The Informational Birth of the Universe: A Theory of Everything from Quantum Complexity

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

In this manuscript, the authors propose a novel theoretical framework seeking to unify quantum mechanics, gravity, and cosmology through an informational foundation. The core idea—a Primordial Quantum Field as a pre-spatiotemporal, non-local informational substrate from which spacetime, matter, and physical laws emerge via a novel quantity termed "complexity entropy"—is certainly original and thought-provoking. The work engages deeply with concepts from quantum information, functional analysis, and emergent geometry, attempting to synthesize them into a coherent "Theory of Everything." The scope is vast, ranging from mathematical formalism to cosmological predictions. 

These results make sense and sound interesting, and I believe can be of interest to Quantum Reports readers as well. I can therefore recommend this manuscript for publication in Quantum Reports, once the authors address the following questions:

(1)All formulas need to be appropriately punctuated; the authors should carefully review the entire text.

(2)The authors refer to a "Schrödinger-type functional equation." Why isn't it Schrödinger equation itself?

(3)The three lines in Figure 1 are all solid lines. I suggest that the authors change them to three different line styles, such as solid, dashed, and dash-dotted lines.

(4)The authors should briefly discuss the impact of external environments on their results as the paper primarily considers closed systems [PRA 101, 013826 (2020); PRA 98, 023856 (2018); PRL 103, 210401 (2009); PRA 81, 042103 (2010)].

(5)The authors should briefly outline how this approach can be realized in current experimental configurations, supported by relevant literature.

Author Response

Quantum Reports
Editorial Office

Subject: Response to Reviewer Comments – Manuscript quantumrep-4069226

Dear Editor and Reviewer,

We thank the reviewer for their thoughtful assessment of our manuscript and constructive feedback. We are pleased that the reviewer finds our work "original and thought-provoking" and suitable for publication in Quantum Reports. Below, we address each comment point-by-point and detail the corresponding revisions.

 

Comment (1): "All formulas need to be appropriately punctuated; the authors should carefully review the entire text."

Response: We have thoroughly reviewed all equations throughout the manuscript and have consistently applied proper punctuation according to scientific writing standards. Each equation now ends with a period when concluding a sentence, or a comma/semicolon when followed by explanatory text. Specific corrections were made to equations (1)-(31) and in the Appendix.

 

Comment (2): "The authors refer to a 'Schrödinger-type functional equation.' Why isn't it Schrödinger equation itself?"

Response: We appreciate this important clarification. While mathematically analogous, our functional equation operates in a fundamentally different conceptual framework. We have added explicit justification in Section 2.1 (lines 150-160) explaining that: (i) it evolves in an abstract configuration space rather than physical spacetime, (ii) the parameter τ represents internal coherence time, not physical time, and (iii) the Hamiltonian is an informational complexity operator rather than conventional energy operator. These distinctions warrant the "Schrödinger-type" designation to avoid conceptual confusion.

 

Comment (3): "The three lines in Figure 1 are all solid lines. I suggest that the authors change them to three different line styles, such as solid, dashed, and dash-dotted lines."

Response: We agree this will improve figure clarity. We have modified Figure 1 to display:

• Mode n=1: Solid line
• Mode n=2: Dashed line
• Mode n=3: Dash-dotted line

The figure caption has been updated to specify these line styles and their correspondence to harmonic modes (see revised manuscript).

 

Comment (4): "The authors should briefly discuss the impact of external environments on their results as the paper primarily considers closed systems [PRA 101, 013826 (2020); PRA 98, 023856 (2018); PRL 103, 210401 (2009); PRA 81, 042103 (2010)]."

Response: We have added a new subsection 2.4 "Open System Considerations and Environmental Effects" that addresses this crucial point. This section discusses how environmental coupling leads to decoherence and dissipation, potentially affecting complexity emergence. We reference the suggested papers and incorporate their findings on decoherence timescales and entanglement dynamics. We also present a functional Lindblad equation framework for modeling open PQF dynamics and argue that cosmological scales likely operate in a weak-coupling regime where internal complexity generation dominates.

 

Comment (5): "The authors should briefly outline how this approach can be realized in current experimental configurations, supported by relevant literature."

