The Symmetry Dial: A Physical Origin for the P vs. NP Problem and the Polynomial Hierarchy
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| Natura: | Recurso digital |
| Lingua: | inglese |
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Zenodo
2025
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| _version_ | 1866902236819357696 |
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| author | Babulik, Peter |
| author_facet | Babulik, Peter |
| contents | <p>The P vs. NP problem is one of the most profound unsolved questions in mathematics and com-<br>puter science. This paper proposes a new physical, rather than purely mathematical, origin for the<br>separation of these complexity classes. We posit the existence of a timeless, ”Platonic Computa-<br>tional Substrate” where information is unprocessed and all problems are equivalent, a state where<br>P=NP. We argue that the Big Bang was a cosmological symmetry-breaking event that initiated<br>a universal quantum computation. This act of computation, which creates the arrow of time, is<br>what breaks the symmetry and separates P from NP in our local universe. The ”hardness” of an<br>NP problem is a direct measure of the ”processional cost” (Information-Energy) required to locally<br>reverse this fundamental symmetry break. We extend this model to the Polynomial Hierarchy,<br>proposing that its higher levels correspond to fundamental principles of our universe’s structure.<br>We predict that the existence of stable, self-replicating systems (life) is a physical manifestation of<br>the universe solving a Σ2-type problem, while the stability of its physical laws is a manifestation<br>of it solving a Π2-type problem. This framework reframes computational complexity not as an<br>abstract mathematical property, but as a fundamental feature of the physics of our cosmos.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_16265474 |
| institution | Zenodo |
| language | eng |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | The Symmetry Dial: A Physical Origin for the P vs. NP Problem and the Polynomial Hierarchy Babulik, Peter Quantum mechanics Computational psychics <p>The P vs. NP problem is one of the most profound unsolved questions in mathematics and com-<br>puter science. This paper proposes a new physical, rather than purely mathematical, origin for the<br>separation of these complexity classes. We posit the existence of a timeless, ”Platonic Computa-<br>tional Substrate” where information is unprocessed and all problems are equivalent, a state where<br>P=NP. We argue that the Big Bang was a cosmological symmetry-breaking event that initiated<br>a universal quantum computation. This act of computation, which creates the arrow of time, is<br>what breaks the symmetry and separates P from NP in our local universe. The ”hardness” of an<br>NP problem is a direct measure of the ”processional cost” (Information-Energy) required to locally<br>reverse this fundamental symmetry break. We extend this model to the Polynomial Hierarchy,<br>proposing that its higher levels correspond to fundamental principles of our universe’s structure.<br>We predict that the existence of stable, self-replicating systems (life) is a physical manifestation of<br>the universe solving a Σ2-type problem, while the stability of its physical laws is a manifestation<br>of it solving a Π2-type problem. This framework reframes computational complexity not as an<br>abstract mathematical property, but as a fundamental feature of the physics of our cosmos.</p> |
| title | The Symmetry Dial: A Physical Origin for the P vs. NP Problem and the Polynomial Hierarchy |
| topic | Quantum mechanics Computational psychics |
| url | https://doi.org/10.5281/zenodo.16265474 |