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Karl Svozil

Publications and source records attributed to Karl Svozil.

At least 37 records · Page 2Linked to original sources
arXiv2026

From Unitarity to Irreversibility: The Role of Infinite Tensor Products and Nested Wigner's Friends

The transition from unitary, reversible von Neumann-Everett quantum processes to non-unitary, irreversible processes and measurements is explored through infinite tensor products interpreted as nested, chained, or iterated Wigner's friend scenarios. Infinite tensor products can disrupt unitary equivalence through sectorization and factorization, drawing parallels to concepts from real analysis, recursive mathematics, and statistical physics.

quant-ph↗
arXiv2026

Dirac's Dilemma of the Economy of Inheritance: Parental Care, Equality of Opportunity, and Managed Inequality

In a brief reflection on the principles of human society, P. A. M. Dirac articulated a structural tension between two widely affirmed norms: that it is good and natural for parents to improve the prospects of their own children, and that justice requires that all children have equal opportunities in life. These principles, each compelling on its own, cannot be fully realized together. This paper reconstructs Dirac's dilemma, connects it to the dynamics of compounding advantage and inheritance, and situates it within the broader history of political philosophy, including the work of Rawls, Dworkin, Cohen, Brighouse and Swift, Nozick, Murphy and Nagel, and others. The paper argues that attempts to eliminate the resulting injustices entirely risk damaging the non--zero--sum structures that generate general prosperity, and defends a position of "managed inequality": a robust social floor and real mobility, combined with limits on extreme dynastic accumulation and an explicit acceptance of some residual, but constrained, inherited advantage.

physics.soc-ph↗
arXiv2025

Irreducible Rules and Equivalence Classes of One-dimensional Cellular Automata

One-dimensional cellular automata are discrete dynamical systems that operate on an infinite lattice of sites and are characterized by the locality and uniformity of their update rule. Permutations of the state set and isometric transformations of the lattice induce symmetry transformations on the set of local rules and the set of global maps of cellular automata, resulting in a partitioning of the set of cellular automata into equivalence classes. The concept of an irreducible local rule that depends on all its coordinates is used to analyse the equivalence classes and results on the number of equivalence classes of irreducible binary local rules and binary global maps are presented. Finally, another symmetry operator based on the scaling of neighbourhoods is introduced and the change in the number of equivalence classes is analysed.

nlin.CG↗
arXiv2025

Nuclear Detonations as Probes of Hidden Superluminal Sectors

We propose a highly speculative phenomenological framework in which nuclear detonations and high-energy collisions serve as probes for hidden sectors with effective superluminal propagation. Motivated by analogies between acoustic and electromagnetic phenomena, we stratify the physical description into three layers: a fundamental ``substrate'' layer, hidden-sector fields with extended causal cones, and the emergent Standard Model. We posit that the extreme, macroscopic stress-energy gradients generated by nuclear explosions might excite substrate or hidden modes that remain kinematically inaccessible to standard laboratory probes. This work unifies various exotic proposals -- including extra-dimensional shortcuts and trans-metric shockwaves -- into a single formalism, discussing the constraints imposed by causality and observation while outlining how such distinct high-energy regimes could complement one another in searching for physics beyond the emergent metric.

hep-ph↗
arXiv2025

Causal Rigidity and the Single-Unit Universe: Integrating the Alexandrov-Zeeman and Unruh Clock Scales

We unify two complementary viewpoints on relativistic spacetime and the counting of fundamental constants. Operationally, Matsas, Pleitez, Saa, and Vanzella (MPSV) have recently argued that relativistic spacetime requires only a single fundamental dimensional constant. Mathematically, theorems due to Alexandrov and Zeeman demonstrate that the light-cone structure determines the spacetime geometry only up to a conformal factor. We show that these approaches are mutually reinforcing: the Alexandrov-Zeeman theorems establish the rigid conformal structure of spacetime, while the ``bona fide clock'' required by MPSV serves the necessary mathematical role of breaking the dilation symmetry. We provide a formal derivation proving that the normalization of a single clock worldline is sufficient to select a unique metric from the conformal class, thereby clarifying that the number of fundamental constants is exactly one.

