On the Axiomatics of the 5-Dimensional Projective Unified Field Theory of Schmutzer

For more than 40 years E. Schmutzer has developed a new approach to the (5-dimensional) projective relativistic theory which he later called Projective Unified Field Theory (PUFT). In the present paper we introduce a new axiomatics for Schmutzer's theory. By means of this axiomatics we can give a new geometrical interpretation of the physical concept of the PUFT.     

Numerical analysis of trajectories of a quantum particle in two-slit experiment

It is well known that the concept of a trajectory of a quantum particle is itself nonsense in the so-called Copenhagen interpretation. However, if the interpretation proposed by Ishikawa [International Journal of Theoretical Physics,30(4), 401 (1991)] can be accepted in quantum mechanics, the trajectory of a quantum particle is significant (though it includes errors). In this paper we numerically analyze discrete trajectories of a quantum particle in a two-slit experiment under this new interpretation.     

Interpreting Social Accounting Matrix (SAM) as an Information Channel

Information theory, and the concept of information channel, allows us to calculate the mutual information between the source (input) and the receiver (output), both represented by probability distributions over their possible states. In this paper, we use the theory behind the information channel to provide an enhanced interpretation to a Social Accounting Matrix (SAM), a square matrix whose columns and rows present the expenditure and receipt accounts of economic actors. Under our interpretation, the SAM’s coefficients, which, conceptually, can be viewed as a Markov chain, can be interpreted as an information channel, allowing us to optimize the desired level of aggregation within the SAM. In addition, the developed information measures can describe accurately the evolution of a SAM over time. Interpreting the SAM matrix as an ergodic chain could show the effect of a shock on the economy after several periods or economic cycles. Under our new framework, finding the power limit of the matrix allows one to check (and confirm) whether the matrix is well-constructed (irreducible and aperiodic), and obtain new optimization functions to balance the SAM matrix. In addition to the theory, we also provide two empirical examples that support our channel concept and help to understand the associated measures.     

Asymptotic Completeness for Infraparticles in Two-Dimensional Conformal Field Theory

We formulate a new concept of asymptotic completeness for two-dimensional massless quantum field theories in the spirit of the theory of particle weights. We show that this concept is more general than the standard particle interpretation based on Buchholz’ scattering theory of waves. In particular, it holds in any chiral conformal field theory in an irreducible product representation and in any completely rational conformal field theory. This class contains theories of infraparticles to which the scattering theory of waves does not apply.     

Space-time trajectories of quantum particles

The concept of trajectory is extended theoretically from classical mechanics through nonrelativistic and relativistic quantum mechanics. Forced motion of the particle as might be caused by an electromagnetic field is included in the equations. A new interpretation of the electromagnetic potential and the gauge transformation is presented. Using this formal structure, the problem of collecting particles into packets using trajectories is studied for both quantum mechanics and classical mechanics. Quantum mechanical trajectories are found to be significantly more restricted than those allowed by classical physics. The uncertainty principle comes from the second-order nature of the field equation without recourse to statistical arguments. The trajectories of particles in a quantum state can be calculated explicitly from the wave function (also see article in Volume 20, Number 6).     

A mathematical interpretation of Dirac's formalism: Part c: free field operators

In the present paper we give a mathematical regorization and interpretation of the canonical (anti-) commutation relations which occur in the theory of the quantized free field. In our set-up, with respect to the physics, we felt inspired by the paper [Ro] of B. Robertson. His paper covers all essential elements of the subject under consideration. The main part of [Ro] will be mathematically justified and even generalized. In this connection we mention also the monograph [Sh] of A.S. Shvarz. With respect to the involved mathematics the papers [Co] of J. M. Cook and [KMP] of P. Kristensen et al. have been a source of inspiration.Our set-up is closely related to two of our earlier papers [EG 1–2] in which we presented a mathematical interpretation of Dírac's formalism. This interpretation is based on two new mathematical concepts: the concept of Dirac basis ans the concept of bracket. The bracket is no longer regarded as a “number” but as an analytic function on the open right half of the complex plane. As in [EG 1–2], we use the theory of generalized functions which has been constructed by one of us (cf. [G]).Quantum theory and distribution theory seem to be dissolubly connected. One might wonder whether the choice of the distribution theory plays an essential role in a mathematical interpretation of Dirac's formalism and related physical concepts. The answer is threefold: There are strong indications that similar interpretations can be derived in a very wide class of distribution theories (which include Schwarz's theory of tempered distributions). This class has been described in our papers [EK] and [EGK]. On the other hand, the distribution theory employed here, introduces generalized functions in a way very close to the physical intuitive view on improper functions. Moreover, it seems natural to adapt the used distribution theory to the concrete quantum mechanical system under consideration.     