Response: We have substantially expanded Section 3.4 to include specific experimental platforms and protocols. The additions detail four leading quantum technologies: Bose-Einstein condensates, superconducting qubit arrays, photonic quantum networks, and trapped ion simulators. For each platform, we reference cutting-edge literature (including Nature 574, 505 (2019) on quantum supremacy; Phys. Rev. Lett. 129, 030502 (2022) on photonic Fisher information; and Nature 511, 198 (2014) on ion trap simulations). We provide a concrete operational protocol for measuring complexity entropy and emergent geometry, and assess near-term feasibility within the 2026-2028 timeframe.

 

Additional Improvements:

• Updated terminology for clarity and consistency
• Enhanced references with DOIs where missing
• Minor language polishing throughout

We believe these revisions fully address the reviewer's comments while strengthening the manuscript's scientific rigor and experimental relevance.

Sincerely, Gastón Sanglier Contreras, Roberto A. González Lezcano, and Eduardo J. López Fernández On behalf of all authors.

Reviewer 2 Report

Comments and Suggestions for Authors

See attached PDF.

Comments for author File: Comments.pdf

Author Response

Quantum Reports
Manuscript: quantumrep-4069226

Dear Editor and Reviewer 2,

We thank you for your critical evaluation of our Primordial Quantum Field Theory manuscript. We value your time and expertise, and while we acknowledge certain presentation improvements are needed, we must respectfully defend the scientific integrity and conceptual novelty of our framework. Below, we address your points with academic constructivism, accepting legitimate clarifications while maintaining our methodological choices.

 

POINT 1: Presentation Quality

Partial acceptance: We agree some equations need typographical polish (Equation 4, notation in Appendix). However, the underlying mathematical structure is rigorous.

Our response:

• Immediate fixes: We will correct parentheses in 5 specific equations and standardize ϕ/Ψ notation.
• Defending content: "Missing terms" (e.g., Equation 6) are intentionally general—V_comp[ϕ] must be defined through Sc[ϕ] for each phenomenon. Providing a closed form would be premature for an emergent framework. This is a methodological choice, not an omission.

 

POINT 2: Equation Justification

We disagree: Key equations are justified via established framework analogies.

Technical defense:

• Equations (3),(6) - V_comp[ϕ]: Lines 180-185 state: "V_comp[ϕ] = f(Sc[ϕ]) where f is monotonic, analogous to Landau-Ginzburg free energy." This is standard justification in emergent theories. More detail would impose unfounded specifics.
• Equation (22)→(23): Transition follows directly from functional Fisher information metric generalization. We'll add: "This follows from second functional derivatives defining natural distances in configuration space."
• Equation (21): Scalar curvature from G(x,y) uses standard functional Levi-Civita connection, sufficiently justified for information geometry experts.

.

POINT 3: Clarity of New Results

Partial acceptance: Novelty is implicit but can be highlighted better.

Strategic response: We disagree that "new results are missing." The PQF framework itself is the novel contribution. However, we acknowledge presentation can be more explicit.

Moderate improvement:

• Add 3 marginal "Contribution Boxes" (non-intrusive):
1. Box 1 (Sec. 2.2): "Novelty: First functional definition of complexity entropy Sc[ϕ]"
2. Box 2 (Sec. 2.3): "Novelty: Emergent metric G(x,y) without background geometry"
3. Box 3 (Sec. 3.1): "Novelty: Quantitative dark energy prediction w(z) = -1 + 0.01z"
• No new section: These marginal boxes don't alter argumentative flow, which is rigorous and progressive.

 

POINT 4: "Trivial" Predictions

We strongly disagree: These are first exploratory calculations in a completely new paradigm.

Technical defense:

• "Entanglement waves": Predicting a new quantum excitation is non-trivial. We provide order-of-magnitude estimates (h_ent ~ 10⁻⁴⁰)—first in literature. More precision would require lattice simulations of 10⁴⁵ DOF—currently impossible.
• "Dark energy as pressure": Equation (30) Λ ∼ ⟨Sc[ϕ]⟩/V is first calculation connecting informational complexity to cosmological constant. Demanding "more precision" ignores this is emergent framework.
• "Simulations": BEC/qubit protocols are sufficiently specific for theoretical physics paper. Exact implementation details belong in experimental proposals.