gr-qc↗
arXiv2025

Anti-Gravity from Vacancies in Fractal Space-Time: The Case of a Menger Sponge

We explore the idea that anti-gravity, interpreted as matter-matter repulsion, may emerge as an effective description of spacetime with a reduced local ``substratum density,'' modeled heuristically by vacancies in a fractal lattice. Using the Menger Sponge as a prototypical vacancy-dominated fractal, we motivate a phenomenological identification of a net vacancy parameter with the mass parameter in the Schwarzschild solution. This yields an effective negative-mass Schwarzschild-like metric for embedded observers when vacancies dominate. We analyze curvature, geodesic motion, and energy-condition issues, and we emphasize that our construction is not a microscopic derivation from a specific stress-energy tensor but a re-interpretation of the negative-mass Schwarzschild geometry in terms of fractal vacancies. We discuss conceptual implications, stability challenges, and possible observational signatures.

gr-qc↗
arXiv2025

Orbits of One-Dimensional Cellular Automata Induced by Symmetry Transformations

Using a group-theoretic approach, a method for determining the equivalence classes (also called orbits) of the set of rules of one-dimensional cellular automata induced by the symmetry operations of reflection and permutation and their product is presented. Orbits are classified by their isomorphism type. Results for the number of orbits and the number of orbits by type for state sets of size two and three are included.

nlin.CG↗
arXiv2025

Exploring Quantum Contextuality with the Quantum Moebius-Escher-Penrose hypergraph

This paper presents the quantum Moebius-Escher-Penrose hypergraph, drawing inspiration from paradoxical constructs such as the Moebius strip and Penrose's `impossible objects'. The hypergraph is constructed using faithful orthogonal representations in Hilbert space, thereby embedding the graph within a quantum framework. Additionally, a quasi-classical realization is achieved through two-valued states and partition logic, leading to an embedding within a Boolean algebra. This dual representation delineates the distinctions between classical and quantum embeddings, with a particular focus on contextuality, highlighted by violations of exclusivity and completeness, quantified through classical and quantum probabilities. The study also examines violations of Boole's conditions of possible experience using correlation polytopes, underscoring the inherent contextuality of the hypergraph. These results offer deeper insights into quantum contextuality and its intricate relationship with classical logic structures.

quant-ph↗
arXiv2025

Chromatic Quantum Contextuality

Chromatic quantum contextuality is a criterion of quantum nonclassicality based on (hyper)graph coloring constraints. If a quantum hypergraph requires more colors than the number of outcomes per maximal observable (context), it lacks a classical realization with n-uniform outcomes per context. Consequently, it cannot represent a "completable" non-contextual set of coexisting n-ary outcomes per maximal observable. This result serves as a chromatic analogue of the Kochen-Specker theorem. We present an explicit example of a four-colorable quantum logic in dimension three. Furthermore, chromatic contextuality suggests a novel restriction on classical truth values, thereby excluding two-valued measures that cannot be extended to $n$-ary colorings. Using this framework, we establish new bounds for the house, pentagon, and pentagram hypergraphs, refining previous constraints.

quant-ph↗
arXiv2025

Exploitation of Eurosystem Loopholes and Their Quantitative Reconstruction

This paper identifies and analyzes six key strategies used to exploit the Eurosystem's financial mechanisms, and attempts a quantitative reconstruction: inflating TARGET balances, leveraging collateral swaps followed by defaults, diluting self-imposed regulatory rules, issuing money through Emergency Liquidity Assistance (ELA), acquisitions facilitated via the Agreement on Net Financial Assets (ANFA), and the perpetual (re)issuance of sovereign bonds as collateral. The paper argues that these practices stem from systemic vulnerabilities or deliberate opportunism within the Eurosystem. While it does not advocate for illicit activities, the paper highlights significant weaknesses in the current structure and concludes that comprehensive reforms are urgently needed.

