Spontaneous Wave Function Collapse with Frame Dragging and Induced Gravity

Round 1

Reviewer 1 Report

The author examines a refined concept of spontaneous wave function collapse leveraging a modified stochastic Schrodinger equation, thereby introducing nonlinearities, to maintain both the continuity of the spatial particle trajectory and the conservation of momentum. This is accomplished by using a coordinate transformation to maintain a local inertial frame. The constant updating of the coordinates is referred to as “frame dragging.”  This is an insightful way to approach the problem however the terminology is too easily confused with general relativistic frame dragging in rotating noninertial frames and given the connections between wavefunction collapse and induced gravity, as alluded to by the author, it might be clearer to not use the frame dragging term in this context as well, but I would let the author decide. Although there may be issues with using this approach in non-asymptotically flat spacetime manifolds, it should be useful for similar concepts in quantum optics, this approach is an interesting contribution to the wave function collapse issues.

Author Response

RESPONSE TO REVIEWER 1 COMMENTS

Point 1: the terminology is too easily confused with general relativistic frame dragging in rotating noninertial frames and given the connections between wavefunction collapse and induced gravity, as alluded to by the author, it might be clearer to not use the frame dragging term in this context as well, but I would let the author decide.

Response 1: I prefer to keep "frame dragging". The Abstract is now completed by a clarifying sentence.

Point 2: ... there may be issues with using this approach in non-asymptotically flat spacetime manifolds, it should be useful for similar concepts in quantum optics, this approach is an interesting contribution to the wave function collapse issues.

Response 2: If the whole concept survives forthcoming tests like e.g. the promised Ref. 19. 

Reviewer 2 Report

See attached review

Comments for author File: Comments.pdf

Author Response

RESPONSE TO REVIEWER 2 COMMENTS

(1) If the frame is changed, it would be natural to redefine the physical position and momentum operators for such a transformation. Then the derived equation (12) should be re-expressed in terms of the newly defined physical operators. However this procedure seems to be ignored in the present work. I did not find any convincing discussion about this.

Response: Below Eq.(9) I added two clarifying sentences why (12) is valid in x,p which are already  the inertial variables.

(2) On the left panel of Fig. 1, the stochastic trajectory becomes discontinuous. It means that
a Levy process is involved. However, the equations (5) and (6) use only the continuous
Wiener processes and thus I do not understand why the discontinuity of the trajectory
appears. It should be explained.

Response: This is an important remark because my use of continuity contradicts to the mathematical continuity of the Wiener process. I changed "discontinuity" for "random jumps", "continuity" for "smoothness" (twice), hence remove the observed conflict.  

(3) I cannot help thinking that the success of the procedure of the submitted work is just
accidental and that it does not work for other cases. To wipe out such a doubt, the author
should consider, for example, the free particle in a rotating frame and discuss the present
procedure. In fact, the main mathematical result of this paper was already shown in Ref.
7 as is mentioned above Eq. (11) and thus I am not satisfied with the present content of
the paper.

Response: Since SC theories and the proposed frame-drag are covariant for smooth coordinate transformations, like that of rotating the frame, the results are also covariant. This not an issue. (However, the success of the procedure for other cases is yet to be confirmed, to see "whether the new concept is new physics or a deadlock" - I wrote in the last Section.

(4) The discussion for relativistic systems in Sec. 6 is not sufficient because of the following
reasons.
(a) As is well known, there is no fully consistent space localisation, i.e., satisfying definition
of a position operator, for relativistic systems (not only for particles but also for fields).

This was pointed out by Newton-Wigner [1], Wightman [2], and many others, see for
instance the review by K´alnay [3] and the no-go results by Hegerfeld [4].
(b) Normally the Lorentz-covariant noise is not known.
(c) As is considered by Ito [5], the metric is not necessarily sufficient to treat stochastic
variable in curvilinear systems and we need the vierbeins (tetrads).
These above problems should be mentioned in Sec. 6.

Response: Although all these comments may become relevant in some relativistic theories,  at the current status  my proposal one can not predict which one might become so and which one remains irrelevant. Still,  point (b) is already a known bottle-neck for relativistic SC.

(5) Although SC is not considered in the recent article [6], the correlation between quantum
fluctuation and classical spacetime curvature is also discussed in this paper. .

Response: This work is related to the general issue, but it's approach is unrelated to my work.

The author is invited to correct the written English and the following misprints or confusions,
for instance

(1) Page 2, line 2, the expression microscopic theories looks bizarre

Response: Does not, I think. I found it in 221 titles on arxiv.org physics.

