Nine selection‐survival strategies were implemented in a genetic algorithm experiment, and differences in terms of evolution were assessed. The moments of evolution (expressed as generation numbers) were recorded in a contingency of three strategies (i.e., proportional, tournament, and deterministic) for two moments (i.e., selection for crossover and mutation and survival for replacement). The experiment was conducted for the first 20,000 generations in 46 independent runs. The relative moments of evolution (where evolution was defined as a significant increase in the determination (...) coefficient relative to the previous generation) when any selection‐survival strategy was used fit a Log‐Pearson type III distribution. Moreover, when distributions were compared to one another, functional relationships were identified between the population parameters, revealing a degeneration of the Log‐Pearson type III distribution in a one‐parametrical distribution that can be assigned to the chosen variable—evolution strategy. The obtained theoretical population distribution allowed comparison of the selection‐survival strategies that were used. © 2012 Wiley Periodicals, Inc. Complexity, 2012. (shrink)

The case of ungapped alignment of two literal sequences under constrains is considered. The analysis lead to general formulas for probability mass function and cumulative distribution function for the general case of using an alphabet with a chosen number of letters in the expression of the literal sequences. Formulas for three statistics including mean, mode, and standard deviation were obtained. Distributions are depicted for three important particular cases: alignment on binary sequences, alignment of trinomial series, and alignment of genetic sequences. (...) A particular case when sequences contain each letter of the alphabet at least once in both sequences has also been analyzed and some statistics for this restricted case are given. (shrink)

This is a reproduction of the original artefact. Generally these books are created from careful scans of the original. This allows us to preserve the book accurately and present it in the way the author intended. Since the original versions are generally quite old, there may occasionally be certain imperfections within these reproductions. We're happy to make these classics available again for future generations to enjoy!

The Lorentz transformation of space and time between two reference frames is one of the pillars of the special relativity theory. As a result of the Lorentz transformation, space and time are only relative and are entangled, while the Minkowski metric is Lorentz invariant. For this reason, the Lorentz transformation is one of the major obstructions in the development of physical theories with quantized space and time. Here is described the Lorentz transformation of a physical (...) system with a discrete dynamical time and a continuous space that fulfills Lorentz invariance while approximating the Lorentz transformation at the time continuous limit and the Galilei transformation at the classical limit. Furthermore, the discreteness of time is not mixed with the continuous nature of space, making time distinct from space. (shrink)

The meaning of Lorentz contraction in special relativity and its connection with Bell’s spaceships parable is discussed. The motion of Bell’s spaceships is then compared with the accelerated motion of a rigid body. We have tried to write this in a simple form that could be used to correct students’ misconceptions due to conflicting earlier treatments.

In this paper I will present conceptions of state reduction and particle and/or system localization which render these subjects fully compatible with the general requirements of a relativistic, i.e. Lorentz invariant, quantum theory. The approach consists of a systematic generalization of the concepts of initial data assignment at definite times, initiation and completion of measurements at definite times, and dynamical evolution as time dependence, to the concepts of initial data assignment on arbitrary space-like hyperplanes, initiation and completion of measurements (...) on arbitrary space-like hyperplanes, and dynamical evolution as space-like hyperplane dependence, respectively. I also briefly discuss the superluminal propagation which emerges from the localization study and the manner in which causal anomalies are nevertheless avoided. (shrink)

Inertial frames and Lorentz transformations have a preferred status in the special theory of relativity (STR). Lorentz transformations, in turn, embody Einstein's convention that the velocity of light is isotropic, a convention that is necessary for the establishment of a standard signal synchrony. If the preferred status of Lorentz transformations in STR is not due to some particular bias introduced by a convention on signal synchronism, but to the fact that the Lorentz transformation group is the (...) symmetry group of the theory, then the signal synchronism is not a matter of convention but rather a matter of fact. In order to explore the conventionalist thesis, that within the frame of STR isotropy in the velocity of light and, hence, signal synchronism is a matter of convention, we need a generalized Lorentz transformation group that does not embody Einstein's isotropy convention, and upon which STR can be based. We present here a new approach to the resulting search for a generalized STR, which is well suited for establishing some well-known results of Winnie as well as some new results. (shrink)