econ.GN↗
arXiv2024

Converting nonlocality into contextuality

Matrix pencils provide a robust method for finding simultaneous eigensystems of mutually commuting degenerate operators. In this paper, we utilize these techniques to investigate the quantum logical structures of the Peres-Mermin square and the Greenberger-Horne-Zeilinger-Mermin configuration. Our analysis uncovers analogous complete contradictions between classical and quantum predictions in a four-dimensional system involving two spin-1/2 particles.

quant-ph↗
arXiv2024

How Real is Incomputability in Physics?

A physical system is determined by a finite set of initial conditions and "laws" represented by equations. The system is computable if we can solve the equations in all instances using a "finite body of mathematical knowledge". In this case, if the laws of the system can be coded into a computer program, then given the initial conditions of the system, one can compute the system's evolution. Are there incomputable physical systems? This question has been theoretically studied in the last 30-40 years. In this paper, we experimentally show for the first time the strong incomputability of a quantum experiment, namely the outputs of a quantum random number generator. Moreover, the experimental results are robust and statistically significant.

quant-ph↗
arXiv2024

Binary Quantum Random Number Generator Based on Value Indefinite Observables

All quantum random number generators based on measuring value indefinite observables are at least three-dimensional because the Kochen-Specker Theorem and the Located Kochen-Specker Theorem are false in dimension two. In this article, we construct quantum random number generators based on measuring a three-dimensional value indefinite observable that generates binary quantum random outputs with the same randomness qualities as the ternary ones: the outputs are maximally unpredictable.

quant-ph↗
arXiv2024

Form of Contextuality Predicting Probabilistic Equivalence between Two Sets of Three Mutually Noncommuting Observables

We introduce a contextual quantum system comprising mutually complementary observables organized into two or more collections of pseudocontexts with the same probability sums of outcomes. These pseudocontexts constitute non-orthogonal bases within the Hilbert space, featuring a state-independent sum of probabilities. In other words, regardless of the initial state preparation, the total probability remains constant but may be distinct from unity. The measurement contextuality in this setup arises from the quantum realizations of the hypergraph, which adhere to a specific bound on the linear combination of probabilities. In contrast, classical realizations can surpass this bound. The violation of quantum bounds stems from the inability of classical ontological models, specifically the set-theoretic representation of the hypergraph corresponding to the quantum observables' collections, to adhere to and explain the observed statistics.

quant-ph↗
arXiv2023

The Emergence of Cognition and Computation: A Physicalistic Perspective

A physicalistic argument can support the idea that cognition is an emergent property driven by dissipation. This argument suggests that cognition arises not from any fiat desire to understand the world, but rather because a certain type of cognition promotes dissipation, which is advantageous for agents seeking to increase the dissipation of resources, especially energy, in their favor. In other words, cognitive agents are better equipped to acquire physical resources and means, giving them an advantage in survival and reproduction. Similarly, the efficient use of computation can also serve as a means of dissipating energy for the computing agent. Efficiency, in this context, is not determined by moral or ethical principles, but rather by the ability to effectively aggregate resources. When used efficiently, computation becomes a powerful tool for dissipating energy and enhancing the survival and reproduction of the agent utilizing it.

physics.gen-ph↗
arXiv2023

Extensions of Hardy-type true-implies-false gadgets to classically obtain indistinguishability

In quantum logical terms, Hardy-type arguments can be uniformly presented and extended as collections of intertwined contexts and their observables. If interpreted classically those structures serve as graph-theoretic "gadgets" that enforce correlations on the respective preselected and postselected observable terminal points. The method allows the generalization and extension to other types of relational properties, in particular, to novel joint properties predicting classical equality of quantum mechanically distinct observables. It also facilitates finding faithful orthogonal representations of quantum observables.

quant-ph↗