Evidence of Predictive Power and Experimental Relevance of Weak-Values Theory
Round 1
Reviewer 1 Report
Evidence of Predictive Power and Experimental Relevance of
Weak-Values Theory by C. Aris Chatzidimitriou-Dreismann
This manuscript deals with teh theoretical frame of Weak Values (WV) and Two-State-Vector Formalism (TSVF)
to provide more insight into quantum mechanics in various physical and technological fields. In the paper, the focus is on the question of whether the WV-TSVF theory possesses predictive power beyond widely used standard quantum mechanics. As a test case the author considers the dynamics of hydrogen in nanostructured materials like carbon nanotubes by employing incoherent scattering of thermal neutrons (INS). As a result the measured energy and momentum transfers are shown to contradict qualitatively the associated expectations of conventional scattering theory. Many other theoretical and experimental implications are discussed in the paper. In summary, the study seems relevant and promising tool for investigating new effects. I believe the study deserves publication in its present form.
Author Response
I thank the Reviewer 1 for his kind comments and encouraging reemarks.
Although there is no comment to address, perhaps I may notice the following detail. Due to the comments and views of Reviewers 2 and 3 concerning the status of WV and TSVF, I re-analysed my unterstanding of Ref [8] by Aharonov et al. My surprising conclusion is that TSVF is here necessarily applied, in order to derive the new effect of [8]. Consequently, one may conclude that WV and TSVF represent new physics that goes beyong standard QM. This of course conttadicts the views of Reviewers 2 and 3.
This result is now included in the new " Subsection 2.1. A Digression: Is the Result Based on WV theory alone, or on both WV and TSVF? "
Reviewer 2 Report
[Quantum Reports] Manuscript ID: quantumrep-1146498
Evidence of Predictive Power and Experimental Relevance of
Weak-Values Theory
- Aris Chatzidimitriou-Dreismann
This paper claims to present experimental evidence in molecular (graphene-like and small molecule combinations) systems for effects related to "weak values" and the associated "two-state" formalism. (WV and TS hereafter.) I believe the paper may be of value, but it needs considerable revision. In some ways, it is quite interesting.
First, the paper ties itself not only to the WV TS formalism, but also to claims about the "ontic status" of this. These lead into ideas of retrocausality or retrocausation that are not at all universally accepted. I think it is fine for the author to adopt the formalism, but not necessary to tie himself to the more extravagant ideas. (Personally, I'm open to new ideas about quantum mechanics, because I don't feel that any of the existing ideas are completely satisfactory.)
Now, the author makes some extravagant-sounding claims about seeing effects that can't be explained by the "conventional" formalism but which are understood in terms of the WV TS formalism. But isn't this misleading? As far as I can tell, WV TS is all based on conventional quantum formalism; it makes no new predictions? Its claim seems to be that it helps guide new ideas and intuitions; I'm fine with that.
From this, I go on to be somewhat puzzled about a seeming lack in the manuscript. WV TS makes much use of "postselection" which is mentioned several times in the early, introductory part of the paper, and once at the end, from what I can tell. But the author never seems to spell out what kind of postselection he is using in analyzing the actual data here.
In sum, there may be interesting work here, but I'm left with too many apprehensions of misleading statements, and missing things.
Author Response
see attached PDF Reviewer2.pdf
Author Response File: 
Author Response.pdf
Reviewer 3 Report
The paper deals with a weak measurement based account of results in inelastic neutron scattering that the author finds anomalous. The work might be publishable in Quantum Reports, but the present manuscript suffers from several problems: substantial overlaps with previous works by the same author, digressions on topics that are not analyzed in the paper, and lack of a contextualized discussion on the problems that the author finds “anomalous”.
1. As far as I can see, only Sec 7 contains original results; the other sections largely borrow text from previous works by the author (Refs 11-14 of the ms). I believe it would be more appropriate to shorten the paper by recalling the basics from INS, citing past work, and presenting the novel results, rather than repeating at length (and in the same form) what the author has written in previous works (including displaying the same figures already shown in these previous Refs).
2. There are many digressions in the paper on important topics (meaning of the wavefunction, of weak values…) in which the author simply gives their opinion without justifying or analyzing what they assert. Not only is this probably uninteresting from a reader’s point of view, but it makes the paper harder to read, and at some point confusing. In particular, Sec. 3 (in which the author gives some personal remarks, 3 or 4 lines each time on several topics – Google’s computer, DFT...) is irrelevant to the rest of the paper and should be removed.