Michel Janssen and Harvey Brown have driven a prominent recent debate concerning the direction of an alleged arrow of explanation between Minkowski spacetime and Lorentz invariance of dynamical laws in special relativity. In this article, I critically assess this controversy with the aim of clarifying the explanatory foundations of the theory. First, I show that two assumptions shared by the parties—that the dispute is independent of issues concerning spacetime ontology, and that there is an urgent need for a constructive (...) interpretation of special relativity—are problematic and negatively affect the debate. Second, I argue that the whole discussion relies on a misleading conception of the link between Minkowski spacetime structure and Lorentz invari-ance, a misconception that in turn sheds more shadows than light on our understand-ing of the explanatory nature and power of Einstein’s theory. I state that the arrow connecting Lorentz invariance and Minkowski spacetime is not explanatory and uni-directional, but analytic and bidirectional, and that this analytic arrow grounds the chronogeometric explanations of physical phenomena that special relativity offers. (shrink)

We consider a representation of the state reduction which depends neither on its reality nor on the details of when and how it emerges. Then by means of the representation we find necessary conditions, even if not the sufficient ones, for a decomposition of the state vector space to be a solution to the basis problem. The conditions are that the decomposition should be Lorentz invariant and orthogonal and that the associated projections should be continuous. They are shown to (...) be able to determine a decomposition in each of a few examples considered if the other circumstances are taken into account together. (shrink)

Relative distance and velocity magnitudes between two arbitrarily moving particles are independent of an observer's reference frame, and may be used to construct theoretically a clock whose rate is Lorentz-invariant. This result is in accord with the principle of relativity, using the interaction interpretation: Relativistic changes arise in association with momentum-energy transfer, rather than in consequence of velocity-induced changes in measuring clocks and rods.

We review several no-go theorems attributed to Gisin and Hardy, Conway and Kochen purporting the impossibility of Lorentz-invariant deterministic hidden-variable model for explaining quantum nonlocality. Those theorems claim that the only known solution to escape the conclusions is either to accept a preferred reference frame or to abandon the hidden-variable program altogether. Here we present a different alternative based on a foliation dependent framework adapted to deterministic hidden variables. We analyse the impact of such an approach on Bohmian mechanics (...) and show that retrocausation necessarily comes out without time-loop paradox. (shrink)

The Lorentz-formulae are deduced from three factual statements the physical meaning of which is explained in terms of operations with clocks, light-signals and measuring rods. These statements are: (1) The time-length of a process is invariant. (2) The velocity of light is the same in all inertial systems. (3) The velocity of light is independent of the source. It is also shown that these statements can be deduced from the Lorentz-formulae. They are the physical content of the latter. (...) The principle of relativity and the light-principle together, however, contain more physical meaning than the Lorentz-formulae. Operational definitions are given for all relevant concepts. (shrink)

It is shown that the Lorentz-deformation property discussed in previous papers is consistent with the hadronic jet phenomenon in high-energy production processes.

In support of their contention that it is the absence of a subsisting medium that imbues the speed of light with fundamentality, Bryan Cheng and James Read discuss certain “fishbowl universes” in which physical influences evolve, not at the speed of light, but that of sound. The Lorentz transformation simulated in these sonic universes, which the authors cite from the literature of analogue gravity, is not that of Einstein, for whom an aether was “superfluous”, but that of the earlier (...) relativity of Lorentz and Poincaré, which did suppose such a medium. The authors’ intention is not to argue analogically, but simply to contrast the situation of light with that of sound. However, I argue that these universes are too successful as analogues to support the authors’ case. By reducing Lorentzian relativity to its bare essentials, they provide a compelling demonstration of the viability and explanatory strengths of the earlier theory. They show how a thoroughly wave-theoretic treatment of the elementary particles would explain why all aspects of matter transform in like manner, thereby avoiding a difficulty that was a significant reason for the demise of Lorentzian relativity after 1905. Importantly, these sonic universes suggest a unifying explanation, not only of the Lorentz transformation and de Broglie wave, but of the principle of relativity, which was merely postulated, rather than explained, by Einstein in 1905. (shrink)

The purpose of this paper is to show that the Lorentz contraction of a rod is possible only if the rod’s world path is a real four-dimensional object. This result demonstrates that special relativity does require reality at the microscopic level to be a four-dimensional world represented by Minkowski spacetime.

