In 1885, during initial discussions of J. C. Maxwell's celebrated thermodynamic demon, Whiting (1) observed that the demon-like velocity selection of molecules can occur in a gravitationally bound gas. Recently, a gravitational Maxwell demon has been proposed which makes use of this observation [D. P. Sheehan, J. Glick, and J. D. Means, Found. Phys. 30, 1227 (2000)]. Here we report on numerical simulations that detail its microscopic phase space structure. Results verify the previously hypothesized mechanism of its paradoxical (...) behavior. This system appears to be the only example of a fully classical mechanical Maxwell demon that has not been resolved in favor of the second law of thermodynamics. (shrink)

The category of coherent phase spaces introduced by the author is a refinement of the symplectic “category” of A. Weinstein. This category is *-autonomous and thus provides a denotational model for Multiplicative Linear Logic. Coherent phase spaces are symplectic manifolds equipped with a certain extra structure of “coherence”. They may be thought of as “infinitesimal” analogues of familiar coherent spaces of Linear Logic. The role of cliques is played by Lagrangian submanifolds of ambient spaces. Physically, a symplectic manifold (...) is the phase space of a classical dynamical system, and a Lagrangian submanifold is a phase of a short-wave oscillation. Typically, Lagrangian submanifolds represent such objects as short-wave approximations of wave functions in asymptotic quantization and wave fronts in geometrical optics. The coherent phase space semantics was motivated to a large extent by methods of geometric and asymptotic quantization and suggests some interesting intuitions on Linear Logic. In particular Lagrangian submanifold-cliques of types A and A can be interpreted as semiclassical limits of eigenstates of respectively position and momentum observables. These observables being canonically conjugate cannot be measured simultaneously, which corresponds to the idea that a formula A and its negation A cannot both simultaneously have proofs . We show that the coherent phase space semantics of Linear Logic enjoys several completeness properties in general much stronger than the usual full completeness with respect to the class of dinatural transformations. These properties of completeness in conjunction with a quite natural -physical meaning make the coherent phase space semantics an interesting object of investigation. (shrink)

Often it is assumed that a quantum state or a phase-space distribution must be normalizable. Here it is shown that even if it is not normalizable, one may be able to extract normalized observational probabilities from it.

In 1885, during initial discussions of J. C. Maxwell's celebrated thermodynamic demon, Whiting(1) observed that the demon-like velocity selection of molecules can occur in a gravitationally bound gas. Recently, a gravitational Maxwell demon has been proposed which makes use of this observation [D. P. Sheehan, J. Glick, and J. D. Means, Found. Phys. 30, 1227 (2000)]. Here we report on numerical simulations that detail its microscopic phase space structure. Results verify the previously hypothesized mechanism of its paradoxical behavior. (...) This system appears to be the only example of a fully classical mechanical Maxwell demon that has not been resolved in favor of the second law of thermodynamics. (shrink)

A (to our knowledge) novel Generalized Nonlinear Schrödinger equation based on the modifications of Nottale-Cresson’s fractal-scale calculus and resulting from the noncommutativity of the phase space coordinates is explicitly derived. The modifications to the ground state energy of a harmonic oscillator yields the observed value of the vacuum energy density. In the concluding remarks we discuss how nonlinear and nonlocal QM wave equations arise naturally from this fractal-scale calculus formalism which may have a key role in the final (...) formulation of Quantum Gravity. (shrink)

The quantum transition probability assignment is an equiareal transformation from the annulus of symplectic spinorial amplitudes to the disk of complex state vectors, which makes it equivalent to the equiareal projection of Archimedes. The latter corresponds to a symplectic synchronization method, which applies to the quantum phase space in view of Weyl’s quantization approach involving an Abelian group of unitary ray rotations. We show that Archimedes’ method of synchronization, in terms of a measure-preserving transformation to an equiareal disk, (...) imposes the integrality of the quantum of action, and requires the extension of the classical moment map from the real line to the circle. Additionally, the same synchronization method is encoded in the structure of the Heisenberg group, viewed as a principal bundle with a connection, whose curvature and anholonomy is expressed in terms of area bounding loops in relation to the underlying Abelian shadow on a symplectic plane. In this manner, we show that the geometric phase pertains to the minimal synchronized area \ of the 2-d symplectic Abelian shadow of the symplectic ball, modulo \. The integrality condition naturally leads to the consideration of modular commutative observables pertaining to the role of the discrete Heisenberg group. We prove that the structural transition from non-commutativity to modular commutativity in accordance to Weyl’s group-theoretic commutation relations takes place via universal factorization through the discrete Heisenberg group. In this way, we derive a homology-theoretic formulation of the synchronization method in terms of the area-bounding cells of the modular lattice \ in relation to any Abelian symplectic shadow. Thus, we finally obtain the physical interpretation of the analytic representation of quantum states as theta functions corresponding to the sections of a complex line bundle with an integral symplectic structure. (shrink)

