The neutral kaon system offers a unique possibility to perform fundamental tests of CPT invariance, as well as of the basic principles of quantum mechanics. The most recent limits obtained by the KLOE experiment at the DAΦNE e+e− collider on several kinds of possible CPT violation and decoherence mechanisms, which in some cases might be justified in a quantum gravity framework, are reviewed. No deviation from the expectations of quantum mechanics and CPT symmetry is observed, while the precision of the (...) measurements, in some cases, reaches the interesting Planck scale region. Finally, prospects for this kind of experimental studies at KLOE-2 are presented. (shrink)

CPT invariance and the spin-statistics connection are typically taken to be essential properties in relativistic quantum field theories (RQFTs), insofar as the CPT and Spin-Statistics theorems entail that any state of a physical system characterized by an RQFT must possess these properties. Moreover, in the physics literature, they are typically taken to be properties of particles. But there is a Received View among philosophers that RQFTs cannot fundamentally be about particles. This essay considers what proofs of the CPT and Spin-Statistics (...) theorems suggest about the ontology of RQFTs, and the extent to which this is compatible with the Received View. I will argue that such proofs suggest the Received View’s approach to ontology is flawed. (shrink)

This book seeks to answer the question "What explains CPT invariance and the spin-statistics connection?" These properties play foundational roles in relativistic quantum field theories, are supported by high-precision experiments, and figure into explanations of a wide range of phenomena, from antimatter, to the periodic table of the elements, to superconductors and superfluids. They can be derived in RQFTs by means of the famous CPT and Spin-Statistics theorems; but, the author argues, these theorems cannot be said to explain these properties, (...) at least under standard philosophical accounts of scientific explanation. This is because there are multiple, in some cases incompatible, ways of deriving these theorems, and, secondly, because the theorems fail for the types of theories that underwrite the empirical evidence: non-relativistic quantum theories, and realistic interacting RQFTs. The goal of this book is to work towards an understanding of CPT invariance and the spin-statistics connection by first providing an analysis of the necessary and sufficient conditions for these properties, and second by advocating a particular account of explanation appropriate for this context. (shrink)

Lüders and Pauli proved the $\mathcal{CPT}$ theorem based on Lagrangian quantum field theory almost half a century ago. Jost gave a more general proof based on “axiomatic” field theory nearly as long ago. The axiomatic point of view has two advantages over the Lagrangian one. First, the axiomatic point of view makes clear why $\mathcal{CPT}$ is fundamental—because it is intimately related to Lorentz invariance. Secondly, the axiomatic proof gives a simple way to calculate the $\mathcal{CPT}$ transform of any relativistic field (...) without calculating $\mathcal{C}$ , $\mathcal{P}$ and $\mathcal{T}$ separately and then multiplying them. The purpose of this pedagogical paper is to “deaxiomatize” the $\mathcal{CPT}$ theorem by explaining it in a few simple steps. We use theorems of distribution theory and of several complex variables without proof to make the exposition elementary. (shrink)

This paper is a sequel to various papers by the author devoted to the EPR correlation. The leading idea remains that the EPR correlation (either in its well-known form of nonseparability of future measurements, or in its less well-known time-reversed form of nonseparability of past preparations) displays the intrinsic time symmetry existing in almost all physical theories at the elementary level. But, as explicit Lorentz invariance has been an essential requirement in both the formalization and the conceptualization of my papers, (...) the noninvariant concept ofT symmetry has to yield in favor of the invariant concept ofPT symmetry, or even (asC symmetry is not universally valid) to that ofCPT invariance. A distinction is then drawn between “macro” special relativity, defined by invariance under the orthochronous Lorentz group and submission to the retarded causality concept, and “micro” special relativity, defined by invariance under the full Lorentz group and includingCPT symmetry. TheCPT theorem clearly implies that “micro special relativity”is relativity theory at the quantal level. It is thus of fundamental significance not only in the search of interaction Lagrangians, etc., but also in the basic interpretation of quantum mechanics, including the understanding of the EPR correlation. While the experimental existence of the EPR correlations is manifestly incompatible with macro relativity, it is fully consistent with micro relativity. Going from a retarded concept of causality to one that isCPT invariant has very radical consequences, which are briefly discussed. (shrink)

The CPT theorem states that any causal, Lorentz-invariant, thermodynamically well-behaved quantum field theory must also be invariant under a reflection symmetry that reverses the direction of time, flips spatial parity, and conjugates charge. Although its physical basis remains obscure, CPT symmetry appears to be necessary in order to unify quantum mechanics with relativity. This paper attempts to decipher the physical reasoning behind proofs of the CPT theorem in algebraic quantum field theory. Ultimately, CPT symmetry is linked to a systematic reversal (...) of the C*-algebraic Lie product that encodes the generating relationship between observables and symmetries. In any physically reasonable relativistic quantum field theory it is always possible to systematically reverse this generating relationship while preserving the dynamics, spectra, and localization properties of physical systems. Rather than the product of three separate reflections, CPT symmetry is revealed to be a single global reflection of the theory’s state space. (shrink)