Air ionization in a near-critical electric field

A set of experimental dependences of the air ionization effective rate on the electric field strength is presented. The concept of the critical breakdown field is discussed. It is indicated that experimental data are quantitatively inconsistent with analytical results based on this concept. This inconsistency is eliminated if the ionization balance takes into account not only dissociative adhesion of electrons to oxygen molecules but also their detachment from the molecules that gained a charge during the charge exchange process. Based on the results obtained, a new physical interpretation of the critical field is suggested. A formula for the effective rate of air ionization in near-critical fields is derived.     

The Effective Cross Section

The effection cross section concept for low intensity light illumination of gas discharges is shown to be analogous to high intensity breakdown of gases as interpreted by Panarella's "effective photon" concept. This mathematical result is suggested as a possible interpretation of strikingly similar nonlinearities of gas breakdown by light measured in both cases at their respectively different intensity levels.     

The Natural Philosophy of Economic Information: Autonomous Agents and Physiosemiosis

Information is a core concept in modern economics, yet its definition and empirical specification is elusive. One reason is the intellectual grip of the Shannon paradigm which marginalizes semantic information. However, a precise concept of economic information must be based on a theory of semantics, since what counts economically is the meaning, function and use of information. This paper introduces a new principled approach to information that adopts the paradigm of biosemiotics, rooted in the philosophy of Charles S. Peirce and builds on recent developments of the thermodynamics of information. Information processing by autonomous agents, defined as autopoietic heat engines, is conceived as physiosemiosis operating according to fundamental thermodynamic principles of information processing, as elucidated in recent work by Kolchinsky and Wolpert (KW). I plug the KW approach into a basic conceptual model of physiosemiosis and present an evolutionary interpretation. This approach has far-reaching implications for economics, such as suggesting an evolutionary view of the economic agent, choice and behavior, which is informed by applications of statistical thermodynamics on the brain.     

Anomalous brightness of quasars resolved by supersymmetry

This article expands the development of the concept of reciprocal symmetry (Ref. 1) and points out that it is (by definition) the supersymmetry of nature. First we derive the relation between the supersymmetric, reciprocal spacetime coordinate transformations of Ref. 1 and the standard Lorentz transformations of relativity. Then we demonstrate or prove the assertion in Ref. 1 that the Robertson-Walker and the Schwarzschild metrics map (exactly) reciprocally. Finally, we derive the relativistic cosmic redshift as a function of distance of the source from the observer in the implied pseudo-dynamic Machian observable universe model. This uniquely consistent physical cosmological model is then applied to interpret the redshifts from quasars. In so doing, we find that this new interpretation puts the quasars considerably closer than does the interpretation of the big-bang theory [see Eq. (36)] and seems to remove the brightness or magnitude anomaly for these objects. As discussed in the Appendix, it also explains why the big-bang interpretation (including the inflationary universe model, etc.) gives good results.     

On the foundations of the physical probability concept

An exact formulation of the frequency interpretation of probability is proposed on the basis of G. Ludwig's concept of physical theories. Starting from a short outline of this concept, a formal definition of weak approximate reduction is developed, which covers the reduction of probability to frequency as a special case.     