(2) Page 2, line 12, idem for extreme small

Response: Looks an oxymoron, indeed. But I found 721 "extreme small" and "extremely small" in abstracts on arxiv.org physics.

(3) In Eq. (21), ~/m 7→ ~/M

Response: Thanks, corrected.

(4) In the second paragraph from the last in Page 5, x2 = hxi1 will be x2 = hxi2.

Response: Thanks, corrected.

Reviewer 3 Report

The present paper is in the general genre of beyond-quantum-mechanics theories which feature spontaneous collapse of the wavefunctionwavefunction.

Given the somewhat esoteric nature of the subject, it would be nice to include some brief motivation for the entire approach. In particular, as a relative outsider to these discussions, it is unclear to me what spontaneous collapse has to add on top of what we already understand, within standard QM, as decoherencedecoherence. In particular, the generic drive away from SchrodingerSchrodinger-cat-like states appears equally well-understood, while the Born rule appears equally mysterious, with or without the clunky addition of stochastic and non-linear terms. 

The paper offers a modification of the "standard" spontaneous-collapse story, which remedies some problems vis. energy-momentum conservation and deviations from classical motion. Again, this point could appear more powerful, if it were made clear in the Introduction what it is we're gaining from the spontaneous-collapse machinery in the first place.

That being said, the paper then goes on to hint at some real, independent merit of spontaneous collapse: together with the proposed "frame-dragging" idea, it may function as a mechanism for gravity. This may provide the entire framework with a crucial dose of both testability and explanatory power. 

Before publication, I recommend the following additions/clarifications:

1. The author suggests that local coordinate transformations don't have enough freedom to fix the conservation of energy-momentum, and therefore we should resort to genuinely altering the metric. Can this reasoning be presented in more detail? In particular, from naive degrees-of-freedom counting, coordinate transformations have as many degrees of freedom (4 per point) as the energy-momentum conservation law. On the other hand, if $\nabla_a T^{ab}$ transforms as a tensor under coordinate changes, then indeed one cannot use a coordinate transformation to set it to zero.

2. The author avoids any attempt to quantitatively analyze the proposed notion of emergent gravity, and compare it to (Newtonian or Einsteinian) gravity as we know it. While the difficulty is understandable, this makes the argument rather sterile. Perhaps one can do at least some order-of-magnitude estimate of the required relationship between e.g. the spontaneous-collapse parameters and an emergent Newton's constant?

 

Author Response

Points unnumbered: The paper offers a modification of the "standard" spontaneous-collapse story, which remedies some problems vis. energy-momentum conservation and deviations from classical motion. Again, this point could appear more powerful, if it were made clear in the Introduction what it is we're gaining from the spontaneous-collapse machinery in the first place.

That being said, the paper then goes on to hint at some real, independent merit of spontaneous collapse: together with the proposed "frame-dragging" idea, it may function as a mechanism for gravity. This may provide the entire framework with a crucial dose of both testability and explanatory power.

Response: Introduction is inserted by 1.5 new clarifying sentence right after the first one.

Point 1: The author suggests that local coordinate transformations don't have enough freedom to fix the conservation of energy-momentum, and therefore we should resort to genuinely altering the metric. Can this reasoning be presented in more detail? In particular, from naive degrees-of-freedom counting, coordinate transformations have as many degrees of freedom (4 per point) as the energy-momentum conservation law. On the other hand, if $\nabla_a T^{ab}$ transforms as a tensor under coordinate changes, then indeed one cannot use a coordinate transformation to set it to zero.

Response 1: My preliminary calculations in DP-model show that local-frame dragging is not sufficient to recover momentum conservation. These results are not yet safe enough to publish neither to mention. 

Point 2: The author avoids any attempt to quantitatively analyze the proposed notion of emergent gravity, and compare it to (Newtonian or Einsteinian) gravity as we know it. While the difficulty is understandable, this makes the argument rather sterile. Perhaps one can do at least some order-of-magnitude estimate of the required relationship between e.g. the spontaneous-collapse parameters and an emergent Newton's constant?

Response 2: In the last but one paragraph a new sentence tries meeting the suggestion.

Round 2

Reviewer 2 Report

The author has considered my comments in a constructive way and has significantly amended the submission. In my opinion the revised manuscript deserves to be published in Quantum Reports

Reviewer 3 Report

The author did not quite address my points, but that is perhaps unavoidable. I declare my job as done, and the paper can move on to publication.

Before signing off, I must observe that the author added to the Introduction a sentence about the "merits" of spontaneous collapse, which is actually a list of its properties. Why are these desirable? Why are they merits?