The main features of how to build a Born’s Reciprocal Gravitational theory in curved phase-spaces are developed. By recurring to the nonlinear connection formalism of Finsler geometry a generalized gravitational action in the 8D cotangent space (curved phase space) can be constructed involving sums of 5 distinct types of torsion squared terms and 2 distinct curvature scalars ${\mathcal{R}}, {\mathcal{S}}$ which are associated with the curvature in the horizontal and vertical spaces, respectively. A Kaluza-Klein-like approach to the (...) construction of the curvature of the 8D cotangent space and based on the (torsionless) Levi-Civita connection is provided that yields the observed value of the cosmological constant and the Brans-Dicke-Jordan Gravity action in 4D as two special cases. It is found that the geometry of the momentum space can be linked to the observed value of the cosmological constant when the curvature in $\mathit{momentum}$ space is very large, namely the small size of P is of the order of $( 1/R_{\mathit{Hubble}})$ . Finally we develop a Born’s reciprocal complex gravitational theory as a local gauge theory in 8D of the $\mathit{deformed}$ Quaplectic group that is given by the semi-direct product of U(1,3) with the $\mathit{deformed}$ (noncommutative) Weyl-Heisenberg group involving four $\mathit{noncommutative}$ coordinates and momenta. The metric is complex with symmetric real components and antisymmetric imaginary ones. An action in 8D involving 2 curvature scalars and torsion squared terms is presented. (shrink)

We construct the Extended Relativity Theory in Born-Clifford-Phase spaces with an upper R and lower length λ scales (infrared/ultraviolet cutoff). The invariance symmetry leads naturally to the real Clifford algebra Cl (2, 6, R) and complexified Clifford Cl C (4) algebra related to Twistors. A unified theory of all Noncommutative branes in Clifford-spaces is developed based on the Moyal-Yang star product deformation quantization whose deformation parameter involves the lower/upper scale $$(\hbar \lambda / R)$$. Previous work led us to show (...) from first principles why the observed value of the vacuum energy density (cosmological constant) is given by a geometric mean relationship $$\rho \sim L_{\rm Planck}^{-2}R^{-2} = L_{P}^{-4} (L_{\rm Planck} / R)^{2} \sim 10^{-122}M_{\rm Planck}^4$$, and can be obtained when the infrared scale R is set to be of the order of the present value of the Hubble radius. We proceed with an extensive review of Smith’s 8D model based on the Clifford algebra Cl (1, 7) that reproduces at low energies the physics of the Standard Model and Gravity, including the derivation of all the coupling constants, particle masses, mixing angles,....with high precision. Geometric actions are presented like the Clifford-Space extension of Maxwell’s Electrodynamics, and Brandt’s action related to the 8D spacetime tangent-bundle involving coordinates and velocities (Finsler geometries). Finally we outline the reasons why a Clifford-Space Geometric Unification of all forces is a very reasonable avenue to consider and propose an Einstein-Hilbert type action in Clifford-Phase spaces (associated with the 8D Phase space) as a Unified Field theory action candidate that should reproduce the physics of the Standard Model plus Gravity in the low energy limit. (shrink)

Several versions exist of pseudo-classical models of the electron using Grassmann variables. Most of these require additional constraints on the variables, and it is these which, when quantized, lead to Dirac's equation. In addition, the Grassmann variables do not have physical interpretations. In this article a model is constructed which does not require constraints and in which the Grassmann variables can be interpreted as observables. Dirac's equation is obtained directly from quantization.

The quasiclassical representations of quantum theory, generalizing the concept of a phase-space representation of quantum mechanics, are studied with particular emphasis on some questions connected with the Jordan structure of the classical and quantum algebras of observables. A generalized version of the theorem of Gleason, Kahane, and Zelazko is used to establish some nonclassical features of these representations.

Phase separation underlies the formation of biomolecular condensates. We hypothesize the cellular processes that occur within condensates shape their structural features. We use the example of transcription to discuss structure–function relationships in condensates. Various types of transcriptional condensates have been reported across the evolutionary spectrum in the cell nucleus as well as in mitochondrial and bacterial nucleoids. In vitro and in vivo observations suggest that transcriptional activity of condensates influences their supramolecular structure, which in turn affects their function. Condensate (...) organization thus becomes driven by differences in miscibility among the DNA and proteins of the transcription machinery and the RNA transcripts they generate. These considerations are in line with the notion that cellular processes shape the structural properties of condensates, leading to a dynamic, mutual interplay between structure and function in the cell. (shrink)

In this paper we investigate the coupling properties of pairs of quadrature observables, showing that, apart from the Weyl relation, they share the same coupling properties as the position-momentum pair. In particular, they are complementary. We determine the marginal observables of a covariant phase space observable with respect to an arbitrary rotated reference frame, and observe that these marginal observables are unsharp quadrature observables. The related distributions constitute the Radon transform of a phase (...) space distribution of the covariant phase space observable. Since the quadrature distributions are the Radon transform of the Wigner function of a state, we also exhibit the relation between the quadrature observables and the tomography observable, and show how to construct the phase space observable from the quadrature observables. Finally, we give a method to measure together with a single measurement scheme any complementary pair of quadrature observables. (shrink)

Starting from the phase space representation of quantum mechanics we provide an Euclidean system of covariance for the photon. In particular, we consider systems with the Poincaré group as the symmetry group and use a standard procedure in order to build a phase space and a localization observable on the phase space. Then we focus on the massless representations of the Poincaré group that we use to build a space localization observable for the (...) photon. (shrink)

We care not just how things are but how they could have been otherwise – about possibility and necessity as well as actuality. Many philosophers regard such talk as beyond the reach of respectable science, since observation tells us how things are but not how they could have been otherwise. I argue that, on the contrary, such criticisms are ill-founded: possibility and necessity are studied in natural science, for example through phase spaces, abstract mathematical representations of the possible states (...) of a physical system. The possibility is objective, not merely epistemic, though it may be more restricted than pure metaphysical possibility. The elements of a phase space are very similar to Kripke's possible worlds, despite being time slices rather than total histories. The absence of explicit modal operators in the mathematical models used by scientists does not show science to be non-modal; rather, it manifests reliance on a mathematical framework for theorizing about objective possibility similar to the mathematical framework of possible worlds model theory. (shrink)