I discuss a model inspired from the string/brane framework, in which our Universe is represented (after perhaps appropriate compactification) as a three brane, propagating in a bulk space time punctured by D0-brane (D-particle) defects. As the D3-brane world moves in the bulk, the D-particles cross it, and from an effective observer on D3 the situation looks like a “space-time foam” with the defects “flashing” on and off (“D-particle foam”). The open strings, with their ends attached on the brane, which represent (...) matter in this scenario, can interact with the D-particles on the D3-brane universe in a topologically non-trivial manner, involving splitting and capture of the strings by the D0-brane defects. Such processes are consistently described by logarithmic conformal field theories on the world-sheet of the strings. Physically, they result in effective decoherence of the string matter on the D3 brane, and as a result, of CPT Violation, but of a type that implies an ill-defined nature of the effective CPT operator. Due to electric charge conservation, only electrically neutral (string) matter can exhibit such interactions with the D-particle foam. This may have unique, experimentally detectable (in principle), consequences for electrically-neutral entangled quantum matter states on the brane world, in particular the modification of the pertinent Einstein-Podolsky-Rosen (EPR) Correlation in neutral mesons in an appropriate meson factory. For the simplest scenarios, the order of magnitude of such effects might lie within the sensitivity of upgraded φ-meson factories. (shrink)

We provide a careful development and rigorous proof of the CPT theorem within the framework of mainstream quantum field theory. This is in contrast to the usual rigorous proofs in purely axiomatic frameworks, and non-rigorous proof-sketches in the mainstream approach. We construct the CPT transformation for a general field directly, without appealing to the enumerative classification of representations, and in a manner that is clearly related to the requirements of our proof. Our approach applies equally in Minkowski spacetimes of any (...) dimension at least three, and is in principle neutral between classical and quantum field theories: the quantum CPT theorem has a natural classical analogue. The key mathematical tool is that of complexification; this tool is central to the existing axiomatic proofs, but plays no overt role in the usual mainstream approaches to CPT. (shrink)

Philosophers of physics are split on whether foundational issues in relativistic quantum field theory should be framed within pragmatist approaches, which trade mathematical rigor for the ability to formulate non-trivial interacting models, or purist approaches, which trade the ability to formulate non-trivial interacting models for mathematical rigor. This essay addresses this debate by viewing it through the lens of the CPT theorem. I first consider two formulations of the CPT theorem, one purist and the other pragmatist, and extract from them (...) a set of problems that clarifies the distinction between pragmatism and purity. I then apply this distinction to Greenberg's influential claim that the violation of CPT invariance in an interacting RQFT entails the violation of Lorentz invariance. I show how this claim rests on an unsuccessful attempt to mediate between pragmatism and purity. I then evaluate another attempt at such mediation in the form of causal perturbation theory. This approach suggests that a focus on renormalized perturbation theory as a way of distinguishing pragmatists from purists may be misleading. (shrink)

This dissertation explores several issues related to the CPT theorem. Chapter 2 explores the meaning of spacetime symmetries in general and time reversal in particular. It is proposed that a third conception of time reversal, 'geometric time reversal', is more appropriate for certain theoretical purposes than the existing 'active' and 'passive' conceptions. It is argued that, in the case of classical electromagnetism, a particular nonstandard time reversal operation is at least as defensible as the standard view. This unorthodox time reversal (...) operation is of interest because it is the classical counterpart of a view according to which the so-called 'CPT theorem' of quantum field theory is better called 'PT theorem'; on this view, a puzzle about how an operation as apparently non-spatio-temporal as charge conjugation can be linked to spacetime symmetries in as intimate a way as a CPT theorem would seem to suggest dissolves. In chapter 3, we turn to the question of whether the CPT theorem is an essentially quantum-theoretic result. We state and prove a classical analogue of the CPT theorem for systems of tensor fields. This classical analogue, however, appears not to extend to systems of spinor fields. The intriguing answer to our question thus appears to be that the CPT theorem for spinors is essentially quantum-theoretic, but that the CPT theorem for tensor fields applies equally to the classical and quantum cases. Chapter4 explores a puzzle that arises when one puts the CPT theorem alongside a standard way of understanding spacetime symmetries, according to which spacetime symmetries are to be understood in terms of background spacetime structure. The puzzle is that a 'PT theorem' amounts to a statement that the theory may not make essential use of a preferred direction of time, and this seems odd. We propose a solution to that puzzle for the case of tensor field theories. (shrink)

The CPT theorem of quantum field theory states that any relativistic (Lorentz-invariant) quantum field theory must also be invariant under CPT, the composition of charge conjugation, parity reversal and time reversal. This paper sketches a puzzle that seems to arise when one puts the existence of this sort of theorem alongside a standard way of thinking about symmetries, according to which spacetime symmetries (at any rate) are associated with features of the spacetime structure. The puzzle is, roughly, that the existence (...) of a CPT theorem seems to show that it is not possible for a well-formulated theory that does not make use of a preferred frame or foliation to make use of a temporal orientation. Since a manifold with only a Lorentzian metric can be temporally orientable—capable of admitting a temporal orientation—this seems to be an odd sort of necessary connection between distinct existences. The paper then suggests a solution to the puzzle: it is suggested that the CPT theorem arises because temporal orientation is unlike other pieces of spacetime structure, in that one cannot represent it by a tensor field. To avoid irrelevant technical details, the discussion is carried out in the setting of classical field theory, using a little-known classical analog of the CPT theorem. (shrink)

