Errors in Ballentine (QM Textbook)?

[vanhees71]

No, standard (orthodox) quantum mechanics is about proving locality, whatever it takes. Sometimes it takes cause and effect, sometimes it takes denying cause and effect, sometimes it takes objective reality, sometimes it takes denying objective reality.

This confusion is by leaving the minimal physical meaning into the realm of vague philosophical speculation

 

[A. Neumaier]

Quantum mechanics is not about cause and effect. It is only about predicting the probabilities of measurement outcomes.

But even measurements respect causality. You cannot measure an effect before it was caused.

 

[vanhees71]

And of course, as any physical dynamical theory also QT must be causal. If nature weren't describable by causal laws, there'd be no natural sciences to begin with!

 

[atyy]

Yes, but assuming a measurement causes a collapse, i.e., a change of the state, implies a causal influence of the measurement on the state, and that's the problem particularly in this context.

No it does not.

It's contradicting the very assumptions you make about the dynamics of the system (microcausality condition), which by construction cannot violate causality, i.e., space-like separated events cannot be causally connected.

No it does not. Microcausality means that one cannot information faster than light. Collapse does not allow information to be sent faster than light, so it is consistent with microcausality.

 

[atyy]

But even measurements respect causality. You cannot measure an effect before it was caused.

We can use terminology in which we accept some notion of causality, but reject another form. So to use the terminology of Wiseman and Cavalcanti, we accept relativistic causality and agent causation, but reject Reichenbach's principle.
https://arxiv.org/abs/1503.06413 (Fig. 5, Operationalist Version)

When vanhees71 is talking about collapse as a cause, he is using it in the sense of (for example), collapse explaining the Bell correlations in the sense of Reichenbach's principle.

 

[vanhees71]

All I'm saying is that there is no general rule, i.e., no general postulate, to say which state a quantum system is in when doing a measurement. One has to analyze the specific experiment for this.

What's also clear is that a naive collapse assumption in the context of far-distant experiments on an entangled system (e.g., two entangled photons measured at far distant positions) with measurement events that are space-like separated, doesn't make sense and contradicts the fundamental property of microcausality which excludes the possibility that the observed correlations of the outcomes at the far distant places are due to a causal connection between these far-distant measurements.

My solution is trivial: We have prepared the entangled state, and thus the observed correlation is already there from the very beginning. Though the single-photon polarizations are totally indetermined in such an entangled state, they are strongly correlated, no matter how far away the photon measurements, but it's a correlation due to the state preparation in the beginning and not mutually caused by the two measurments made. There's thus no need for a collapse in analyzing this experiment.

 

[PeterDonis]

According to local relativistic QFT (in this case particularly QED) describes all findings correctly. This implies that there can be no causal effect between measurement events that are spacelike separated (that's a mathematical statement!).

No, it doesn't; "no causal effect" is not correct because there is no rigorous definition of "causal effect" in QFT. What QFT does say rigorously is that measurements at spacelike separated events must commute--the results must not depend on the order in which the measurements are made.

You can, of course, define "no causal effect" to mean "the measurements commute"; but then you are just inviting argument about your definition of "causal effect".

 

[PeterDonis]

a naive collapse assumption in the context of far-distant experiments on an entangled system (e.g., two entangled photons measured at far distant positions) with measurement events that are space-like separated, doesn't make sense and contradicts the fundamental property of microcausality

What, mathematically, is "the fundamental property of microcausality"? Does it just refer to the fact that spacelike separated measurements must commute? Or something else?

 

[Demystifier]

We have prepared the entangled state, and thus the observed correlation is already there from the very beginning.

This statement doesn't make sense because it doesn't say - correlation of what? In experiments we observe correlations of measurement outcomes, but certainly measurement outcomes do not exist from the very beginning. So if there is something which is correlated from the beginning, and if that something can be described by math,
then various Bell-like theorems (many of which do not assume determinism, contrary to what you repeat over and over again) show that measured correlations cannot be explained by correlations of something from the very beginning. Of course, you refuse such theorems because they introduce a mathematical symbol for that something (e.g. $\lambda$) which is not a part of the standard QM formalism. You want to use just standard QM and nothing else. Hence you are confident with saying "correlation", but not confident with saying "correlation of what". But as long as you refuse to say what is correlated from the beginning, for many of us your statement quoted above does not make sense.

 

[A. Neumaier]

What, mathematically, is "the fundamental property of microcausality"? Does it just refer to the fact that spacelike separated measurements must commute? Or something else?

Measurement is not a notion of QFT. Microcausality says by definition that field operators commute or anticommute at spacelike pairs of arguments. This implies (and is indeed equivalent to) the statement that arbitrary observables with spacelike separated support commute.

 

[bhobba]

I have read the thread, and since Ballentine is my 'Bible' on QM I believe I can make some comments.