We propose a group-theoretical interpretation of the fact that the transition from classical to quantum mechanics entails a reduction in the number of observables needed to define a physical state and \ to \ or \ in the simplest case). We argue that, in analogy to gauge theories, such a reduction results from the action of a symmetry group. To do so, we propose a conceptual analysis of formal tools coming from symplectic geometry and group representation theory, notably Souriau’s (...) moment map, the Mardsen–Weinstein symplectic reduction, the symplectic “category” introduced by Weinstein, and the conjecture according to which “quantization commutes with reduction”. By using the generalization of this conjecture to the non-zero coadjoint orbits of an abelian Hamiltonian action, we argue that phase invariance in quantum mechanics and gauge invariance have a common geometric underpinning, namely the symplectic reduction formalism. This stance points towards a gauge-theoretical interpretation of Heisenberg indeterminacy principle. We revisit this principle in the light of the difference between the set-theoretic points of a phase space and its category-theoretic symplectic points. (shrink)

Classical mechanics in phase space as well as quantum mechanics in Hilbert space lead to states and observables but not to objects that may be considered as carriers of observable quantities. However, in both cases objects can be constituted as new entities by means of invariance properties of the theories in question. We show, that this way of reasoning has a long history in physics and philosophy and that it can be traced back to the transcendental (...) arguments in Kant’s critique of pure reason. (shrink)

Development strategy of using modern portfolio theory focused on the short term. However, macroeconomic uncertainty and geopolitical environment makes their use ineffective. And challenge is to provide a reasonable balance between the short and long term profitability. Another issue, which is to some extent related to the previous observation is the absence in most matrices strategic recommendations for non-standard "behavior" of business units with dynamic analysis. This applies to the use of a relatively new tool matrix approach to development strategies (...) the company and its strategic business units - SPACE-analysis that also takes into account not forecasts of changes in the environment impact on the company. The aim of this paper is to develop methods of portfolio analysis on the basis of SPACE-dynamic analysis and formation of the list of possible strategic initiatives for definite basic trajectories of its strategic business units energy holding DTEK. Methods. SPACE-analysis, analytic hierarchy process, expert analysis. Results. The authors proposed a methodological approach to the implementation of dynamic SPACE-analysis company. The technique involves a strategic segmentation of the company, the formation of an expert group to assess reliable energy holding the current forecast period and on four aspects of SPACE-analysis. Also, using the analytic hierarchy determined by weighting the partial evaluation criteria. Methodology offers a "weighting" expert estimates within a particular group of partial criteria: sectors to "competitive advantage" and "stability branch" scale ratings is positive. The next phase involves the construction of vectors for the current and projected state holding that can be placed in one of four quadrants. Each quadrant has 4 basic strategic trajectory states, they can also be interpreted as a strategic gaps. In other words diagnosis of trajectories allows to identify and evaluate strategic gaps company or its individual business units according to specific criteria and receive partial numerical values of generalized gaps on key evaluation criteria. Conclusions. The authors matrix formed strategic decisions SPACE-dynamic analysis. The article graphically interpreted SPACE-analysis for the energy holding in three strategic business units. The study offers an integrated approach to the definition of policy recommendations for each strategic unit based on an analysis of superposition defined basic trajectories. S-trajectory or S-vectors can be represented as the sum of two vectors : numbers and appropriate call intensity factors relevant basic trajectories since their values determine the degree of contribution of each of these basic paths in the integrated S-vector is a vector strategic set of strategic business units to achieve strategic objectives, transfered into numerical form by partial criteria by expert predictive testing. These coefficients also make it possible to calculate the value of integrated strategic gaps generalized criteria. (shrink)

Quantum theory does not only predict probabilities, but also relative phases for any experiment, that involves measurements of an ensemble of systems at different moments of time. We argue, that any operational formulation of quantum theory needs an algebra of observables and an object that incorporates the information about relative phases and probabilities. The latter is the (de)coherence functional, introduced by the consistent histories approach to quantum theory. The acceptance of relative phases as a primitive ingredient of any quantum (...) theory, liberates us from the need to use a Hilbert space and non-commutative observables. It is shown, that quantum phenomena are adequately described by a theory of relative phases and non-additive probabilities on the classical phase space. The only difference lies on the type of observables that correspond to sharp measurements. This class of theories does not suffer from the consequences of Bell's theorem (it is not a theory of Kolmogorov probabilities) and Kochen–Specker's theorem (it has distributive “logic”). We discuss its predictability properties, the meaning of the classical limit and attempt to see if it can be experimentally distinguished from standard quantum theory. Our construction is operational and statistical, in the spirit of Copenhagen, but makes plausible the existence of a realist, geometric theory for individual quantum systems. (shrink)

The numerical study of a glycolytic model formed by a system of three delay differential equations reveals a multiplicity of stable coexisting states: birhythmicity, trirhythmicity, hard excitation and quasiperiodic with chaotic regimes. For different initial functions in the phase space one may observe the coexistence of two different quasiperiodic motions, the existence of a stable steady state with a stable torus, and the existence of a strange attractor with different stable regimes (chaos with torus, chaos with bursting motion, (...) and chaos with different periodic regimes). For a single range of the control parameter values our system may exhibit different bifurcation diagrams: in one case a Feigenbaum route to chaos coexists with a finite number of successive periodic bifurcations, in other conditions it is possible to observe the coexistence of two quasiperiodicity routes to chaos. These studies were obtained both at constant input flux and under forcing conditions. (shrink)

