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| Κύριοι συγγραφείς: | , |
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| Μορφή: | Recurso digital |
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Zenodo
2026
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| Θέματα: | |
| Διαθέσιμο Online: | https://doi.org/10.5281/zenodo.20032310 |
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Πίνακας περιεχομένων:
- <p>Physics history repeatedly exhibits a striking phenomenon: two seemingly inde<br>pendent theoretical frameworks, developed separately, are eventually shown to be<br>equivalent at a deep structural level. The discovery of such “theoretical dualities”<br>often marks major theoretical breakthroughs, yet the structural conditions for du<br>ality itself are rarely analyzed in a systematic front-facing manner. This paper pro<br>poses that theoretical duality is essentially an information-preserving translation<br>operation: two theories stand in a dual relation if and only if their mutual trans<br>lation process is information-lossless under an economic metric. This framework<br>maps the strength of duality to the degree of information loss in the translation<br>operation, identifying strong duality with fully reversible functorial equivalence<br>and weak duality with adjoint relations involving partial information loss. Fur<br>thermore, this paper models the cognitive operation of “discovering a duality” as a<br>meta-learning process: a cognitive system alternates exploration and exploitation in<br>duality space, gradually converging to the mapping relation with the lowest trans<br>lation cost. The dynamics of this process are jointly characterized by the structural<br>hierarchy of category theory and the gradient dynamics of cognitive search, leading<br>to an open, structured spectrum of duality types. The paper argues that logical<br>translation cost and physical discovery cost belong to distinct categories: the for<br>mer is determined by the functor’s faithfulness, fullness, and essential surjectivity,<br>while the latter is constrained by Landauer’s principle and the Bekenstein bound,<br>and the two must not be conflated. On this basis, the paper provides a princi<br>pled method for mapping theoretical dualities to assessable structural levels, and<br>demonstrates its operation through complete evaluations of electromagnetic duality<br>and the AdS/CFT correspondence.</p>