3. The author finds problematic the low value of the effective mass deduced from data in IINS experiments (and this is where they claim weak values play a role). However no mention is made of (i) whether this is seen as a problem in the IINS community; and (ii) whether there are other interpretations for this “anomalous” low value fo the effective mass. Indeed, intuitively it seems to me that this effective mass value is obtained by fitting experimental results to a specific model, so it is not necessarily a problem to have a low value of a parameter if one understands the meaning it has within the model (actually, effective masses lower than the free molecule mass have been computed within these models for decades). This point should be clarified.
4. Other concerns:
a) WV and TSVF are presented in the text (including in the Introduction) as going beyond standard QM. I think this is incorrect and potentially confusing: the Weak measurements framework is entirely contained within standard QM (the WV is indeed derived from standard perturbation theory). On the other hand TSVF is a specific interpretation of pre-post-selected systems, different from the Copenhagen interpretation of QM. So WV and TSVF should be distinguished.
b) It should be mentioned that the interpretation of WV within TSVF is not consensual – for instance the first critcism (Phys. Rev. Lett. 62, 2325 (1989)) of the WV as representing a measurement of the system (rather than a perturbation of the pointer) could be mentioned. Actually the conditions under which WV can be related to the system properties are rather stringent, a point the reader should be made aware of (see Found. Phys. 49 298 (2019) for a recent discussion).
c) Another relevant Ref that could be cited is the connection between scattering theory and weak values (Annals of Physics 392, 2018, 272).
Author Response
see attached file Reviewer3.pdf
Author Response File: Author Response.pdf
Round 2
Reviewer 2 Report
Review of revision:
The author obviously has made a serious effort to respond to my earlier criticisms. I think the paper should be published with the revisions already at hand. I would ask the author to consider these further remarks about the three points numbered in his response:
1) I agree that an author has the right to express his theoretical views, as long as they are not demonstrably wrong, especially as regards a subject whose real foundations are as unsettled as quantum mechanics. Getting a little ahead, I am certainly not a proponent of the "Copenhagen view" which the author mentions in point (2), to which I turn.
2) In my opinion, I can get the results for weak values and two-state formalism using the "standard" quantum formalism. This in no way implies an endorsement of the "orthodox" or "Copenhagen" view, of which I have always been suspicious. But that's OK – if the author finds the WV and especially the TSVF formalism helpful, who am I say he shouldn't use it? I might suggest however that the author tone down his endorsement a bit, in that this might gain receptivity among the many who are skeptical of some of the claims made by the TSVF school.
3) The author obviously has taken to heart my criticism about the former lack of adequate explication of the "postselection" aspect of his work.
Author Response
Response to Reviewer 2:
I thank the Reviewer for his/her three additional stimulating points of his/her second review. My responses are as follows
Point 1. I agree with all remarks of this Point, and of course with the remark that the real foundations of the theoretical frame under consideration are "...as unsettled as quantum mechanics".
Point 2. First, I agree with the wordings and the spirit of these remarks and suggestions. To be more specific and explicit, I even agree with the Reviewer about the possibility "...[to] get the results for weak values and two-state formalism using the "standard" quantum formalism." However there is a subtle and/or crucial issue here, concerning the meaning of "standard quantum formalism".
Concretely, the paper does not considers this question, but rather another (much more limited) one which is "...[to] get the results for weak values and two-state formalism using the "standard" quantum formalism of INS." According to the explanations of Sect 4, in particular LInes 299-307, this seems highly improbable. . Moreover, I added a new item (A) in „Section 8. Additional Remarks…“ addressing this problem explicitly.
Point 3. It is a pleasure to acknowledge the validity and relevance of this point, and I am happy for the opportunity to amend the paper accordingly (that is, with the additional Subsection 6.3 treating this point).
Reviewer 3 Report
The author has adequately replied to the criticism by amending the text. In particular, I still believe that most of the material contained in the manuscript has already been exposed in previous papers by the author, but the author specified he intends the present manuscript to be a sort of review.
Overall I can therefore recommend publication.
Author Response
Response to Reviewer 3:
I thank the Reviewer for his/her constructive criticisms, which have been helpful to me in the process of revision, and his/her final positive recommendation. As concerns the type of the paper, I suggested to the Editors to consider it as a "comprehensive review paper" (cf. instructions to authors of the Special Issue Information).
