How to Avoid Absolute Determinismin Two Boundary Quantum Dynamics
Round 1
Reviewer 1 Report
The paper is about the incorporation of willful decisions in time symmetric formalism of quantum mechanics. The author expresses his opinion that this is possible by taking into account the Big Bang and the Final Crunch of the universe and holds in our epoch. While the problem is interesting and relevant I do not recommend the publication in Quantum Reports because the proposed solution is highly speculative, contradicts actual understanding and is lacking of justification.
The more detailed points are the following:
The explanation of Fig. 1. suggests that the author believes that the macroscopic world arises because the past of the Universe is shorter than the future. This is in sharp contrast with observation where a microscopic event triggers a macroscopic phenomenon, like the appearance of a particle track in Wilson's stream chamber. The relevance of the state of the universe in the emergence of classical physics makes astrophysical time scales important in laboratory observations. That has not been seen.
The statement "The two boundary description is meant for the whole universe." is not right. What is called by the author as "two boundary quantum mechanics" is the expression of the probability before line 32, the conditional probability of measuring the projector M assuming that the measurement of another observable, represented in this case by the final density matrix, is performed, as well. Who performs performs the measurements when the system in question is the whole universe? Does the author place the free will beyond the universe? What is the initial or final state of the universe? If the universe is a singular point at the beginning and at the end then its state is ill defined. If one assumes a finite structure then what is that state? Why would that state be simpler than the state of say today?
The main point of the argument, presented around line 99, holds if the universe is about the half of its age. Otherwise the time arrow flips as the half life-time of the universe is passed.
There are further minor points which need polishing:
- The meaning of the paragraph after line 33 is unclear.
- The sentence starting in line 38 is incomprehensible.
- The universe starts as a singular point and follows quantum evolution at the beginning. Why is the initial state of Fig. 1 is macroscopic?
Finally, how does the result Jacques et al. Phys. Rev. Let. 100 220402 fit into the vision presented here?
Author Response
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Technical points:
Line numbers are given in pairs. The first one is the one obtained with the provided tex file, the second to that of the provided pdf file.
The changes done in response to the reports are indicated in red. Before publication all '\textcolor{red}'will have to be replaced by '\textcolor{black}'
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The paper is about the incorporation of willful decisions in time symmetric
formalism of quantum mechanics. The author expresses his opinion that this
is possible by taking into account the Big Bang and the Final Crunch of the
universe and holds in our epoch. While the problem is interesting and
relevant I do not recommend the publication in Quantum Reports because the
proposed solution is highly speculative, contradicts actual understanding
and is lacking of justification.
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The comments and changes below intend to answer the objections.
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The more detailed points are the following:
The explanation of Fig. 1. suggests that the author believes that the
macroscopic world arises because the past of the Universe is shorter than
the future. This is in sharp contrast with observation where a microscopic
event triggers a macroscopic phenomenon, like the appearance of a particle
track in Wilson's stream chamber. The relevance of the state of the universe
in the emergence of classical physics makes astrophysical time scales
important in laboratory observations. That has not been seen.
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I don't completely understand the point.
If the microscopic world stays in the domain of classical physics it
somehow reflects the size of the Ljapunow-Exponent. To me, the
thermodynamic time arrow reflects the expanding universe and is a
solved problem. In any case. it is unrelated to the problem
considered.
Presumably microscopic is meant as a quantum decision triggering a
macroscopic phenomenon. The transition to an extended macroscopic
phenomenon enables the selection by the final state. In the two
boundary QM - in the way I use it - the past is immediately fixed
by the final state and there is no collapse or jump to macroscopic
physics. The emergence of classical physics has no astrophysical
time scale as it does not exist.
It seems, of course, counter-intuitive that a track in a streamer
chamber of Wilson's days is still available in some way. One tends
not to fully take into account the abundance of witnesses and the
hugeness of the universe. Excepting the early universe, the extend
of things is given by mass scales so the expanding universe leads to
a huge number of available states.
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The statement "The two boundary description is meant for the whole
universe." is not right. What is called by the author as "two boundary
quantum mechanics" is the expression of the probability before line 37/32, the
conditional probability of measuring the projector M assuming that the
measurement of another observable, represented in this case by the final
density matrix, is performed, as well. Who performs performs the
measurements when the system in question is the whole universe?
---------------------------
The term "two boundary quantum mechanics" is taken literally as a quantum dynamics with two boundaries. It contains no jumps or collapses, no causality, and except for gauge effects wavefunctions or fields can be considered ontological real. The physics is not defined by measurement done by somebody living inside or outside the universe. The measurement operator in the equation is just a projection operator.
I agree with the referee that the equation is careless with priors. I replaced it with a formula for the probability of a specific measurement if all other decisions are taken.
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Does the author place the free will beyond the universe?
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Neither the author nor anybody else in his opinion understands free will (line 95/92) so this question cannot be answered. However, whatever it is, a resulting time-ordered structure of sudden, seemingly "free will" decisions will have to be implementable. For this purpose, an interaction term with hypothetical free will fields beyond the universe of the known fields would do.
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What is the initial or final
state of the universe? If the universe is a singular point at the beginning
and at the end then its state is ill-defined. If one assumes a finite
structure then what is that state? Why would that state be simpler than the
state of say today?