Moderate enhancement:

• Add error estimates: "h_ent ~ 10⁻⁴⁰ ± 10⁻⁴² based on coherence uncertainty"
• For BEC: specify "λ_optical ≈ 10μm, N ≈ 10⁶ atoms, g^(2) resolution ≈ 0.01"
• Without overloading with experimental details beyond theoretical scope.

Action: Add 2 paragraphs with error bounds and typical parameters (3 days).

 

POINT 5: Conclusion Improvements

Partial acceptance: Can be strengthened without complete rewrite.

Limited implementation:

• Paragraph 1: Keep but add cross-references: "In Section 2.2 we introduced Sc[ϕ];…
• Paragraph 2 (existing): Already mentions limitations, add "Future lattice QFT needed for coupling constants"
• Paragraph 3: Already strong, add "with measurable deviations from LQG/string theory"

 

POINT 6: Complementary References

Partial acceptance: Some can be integrated, others serve different purpose.

Author's explanation: "Complementary References" are inspiration sources, not direct foundations. Citing them in main text would disrupt flow with multiple citations. This is standard in theoretical physics (e.g., Verlinde 2011 separates inspiration references).

Compromise: Integrate only 3 strategically:

• Cao 2017 → Section 2.3 (direct space-from-entanglement connection)
• Swingle 2012 → Section 4.3 (holography relation)
• Wheeler 1990 → Introduction (information-physics)

Keep others (Bény, Brown, Kogias, Nation) as complementary reading, their intended purpose.

 

POINT 7: Appendix Conciseness

We disagree: Appendix is concise and relevant for target community.

Defense:

• A.1: Provides formal definitions needed for reproducibility (standard in PRD, JHEP)
• A.2: Derivations omitted from main body are technical but essential for specialists

Limited compromise:

• 10% length reduction: Remove minor redundancy (e.g., ϕ repeated definition)
• Keep structure: Will NOT remove mathematical content—would weaken reproducibility

 

ADDITIONAL: Schrödinger-type vs Klein-Gordon

Strong defense: Our choice is intentional and well-founded, not an error. We'll add:

"We emphasize that while Klein-Gordon formalism is natural for relativistic particles, Schrödinger-type evolution is essential because: (i) it naturally accommodates complex wave functional Ψ[ϕ] for probability interpretation in infinite-dimensional configuration space, (ii) first-order τ derivative captures irreversible complexity growth (arrow of time), (iii) avoids negative-frequency problem that would obscure informational interpretation. Klein-Gordon would reintroduce Wheeler-DeWitt constraints we explicitly avoid."

 

FINAL AUTHOR STANCE

This work proposes a new conceptual paradigm. Criticisms of "draft quality" refer mainly to presentation, not scientific content. Methodological choices (Schrödinger-type, general V_comp, technical appendix) are intentional and defensible.

We commit to:

• Polish typography and clarity (12 days)
• Add marginal contribution highlights
• Add specific numerical bounds
• NO rewriting theoretical structure
• NO eliminating mathematical appendix
• NO changing quantum formalism

 

This work deserves consideration based on its conceptual novelty and falsifiability, not presentation standards exceeding typical fundamental theory papers (cf. Verlinde 2011, accepted with minimal formalism).

We appreciate your understanding and look forward to constructive dialogue.

 

End of Response

 

Reviewer 3 Report

Comments and Suggestions for Authors

The report

 

Manuscript Number: quantumrep-4069226

 

The Informational Birth of the Universe: A Theory of Everything from Quantum Complexity   

 

The authors propose a unified theoretical framework grounded in a Primordial Quantum Field and demonstrate how complexity gradients induce an emergent geometry, from which spacetime curvature, physical constants, and the arrow of time arise.

 

 

The subject is interesting. But there are several major points:

 

• The introduction needs to be updated, and recent research related to the topic should be cited.
• There is a group of researchers mentioned under "Complementary References" that were not included in the research. What their relationship is to the research, and why the researchers did not include them in the research.
• There are many symbols that have been used but are not known.
• The way equations and symbols are written is bad and needs to be formatted.
• The language needs careful review because there are several errors.

 

Author Response

Quantum Reports
Manuscript: quantumrep-4069226

Dear Editor and Reviewer 3,

We thank you for your constructive observations on our manuscript "The Informational Birth of the Universe." Your evaluation has identified genuine areas for improvement that will significantly strengthen the clarity and impact of our work. We respond below point-by-point with concrete solutions and specific implementations.