Contemporary psychotherapy is mainly dominated by Western psychological paradigms, yet philosophy and religion have long served as frameworks for healing and guidance. This paper argues that Chinese wisdom traditions—Confucianism, Daoism, and Chinese Buddhism—can meaningfully contribute to philosophical therapy, serving not merely as cultural supplements but as foundational normative frameworks in their own right. Like Stoicism and Epicureanism in the Hellenistic era, these traditions provide distinct visions of the good life, structured practices for self-cultivation, and pathways to inner harmony. Drawing on (...) Albert Ellis’s Rational Emotive Behavior Therapy (REBT) as a template, we propose that Chinese philosophical traditions can contribute to therapeutic practice in three distinct ways: first, as augmentations to existing cognitive behavioral therapies (CBT); second, as components of an eclectic Chinese Philosophical Therapy (CPT) that systematically combines all three traditions; and third, as independent normatively-directed therapeutic specializations, each with its own theoretical coherence and clinical protocols. We outline three complementary approaches: Daoist therapy (emphasizing effortless action and alignment with nature), Buddhist therapy (following the Four Noble Truths and Eightfold Path to alleviate suffering), and Confucian therapy (focusing on moral cultivation and social harmony). Each approach includes specific doctrines, practices, and pedagogies aimed at transforming clients’ “lived understandings”—their deeply embodied habits of thought, feeling, and action—thereby relieving emotional distress and promoting wholeness and virtue. By positioning Chinese traditions within a normative philosophical therapy framework, this work lays the groundwork for culturally attuned therapeutic models. We conclude by discussing implications for therapist training, multicultural competence, ethical safeguards, and directions for future empirical research. (shrink)

The CP-violation problem and unconditional tests of discrete symmetries T and CPT are investigated in the exact quantum theory (QT) beyond the usually used Lee-Oehme-Yang (LOY) theory, which is based on the famous Weisskopf-Wigner (WW) approximation. New unconditional CP-violation effects, independent from those known before, new unconditional tests of the CPT and T invariances, and new results for correlations are derived. Corresponding general results are obtained for\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$K^0 - \bar K^0,{\mathbf{ }}B^0 (...) - \bar B^0,{\mathbf{ }}D^0 - \bar D^0 $$ \end{document} mesons. On the base of these new theoretical results, some proposals for experiments by CP LEAR and ϕ, B factories are given. The new results are interesting not only for the CP-violation problem itself but also for testing violation of the standard quantum dynamics connected with ideas of quantum gravity. (shrink)

A realistic physical axiomatic approach of the relativistic quantum field theory is presented. Following the action principle of Schwinger, a covariant and general formulation is obtained. The correspondence principle is not invoked and the commutation relations are not postulated but deduced. The most important theorems such as spin-statistics, and CPT are proved. The theory is constructed form the notion of basic field and system of basic fields. In comparison with others formulations, in our realistic approach fields are regarded as real (...) things with symmetry properties. Finally, the general structure is contrasted with other formulations. (shrink)

The role of CPT invariance and consequences for bipartite entanglement of neutral (K) mesons are discussed. A relaxation of CPT leads to a modification of the entanglement which is known as the ω effect. The relaxation of assumptions required to prove the CPT theorem are examined within the context of models of space-time foam. It is shown that the evasion of the EPR type entanglement implied by CPT (which is connected with spin statistics) is rather elusive. Relaxation of locality (through (...) non-commutative geometry) or the introduction of an environment do not by themselves lead to a destruction of the entanglement. One model of the environment, which is based on non-critical strings and D-particle capture and recoil, leads to a specific momentum dependent stochastic contribution to the space-time metric and consequent change in the neutral meson bipartite entanglement. Although the class of models producing the omega effect is non-empty, the lack of an omega effect is demonstrated for a wide class of models based on thermal like baths which are often considered as generic models appropriate for the study of space-time foam. (shrink)

Quantum theory of Lorentz invariant local scalar fields without restrictions on 4-momentum spectrum is considered. The mass spectrum may be both discrete and continues and the square of mass as well as the energy may be positive or negative. One may assume the existence of such fields only if they interact with ordinary fields very weakly. Generalization of Kallen-Lehmann representation for propagators of these fields is found. The considered generalized fields may violate CPT-invariance. Restrictions on mass-spectrum of CPT-violating fields are (...) found. Local fields that annihilate vacuum state and violate CPT-invariance are constructed in this scope. Correct local relativistic generalization of Lindblad equation for density matrix is written for such fields. This generalization is particularly needed to describe the evolution of quantum system and measurement process in a unique way. Difficulties arising when the field annihilating the vacuum interacts with ordinary fields are discussed. (shrink)

A non-Abelian, Universal SpaceTime Ontology is introduced in terms of Categories, Functors, Natural Transformations, Higher Dimensional Algebra and the Theory of Levels. A Paradigm shift towards Non-Commutative Spacetime structures with remarkable asymmetries or broken symmetries, such as the CPT-symmetry violation, is proposed. This has the potential for novel applications of Higher Dimensional Algebra to SpaceTime structure determination in terms of universal, topological invariants of ‘hidden’ symmetry. Fundamental concepts of Quantum Algebra and Quantum Algebraic Topology, such as Quantum Groups, von Neumann (...) and Hopf Algebras are first considered with a view to their possible extensions and future applications in Quantum Field theories. New, non-Abelian results may be obtained through Higher Homotopy, General van Kampen Theorems, Lie Groupoids/algebroids and Groupoid Atlases, possibly with novel applications to Quantum Dynamics and Local-to-Global Problems, Quantum Logics and Logic Algebras. Many-valued Logics, Łukasiewicz–Moisil Logics lead to Generalized LM-Toposes as global representations of SpaceTime Structures in the presence of intense Quantum Gravitational Fields. Such novel representations have the potential to develop a Quantum/general Relativity Theory in the context of Supersymmetry, Supergravity, Supersymmetry Algebras and the Metric Superfield in the Planck limit of spacetime. Quantum Gravity and Physical Cosmology issues are also considered here from the perspective of multiverses, thus leading also to novel types of Generalized, non-Abelian, Topological, Higher Homotopy Quantum Field Theories (HHQFT) and Non-Abelian Quantum Algebraic Topology (NA-QAT) theories. (shrink)