The paper aims to spell out the relevance of the Berry phase in view of the question what the minimal mathematical structure is that accounts for all observable quantum phenomena. The question is both of conceptual and of ontological interest. While common wisdom tells us that the quantum structure is represented by the structure of the projective Hilbert space, the appropriate structure rich enough to account for the Berry phase is the U(1) bundle over that projective (...) class='Hi'>space. The Berry phase is ultimately rooted in the curvature of this quantum bundle, it cannot be traced back to the Hamiltonian dynamics alone. This motivates the ontological claim in the final part of the paper that, if one strives for a realistic understanding of quantum theory including the Berry phase, one should adopt a form of ontic structural realism. (shrink)

Defining the observable φ canonically conjugate to the number observable N has long been an open problem in quantum theory. The problem stems from the fact that N is bounded from below. In a previous work we have shown how to define the absolute phase observable Φ≡|φ| by suitably restricting the Hilbert space of x and p like variables. Here we show that also from the classical point of view, there is no rigorous definition for the phase (...) even though it's absolute value is well defined. (shrink)

Uniformities describing the distinguishability of states and of observables are discussed in the context of general statistical theories and are shown to be related to distinguished subspaces of continuous observables and states, respectively. The usual formalism of quantum mechanics contains no such physical uniformity for states. Using recently developed tools of quantum harmonic analysis, a natural one-to-one correspondence between continuous subspaces of nonrelativistic quantum and classical mechanics is established, thus exhibiting a close interrelation between physical uniformities for quantum (...) states and compactifications of phase space. General properties of the completions of the quantum state space with respect to these uniformities are discussed. (shrink)

This is a pdf of a Mathematica calculation that supplements the paper "Presentist Fragmentalism and Quantum Mechanics" forthcoming in Foundations of Physics. In that paper the Born rule (or at least a progenitor) is derived from experimental conditions on the mutual observations of two fragments. In this pdf the experimental conditions are applied to Hilbert space dimensions 3, 4, and 5. It turns out each of these have a 1-dimensional solution space which, it is hoped, can be interpretated (...) as the phase. (shrink)

We examined whether variations in contextual diversity, spacing, and retrieval practice influenced how well adults learned new words from reading experience. Eye movements were recorded as adults read novel words embedded in sentences. In the learning phase, unfamiliar words were presented either in the same sentence repeated four times (same context) or in four different sentences (diverse context). Spacing was manipulated by presenting the sentences under distributed or non‐distributed practice. After learning, half of the participants were asked to retrieve (...) the new words, and half had an extra exposure to the new words. Although words experienced in diverse contexts were acquired more slowly during learning, they enjoyed a greater benefit of learning at immediate posttest. Distributed practice also slowed learning, but no benefit was observed at posttest. Although participants who had an extra exposure showed the greatest learning benefit overall, learning also benefited from retrieval opportunity, when words were experienced in diverse contexts. These findings demonstrate that variation in the content and structure of the learning environment impacts on word learning via reading. (shrink)

The macroscopic properties of a many-particle quantum system are revealed by an embedding of the macroscopic classical into the microscopic quantum description of the system. Such an embedding is based on the assumption that the experiments to which the classical theory applies may also be described quantum mechanically. It results from the existence of an injective trajectory observable. For photon quantum systems with a finite number of modes an embedding is explicitly constructed using the well- known phase space (...) observable for quantum systems of finite degrees of freedom. For the general case of photon quantum fields the existence of a phase space observable is shown which, restricted to a finite number of modes, coincides with the mentioned one. (shrink)

Non-commuting quantities and hidden parameters – Wave-corpuscular dualism and hidden parameters – Local or nonlocal hidden parameters – Phase space in quantum mechanics – Weyl, Wigner, and Moyal – Von Neumann’s theorem about the absence of hidden parameters in quantum mechanics and Hermann – Bell’s objection – Quantum-mechanical and mathematical incommeasurability – Kochen – Specker’s idea about their equivalence – The notion of partial algebra – Embeddability of a qubit into a bit – Quantum computer is not Turing (...) machine – Is continuality universal? – Diffeomorphism and velocity – Einstein’s general principle of relativity – „Mach’s principle“ – The Skolemian relativity of the discrete and the continuous – The counterexample in § 6 of their paper – About the classical tautology which is untrue being replaced by the statements about commeasurable quantum-mechanical quantities – Logical hidden parameters – The undecidability of the hypothesis about hidden parameters – Wigner’s work and и Weyl’s previous one – Lie groups, representations, and psi-function – From a qualitative to a quantitative expression of relativity − psi-function, or the discrete by the random – Bartlett’s approach − psi-function as the characteristic function of random quantity – Discrete and/ or continual description – Quantity and its “digitalized projection“ – The idea of „velocity−probability“ – The notion of probability and the light speed postulate – Generalized probability and its physical interpretation – A quantum description of macro-world – The period of the as-sociated de Broglie wave and the length of now – Causality equivalently replaced by chance – The philosophy of quantum information and religion – Einstein’s thesis about “the consubstantiality of inertia ant weight“ – Again about the interpretation of complex velocity – The speed of time – Newton’s law of inertia and Lagrange’s formulation of mechanics – Force and effect – The theory of tachyons and general relativity – Riesz’s representation theorem – The notion of covariant world line – Encoding a world line by psi-function – Spacetime and qubit − psi-function by qubits – About the physical interpretation of both the complex axes of a qubit – The interpretation of the self-adjoint operators components – The world line of an arbitrary quantity – The invariance of the physical laws towards quantum object and apparatus – Hilbert space and that of Minkowski – The relationship between the coefficients of -function and the qubits – World line = psi-function + self-adjoint operator – Reality and description – Does a „curved“ Hilbert space exist? – The axiom of choice, or when is possible a flattening of Hilbert space? – But why not to flatten also pseudo-Riemannian space? – The commutator of conjugate quantities – Relative mass – The strokes of self-movement and its philosophical interpretation – The self-perfection of the universe – The generalization of quantity in quantum physics – An analogy of the Feynman formalism – Feynman and many-world interpretation – The psi-function of various objects – Countable and uncountable basis – Generalized continuum and arithmetization – Field and entanglement – Function as coding – The idea of „curved“ Descartes product – The environment of a function – Another view to the notion of velocity-probability – Reality and description – Hilbert space as a model both of object and description – The notion of holistic logic – Physical quantity as the information about it – Cross-temporal correlations – The forecasting of future – Description in separable and inseparable Hilbert space – „Forces“ or „miracles“ – Velocity or time – The notion of non-finite set – Dasein or Dazeit – The trajectory of the whole – Ontological and onto-theological difference – An analogy of the Feynman and many-world interpretation − psi-function as physical quantity – Things in the world and instances in time – The generation of the physi-cal by mathematical – The generalized notion of observer – Subjective or objective probability – Energy as the change of probability per the unite of time – The generalized principle of least action from a new view-point – The exception of two dimensions and Fermat’s last theorem. (shrink)