Ballentine has a few errors, but so do many textbooks. The errors are the type you can spot with a bit of thought and in doing so actually helps in your understanding. For example he makes the mistake of in Copenhagen thinking the only version is one in which the state is real and an instantaneous collapse violates relativity. Of course that is not the case - the state can simply be something that helps in calculating things. The huge advantage of the book IMHO is he only states two actual axioms (the second - he calls the Born Rule) being at least partially derivable from the first via Gleason (which strangely he doesn't mention). There are of course more rules than just 2 but he introduces them in such a way they seem natural. That way we see the fundamental assumption of QM is Axiom 1 about observables and eigenvalues. The Born Rule is automatically true if we make a few reasonable assumptions, the main one being non-contextuality. The other is Chapter 3 which is unique in all other QM books I have read in deriving Schrodinger's Equation rather than postulating it. For me that was simply eye opening. You learn a lot from thinking about the derivation. The actual content is you notice that if you use Ehrenfest's Theorem you get the classical Hamiltonian equation so you understand why the momentum and energy operators are defined the way they are. It lies at the heart of QM how a classical system is quantized. This derivation is the reason we do it by replacing classical variables with operators - usually the momentum, position and energy operators. But we see there is an ambiguity in doing it because the operators may not commute so what order are they in? However as Ballentine comments it does not seem to cause problems in practice.

Yes it is advanced - I would study Modern Quantum Mechanics by Sakurai first, and Susskind before that (I just love Susskind's books). But if you do study it, and think about it, you will have a very good understanding of QM.

Thanks
Bill

 

[bhobba]

Measurement is not a notion of QFT.

I agree. But since QM is a limiting case of QM how does it emerge? Or is it an actual limiting case?

Thanks
Bill

 

[PeterDonis]

Measurement is not a notion of QFT. Microcausality says by definition that field operators commute or anticommute at spacelike pairs of arguments. This implies (and is indeed equivalent to) the statement that arbitrary observables with spacelike separated support commute.

Yes, agreed, this is a better way of saying what I was trying to say.

 

[atyy]

Here is a paper that includes discussion of state reduction in the context of AQFT.
https://arxiv.org/abs/1810.06512
https://link.springer.com/article/10.1007/s00220-020-03800-6
Quantum fields and local measurements
Christopher J. Fewster, Rainer Verch

"(The term ‘post-selected’ is used in various different ways in the literature – the precise meaning we have in mind, which amounts to updating the state based on the measurement outcome, will be spelled out in detail.)"

State reduction is given in Eq. 3.20.

 

[vanhees71]

No, it doesn't; "no causal effect" is not correct because there is no rigorous definition of "causal effect" in QFT. What QFT does say rigorously is that measurements at spacelike separated events must commute--the results must not depend on the order in which the measurements are made.

You can, of course, define "no causal effect" to mean "the measurements commute"; but then you are just inviting argument about your definition of "causal effect".

But that's indeed what's usually understood to be "no causal effect" and that's why you impose the microcausality condition which then leads to unitarity and Poincare covariance of the S-matrix, the cluster-decomposition principle.

It's, maybe, only a sufficient but not necessary condition for a relativistic QFT to have all these desired features, but I'm not aware of any example that's not in this sense a "local/microcausal relativistic QFT".

See Weinberg, QT of fields vol. 1 for a comprehensive treatment of these issues for fields of arbitrary spin.

 

[vanhees71]

Measurement is not a notion of QFT. Microcausality says by definition that field operators commute or anticommute at spacelike pairs of arguments. This implies (and is indeed equivalent to) the statement that arbitrary observables with spacelike separated support commute.

I don't understand the first sentence. QFT as any physical theory is about the mathematical description of observable facts of nature and thus it makes observable predictions (cross sections for scattering, the blackbody spectrum, etc.). Measurement is as much a notion of QFT as it is for non-relativistic QM.

 

[PeterDonis]

that's indeed what's usually understood to be "no causal effect"

Not in the many papers in the literature that struggle with how to interpret correlations that violate the Bell inequalities. Perhaps that's not a problem for you, but it is for many.

 

[vanhees71]

It's a problem for proponents of the collapse assumption. It's no problem for proponents of the ensemble interpretation.

 

[PeterDonis]

Moderator's note: Some posts have been moved to the "Difference Between Collapse and Projection" thread in the interpretations forum.

 

[atyy]

No, you need to take a partial trace and describe the evolution by some master equation. That can be FAPP a kind of "state reduction", but it's nothing outside the dynamical laws of QT!

This is wrong. The partial trace does not derive state reduction. The partial trace derives the state update for non-selective measurements. It does not derive the state update for selective measurements. Mathematically, this is because a mixed density matrix does not have a unique decomposition as a mixture of pure states.
https://pages.uoregon.edu/svanenk/solutions/Mixed_states.pdf (see comments #22 and #55-57)

 

[atyy]

See Weinberg, QT of fields vol. 1 for a comprehensive treatment of these issues for fields of arbitrary spin.

This QFT reference also give the state reduction postulate in Eq 2.1.7 (in the old fashioned way as part of the Born rule). Earlier in the chapter, he also writes that QFT is based on the same postulates as QM.

 

[PeterDonis]

The thread has gotten far away from just discussing errors in Ballentine, and we already have another thread in the interpretations forum for discussing different concepts of what "state reduction" means.

Thread closed.