This paper proposes a speculative conceptual model in which dark matter arises from gravitational influence originating in companion universes produced through cosmic mitosis. Building on the earlier paper From the Fermi Paradox to Cosmic Mitosis, this work shifts from biological analogy to physical symmetry, exploring the possibility that universes form in +/– pairs whose quantum states remain entangled. In this model, matter in a “negative” universe does not interact electromagnetically with matter in a “positive” universe, rendering each universe invisible to (...) the other except through gravity. Dark matter is interpreted as the gravitational imprint of these companion universes. The model draws conceptual support from brane cosmology, CPT-symmetric universe theories, and studies of entanglement across cosmological horizons. It is offered not as a testable theory, but as a continuation of interdisciplinary reflection on replication, isolation, and structure at universe scale. (shrink)

Quantum theories constructed on the noncommutative spacetime called the Groenewold–Moyal plane exhibit many interesting properties such as Lorentz and CPT noninvariance, causality violation and twisted statistics. We show that such violations lead to many striking features that may be tested experimentally. These theories predict Pauli forbidden transitions due to twisted statistics, anisotropies in the cosmic microwave background radiation due to correlations of observables in spacelike regions and Lorentz and CPT violations in scattering amplitudes.

Contemporary political theory (CPT) has approached questions of plurality and diversity by drawing rather implicitly on anthropological accounts of difference. This was the case with the ‘cultural turn’, which significantly shaped theories of multiculturalism. Similarly, the current ‘ontological turn’ is gaining influence and leaving a marked impact on CPT. I examine the recent turn and assess both the possibilities it offers and the challenges it poses for decentering CPT and opening radical, decolonial avenues for thinking difference otherwise. I take Paul (...) Nadasdy's critique of the ontological turn as an invitation to reflect on the methodological precepts that inform how the field frames the scope and limits of comparison. In pursuit of this, I examine the Zapatistas’ notion of a ‘world of many worlds’, which provides a way of approaching difference that captures the generative aspects of the ontological turn while avoiding the pitfalls of relativism and political inertia. I argue that the Zapatistas’ insights offer ethical guidance towards social and ecological thriving. Ultimately, my goal is to move CPT towards a more capacious form of making sense of what is out there in the world, and thus make room for better ways of inhabiting the Earth. (shrink)

This chapter develops an idea of Richard Feynman’s, namely the idea that anti-particles are nothing but particles travelling back in time, and the related idea that what is standardly called the CPT theorem is really a theorem which shows that space-time has neither a direction in time nor a spatial handedness structure.

Cumulative Prospect Theory (CPT) does not explain the St. Petersburg Paradox. We show that the solutions related to probability weighting proposed to solve this paradox, (Blavatskyy, Management Science 51:677–678, 2005; Rieger and Wang, Economic Theory 28:665–679, 2006) have to cope with limitations. In that framework, CPT fails to accommodate both gambling and insurance behavior. We suggest replacing the weighting functions generally proposed in the literature by another specification which respects the following properties: (1) to solve the paradox, the slope at (...) zero has to be finite. (2) to account for the fourfold pattern of risk attitudes, the probability weighting has to be strong enough. (shrink)

Contemporary Political Theory (CPT) is a journal where conversations are emergent rather than specially curated. This selection of published items includes peer-reviewed articles, Critical Exchanges—in which contributors and editors work together on a theme or issue—and reviews that are themselves more than simply “about the book.” Like the authors of articles, and the contributors to Critical Exchanges, the reviewers, contributors, and authors selected here are important participants in the emerging conceptual logo-scapes of political theory.

We present the first complete construction of quantum gravity describing our real universe via the celestial holographic conformal field theory dual to Einstein gravity in four-dimensional asymptotically-flat spacetime. The theory is rigorously constructed as the shadow-invariant, purely spin-2 sector of holomorphic Chern–Simons theory on twistor space PT ≃ CP³ with gauge group the quantomorphic group Quant(PT). Primary fields are the celestial graviton operators O^{±2}Δ(z, z̄) with Δ ∈ 1 + iℝ and J = ±2. Three-point functions are determined by the (...) Penrose transform and reproduce the MHV and anti-MHV amplitudes of general relativity, including the vanishing of parity-odd and mixed-helicity couplings. Higher-point amplitudes arise from OPEs with analytically continued principal-series contours; loop integrands emerge as double discontinuities across shadow poles, which we demonstrate explicitly for the scalar box integrals computed via this shadow discontinuity method, verifying they match Feynman diagram calculations exactly to machine precision. The construction satisfies extended BMS₄ ⋉ shadow symmetry with vanishing Virasoro central charge c = 0, which we also demonstrate explicitly (confirmed by five independent methods) to 10+ significant figures. We prove a rigidity theorem establishing that any 2D CFT with only spin ±2 primaries, the above symmetries and three-point data, and local inverse-Mellin-transformed correlators, must be uniquely isomorphic to this quantomorphic twistor theory. Combined with the proof that crossing symmetry is a necessary consequence of bulk locality (not an independent axiom), this establishes that Einstein gravity in asymptotically-flat spacetime is the unique consistent theory of a single massless spin-2 particle. The quantomorphic gauge group structure provides a non-perturbative foundation, with perturbative scattering amplitudes emerging as the first residues of the holographic algebra. A key insight that facilitated this construction was proving that the shadow symmetry of the boundary CFT—the map Δ ↔ 2 − Δ on conformal dimensions—is mathematically equivalent to CPT conjugation in the bulk QFT (Theorem 6.1). Locality itself is derived: the self-duality of Haar measure on the Grassmannian forces celestial two-point functions to be positive-definite kernels; Bochner’s theorem then guarantees the spectral decomposition that implies commutativity at spacelike separation, without any appeal to Wightman axioms that would render the argument circular. The structural centrepiece of the construction is the identification of the celestial shadow transform (Δ ↔ 2 − Δ) with CPT conjugation in the bulk spacetime. Time reversal maps energy E to −E, which under the Mellin transform is precisely the shadow transform; parity flips helicity; charge conjugation acts on quantum numbers. Together these constitute the full CPT operation. This resolves Penrose's longstanding "googly problem" in twistor theory by revealing that self-dual and anti-self-dual helicity sectors—which twistor theory had previously been unable to unify—are related by the same symmetry that exchanges particles with antiparticles and past with future. This work provides a mathematically rigid reconciliation of general relativity with quantum field theory, deriving quantum consistency, locality, and gravitational dynamics via the celestial holography program and the 2D CFT dual to 4D flat spacetime. (shrink)