We discuss the possible breakdown of Lorentz invariance—at distances greater than the Planck length—from both the theoretical and the phenomenological point of view. The theoretical tool to deal with such a problem is provided by a “deformation” of the Minkowski metric, with parameters dependent on the energy of the physical system considered. Such a deformed metric realizes, for any interaction, the “solidarity principle” between interactions and spacetime geometry (usually assumed for gravitation), according to which the peculiar features of every (...) interaction determine—locally—its own spacetinie structure. The generalized theory of relativity, based on the locally deformed Minkowski spacetime, is called “deformed special relativity” (DSR). In the first part of the paper, we give the foundations and the basic laws of DSR. In the second part, we analyze some experimental data, which admit an interpretation in terms of the DSR formalism and are, therefore, candidates for displaying a breakdown of the Lorentz symmetry. They are (i) the superluminal propagation of evanescent electromagnetic waves in waveguides, (ii) the meanlife of the KS 0, (iii) the Bose-Einstein correlation in pion production and (iv) the comparison of clock rates in the gravitational field of Earth. Such analysis provides us with the explicit forms of the related deformed metrics as functions of the energy, thus putting in evidence, in all four cases (and therefore for all four fundamental interactions), departures from the usual Minkowski metric. This preliminary evidence for a broken Lorentz invariance may be regarded as the signature of possible nonlocal effects involved in the processes examined. Moreover, the corresponding deformed metrics obtained by our analysis provide an effective dynamical description of the interactions (at least in the energy range considered). (shrink)

A torsional-antenna and a log-periodic antenna are used as a source and an analyzer, respectively, to investigate the possible anomalies of an electro-magnetic field. An unexpected isotropic signal has been detected using those torsion angles, which correspond to a breakdown of the Local Lorentz Invariance, which was found in the past. This coincidence is interpreted as the recovery of a lost symmetry by torqueing the antenna, thus putting in evidence that this Lorentz violation is of angular nature. Introducing (...) a new physical dimension—not only a mathematical dimension as a way to rearrange some equations—is here proposed as a general rule to recover the lost symmetry. (shrink)

In a recent paper in this journal which was part of a panel discussion of Grünbaum's philosophy of science, M. G. Evans discusses the Lorentz-Fitzgerald contraction hypothesis and related matters [2]. The purpose of this note is to clarify and correct some of the points in Evans' paper.

A velocity-orientation formalism to deal with compositions of successive Lorentz transformations, emphasizing analogies shared by Lorentz and Galilean transformations, has recently been developed. The emphasis in the present article is on the convenience of using the velocity-orientation formalism by resolving a paradox in the study of successive Lorentz transformations of the electromagnetic field that was recently raised by Mocanu. The paradox encountered by Mocanu results from the omission of the Thomas rotation (or, precession) which is involved in (...) the composition of two Lorentz transformations with corresponding noncollinear velocity parameters. By resolving this paradox, we expose (i) the central role that the Thomas rotation plays in special relativity, (ii) the need to consider in special relativity orientations in addition to velocities between inertial frames, and (iii) the power and elegance of the novel velocity-orientation formalism. A similar paradox in STR that Mocanu pointed out, also resulting from the omission of the Thomas rotation, has been resolved in a previous communication. (shrink)

We show the existence of Lorentz invariant Berry phases generated, in the Stueckelberg–Horwitz–Piron manifestly covariant quantum theory (SHP), by a perturbed four dimensional harmonic oscillator. These phases are associated with a fractional perturbation of the azimuthal symmetry of the oscillator. They are computed numerically by using time independent perturbation theory and the definition of the Berry phase generalized to the framework of SHP relativistic quantum theory.

It is shown that the jet mechanism derivable from the Lorentz deformation picture leads to a nearly constant average jet transverse momentum. It is pointed out that this is consistent with the high-energy experimental data. It is pointed out further that this result strengthens the physical basis for the minimal time-energy uncertainty combined covariantly with Heisenberg's space-momentum uncertainty relation.

