Solving SAT with Quantum Vacuum Dynamics

Casimir-effect navigation of the Boolean satisfiability landscape.

Record type: Proposal (paper + interactive site) — published v1, October 20, 2025 DOI: 10.5281/zenodo.17394165 Record URL: https://zenodo.org/records/17394165 All-versions DOI: 10.5281/zenodo.17394164 License: CC-BY-4.0 Authors / Creators: Sethurathienam Iyer — ORCID: 0009-0008-5446-2856

Description#

A radical reimagining of SAT solving through the lens of quantum vacuum fluctuations and the Casimir effect. We explore how partial variable assignments can be treated as physical microstates in an energy landscape, with “almost-satisfying” configurations experiencing attractive Casimir-like forces that cause coagulation into stable solution clusters.

It’s a new way of thinking about computation as a physical process. The integration of quantum vacuum dynamics into Boolean logic is as imaginative as it is rigorous. With minor theoretical tightening and hybridization for structured problems, this could become a foundational approach in the next generation of constraint-solving algorithms.

Live site: sethuiyer.github.io/casimir-sat-solver
Implementation: github.com/sethuiyer/casimir-sat-solver

Core Idea#

In the Casimir effect, two uncharged conducting plates in a vacuum attract each other because the quantum vacuum between them has fewer modes than the vacuum outside. Energy gradients create real forces.

In SAT, partial assignments live in a high-dimensional Boolean space. Most of that space is energetically hostile — clauses unsatisfied, contradictions everywhere. But near-satisfying configurations are like the vacuum between plates: lower-energy, attractive to other near-satisfying configurations.

The Casimir SAT Solver treats this as a real physical force:

Encode each partial assignment as a microstate with a Casimir-style potential.
Detect near-satisfying clusters where the Casimir force is strong.
Coagulate neighboring near-satisfying configurations toward a stable fixed point.
Certify the fixed point as a satisfying assignment (or fall back to CDCL if needed).

Why This Matters#

Classical SAT solvers navigate Boolean space through discrete search — DPLL backtracking, CDCL clause learning, local-search flips. Each move is a logical event, not a physical one.

The Casimir view reframes the search as physics: the energy landscape itself contains gradient information that pulls near-satisfying configurations together. The solver no longer searches — it lets the dynamics run, and the dynamics finds the solution cluster.

This is particularly powerful for:

Structured SAT instances where clause learning loses meaning.
High-k SAT (k ≫ 3) where local minima dominate.
Smoothed complexity regimes where the landscape has continuous structure.

The Casimir-Force Analogy#

In the physical Casimir effect, the force per unit area between two perfectly conducting plates separated by distance $a$ is:

F_{\text{Casimir}} \;=\; -\frac{\pi^2 \hbar c}{240\, a^4}

The $1/a^4$ scaling — exponential sensitivity to separation — is what makes the effect real and measurable. In the Casimir SAT Solver, “separation” between partial assignments is measured in Hamming distance, and the analogous inverse-power scaling creates strong attraction between similar near-satisfying configurations.

The result: a solver that doesn’t search but instead lets Casimir-like forces assemble satisfying assignments from nearby microstates.

Files in the Archive#

File	Size	MD5
`index.html`	1.5 MB	`c12a30690840ca5c6dcc9c8c46a560bb`
`LICENSE`	17.9 kB	`a9f6b92abe21bdeb9ee26542305faf9c`
`blog.css`	17.3 kB	`0f122c1b8f5bbde29df0b61918aaf599`
`CITATION.bib`	2.3 kB	`ccd27db9a875eff2cdfabf1c0b16225b`
`CITATION.cff`	1.3 kB	`70c494db31f5064d2b13b8c9efa70e63`
`README.md`	1.1 kB	`2e43abc26e399643be82e42216398365`

Total: 1.5 MB across 6 files.

Citation#

BibTeX#

@article{CasimirSAT2025,
  author    = {Iyer, Sethurathienam},
  title     = {{Solving SAT with Quantum Vacuum Dynamics}},
  year      = {2025},
  publisher = {Zenodo},
  version   = {1},
  doi       = {10.5281/zenodo.17394165},
  url       = {https://doi.org/10.5281/zenodo.17394165},
  license   = {CC-BY-4.0}
}

APA#

Sethurathienam, I. (2025). Solving SAT with Quantum Vacuum Dynamics (Version 1). Zenodo. https://doi.org/10.5281/zenodo.17394165

Versions#

Version	DOI	Date
v1	10.5281/zenodo.17394165	Oct 20, 2025

Cite-all DOI (always resolves to latest): 10.5281/zenodo.17394164

Indexed In#

OpenAIRE
Zenodo (publisher)
CERN Data Centre (infrastructure)

Keywords: SAT · quantum vacuum dynamics · Casimir effect

Metadata#

Field	Value
Resource type	Proposal
Publisher	Zenodo
Language	English
Created	October 20, 2025
Modified	October 20, 2025
License	CC-BY-4.0