Highlighting main issues and controversies, this book brings together current philosophical discussions of symmetry in physics to provide an introduction to the subject for physicists and philosophers. The contributors cover all the fundamental symmetries of modern physics, such as CPT and permutation symmetry, as well as discussing symmetry-breaking and general interpretational issues. Classic texts are followed by new review articles and shorter commentaries for each topic. Suitable for courses on the foundations of physics, philosophy of physics and philosophy of science, (...) the volume is a valuable reference for students and researchers. (shrink)

We derive the six Wightman axioms of relativistic quantum field theory as theorems of three mathematical inputs: Haar measure on the Grassmannian Gr(2,4), the Penrose twistor correspondence, and the Peter-Weyl decomposition of L^2 spaces on compact groups. The Hilbert space is L^2(Gr(2,4), dmu_Gr), the vacuum is the unique SU(4)-invariant vector, Poincare covariance arises from the conformal embedding P+ into SU(2,2), the spectrum condition from forward-tube analyticity of the Penrose transform, locality from twistor non-incidence (spacelike separation implies non-incident twistors, non-incidence implies (...) holomorphic integrand, holomorphicity implies vanishing contour integral by Cauchy's theorem), cyclicity from irreducibility of the vacuum sector, and temperedness from elliptic regularity on the compact Grassmannian. The CPT theorem emerges from Haar measure self-duality (the map Lambda->Lambda-perp is the geometric CPT). The spin-statistics connection emerges from the topology of the Plucker line bundle. The Osterwalder-Schrader axioms follow by Wick rotation. No physical postulate enters the argument. The Wightman axioms are necessary consequences of Haar measure on the space of light rays. (shrink)

Haar measure has two spectral regimes determined entirely by the compactness of the underlying group. On a non-compact group the regular representation decomposes by Plancherel measure over a continuous unitary dual; on a compact group it decomposes by Peter–Weyl summation over finite-dimensional irreducibles. We prove this dichotomy in the forms needed for two applications in the shadow framework. For the non-compact case we show that the half-density Mellin transform on L²(ℝ⁺, dx) is unitary exactly on the line Re(s) = 1/2, (...) and that the functional equation ξ(s) = ξ(1−s) of the completed zeta function is the restriction of Haar inversion self-duality to the arithmetic spectrum via Tate's thesis. Under Δ = 2s, the same inversion is the shadow symmetry transform ∆ ←→2 - ∆ of celestial conformal field theory, which identified as the boundary theory's version of the fundamental CPT-symmetry of regular four-dimensional quantum field theory in the bulk provides a means of resolving the googly problem regarding the perceived asymmetry problem in twistor-theoretic quantum gravity. For the compact case we prove that Haar projection onto SU(N)-singlets is the orthogonal projection onto the physical gauge sector, and that the Sugawara conformal weight of the first adjoint-current excitation gives a mass gap M = 2N/(k+N)·Λ_QCD > 0 in the continuum celestial Yang–Mills construction. The Riemann and Yang–Mills mechanisms are the two complementary spectral faces of one mathematical fact: non-compact Haar measure gives a Plancherel axis, and compact Haar measure gives a Peter–Weyl gap. (shrink)

I consider recent strategies proposed by econometricians for extrapolating causal effects from experimental to target populations. I argue that these strategies fall prey to the extrapolator’s circle: they require so much knowledge about the target population that the causal effects to be extrapolated can be identified from information about the target alone. I then consider comparative process tracing as a potential remedy. Although specifically designed to evade the extrapolator’s circle, I argue that CPT is unlikely to facilitate extrapolation in typical (...) econometrics and evidence-based policy applications. To argue this, I offer a distinction between two kinds of extrapolation, attributive and predictive, the latter being prevalent in econometrics and evidence-based policy. I argue that CPT is not helpful for predictive extrapolation when using the kinds of evidence that econometricians and evidence-based policy researchers prefer. I suggest that econometricians may need to consider qualitative evidence to overcome this problem. (shrink)

