Non-Deterministic Gravity

  1. Angshuman Roy

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Abstract

This article explores the application of conditional probability theory within the framework of General Relativity. It reveals that uncertainties in particle momentum and position induce corresponding uncertainties in spacetime metric. The findings demonstrate an energy-dependent transition from deterministic spacetime to a probabilistic regime, occurring at scales defined by the particle’s wavelength, as distances approach Gℏ/c^3 λ. The study also provides a methodology for determining wavefunction evolution in regimes where quantum particles induce significant uncertainty in the spacetime geometry.

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  1. PREreview

    This Zenodo record is a permanently preserved version of a PREreview. You can view the complete PREreview at https://prereview.org/reviews/15384363.

    Review of the Article: "Non-Deterministic Gravity" by Angshuman Roy

    DOI: 10.20944/preprints202505.0285.v1

    Date Posted: May 6, 2025

    General Evaluation

    This manuscript presents an original and intriguing investigation into the interplay between quantum uncertainty and general relativistic curvature. By applying conditional probability theory and Bayesian reasoning, the author introduces the concept of non-deterministic spacetime — a framework in which uncertainties in particle momentum and position influence the geometry of spacetime itself. The work is clearly motivated and contributes to an important area of ongoing theoretical research.

    Strengths

    • Conceptual Novelty: The proposal to treat spacetime curvature probabilistically, conditioned on the quantum state of matter, offers a refreshing and creative perspective that departs from traditional deterministic assumptions in general relativity. • Logical Organization: The manuscript follows a clear and coherent structure, progressing from foundational principles to their application in the gravitational context. • Pedagogical Clarity: The illustrative analogy using colored balls and boxes provides a helpful bridge between abstract probability concepts and physical interpretation, making the core ideas more accessible. • Theoretical Ambition: The article contributes meaningfully to the broader discussion on reconciling general relativity with quantum mechanics, particularly in regimes where quantum fluctuations may affect spacetime itself.

    Suggestions for Improvement

    To further strengthen the manuscript and increase its relevance for researchers in the field, the following refinements are recommended:

    Formalism and Mathematical Structure: The current presentation would benefit from a more rigorous mathematical framework. Key quantities such as the spacetime metric g_μν and the probability distributions over manifolds could be formally defined using stochastic geometry or perturbative methods.

    Dimensional Clarification: The expression involving Għ / (c³λ) is mentioned as a transition scale, but its dimensional meaning is unclear. The author is encouraged to verify the units and clarify whether this represents a length, curvature, or another physical quantity.

    Relation to Existing Theories: A more explicit comparison with semiclassical gravity, stochastic gravity, and quantum field theory in curved spacetime would enhance the reader's understanding of how this proposal fits within the landscape of existing approaches.

    Practical Application or Toy Model: A worked example or simplified model could illustrate how the probabilistic curvature evolves in time and how it affects a test particle's quantum state. Even a one-dimensional or weak-field case could serve as a concrete demonstration of the framework.

    Expanded Citations: The references could be extended to include relevant foundational works and developments in quantum gravity and stochastic spacetime models. This would anchor the manuscript more firmly in ongoing research.

    Conclusion

    "Non-Deterministic Gravity" explores a compelling and highly original idea: that the probabilistic nature of quantum mechanics may directly induce uncertainty in the structure of spacetime. The approach opens a new conceptual pathway for thinking about the intersection of gravitational theory and quantum mechanics. With additional mathematical precision, contextual integration, and illustrative development, this work has the potential to make a valuable contribution to the theoretical physics community.

    Competing interests

    The author declares that they have no competing interests.

  2. Version published to 10.20944/preprints202505.0285.v1