Uncertainty measures must not depend on the choice of origin of the measurement scale; it is therefore argued that quantum-mechanical uncertainty relations, too, should remain invariant under changes of origin. These points have often been neglected in dealing with angle observables. Known measures of location and uncertainty for angles are surveyed. The angle variance angv {ø} is defined and discussed. It is particularly suited to the needs of quantum theory, because of its affinity to the Hilbert space metric, (...) and its use of the basic sine and cosine operators. Corresponding uncertainty relations involving azimuthal or phase angles are indicated, and their relevance to study and definition of coherent states is briefly reviewed. (shrink)

Modern observations based on general relativity indicate that the spatial geometry of the expanding, large-scale Universe is very nearly Euclidean. This basic empirical fact is at the core of the so-called “flatness problem”, which is widely perceived to be a major outstanding problem of modern cosmology and as such forms one of the prime motivations behind inflationary models. An inspection of the literature and some further critical reflection however quickly reveals that the typical formulation of this putative problem is fraught (...) with questionable arguments and misconceptions and that it is moreover imperative to distinguish between different varieties of problem. It is shown that the observational fact that the large-scale Universe is so nearly flat is ultimately no more puzzling than similar “anthropic coincidences”, such as the specific values of the gravitational and electromagnetic coupling constants. In particular, there is no fine-tuning problem in connection to flatness of the kind usually argued for. The arguments regarding flatness and particle horizons typically found in cosmological discourses in fact address a mere single issue underlying the standard FLRW cosmologies, namely the extreme improbability of these models with respect to any “reasonable measure” on the “space of all spacetimes”. This issue may be expressed in different ways and a phase space formulation, due to Penrose, is presented here. A horizon problem only arises when additional assumptions—which are usually kept implicit and at any rate seem rather speculative—are made. (shrink)

This paper is a further consideration of Hemmo and Shenker’s ideas about the proper conceptual characterization of macrostates in statistical mechanics. We provide two formulations of how macrostates come about as elements of certain partitions of the system’s phase space imposed on by the interaction between the system and an observer, and we show that these two formulations are mathematically equivalent. We also reflect on conceptual issues regarding the relationship of macrostates to distinguishability, thermodynamic regularity, observer dependence, and (...) the general phenomenon of measurement. (shrink)

Brian Pitts has recently claimed to show via straightforward calculation that, at least in the case of Hamiltonian electromagnetism, an arbitrary first-class constraint ``generates not a gauge transformation, but a bad physical change'' (Annals of Physics 351 (2014) pp.382-406; arXiv:1310.2756). We show, via a straightforward calculation, that a transformation generated by an arbitrary first-class constraint relates gauge-equivalent phase space points, vindicating orthodoxy. Pitts, however, is primarily concerned with transformations of entire histories, rather than of instantaneous states. We show (...) that, even in this context, a transformation generated by an arbitrary first-class constraint is also a gauge transformation, once the empirically observed electric field is correctly identified via its dynamical interactions with charge, and not simply given stipulatively as a certain combination of the potential and its derivatives. (shrink)

Spontaneous brain activity has received increasing attention as demonstrated by the exponential rise in the number of published papers on this topic over the last thirty years. Such “intrinsic” brain activity, generated in the absence of an explicit task, is frequently associated with resting-state or default-mode networks. The focus on characterizing spontaneous brain activity promises to shed new light on questions concerning the structural and functional architecture of the brain and how they are related to “mind”. However, many critical questions (...) have yet to be addressed. In this review, we focus on a scarcely explored area, specifically the energetic requirements and constraints of spontaneous activity, taking into account both thermodynamical and informational perspectives. We argue that the “classical” definitions of spontaneous activity do not take into account an important feature, that is, the critical thermodynamic energetic differences between spontaneous and evoked brain activity. Spontaneous brain activity is associated with slower oscillations compared with evoked, task-related activity, hence it exhibits lower levels of enthalpy and “free-energy” (i.e. the energy that can be converted to do work), thus supporting noteworthy thermodynamic energetic differences between spontaneous and evoked brain activity. Increased spike frequency during evoked activity has a significant metabolic cost, consequently, brain functions traditionally associated with spontaneous activity, such as mind wandering, require less energy that other nervous activities. We also review recent empirical observations in neuroscience, in order to capture how spontaneous brain dynamics and mental function can be embedded in a non-linear dynamical framework, which considers nervous activity in terms of phase spaces, particle trajectories, random walks, attractors and/or paths at the edge of the chaos. This takes us from the thermodynamic free-energy, to the realm of “variational free-energy”, a theoretical construct pertaining to probability and information theory which allows explanation of unexplored features of spontaneous brain activity. (shrink)