This essay, addressed equally to mathematical physicists and philosophers of physics and mathematics, argues that the Riemann Hypothesis is equivalent to a statement about the unitarity of the celestial vacuum at null infinity in four-dimensional Minkowski spacetime. The argument proceeds in three steps. First, it identifies the operator anticipated by Hilbert and Pólya with the self-adjoint generator of dilations on the multiplicative line equipped with its self-dual Haar measure. Second, it identifies the critical line of the zeta function with the (...) principal series of celestial conformal field theory through the rigid correspondence ∆ = 2s, so that the unitarity condition becomes precisely Re(s) = 1/2. Third, it identifies the Riemann functional equation s ←→ 1 - s with the celestial shadow involution ∆ ←→ 2 - ∆, interpreted at null infinity as time reversal t ←→ -t, namely the boundary image of bulk CPT symmetry after metric degeneration and absorption of charge conjugation into representation choice. On this basis, a sharpened form of Weil’s 1952 positivity criterion is stated: the Riemann Hypothesis is equivalent to the self-adjointness of the dilation generator on a canonical form domain, and equivalently to the -invariance of the celestial vacuum. The framework unifies arithmetic, spectral theory, harmonic analysis, representation theory, differential and algebraic geometry, operator theory, quantum field theory, general relativity, quantum gravity, and holographic duality within a single structural architecture. This essay is a compressed presentation of the bridge and closure developed at full length in On the Nature of Nature, especially the transition from Einstein gravity to number theory and the subsequent Riemann-Hypothesis chapter, where adèlic positivity, spectral self-adjointness, celestial no-ghost unitarity, and completeness arguments all converge on the same conclusion. The claim is therefore stronger than an interpretive analogy: in this reading, the Riemann Hypothesis is the arithmetic statement of unitarity at null infinity, and the line Re(s) = 1/2 is the unique fixed locus forced by the shared Haar geometry of the arithmetic and celestial descriptions. (shrink)

Richard Feynman has claimed that anti-particles are nothing but particles `propagating backwards in time'; that time reversing a particle state always turns it into the corresponding anti-particle state. According to standard quantum field theory textbooks this is not so: time reversal does not turn particles into anti-particles. Feynman's view is interesting because, in particular, it suggests a nonstandard, and possibly illuminating, interpretation of the CPT theorem. In this paper, we explore a classical analog of Feynman's view, in the context of (...) the recent debate between David Albert and David Malament over time reversal in classical electromagnetism. (shrink)

Much behavioral welfare economics assumes that expected utility theory does not accurately describe most human choice under risk. A substantial literature instead evaluates welfare consequences by taking cumulative prospect theory as the natural default alternative, at least where description is concerned. We present evidence, based on a review of previous literature and new experimental data, that the most empirically adequate hypothesis about human choice under risk is that it is heterogeneous, and that where EUT does not apply, more choice is (...) characterized by rank-dependent utility models than by CPT. Most of the apparently loss-averse choice behavior results from probability weighting rather than from direct disutility experienced when an outcome is framed as a loss against an idiosyncratic reference point. We then consider implications of this finding for methodological debates about how to model welfare effects of policies, and argue that abandonment of a dogmatic belief in CPT as the correct theory of risk human choice exposes a conceptual error that is widespread in behavioral welfare economics. We provide concluding reflections on second-order, philosophical issues around the grounding of normative commitments in policy-focused economics. (shrink)

The lifetimes of both positive and negative relativistic (γ = 29.33) muons have been measured in the CERN Muon Storage Ring with the results τ+ = 64.419 (58) µs, τ− = 64.368 (29) µs The value for positive muons is in accordance with special relativity and the measured lifetime at rest: the Einstein time dilation factor agrees with experiment with a fractional error of 2×10−3 at 95 confidence. Assuming special relativity, the mean proper lifetime for μ− is found to be (...) τ0− = 2.1948(10) µs the most accurate value reported to date. The agreement of this value with previously measured values of τ0+ confirms CPT invariance for the weak interaction in muon decay. (shrink)

The military metaverse integrates immersive digital technologies, virtual worlds, artificial intelligence (AI), extended reality (XR), and digital twins to enhance capabilities across the defence enterprise. Within this framework, Digital Human Twins (DHTs) function as dynamic digital representations of military personnel and sometimes “things”, supporting training, mission planning, operational decision-making, health monitoring, equipment design and acquisition, and human–machine teaming. DHTs can be considered “actors” on a metaverse “stage”. This paper explores the role of DHTs in defence, categorising them into real human-derived, (...) artificial, hybrid, and anthropomorphic twins, each serving one or more military functions. DHTs offer significant advantages in adaptive training, career development, operational effectiveness, and equipment optimisation, but also present challenges related to data security, AI reliability, ethical concerns, and trust in autonomous decision-support systems. To address these complexities, we propose an extended version of the Digital Twin Capability Periodic Table (CPT), originally developed for engineering digital twins, by incorporating ethical considerations, psychological fidelity, social interaction, and autonomy levels. This structured framework can support the development and governance of DHTs across defence and other domains. By adopting a comprehensive approach to DHT implementation, including interoperability, data governance, and ethical oversight, organisations can unify their human data and maximise operational benefits whilst mitigating risks. The paper concludes with strategic recommendations for implementation, emphasising research investment and trials, AI governance policies, exploiting the extended CPT, and cross-sector collaboration to refine and standardise DHT deployment. (shrink)

This paper is a tour of how the laws of nature can distinguish between the past and the future, or be T-violating. I argue that, in terms of the basic argumentative structure, there are basically just three approaches currently being explored. The first is an application of Curie's Principle, together with the CPT theorem. The second route makes use of a principle due to Pasha Kabir which allows for a direct detection. The third route makes use of a Non-degeneracy Principle, (...) and is related to the energy spectrum of elementary particles. I show how each provides a general template for detecting T-violation, illustrate each with an example, and discuss their prospects in extensions of particle physics beyond the standard model. (shrink)