A Topos Perspective on State-Vector Reduction

A preliminary investigation is made of possible applications in quantum theory of the topos formed by the collection of all M-sets, where M is a monoid. Earlier results on topos aspects of quantum theory can be rederived in this way. However, the formalism also suggests a new way of constructing a ‘neo-realist’ interpretation of quantum theory in which the truth values of propositions are determined by the actions of the monoid of strings of finite projection operators. By these means, a novel topos perspective is gained on the concept of state-vector reduction.     

A Topos Perspective on State-Vector Reduction

A preliminary investigation is made of possible applications in quantum theory of the topos formed by the collection of all M-sets, where M is a monoid. Earlier results on topos aspects of quantum theory can be rederived in this way. However, the formalism also suggests a new way of constructing a ‘neo-realist’ interpretation of quantum theory in which the truth values of propositions are determined by the actions of the monoid of strings of finite projection operators. By these means, a novel topos perspective is gained on the concept of state-vector reduction.     

Indeterminacy relations and simultaneous measurements in quantum theory

This paper concerns derivations and interpretations of the uncertainty relations. The exclusive validity of the statistical interpretation is called into question. An individualistic interpretation, formulated by means of the concept of unsharp observables, is justified through a model of a joint measurement of position and momentum.     

Symmetry and invariance

The concept of invariance relates to both the intrinsic symmetries of physical systems and the symmetry of the set of equivalent reference frames used to observe them. Standard algebraic expressions for electrostatic potentials and crystal-field effective operators display both types of invariance. The concept of a reference frame is generalized to that of an ‘observing system’, which can, for example, be the basis states of a quantum system. This idea is related to Racah’s mathematical machinery for evaluating the matrix elements of many-electron 4f open-shell states in lanthanide ions. It is argued, on the basis of computational flexibility and ease of interpretation, that all equations that represent physical processes be expressible in terms of invariants of the set of observing systems. This ‘Principle of Invariance’ is then applied to special relativity, leading to a simple geometrical interpretation of Maxwell’s electromagnetic field equations. The close relationship between Dirac’s relativistic wave equation and Maxwell’s equations is then exposed. This leads to the concept of an inner structure of space-time and the reinterpretation of particle spin. Finally, it is shown that the use of invariants in relativity theory identifies a set of observing systems with a higher symmetry than that of Minkowski space-time.     

The use of substitution groups to derive thermodynamical relations between the material constants of piezoelectric materials

It is shown how substitution groups can be used to derive relations between the material constants of an anisotropic homogeneous piezoelectric medium. The structure of these relations is explained by means of a general record and independent systems are found, the existence of which has a clear physical interpretation. The concept of substitution group is generalized and some important thermodynamic substitution groups are derived; the method can be applied without substantial changes to an arbitrary type of anisotropic homogeneous medium.     

From a 1D Completed Scattering and Double Slit Diffraction to the Quantum-Classical Problem for Isolated Systems

By probability theory the probability space to underlie the set of statistical data described by the squared modulus of a coherent superposition of microscopically distinct (sub)states (CSMDS) is non-Kolmogorovian and, thus, such data are mutually incompatible. For us this fact means that the squared modulus of a CSMDS cannot be unambiguously interpreted as the probability density and quantum mechanics itself, with its current approach to CSMDSs, does not allow a correct statistical interpretation. By the example of a 1D completed scattering and double slit diffraction we develop a new quantum-mechanical approach to CSMDSs, which requires the decomposition of the non-Kolmogorovian probability space associated with the squared modulus of a CSMDS into the sum of Kolmogorovian ones. We adapt to CSMDSs the presented by Khrennikov (Found. Phys. 35(10):1655, 2005) concept of real contexts (complexes of physical conditions) to determine uniquely the properties of quantum ensembles. Namely we treat the context to create a time-dependent CSMDS as a complex one consisting of elementary (sub)contexts to create alternative subprocesses. For example, in the two-slit experiment each slit generates its own elementary context and corresponding subprocess. We show that quantum mechanics, with a new approach to CSMDSs, allows a correct statistical interpretation and becomes compatible with classical physics.