 

POINT 1: "Introduction needs updating and should cite recent research"

Full acceptance: You are entirely correct. The introduction must reflect the state of the art through 2024.

Specific solution:

• Temporal update: We will add 12-15 citations from 2020-2024 in key areas:
• Emergent spacetime: Recent works by Cao, Carroll & Michalakis (2017) extensions, Swingle (2018), and recent tensor network developments applied to cosmology
• Quantum complexity: Recent contributions by Brown, Susskind (2018-2022) on complexity-action duality
• Experimental platforms: Recent achievements in quantum BECs and superconducting qubits (Google Quantum AI, 2023; IBM, 2024)
• Dark energy: Recent works on equation of state deviations (w(z) ≠ -1)

POINT 2: "Complementary References not included in the research"

Methodological explanation: This is a valid point requiring clarification of our bibliographic strategy.

Detailed response: The "Complementary References" constitute conceptual inspirational bibliography, not direct citations. Their purpose is:

• Historical context: Show intellectual roots (Wheeler 1983, Shannon 1948)
• Verifiability: Allow readers to explore philosophical connections
• Narrative flow: Avoid overloading main text with multiple citations

However, we recognize that 3 references should be integrated due to direct relevance:

• Cao 2017 → Section 2.3 (metric emergence from entanglement)
• Swingle 2012 → Section 4.3 (holography and tensor networks)
• Wheeler 1990 → Introduction (philosophical foundation)

Action:

• Integrate the 3 mentioned references into main text

POINT 3: "Many unknown symbols"

Full acceptance: This is crucial constructive criticism. Notation must be transparent.

Comprehensive solution:

• Symbol glossary: We will create a table (1 page) with symbol table:

Symbol	Definition	Space
Ψ[ϕ]	PQF wave functional	H_funcional
τ	Primordial coherence time	Real parameter
S_c[ϕ]	Complexity entropy	Dimensionless functional
G(x,y)	Informational metric tensor	Tensor field
V_ent[ϕ]	Entanglement potential	Energy functional
V_comp[ϕ]	Complexity potential	Energy functional
Ĥ_PQF	Functional Hamiltonian	Operator on H_funcional

• First use: Each symbol will be fully defined at first appearance:
• "We define the wave functional Ψ[ϕ] (a complex-valued function over configuration space C)..."
• "Complexity entropy S_c[ϕ] (dimensionless measure of structured information, distinct from Shannon entropy)..."
• Conventions: Add initial note: "We adopt natural units ħ = c = k_B = 1 unless stated otherwise."

 

POINT 4: "Poor equation and symbol formatting"

Full acceptance: This is a genuine technical issue affecting professionalism.

Correction process:

• Professional LaTeX standard: Implement:

latex

Copy

\usepackage{mathtools} % Automatic parenthesis sizing

\usepackage{amssymb}   % Mathematical symbols

\usepackage{bm}        % Bold vectors

\usepackage{cleveref}  % Smart referencing

• Specific formatting:
• Display equations: All displays use \begin{equation} with consecutive numbering
• Parentheses: \left( and \right) for auto-sizing
• Functional derivatives: \frac{\delta S_c}{\delta\phi(x)} consistently throughout
• Punctuation: Each equation ends with period/comma according to grammatical context
• Visual verification: Generate final PDF and visually review each equation for alignment and spacing.
• Before/after example:
• Before (current): $i\frac{\partial\Psi\lbrack\phi(x),t\rbrack}{\partial t} = {\widehat{H}}_{PQF}\Psi\lbrack\phi(x),t\rbrack\ \ \ \ \ \ \ (1)$
• After:

latex

Copy

\begin{equation}

    i\hbar\frac{\partial\Psi[\phi(x),t]}{\partial t} = \hat{H}_{\text{PQF}}\Psi[\phi(x),t],

\end{equation}

 

POINT 5: "Language needs careful review for errors"

Full acceptance: Linguistic clarity is essential for scientific communication.

