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An Epistemic Analysis of Time Phenomenon

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Abstract

In this work we present an epistemic analysis of time phenomenon using the mathematical machinery of information theory and modular theory. By adopting limited commitment to the ontology of time evolution, and instead by mainly relying on the information that is in principle accessible to the observer, we find that the most primary aspect of the temporal experience, the perceived distinctiveness across the states of the world, emerges as a purely epistemic function. By analyzing the mathematical properties of this epistemic function, we interpret it to be in principle insensitive to any ontic state of the world, which leads to the conclusion that the observer is subject to temporal experience irrespective of whether the underlying state of the world is dynamical or invariant. On the ground of the presented analysis, we also provide a solution to the conceptual challenge of non-equilibrium phenomena that faces the thermal time hypothesis.

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Notes

  1. The reason behind a logarithmic definition of information content of an even is the additivity of the amount of surprise associated with the occurrence of two independent events x and y: \(-\log p_{xy} = -\log p_x -\log p_y\).

  2. The interaction Hamiltonian is bounded.

  3. A state \(\Psi \) is called separating for \({\mathcal {R}}_{{\mathcal {O}}}\) if \(A\vert \Psi \rangle \ne 0\) unless A=0 for all \(A\in {\mathcal {R}}_{{\mathcal {O}}}\).

  4. \(\log \Delta \) is called the modular Hamiltonian.

  5. Note that the relative entropy \(H_{\Psi ;\Phi }\) is a function of the local algebra \({\mathcal {R}}_{{\mathcal {O}}}\), as the modular operator is generated by both the global state and the local algebra.

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Acknowledgements

The authors are grateful to Miklós Rédei, Roberto Longo, Klaus Fredenhagen and Carlo Rovelli for insightful discussions.

Funding

This research has received funding and support from the European Union’s Horizon 2020 research and innovation programme under grant agreement n. 758145 and the project CHRONOS (PID2019-108762GB-I00) of the Spanish Ministry of Science and Innovation.

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Authors and Affiliations

  1. Department of Philosophy, Universidad Autónoma de Barcelona, Barcelona, 08193, Spain

    Farhang Hadad Farshi & Silvia DeBianchi

  2. Department of Philosophy, Università degli Studi di Milano, Milan, 20122, Italy

    Silvia DeBianchi

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  1. Farhang Hadad Farshi
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  2. Silvia DeBianchi
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Correspondence to Farhang Hadad Farshi or Silvia DeBianchi.

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Farshi, F.H., DeBianchi, S. An Epistemic Analysis of Time Phenomenon. Found Phys 52, 63 (2022). https://doi.org/10.1007/s10701-022-00583-9

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