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As said in line 148/139 a macroscopic description is not available close to the initial and final state and so what is known about these states in the real universe is limited. Our consideration is restricted to the situation when a macroscopic description is available.
Initially, evolution does not lead to an increase in the available states. The larger spatial extend is compensated by lower temperatures and more extended states. At temperatures at which the mass is no longer negligible, a second scale enters which changes the situation. The spatial extent of things is now given by the inverse of the mass. In this way, the state of our present universe can be expected to be less simple than the initial one.
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The main point of the argument, presented around line 102/99, holds if the
universe is about the half of its age. Otherwise the time arrow flips as the
half life-time of the universe is passed.
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I don't understand the point. The macroscopic time arrow flips at \tau/2. A few sentences were added to explain the formula after line 102/99.
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There are further minor points which need polishing:
- The meaning of the paragraph after line 33/33 is unclear.
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I rewrote the paragraph.
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- The sentence starting in line 38 is incomprehensible.
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The offending phrase was dropped.
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- The universe starts as a singular point and follows quantum evolution at
- the beginning. Why is the initial state of Fig. 1 is macroscopic?
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The sentence Line 58/56 was expanded to answer the question.
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Finally, how does the result Jacques et al. Phys. Rev. Let. 100 220402 fit
into the vision presented here?
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I added the interesting reference
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Reviewer 2 Report
This paper discusses several issues concerning the two boundary formulation of quantum mechanics in which evolution is in terms of density matrices and a projection only takes place at the end of the studied process. Although this is not a widely studied interpretation of quantum mechanics, some people have considered it and may benefit from some of the concepts discussed here. I recommend publication.
Author Response
I have to thank for the professional report.
Reviewer 3 Report
This paper discusses how one might implement a causal macroscopic theory from two-boundary quantum mechanics. The difficulty of causality is avoided by forcing all decisions to the end of the time interval under consideration. The ideas are implemented in the context of a simple, time symmetric big bang/big crunch universe.
Some of the arguments are difficult to parse because they are presented in a vague and imprecise manner. In particular Section 1 is disjointed and makes use of either vague language or undefined terms, particularly the paragraph on measurements (line 19).
Additionally, in the following paragraphs (line 29+), the definitions of f* and i’’, f’’ need to be made explicit. What is meant by the postponement of measurements to the final time is not clear from the presentation. Also, what is meant by “tiny effective final density matrix”? The smallness of a density matrix show up elsewhere in the text as well.
In section 2, the author conjectures how apparent causal macroscopic dynamics can arise from an underlying non causal quantum theory, but the details of the mechanism are vague. (And the remark about radio waves could potentially serve as a illuminating exemplar, but as is, it’s a non-sequitur.)
There is potential promise in the author’s ideas, but at present, the arguments are not presented with sufficient clarity to fully evaluate their merits.
Author Response
---------------------------
Technical points:
Line numbers are given in pairs. The first one is the one obtained
with the provided tex file, the second to that of the provided pdf
file.
The changes done in response to the reports are indicated in red.
Before publication, all '\textcolor{red}'will have to be replaced by
'\textcolor{black}'
Detailed response:
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This paper discusses how one might implement a causal macroscopic theory
from two-boundary quantum mechanics. The difficulty of causality is avoided
by forcing all decisions to the end of the time interval under
consideration. The ideas are implemented in the context of a simple, time
symmetric big bang/big crunch universe.
Some of the arguments are difficult to parse because they are presented in a
vague and imprecise manner. In particular Section 1 is disjointed and makes
use of either vague language or undefined terms, particularly the paragraph
on measurements (line 19).
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For your general points, please note the numerous revision. I tried to be brief and emphasize the second part. But I might have overdone it.
The paragraph starting with line 19/19 was reformulated to be more precise.
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Additionally, in the following paragraphs (line 29+), the definitions of f*
and i’’, f’’ need to be made explicit.
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The paragraph starting with line 19/19 was reformulated to be more precise. I have to admit i’’, f’’ were typos I overlooked. They were too tiny on my screen. The definitions of density matrices were added. To avoid confusion I left out conjugation of an anyhow hermitian matrix.
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What is meant by the postponement of measurements to the final time
is not clear from the presentation. Also, what is meant by “tiny effective
final density matrix”? The smallness of a density matrix show up elsewhere
in the text as well.
------------------------------------
The paragraph starting with line 19/19 was reformulated to be more precise.
------------------------------------
In section 2, the author conjectures how apparent causal macroscopic
dynamics can arise from an underlying non causal quantum theory, but the
details of the mechanism are vague. (And the remark about radio waves could
potentially serve as a illuminating exemplar, but as is, it’s a
non-sequitur.)
------------------------------------
The remark about radio waves was expanded. A time-reversed picture was discussed to illustrate the selection power of the final state.
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There is potential promise in the author’s ideas, but at present, the
arguments are not presented with sufficient clarity to fully evaluate their
merits.
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I spend considerable time to improve it.
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Round 2
Reviewer 1 Report
I accept the author's response to my questions. It made clear that his view is based on the cosmological origin of the time arrow. However it is not obvious why the quantum mechanical time arrow should be derived from a cosmological concept since it is more natural to base the phenomenons of a composite system on the laws of the elementary, microscopical constituents. In any case the author has right to uphold his conviction but it has to be stated clearly if a key assumption is beyond experimental verification.
Reviewer 3 Report
The author has addressed my concerns.