The analysis of the temporal structure of canonical general relativity and the connected interpretational questions with regard to the role of time within the theory both rest upon the need to respect the fundamentally dual role of the Hamiltonian constraints found within the formalism. Any consistent philosophical approach towards the theory must pay dues to the role of these constraints in both generating dynamics, in the context of phase space, and generating unphysical symmetry transformations, in the context of (...) a hypersurface embedded within a solution. A first denial of time in the terms of a position of reductive temporal relationalism can be shown to be troubled by failure on the first count, and a second denial in the terms of Machian temporal relationalism can be found to be hampered by failure on the second. A third denial of time, consistent with both of the Hamiltonian constraints roles, is constituted by the implementation of a scheme for constructing observables in terms of correlations and leads to a radical Parmenidean timelessness. The motivation for and implications of each of these three denials are investigated. (shrink)

Schwinger’s algebra of microscopic measurement, with the associated complex field of transformation functions, is shown to provide the foundation for a discrete quantum phase space of known type, equipped with a Wigner function and a star product. Discrete position and momentum variables label points in the phase space, each taking \(N\) distinct values, where \(N\) is any chosen prime number. Because of the direct physical interpretation of the measurement symbols, the phase space structure is (...) thereby related to definite experimental configurations. (shrink)

The rich blend of theories and experiences that made the history of physics possible still now enlightens the scientific method. We stress the need to learn from this method the force of making its principles explicit, while developing a rich diversity of theories, which are often incompatible. Unity is preserved by common founding principles and their mathematical form, such as the understanding of conservation properties (energy, momentum etc.) in terms of symmetries. When moving from the inert to the living state (...) of matter, new challenges are posed, beginning with biological “heterogenesis”, as “genesis of and from diversity” in a changing space of pertinent observables and parameters: the Darwinian ecosystem. The question that is posed is how we may consistently embed the theories of the inert into biology. By naturalization we mean an analysis of physics as part of the sciences of nature, not as the science governing them all. In particular, the founding symmetry principles of physical theories, often used to “naturalize” (but, actually, to “physicalize”) other sciences, will instead be framed in more general dynamics which deal with fundamental changes of symmetries, as they apply, in our views, in all historical sciences, beginning with biology. This paper will accordingly explore the notion of (non-)conservative extension of theories in a precise mathematical sense. We stress a perspectival epistemology that promotes a dialogue of theories, in search for bridges or even unity, inspired by the method of “unification” at the core of major theoretical inventions in physics. Our main motivation is the need to go beyond the strong dualistic separation of space (or of the more general “phase space”) as a pre-given container of the dynamics of matter, that biased physics from Aristotle to Newton and, in a technically different way, even Einstein. (shrink)

This paper considers states on the Weyl algebra of the canonical commutation relations over the phase space R^{2n}. We show that a state is regular iff its classical limit is a countably additive Borel probability measure on R^{2n}. It follows that one can "reduce" the state space of the Weyl algebra by altering the collection of quantum mechanical observables so that all states are ones whose classical limit is physical.

Symplectic reduction is a formal process through which degeneracy within the mathematical representations of physical systems displaying gauge symmetry can be controlled via the construction of a reduced phase space. Typically such reduced spaces provide us with a formalism for representing both instantaneous states and evolution uniquely and for this reason can be justifiably afforded the status of fun- damental dynamical arena - the otiose structure having been eliminated from the original phase space. Essential to the (...) application of symplectic reduction is the precept that the first class constraints are the relevant gauge generators. This prescription becomes highly problematic for reparameterization invariant theories within which the Hamiltonian itself is a constraint; not least because it would seem to render prima facie distinct stages of a history physically identical and observable functions changeless. Here we will consider this problem of time within non-relativistic me- chanical theory with a view to both more fully understanding the temporal struc- ture of these timeless theories and better appreciating the corresponding issues in relativistic mechanics. For the case of nonrelativistic reparameterization invariant theory application of symplectic reduction will be demonstrated to be both unnec- essary; since the degeneracy involved is benign; and inappropriate; since it leads to a trivial theory. With this anti-reductive position established we will then examine two rival methodologies for consistently representing change and observable func- tions within the original phase space before evaluating the relevant philosophical implications. We will conclude with a preview of the case against symplectic re- duction being applied to canonical general relativity. (shrink)

I analyse two different methods for the retrieval of a classical notion of spacetime from the theory of quantum cosmology in terms of the different means they employ to bring about the necessary loss of coherence. One method employs a direct coarse graining of the appropriate phase space, whereas the other method is based on decohering the system by the interaction with an environment. Although these methods are equivalent on a phenomenological level, I argue that conceptually the decoherence (...) approach is superior. The coarse graining approach construes the necessary loss of coherence in epistemic terms, whereas the method based on decohering the system by interaction with an environment provides a dynamical explanation for the emergence of classical notions of spacetime. On the latter account the emergence of classical behaviour is an objective property of the physical system under consideration, in contradistinction with the subjective coarse graining account of the retrieval of a classical spacetime in terms of measurements made by an observer. (shrink)