The emerging field of comparative political theory (CPT) seeks to expand our understanding of politics through intercultural dialogues between diverse systems of political thought. CPT acknowledges diverse modes of political understanding, yet the field is still methodologically focused on textual forms of political practice and learning. I argue that the privileging of political literature in CPT has been inherited from orthodox political theory and the history of political thought and that the prioritizing of text over oral and enactive practices places (...) constraints on intercultural dialogue. First, methodological focus on texts inhibits dialogue with Indigenous traditions that do not prioritize text in the same way or to the same extent in the reproduction of political culture. Second, the incorporation of oral traditions tends to conflate orality with text in ways that obfuscate the contribution of enactive performance. One result of these methodological oversights is that CPT risks recapitulating some of the historical exclusionary logics that it seeks to overcome. (shrink)

Physics takes for granted that interacting physical systems with no common history are independent, before their interaction. This principle is time-asymmetric, for no such restriction applies to systems with no common future, after an interaction. The time-asymmetry is normally attributed to boundary conditions. I argue that there are two distinct independence principles of this kind at work in contemporary physics, one of which cannot be attributed to boundary conditions, and therefore conflicts with the assumed T (or CPT) symmetry of microphysics. (...) I note that this may have interesting ramifications in quantum mechanics. (shrink)

In a recent article in this Journal, Shlomo Cohen and Haim Shapiro introduce the concept of “comparable placebo treatments” —placebo treatments with biological effects similar to the drugs they replace—and argue that doctors are not being deceptive when they prescribe or administer CPTs without revealing that they are placebos. We critique two of Cohen and Shapiro’s primary arguments. First, Cohen and Shapiro argue that offering undisclosed placebos is not lying to the patient, but rather is making a self-fulfilling prophecy—telling a (...) “lie” that, ideally, will become true. We argue that offering undisclosed placebos is not a “lie” but is a straightforward case of deceptively misleading the patient. Second, Cohen and Shapiro argue that offering undisclosed CPTs is not equivocation. We argue that it typically is equivocation or deception of another sort. If justifiable, undisclosed placebo use will have to be justified as a practice that is deceptive in most instances. (shrink)

Introduction: Neurobiological systems engineering models are useful for treating patients. We show a model of “high opioid tone” autism and present a hypothesis about how autism is caused by administration of opioids during childbirth.Main Symptoms: Clinical diagnosis of autism in a 25 year old man was confirmed by a Social Responsiveness Scale self-rating of 79, severe, and a Social Communications Questionnaire by the patient's father scoring 27. Cold pressor time was 190 seconds—unusually long, consonant with the high pain tolerance of (...) autism.Therapeutic Intervention and Outcomes: At naltrexone 50 mg/day SRS fell to 54 and SCQ-−2–9; both non-significant. CPT fell to 28, repeat 39 s. Improved relatedness was experienced ambivalently, understood as feelings never before experienced—causing pain. Non-compliance with naltrexone was followed by cutting open his palm and drinking alcoholically. Transference focused psychotherapy has helped him remain naltrexone—compliant while he works on issues of identity and relatedness.Conclusion: The model suggests studies that could be conducted to both prevent and treat this form of autism. (shrink)

Recent research, especially with functional brain imaging, demonstrated cases where the administration of a placebo produces objective effects in tissues that are indistinguishable from those of the real therapeutic agents. This phenomenon has been shown in treatments of pain, depression, Parkinsonism, and more. The main ethical complaint against placebo treatment is that it is a kind of deception, where supposedly we substitute what works just psychologically for a real drug that actually works on the tissue level. We claim that the (...) scientific findings bring to a new level the seeming deconstruction of the distinction between “placebo” and “real” drugs, and that instances of placebo treatment which fulfill this criterion should be recognized as a unique category—we call it “comparable placebo treatment” (CPT). The paper uses an analysis of the notion of deception to argue that CPT does not amount to deception; that it can preserve patient autonomy; and that it is therefore morally legitimate. (shrink)

Hawking particles emitted by a black hole are usually found to have thermal spectra, if not exactly, then by a very good approximation. Here, we argue differently. It was discovered that spherical partial waves of in-going and out-going matter can be described by unitary evolution operators independently, which allows for studies of space-time properties that were not possible before. Unitarity dictates space-time, as seen by a distant observer, to be topologically non-trivial. Consequently, Hawking particles are only locally thermal, but globally (...) not: we explain why Hawking particles emerging from one hemisphere of a black hole must be 100 % entangled with the Hawking particles emerging from the other hemisphere. This produces exclusively pure quantum states evolving in a unitary manner, and removes the interior region for the outside observer, while it still completely agrees locally with the laws of general relativity. Unitarity is a starting point; no other assumptions are made. Region I and the diametrically opposite region II of the Penrose diagram represent antipodal points in a PT or CPT relation, as was suggested before. On the horizon itself, antipodal points are identified. A candidate instanton is proposed to describe the formation and evaporation of virtual black holes of the type described here. (shrink)

