Superluminal Local Operations in Quantum Field Theory: A Ping-Pong Ball Test

Round 1

Reviewer 1 Report

Comments for author File: Comments.pdf

Author Response

Changes in revision

We have implemented the alterations suggested by the referee.

The referee has mentioned that the presentation of the algebraic setting of the classical Klein-Gordon field appears to be ``pedantic´´ to some degree. While we tend to agree, we cannot expect the readership to easily understand the connection between the Hamiltonian approach to classical field theory and the algebraic approach laid out in [13] and [23]. Moreover, these references do not provide simple examples such as the Klein-Gordon field which could just be cited, so we fill this gap in our paper. Summarizing, we think a more detailed exposition than necessary is justified and helps readers to understand the point we wish to make.

In what follows, we provide a list of the changes we have implemented in the revised version.

Note: Changes suggested by the referee are marked with (R).

p. 3, italicized text towards end of first paragraph:

Changed {\it If someone portrays...} to {\it When someone portrays…}

p. 7, line following eqn (2.7):

``it follows that...´´ changed to ``that´´ to achieve grammatical correctness of the sentence.

p. 9, line 4 (R):

Inserted missing ``for all $A \in {\sf A}(O)$´´ as qualifier for the localization property of $T$.

p. 9, last sentence of 1st paragraph (R):

Order of the ``if´´ clause has been changed to express the correct logical order.

p. 12, line following eqn (3.9):

Misplaced indentation removed.

p. 14, 2nd paragraph ( of Sec. 4 (R):

Changed the definition of $\mathcal{S}$ to mean the set of solutions to the KG equation, without requiring compactly supported Cauchy data.

p. 17, last paragraph (R):

Definition of $\mathcal{S}_0$ as the solutions to the KG equation with compactly supported Cauchy-data now appears here, together with some explanations relating to the causal Green operator, symplecticf orm etc. The notation $\mathcal{S}$ and $\mathcal{S}_0$ is adapted accordingly in the text from this point onwards for consistency.

p. 19, eqn (4.14) (R):

definition of $S_\theta$ changed according to recommendation by referee. In the following line, the definition of $q_\theta$ has been changed appropriately.

p. 19, 2nd sentence below eqn (4.15) (R):

Added that $q_\theta = 1$ outside $B(r_2)$.

p. 19, last sentence beginning on page (R):

it is mentioned here that in the symplectic pairing with the compactly supported $f_j$ and

a solution $\varphi \in \mathcal{S}$, one can replace $\varphi$ by $\mathcal{G}h$ for suitable compactly supported test-function $h$ (as pointed out by the referee).

p. 21, 2nd line of 2nd paragraph:

``...act trivially outside of...´´ changed to ``...act trivially in the causal complement of...´´

p. 25:

additional reference [4] added.

Reviewer 2 Report

see the attached .pdf

Comments for author File: Comments.pdf

Author Response

Changes in revision

We have implemented the alterations suggested by the referee.

The referee has mentioned that the presentation of the algebraic setting of the classical Klein-Gordon field appears to be ``pedantic´´ to some degree. While we tend to agree, we cannot expect the readership to easily understand the connection between the Hamiltonian approach to classical field theory and the algebraic approach laid out in [13] and [23]. Moreover, these references do not provide simple examples such as the Klein-Gordon field which could just be cited, so we fill this gap in our paper. Summarizing, we think a more detailed exposition than necessary is justified and helps readers to understand the point we wish to make.

In what follows, we provide a list of the changes we have implemented in the revised version.

Note: Changes suggested by the referee are marked with (R).

p. 3, italicized text towards end of first paragraph:

Changed {\it If someone portrays...} to {\it When someone portrays…}

p. 7, line following eqn (2.7):

``it follows that...´´ changed to ``that´´ to achieve grammatical correctness of the sentence.

p. 9, line 4 (R):

Inserted missing ``for all $A \in {\sf A}(O)$´´ as qualifier for the localization property of $T$.

p. 9, last sentence of 1st paragraph (R):

Order of the ``if´´ clause has been changed to express the correct logical order.

p. 12, line following eqn (3.9):

Misplaced indentation removed.

p. 14, 2nd paragraph ( of Sec. 4 (R):

Changed the definition of $\mathcal{S}$ to mean the set of solutions to the KG equation, without requiring compactly supported Cauchy data.

