Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.08507 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908701500112896 |
|---|---|
| author | Imafuku, Kentaro |
| author_facet | Imafuku, Kentaro |
| contents | Why do local actions and exponential Euclidean weights arise so universally in classical, statistical, and quantum theories? We offer a structural explanation from minimal constraints on finite descriptions of admissible histories. Assume that histories admit finite, self-delimiting (prefix-free) generative codes that can be decoded sequentially in a single forward pass. These purely syntactic requirements define a minimal descriptive cost, interpretable as a smoothed minimal program length, that is additive over local segments. First, any continuous local additive cost whose stationary sector coincides with the empirically identified classical variational sector is forced into a unique Euler--Lagrange equivalence class. Hence the universal form of an action is fixed by descriptional structure alone, while the specific microscopic Lagrangian and couplings remain system-dependent semantic input. Second, independently of microscopic stochasticity, finite prefix-free languages exhibit exponential redundancy: many distinct programs encode the same coarse history, and this redundancy induces a universal exponential multiplicity weight on histories. Requiring this weight to be real and bounded below selects a real Euclidean representative for stable local bosonic systems, yielding the standard Euclidean path-integral form. When Osterwalder--Schrader reflection positivity holds, the Euclidean measure reconstructs a unitary Lorentzian amplitude. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_08507 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Syntactic Structure, Quantum Weights Imafuku, Kentaro Quantum Physics Why do local actions and exponential Euclidean weights arise so universally in classical, statistical, and quantum theories? We offer a structural explanation from minimal constraints on finite descriptions of admissible histories. Assume that histories admit finite, self-delimiting (prefix-free) generative codes that can be decoded sequentially in a single forward pass. These purely syntactic requirements define a minimal descriptive cost, interpretable as a smoothed minimal program length, that is additive over local segments. First, any continuous local additive cost whose stationary sector coincides with the empirically identified classical variational sector is forced into a unique Euler--Lagrange equivalence class. Hence the universal form of an action is fixed by descriptional structure alone, while the specific microscopic Lagrangian and couplings remain system-dependent semantic input. Second, independently of microscopic stochasticity, finite prefix-free languages exhibit exponential redundancy: many distinct programs encode the same coarse history, and this redundancy induces a universal exponential multiplicity weight on histories. Requiring this weight to be real and bounded below selects a real Euclidean representative for stable local bosonic systems, yielding the standard Euclidean path-integral form. When Osterwalder--Schrader reflection positivity holds, the Euclidean measure reconstructs a unitary Lorentzian amplitude. |
| title | Syntactic Structure, Quantum Weights |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2512.08507 |