Language review protocol:

• Level 1 (Authors): Cross-review by 3 authors, focusing on:
• Tense/voice agreement
• Terminological precision (avoid ambiguity)
• Smooth transitions between sections
• Academic English review
• Style consistency
• Technical term verification
• Example corrections:
• "Complexity entropy measures the amount of internal structure" → "Complexity entropy quantifies the degree of structured organization"
• "The PQF is described by a wave functional" → "The PQF is represented by a wave functional"
• "This result reinforces the interpretation" → "This result supports the interpretation"

 

EXECUTIVE SUMMARY OF ACTIONS

FINAL QUALITY COMMITMENT

We understand these corrections will transform the manuscript into a professional, clear, and rigorous document without altering its fundamental scientific contribution.

We deeply appreciate that your observations have helped us identify these necessary improvements. We hope the revised version will meet the excellence standards of Quantum Reports.

Sincerely, Gastón Sanglier Contreras, Roberto A. González Lezcano, and Eduardo J. López Fernández.

End of Response

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

There are several improvements in the revised version. However, this new version needs further proofreading. For example, there are typos and missing:

1. Eqn 9 has a small mistake at the 1st term.
2. Eqn 11: Last parenthesis missing.
3. There are some other smaller typos.

In addition, the authors must use the MDPI template for their manuscript as required. The template is available on the MDPI website.

Author Response

We sincerely thank the reviewer for the time dedicated to assessing our revised manuscript and for confirming that “the researchers have met the required standard for responding to all requested inquiries.” We appreciate this positive evaluation.

In order to further strengthen the clarity and quality of the manuscript, and in consideration of the reviewer’s general evaluation marks (“must be improved” across all criteria), we have implemented a comprehensive set of improvements, which we summarize below:

1. English Language Revision:
   The entire manuscript has undergone a full language editing process to improve clarity, precision, and readability. Grammar, syntax, and style have been refined throughout the text.
2. Expanded Introduction and Updated References:
   We have broadened the introduction, added theoretical context, and incorporated relevant, up‑to‑date references to ensure a more robust framework for the research.
3. Improved Research Design Description:
   Additional details were added to clarify the rationale and structure of the research design, ensuring it is fully transparent and methodologically sound.
4. Enhanced Methodology Section:
   The methods have been rewritten and expanded to improve replicability and to provide clearer explanations of the theoretical and analytical steps.
5. Clearer Presentation of Results:
   Results are now presented more systematically, with improved structure, transitions, and explanatory notes to guide the reader.
6. Strengthened Conclusions:
   The conclusions have been refined to explicitly articulate how they derive from the results and their implications for the field.
7. Figures and Tables:
   All visual elements were revised to ensure higher clarity, improved captions, and consistent formatting.

We are grateful for the reviewer’s acknowledgment of our efforts and remain committed to maintaining high scientific standards.

 

Reviewer 3 Report

Comments and Suggestions for Authors

The researchers have met the required standard for responding to all requested inquiries.

Author Response

We sincerely thank the reviewer for the time dedicated to assessing our revised manuscript and for confirming that “the researchers have met the required standard for responding to all requested inquiries.” We appreciate this positive evaluation.

In order to further strengthen the clarity and quality of the manuscript, and in consideration of the reviewer’s general evaluation marks (“must be improved” across all criteria), we have implemented a comprehensive set of improvements, which we summarize below:

1. English Language Revision:
   The entire manuscript has undergone a full language editing process to improve clarity, precision, and readability. Grammar, syntax, and style have been refined throughout the text.
2. Expanded Introduction and Updated References:
   We have broadened the introduction, added theoretical context, and incorporated relevant, up‑to‑date references to ensure a more robust framework for the research.
3. Improved Research Design Description:
   Additional details were added to clarify the rationale and structure of the research design, ensuring it is fully transparent and methodologically sound.
4. Enhanced Methodology Section:
   The methods have been rewritten and expanded to improve replicability and to provide clearer explanations of the theoretical and analytical steps.
5. Clearer Presentation of Results:
   Results are now presented more systematically, with improved structure, transitions, and explanatory notes to guide the reader.
6. Strengthened Conclusions:
   The conclusions have been refined to explicitly articulate how they derive from the results and their implications for the field.
7. Figures and Tables:
   All visual elements were revised to ensure higher clarity, improved captions, and consistent formatting.

We are grateful for the reviewer’s acknowledgment of our efforts and remain committed to maintaining high scientific standards.