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Is energy conserved when nobody looks?

by Stanisław Sołtan, Mateusz Frączak, Wolfgang Belzig, Adam Bednorz

This is not the latest submitted version.

Submission summary

Authors (as registered SciPost users): Adam Bednorz · Wolfgang Belzig
Submission information
Preprint Link:  (pdf)
Date submitted: 2019-12-20 01:00
Submitted by: Bednorz, Adam
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Quantum Physics
Approach: Theoretical


Conservation principles are essential to describe and quantify mechanical processes. Classically, the conservation holds objectively because the description of reality can be considered independent of observation. In quantum mechanics, however, invasive observations change quantities drastically, even those conserved classically. Interestingly, we find that the non-conservation is manifest even in weakly measured correlations if some of the observables do not commute with the conserved quantity. Our observations show that applications of conservation laws in quantum mechanics should be considered in their specific measurement context.

Author comments upon resubmission

Dear Editor,

We are grateful for the comments of the Referee. We agree that the bottom line of our paper is that it follows from quantum mechanics that conservation laws must be contextual.

We have followed the suggestion of the Referee and changed the last sentence of the abstract. In addition we have applied minor improvements of the manuscript detailed below.

Adam Bednorz
on behalf of all the authors

List of changes

a) Modified the last sentence of the abstract
b) Sightly reordered and modified the paragraph below (8) to emphasize the difference between
classical and quantum case.
c) Minor style changes at the end of Sec. 1 and beginning of Sec. 5.

Current status:
Has been resubmitted

Editorial decision: For Journal SciPost Physics Core: Publish
(status: Editorial decision appealed by authors)

Reports on this Submission

Report 1 by Viktoriia Kornich on 2020-3-25 (Invited Report)


1) Interesting topic.
2) Different models (experiments) are suggested.
3) The authors use short, understandable sentences. The manuscript is indeed written for other people to understand it.
4) The parts of the manuscript are logically ordered and connected.


1) I have doubts about the validity of experiments. Please, see the report.
2) In case the experiments are valid, the importance of the results seem to be exaggerated. From the general intuition, even the weak perturbation of the system (measurement) can be amplified and make a big impact, depending on a system. However, this is not my main concern.


First, the main questions.

1) In the end of Section 3 the authors state that indeed, the measurements destroy the translational symmetry of time and thus energy might be not conserved. The argument that the other quantity is also not conserved (angular momentum component in this case) does not solve this problem. Maybe there are more reliable arguments for this? They should be added into the manuscript.

2) Both experiments for the z-component of angular momentum use square capacitors, which violate rotational symmetry of space. Then the angular momentum should not be conserved in any case. Is there some explanation for this?

Now, less important questions, aimed mainly at improving the readability of the manuscript.

1) On the page 5, it is written that the magnetic field is produced by the particle itself. Is there some reason for this? Why not simply external magnetic field?

2) In Section 5, the authors use macrorealism assumption. Why? The system under consideration is not macroscopic, why does it necessarily have properties (and why particularly q,q',x,y) which can be determined without perturbing the past or future state of the system?

3) In the end of page 7, why the noise D is called large? For the considered limit q->0 it goes to zero.

Requested changes

Please, clarify all the questions described in the report.

  • validity: -
  • significance: good
  • originality: high
  • clarity: high
  • formatting: good
  • grammar: excellent

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