, it can't be correct. On the one hand, one of the rules of the minimal interpretation says that a measurement always results in an eigenvalue of the operator corresponding to the observable being measured. That means that after a measurement, the device is in a definite "pointer state". On the other hand, if you treat the measuring device (plus observer plus the environment plus whatever else is involved) as a quantum mechanical system that evolves under unitary evolution, then unless the observable being measured initially has a definite value, then after the measurement, the measuring device (plus observer, etc) will NOT be in a definite pointer state.

This is just a contradiction. Of course, you can make the use of the quantum formalism consistent by just imposing an ad hoc distinction between measurement devices (or more generally, macroscopic systems) and microscopic systems. But that's not a physical theory, that's a rule of thumb.
In other words your problem is that you don't want to accept the probabilistic nature of the quantum description. That's not a problem of QT, but just prejudice about how nature should be. Science, however, tells us, how nature behave, and the conclusion of the gain of knowledge summarized accurately in the QT-formalism, which lead to correct predictions and descriptions of all objective phenomena observed so far, is that nature is intrinsically probabilistic, i.e. there's no way to prepare a system such that all observables take determined values. Thus, there's no contradiction in the two postulates you claim. To the contrary, indeterminism in the above precise sense of QT makes it a consistent and accurate description of all our experience so far!

vanhees71