1love.works · Theory of Interrelation
The legal-physics framework is the first empirical instrument of the Theory of Interrelation — proposing that human law is a measurable physical variable, present in the equations of thermodynamics, quantum mechanics, and general relativity but never previously identified as such.
The legal-physics framework documented on this page is the original work of Avv. Dr. Gian Marco Solas (Italian/EU qualified lawyer, PhD Maastricht/Cagliari, LLM College of Europe). Published in JLMI 1/25, SSRN 5694423, and Cambridge University Press (2019). All formulas, variables, and their application are © 2019–2026. The methodology is a public scientific contribution — citable and teachable. The instruments are proprietary.
The fundamental legal constant. Its mathematical genealogy begins with Shavell's standard model (Cambridge University Press, 2019), where λ is the legal risk probabilistic factor — the probability of success of a legal claim, used to determine the rational investment threshold c < λ(R). Extended for TPF investment valuation (empirically validated in the European truck cartel, +/- €300M pending settlement), then generalised to entire legal systems as λX = EX/MX in JLMI 2025. The probabilistic nature of λ is preserved throughout: λX measures the probability that a legal system is expressing its full potential value.
Derived from the Greek letter used to denote wavelength (λ) and the cosmological constant (Λ) in Einstein's field equations. The hypothesis proposes these are not merely analogous but unified — human law as a missing variable in physics equations.
The force exerted on a legal actor by a client, investor, or market participant. Triggers legal work cycles. In any legal system, PC manifests as demand for rights enforcement, market pressure for compliance, or litigation by affected parties.
From fluid mechanics and thermodynamics: pressure as vector force applied to a container. Here the container is the legal system, and the fluid is legal-economic activity.
The energy input that enables legal work to begin. The fee is not merely payment — it is the physical energy that removes friction and converts pressure into productive legal work. Without F, no work cycle starts. Applied to regulation: compliance costs are legal friction — the energy actors must expend simply to be permitted to operate, before any productive work begins.
From Joule's 1845 paper On the Mechanical Equivalent of Heat. F links monetary policy to entropy — money as the universal energy carrier in legal-economic systems.
The number of unresolved legal states in a system — undisclosed liabilities, opacity, unexpressed asset value, regulatory ambiguity, governance failures. Critically: W is a function of λ — the applicable law determines which states are unresolved. The higher W(λ), the greater the disorder, the higher the entropy. This is a genuine mathematical extension of Boltzmann's W to legal systems, not a metaphor.
Extends Boltzmann's W (number of physical microstates) to legal systems. The λ-dependence of W is the framework's original contribution: legal microstates are not absolute but relative to the applicable law.
Expected profit from a sustainable investment. π is amplified or destroyed by the legal factor λ — good governance, low legal weight, and SDG alignment increase net return; entropy and inertia reduce it. The formula makes governance mathematically inseparable from return.
Adapted from third-party funding investment models and generalised to any legal investment. Empirically validated in the European truck cartel collective redress initiative.
Any legal system X — a city, company, jurisdiction — is the sum of all its constituent legal acts, contracts, and norms. This makes legal systems mathematically tractable and universally comparable.
Like a vector sum in physics: the total legal force on a body is the sum of all individual legal forces acting upon it.
A local legal system X is embedded within and subject to Provincial (P), Regional (R), State (S), and International (I) law. The full legal weight bearing on any entity is the sum across all jurisdictional layers — from municipal bylaws to international treaties.
Analogous to nested coordinate systems in general relativity: each frame of reference is subject to the curvature imposed by the larger frame.
Both the mass in acceleration (MAλ) and the force (FXλ) are bound by applicable law λ. The car does not stop because of physics alone — it stops because λ (municipal traffic law) acts on both the mass (driver+car system) and the force (legal obligation to stop). Without λ, there is no legal event, only a physical one.
Newton's F=MA: the red light is a legal force vector that decelerates the mass 'driver+car'. CCTV provides the objective measurement of the spatio-temporal legal event.
Applicable law (λ) is proposed as the physical equivalent of the speed of light squared (C²) in Einstein's E=MC². Like light, law has both particle properties (specific legal acts, binding decisions) and wave properties (general principles, jurisprudential influence spreading across systems). Law is the beacon of science — what we can, cannot, and must do in any legal frame of reference.
Einstein's wave-particle duality of light: 'We have two contradictory pictures of reality; separately neither fully explains the phenomena of light, but together they do.' The same applies to law as both specific act and general principle.
Legal weight equals mass multiplied by a λ-dependent gravitational function G(λ). This is formally analogous to Einstein's cosmological constant Λ: excessive legal weight acts as a brake on the expansion of the civilisation progress spiral. When W is optimal, the legal universe expands sustainably — the Fibonacci spiral of civilisation progress.
Einstein's cosmological constant Λ was introduced to prevent universal expansion. Legal weight W = MG(λ) plays the same role in civilisation space-time: at the right level it provides structure; in excess it prevents the expansion of human potential.
Entropy of a legal system equals the Boltzmann constant (k) multiplied by the logarithm of the number of unresolved legal states W(λ) — where W is itself a function of the applicable law λ. The same set of facts produces different entropy in different legal systems. W counts all sources of legal disorder: opacity, undisclosed liabilities, governance failures, regulatory ambiguity, unexpressed asset value.
Boltzmann 1877: S = k log W. In thermodynamics, W counts physical microstates. In legal systems, W(λ) counts unresolved legal states relative to the applicable law — introducing the λ-dependence as the framework's original contribution.
The framework builds on three published contributions. The Shavell standard model (Cambridge University Press, 2019) — the established rational claim condition c < λ(R), where λ is the legal risk probabilistic factor — was extended for third-party funding investment valuation and empirically validated in the European truck cartel collective redress initiative (+/- €300M pending settlement).
This was generalised to entire legal systems in JLMI 2025: λX = EX/MX measures the ratio of expressed potential to total legal mass in any system, using UN SDGs as universal benchmark. Empirically tested in Masainas, Sardinia (270 comuni, €21.65B net unexpressed value identified).
The framework was not built by a physicist. It was built by a lawyer who studied physics and identified a missing variable. Finding out whether that variable belongs in the equations is the work of those who built the equations.
Researchers interested in collaborating — accessing the empirical dataset, co-authoring on the pre-print, or testing the framework — are welcome to reach out.
✉ gmsolas@sustainab-law.euItalian and EU qualified lawyer. Founder of Sustainab-Law and inventor of the 1love.works algorithm and related legal technology — phenography, phenocurrency, and fractal cross-pollination — for the codification of sustainable legal systems.
15+ years of experience in global litigation funds, national and international law firms, and at the European Commission. Leading Expert at the BRICS Competition Law & Policy Centre (Higher School of Economics, Moscow). Counsel at Omni Bridgeway (Amsterdam), consultant at Woodsford Litigation Funding (London).
The author's competence is in the legal and economic foundations: litigation funding, competition law, GDPR, EU regulatory frameworks, and the λX codification methodology. The physics, mathematics and neuroscience validation is explicitly the work of the scientific community.
For complex cases requiring legal remediation, conversion of liabilities into sustainable investments, collective redress, or litigation finance — direct mandate with the author of the legal-physics methodology.
Book consultation →The scanner is designed as a scientific instrument — the same document should produce consistent scores. The current beta version uses LLM-based scoring which introduces variance. Score calibration is in active development. Every scan contributes to the empirical dataset.
© 2019–2026 Avv. Dr. Gian Marco Solas · JLMI 1/25 · SSRN 5694423 · 1love.works · All rights reserved.