In physics, one is often misled in thinking that the mathematical model of a system is part of or is that system itself. Think of expressions commonly used in physics like “point” particle, motion “on the line”, “smooth” observables, wave function, and even “going to infinity”, without forgetting perplexing phrases like “classical world” versus “quantum world”.... On the other hand, when a mathematical model becomes really inoperative in regard with correct predictions, one is forced to replace it with a (...) new one. It is precisely what happened with the emergence of quantum physics. Classical models were superseded by quantum ones through quantization prescriptions. These procedures appear often as ad hoc recipes. In the present paper, well defined quantizations, based on integral calculus and Weyl–Heisenberg symmetry, are described in simple terms through one of the most basic examples of mechanics. Starting from probability distribution on the Euclidean plane viewed as the phase space for the motion of a point particle on the line, i.e., its classical model, we will show how to build corresponding quantum model and associated probabilities or quasi-probabilities distributions. We highlight the regularizing rôle of such procedures with the familiar example of the motion of a particle with a variable mass and submitted to a step potential. (shrink)

It is shown that quantum mechanics cannot be formulated as a stochastic theory involving a probability distribution function of position and momentum. This is done by showing that the most general distribution function which yields the proper quantum mechanical marginal distributions cannot consistently be used to predict the expectations of observables if phase space integration is used. Implications relating to the possibility of establishing a "hidden" variable theory of quantum mechanics are discussed.

We analyze the flow into inflation for generic "single-clock" systems, by combining an effective field theory approach with a dynamical-systems analysis. In this approach, we construct an expansion for the potential-like term in the effective action as a function of time, rather than specifying a particular functional dependence on a scalar field. We may then identify fixed points in the effective phase space for such systems, order-by-order, as various constraints are placed on the Mth time derivative of the (...) potential-like function. For relatively simple systems, we find significant probability for the background spacetime to flow into an inflationary state, and for inflation to persist for at least 60 efolds. Moreover, for systems that are compatible with single-scalar-field realizations, we find a single, universal functional form for the effective potential, $V$, which is similar to the well-studied potential for power-law inflation. We discuss the compatibility of such dynamical systems with observational constraints. (shrink)

The concept of complementarity, originally defined for non-commuting observables of quantum systems with states of non-vanishing dispersion, is extended to classical dynamical systems with a partitioned phase space. Interpreting partitions in terms of ensembles of epistemic states (symbols) with corresponding classical observables, it is shown that such observables are complementary to each other with respect to particular partitions unless those partitions are generating. This explains why symbolic descriptions based on an ad hoc partition of an (...) underlying phase space description should generally be expected to be incompatible. Related approaches with different background and different objectives are discussed. (shrink)

It was shown in Dirac A117, 610; A118, 351, 1928) that the ultra-violet divergence in quantum electrodynamics is caused by a violation of the time-energy uncertainly relationship, due to the implicit assumption of infinitesimal time information. In Wheeler et al. it was shown that Einstein’s special theory of relativity and Maxwell’s field theory have mathematically equivalent dual versions. The dual versions arise from an identity relating observer time to proper time as a contact transformation on configuration space, which leaves (...) phase space invariant. The special theory has a dual version in the sense that, for any set of n particles, every observer has two unique sets of global variables \\) and \\) to describe the dynamics, where \ is the canonical center of mass. In the \\) variables, time is relative and the speed of light is unique, while in the \\) variables, time is unique and the speed of light is relative with no upper bound. In the Maxwell case, the two sets of particle wave equations are not equivalent. The dual version contains an additional longitudinal radiation term that appears instantaneously with acceleration, leading to the prediction that radiation from a cyclotron will not produce photoelectrons. A major outcome is the dual unification of Newtonian mechanics and classical electrodynamics with Einstein’s special theory of relativity, without the need for point particles, without a self-energy divergency and, without need for the problematic Lorentz–Dirac equation. The purpose of this paper is to introduce the dual theory of relativistic quantum mechanics. In our approach, we obtain three distinct dual relativistic wave equations that reduce to the Schrödinger equation when minimal coupling is turned off. We show that the dual Dirac equation provides a new formula for the anomalous magnetic moment of a charged particle. We can obtain the exact value for the electron g-factor and phenomenological values for the muon and proton g-factors. (shrink)

Quantum frameworks for modeling competitive ecological systems and self-organizing structures have been investigated under multiple perspectives yielded by quantum mechanics. These comprise the description of the phase-space prey–predator competition dynamics in the framework of the Weyl–Wigner quantum mechanics. In this case, from the classical dynamics described by the Lotka–Volterra (LV) Hamiltonian, quantum states convoluted by statistical gaussian ensembles can be analytically evaluated. Quantum modifications on the patterns of equilibrium and stability of the prey–predator dynamics can then be identified. (...) These include quantum distortions over the equilibrium point drivers of the LV dynamics which are quantified through the Wigner current fluxes obtained from an onset Hamiltonian background. In addition, for gaussian ensembles highly localized around the equilibrium point, stability properties are shown to be affected by emergent topological quantum domains which, in some cases, could lead either to extinction and revival scenarios or to the perpetual coexistence of both prey and predator agents identified as quantum observables in microscopic systems. Conclusively, quantum and gaussian statistical driving parameters are shown to affect the stability criteria and the time evolution pattern for such microbiological-like communities. (shrink)