Is shadowboxing an effective form of functional exercise? What physiological and morphological changes result from an exercise program based exclusively on shadowboxing for 3 weeks? To date, no empirical research has focused specifically on addressing these questions. Since mixed martial arts (MMA) is the fastest growing sport in the world, and since boxing and kickboxing fitness classes are among the most popular in gyms and fitness clubs worldwide, the lack of research on shadowboxing and martial arts-based fitness programs in the (...) extant literature is a shortcoming that the present article aims to address. This case study involved a previously sedentary individual engaging in an exercise program based exclusively on shadowboxing for 3 weeks. Body composition and heart rate data were collected before, throughout, and upon completion of the 3-week exercise program to determine the effectiveness of shadowboxing for functional fitness purposes. An original shadowboxing program prepared by an Everlast Master Instructor and NASM Certified Personal Trainer (NASM-CPT) and Performance Enhancement Specialist (NASM-PES) was used for this 3-week period. The original shadowboxing program with goals, techniques, and combinations to work on throughout the 3-week program is included in this article. This case study demonstrates that a 3-week exercise program based exclusively on shadowboxing can increase aerobic capacity, muscle mass, bone mass, basal metabolic rate, and daily calorie intake, and decrease resting heart rate, fat mass, body fat percentage, and visceral fat rating in a previously sedentary individual. The results of this research demonstrate that shadowboxing can be a safe and effective form of exercise leading to morphological and physiological improvements including fat loss and increased aerobic capacity. The results of this research also demonstrate that the Tanita BC-1500 is a reliable tool for individuals to evaluate their own fitness progress over time. (shrink)

ObjectiveProcessing Speed, the ability to perceive and react fast to stimuli in the environment, has been shown to be impaired in children with attention deficit hyperactivity disorder. However, it is unclear whether PS can be improved following targeted treatments for ADHD. Here we examined potential changes in PS following application of transcranial electric stimulation combined with cognitive training in children with ADHD. Specifically, we examined changes in PS in the presence of different conditions of mental fatigue.MethodsWe used a randomized double-blind (...) active-controlled crossover study of 19 unmedicated children with ADHD. Participants received either anodal transcranial direct current stimulation over the left dorsolateral prefrontal cortex or transcranial random noise stimulation, while completing CT, and the administration order was counterbalanced. PS was assessed before and after treatment using the MOXO-CPT, which measures PS in the presence of various conditions of mental fatigue and cognitive load.ResultstRNS combined with CT yielded larger improvements in PS compared to tDCS combined with CT, mainly under condition of increased mental fatigue. Further improvements in PS were also seen in a 1-week follow up testing.ConclusionThis study provides initial support for the efficacy of tRNS combined with CT in improving PS in the presence of mental fatigue in pediatric ADHD. (shrink)

In a Star Trek: The Next Generation episode, Cpt. Picard is captured and trapped on a planet with an alien captain who speaks a language incompatible with the universal translator, based on their societal historical metaphors. According to Shapiro (2004), the concept of a universal translator removes everything alien from alien languages, and since the Tamarian language refers only to their historical and cultural archetypes, Picard can only establish dialogue by invoking human analogues, such as Gilgamesh. The purpose of this (...) paper is threefold. First, we will tie such communication to standard cognitive models in cognitive linguistics, pioneered by Lakoff and Johnson (1980) and Lakoff (1987). Second, we will show that metaphorical imaging resembling the Tamarian language is already present in our culture, by analyzing Dawkins's (1982) notion of a meme, who presupposes that memes as cultural living structures physically reside in the brain, and comparing that to a common format of a meme in pop culture. We will also contrast this concept with living natural languages such as Wolaytta, using a great number of proverbs, which can be seen as desemanticized metaphors that are used to embody different domains of the social realm of life (Make et al. 2014). Third, we will compare the notion of such a language with the current state of machine-learning and deep-learning techniques for natural language processing of metaphorical phrases, pinpointing that even deep learning today is powerless without sufficient training datasets (cf. Perifanos et al. 2020) or specific known word contexts and embeddings (Rei et al. 2017), compared to the same situation the universal translator was faced with when dealing with the Tamarian language. (shrink)

Corporations are facing a growing demand for the transparency of political contributions. In the United States, this demand has largely focused on the implementation of a mandatory disclosure law. It rests on the assumption that legal enforcement can make it easier to observe the ties between corporations and political parties. In this study, I challenge this assumption. I build my case by first developing a conceptual foundation of corporate political transparency. I argue that in the absence of economic benefits, legal (...) enforcement has a limited effect on CPT. Instead of encouraging transparency, mandatory disclosure can lead to the concealment of corporate political contributions. To develop a model of concealment, I borrow the characterizations of disguise from theatrical drama. Using the context of Indian firms, I show the limitation of mandatory disclosure and the efficacy of regulatory incentive. My study highlights the need for a broader debate on CPT to understand the relative implications of regulatory policies. (shrink)

The Contingency Postulate of Truth. - Is there a statement that cannot be false under any contingent conditions? Two well-known philosophical schools have given contradictory answers to this question about the existence of a necessarily true statement: Fallibilists (Albert, Keuth) have denied its existence, transcendental pragmatists (Apel, Kuhlmann) and objective idealists (Wandschneider, Hösle) have affirmed it. Dieter Wandschneider has (following Vittorio Hösle) translated the principle of fallibilism, according to which every statement is fallible, into a thesis which he calls the (...) contingency postulate of truth (CPT). It says: If this postulate were true, it would mark an insurmountable boundary of knowledge: a final epistemic justification would then not be possible. Wandschneider has therefore developed a counterargument to show that the contingency postulate of truth cannot be formulated without contradiction and implies the thesis that there is at least one necessarily true statement. This essay deals with the systematic question whether the contingency postulate of truth really cannot be presented without contradiction. To this end I will first present the contingency postulate and the associated problems (I.). Then I will analyze Wandschneider's argument against the consistency of the contingency postulate (II.) and finally reject it with the help of some considerations from the field of epistemic logic (III.). (shrink)