p. 17, last paragraph (R):

Definition of $\mathcal{S}_0$ as the solutions to the KG equation with compactly supported Cauchy-data now appears here, together with some explanations relating to the causal Green operator, symplecticf orm etc. The notation $\mathcal{S}$ and $\mathcal{S}_0$ is adapted accordingly in the text from this point onwards for consistency.

p. 19, eqn (4.14) (R):

definition of $S_\theta$ changed according to recommendation by referee. In the following line, the definition of $q_\theta$ has been changed appropriately.

p. 19, 2nd sentence below eqn (4.15) (R):

Added that $q_\theta = 1$ outside $B(r_2)$.

p. 19, last sentence beginning on page (R):

it is mentioned here that in the symplectic pairing with the compactly supported $f_j$ and

a solution $\varphi \in \mathcal{S}$, one can replace $\varphi$ by $\mathcal{G}h$ for suitable compactly supported test-function $h$ (as pointed out by the referee).

p. 21, 2nd line of 2nd paragraph:

``...act trivially outside of...´´ changed to ``...act trivially in the causal complement of...´´

p. 25:

additional reference [4] added.

Reviewer 3 Report

This manuscript deals with local operators related with study of superluminal phenomena in frameworks of quantum field theory. In Introduction authors give useful review of the problem, grounds of its actuality, point out the developed approach reinforced by needed citations. A main part of the paper is devoted to presentation of formalism and analysis of the developed approach.  In Sect. 2 authors present main formulation of algebraic field theory.  Here, authors give starting definitions and notations. In Sect. 3 authors formulate and study superluminal localized state transformations in quantum field theory. In Sect. 4 authors formulate and study superluminal localized state transformations in classical field theory. Conclusions are summarized in Sect. 5. There are no Appendixes in this manuscript.

Additional positive point of this manuscript is use of presentations, which helps readers. Form of presentation of material is enough clear for readers working in not direct research line. As I able to estimate, material is carefully written, it has proper structure, it is original and can give interesting for journals on mathematical physics, etc. However, I see some difficulties concerning physical issue (see below). A list of references is enough for presentation, including interesting material (for interested reader), but also uses some papers of last years that could be convenient for readers working in other topics. English and grammar seem on level. A volume of the manuscript corresponds to its context.

Summarizing all aspects of analysis, I give the following recommendation:

I do not recommend this manuscript for publication in physical journal.

My main negative arguments are the following:

• I am sorry to tell that I do not feel that this research is focused on study of superluminal effects in quantum physics.
• Different differential equations can be connected with commutation or anti-commutation relations between operators. However, this is not enough to conclude that all these differential equations describe quantum processes in proper way. Actually, one can find that by such a way one can construct two (or more) quantum physics (or quantum mechanics) with different properties.
• A simple example to find that is to check Dirac equation with including interactions and its correspondence with Schrodinger equation for description of strong quantum phenomena. A way to compare is to construct formalism of relativistic corrections for non-relativistic Shrodinger equation, or non-relativistic approximations for Dirac equation (where Pauli equation is the known first such an approximation, but next approximations are known also). But higher orders give different quantum behaves for the same wave function. This means we have two different quantum physics which are in disagreement between each another. Here experiments help.
• It seem this material closer for description of free particle moving in vacuum, without its interactions with something another. However, strong quantum phenomena appear only in cases of not small interactions. For example, tunneling phenomenon is clear demonstration. I feel formalism of authors cannot be applied (not ready) for description of such phenomena (on the level of accurate analysis of wave function for evolution). Authors do not study interference effects between different parts of wave function, that appear after inclusion of interactions. But that analysis was developed by different researchers in past. In result, superluminal effects claimed by ones, then disappeared after more accurate analysis of evolution of shape of wave packet and its interaction with potential. I can understand that different discussions can be there. But, in any case, the submitted manuscript is far from such an analysis with details of superluminal effects. Also note that today inverse theory in quantum mechanics (there is also similar theory for field theory) has formalism for description of strong quantum phenomena with really high accuracy.
• Authors do not develop formalism analyzing properties of wave function, its evolution in time. But many large effects can appear after such study. Authors do not develop such formalism, do not cite on such research lines. But such research lines can cause questions.

Author Response

This referee's request for "major revisions" is scientifically inappropriate.