I analyse two different methods for the retrieval of a classical notion of spacetime from the theory of quantum cosmology in terms of the different means they employ to bring about the necessary loss of coherence. One method employs a direct coarse graining of the appropriate phase space, whereas the other method is based on decohering the system by the interaction with an environment. Although these methods are equivalent on a phenomenological level, I argue that conceptually the decoherence (...) approach is superior. The coarse graining approach construes the necessary loss of coherence in epistemic terms, whereas the method based on decohering the system by interaction with an environment provides a dynamical explanation for the emergence of classical notions of spacetime. On the latter account the emergence of classical behaviour is an objective property of the physical system under consideration, in contradistinction with the subjective coarse graining account of the retrieval of a classical spacetime in terms of measurements made by an observer. (shrink)

The use of idealized models in science is by now well-documented. Such models are typically constructed in a “top-down” fashion: starting with an intractable theory or law and working down toward the phenomenon. This view of model-building has motivated a family of confirmation schemes based on the convergence of prediction and observation. This paper considers how chaotic dynamics blocks the convergence view of confirmation and has forced experimentalists to take a different approach to model-building. A method known as “phase (...) space reconstruction” not only reveals a lacuna in the philosophical literature on models, it also fails to conform to conventional views about how models are used to confirm a theory. (shrink)

Typically, we think of both artificial and natural computing devices as following rules that allow them to alter their behaviour (output) according to their environment (input). This approach works well when the environment and goals are well defined and regular. However, 1) the search time for appropriate solutions quickly becomes intractable when the input is not fairly regular, and 2) responses may be required that are not computable, either in principle, or given the computational resources available to the system. It (...) may seem that there is no way to deal with these conditions, but if we think of systems as dynamical non-equilibrium autonomous entities, there are ways to deal with the unexpected and irregular by taking advantage of self-organising and self-preserving capacities of such systems. A generalised force acting on a system far from equilibrium will cause the system to reorganise itself in the direction of the generalised force in such a way as to minimise its effects (Nicolis and Prigogine, 1977), but there can be unpredictable effects in different generalised directions in the system’s phase space. In order to preserve system integrity, these effects must be damped or used for further self-reorganisation, possibly starting a cascade effect that leaves the system in a substantially different state in which it can handle further instances of this sort of information. This model is similar to and extends the theoretical model of accommodation and assimilation of Piaget, derived from his observations of the development of intelligence in children. (shrink)

We propose the conjecture according to which the fact that quantum mechanics does not admit sharp value attributions to both members of a complementary pair of observables can be understood in the light of the symplectic reduction of phase space in constrained Hamiltonian systems. In order to unpack this claim, we propose a quantum ontology based on two independent postulates, namely the phase postulate and the quantum postulate. The phase postulate generalizes the gauge correspondence between (...) first-class constraints and gauge transformations to the observables of unconstrained Hamiltonian systems. The quantum postulate specifies the relationship between the numerical values of the observables that permit us to individualize a physical system and the symmetry transformations generated by the operators associated to these observables. We argue that the quantum postulate and the phase postulate are formally implemented by the two independent stages of the geometric quantization of a symplectic manifold, namely the prequantization formalism and the election of a polarization of pre-quantum states respectively. (shrink)

In this paper, I want to draw attention to a connection between rigid designation with its consequence that we are able to stipulate worlds and haecceitism, the doctrine that we have possible worlds alike in all qualitative features which nonetheless are metaphysically different, in that two individuals can have all their qualitative features swapped while remaining the same individuals. I shall argue that stipulation leads to haecceitism, which in turn depends upon commitment to haecceity ("primitive thisness"). Haecceitism is, I claim, (...) an unattractive doctrine, but there is one powerful argument for it, drawn from the desire to make sense of observed frequencies of probabilistic events in terms of possible configurations of phase spaces which may be taken to be a form of possible world. However, by paying close attention to classical and quantum statistics, we see that this argument fails. (shrink)

It is argued that the `problem of time' in quantum gravity necessitates a refinement of the local inertial structure of the world, demanding a replacement of the usual Minkowski line element by a 4+2n dimensional pseudo-Euclidean line element, with the extra 2n being the number of internal phase space dimensions of the observed system. In the refined structure, the inverse of the Planck time takes over the role of observer-independent conversion factor usually played by the speed of light, (...) which now emerges as an invariant but derivative quantity. In the relativistic theory based on the refined structure, energies and momenta turn out to be invariantly bounded from above, and lengths and durations similarly bounded from below, by their respective Planck scale values. Along the external timelike world-lines, the theory naturally captures the `flow of time' as a genuinely structural attribute of the world. The theory also predicts expected deviations---suppressed quadratically by the Planck energy---from the dispersion relations for free fields in the vacuum. The deviations from the special relativistic Doppler shifts predicted by the theory are also suppressed quadratically by the Planck energy. Nonetheless, in order to estimate the precision required to distinguish the theory from special relativity, an experiment with a binary pulsar emitting TeV range gamma-rays is considered in the context of the predicted deviations from the second-order shifts. (shrink)

We report on an “anti-Gleason” phenomenon in classical mechanics: in contrast with the quantum case, the algebra of classical observables can carry a non-linear quasi-state, a monotone functional which is linear on all subspaces generated by Poisson-commuting functions. We present an example of such a quasi-state in the case when the phase space is the 2-sphere. This example lies in the intersection of two seemingly remote mathematical theories—symplectic topology and the theory of topological quasi-states. We use this (...) quasi-state to estimate the error of the simultaneous measurement of non-commuting Hamiltonians. (shrink)