Many condensed matter systems are such that their collective excitations at low energies can be described by fields satisfying equations of motion formally indistinguishable from those of relativistic field theory. The finite speed of propagation of the disturbances in the effective fields (in the simplest models, the speed of sound) plays here the role of the speed of light in fundamental physics. However, these apparently relativistic fields are immersed in an external Newtonian world (the condensed matter system itself and the (...) laboratory can be considered Newtonian, since all the velocities involved are much smaller than the velocity of light) which provides a privileged coordinate system and therefore seems to destroy the possibility of having a perfectly defined relativistic emergent world. In this essay we ask ourselves the following question: In a homogeneous condensed matter medium, is there a way for internal observers, dealing exclusively with the low-energy collective phenomena, to detect their state of uniform motion with respect to the medium? By proposing a thought experiment based on the construction of a Michelson-Morley interferometer made of quasi-particles, we show that a real Lorentz-FitzGerald contraction takes place, so that internal observers are unable to find out anything about their ‘absolute’ state of motion. Therefore, we also show that an effective but perfectly defined relativistic world can emerge in a fishbowl world situated inside a Newtonian (laboratory) system. This leads us to reflect on the various levels of description in physics, in particular regarding the quest towards a theory of quantum gravity. (shrink)

We show how a recently introduced retarded version of the Bohm Model evades the Hardy proof that hidden-variable models must violate Lorentz Invariance. We also discuss a possible test of such models.

I address a number of questions concerning the interpretation of local time and the corresponding states theorem (CST) of the Versuch, questions which have been addressed either incompletely or inadequately in the secondary literature. In particular: (1) What is the relation between local time and the behavior of moving clocks? (2) What is the relation between the primed field variables and the electric and magnetic fields in a moving system? (3) What is the relation of the CST to the principle (...) of relativity and requirements of covariance? (4) Does the introduction of local time and the primed field variables constitute a hypothesis, i.e., an addition to or a modification of the basic theory? (shrink)

When Einstein formulated his special relativity, he developed his dynamics for point particles. Of course, many valiant efforts have been made to extend his relativity to rigid bodies, but this subject is forgotten in history. This is largely because of the emergence of quantum mechanics with wave-particle duality. Instead of Lorentz-boosting rigid bodies, we now boost waves and have to deal with Lorentz transformations of waves. We now have some nderstanding of plane waves or running waves in the (...) covariant picture, but we do not yet have a clear picture of standing waves. In this report, we show that there is one set of standing waves which can be Lorentz-transformed while being consistent with all physical principle of quantum mechanics and relativity. It is possible to construct a representation of the Poincaré group using harmonic oscillator wave functions satisfying space-time boundary conditions. This set of wave functions is capable of explaining the quantum bound state for both slow and fast hadrons. In particular it can explain the quark model for hadrons at rest, and Feynman’s parton model hadrons moving with a speed close to that of light. (shrink)

Withdrawn by the author! The main content of this paper has been moved into "Szabó, László E., Does special relativity theory tell us anything new about space and time? (ID Code:1321)".

I show that Albert Einstein’s distinction between principle and constructive theories was predated by Hendrik A. Lorentz’s equivalent distinction between mechanism- and principle-theories. I further argue that Lorentz’s views toward realism similarly prefigure what Arthur Fine identified as Einstein’s ‘‘motivational realism.’’ r 2005 Published by Elsevier Ltd.

Implementing Poincaré’s geometric conventionalism a scalar Lorentz-covariant gravity model is obtained based on gravitationally modified Lorentz transformations (or GMLT). The modification essentially consists of an appropriate space-time and momentum-energy scaling (“normalization”) relative to a nondynamical flat background geometry according to an isotropic, nonsingular gravitational affecting function Φ(r). Elimination of the gravitationally unaffected S 0 perspective by local composition of space–time GMLT recovers the local Minkowskian metric and thus preserves the invariance of the locally observed velocity of light. The (...) associated energy-momentum GMLT provides a covariant Hamiltonian description for test particles and photons which, in a static gravitational field configuration, endorses the four ‘basic’ experiments for testing General Relativity Theory: gravitational (i) deflection of light, (ii) precession of perihelia, (iii) delay of radar echo, (iv) shift of spectral lines. The model recovers the Lagrangian of the Lorentz–Poincaré gravity model by Torgny Sjödin and integrates elements of the precursor gravitational theories, with spatially Variable Speed of Light (VSL) by Einstein and Abraham, and gravitationally variable mass by Nordström. (shrink)

1.Here is a well known theorem. Consider the homogeneous Maxwell equations(where E and H are functions of x, y, z, and t, and ).Use the coordinate substitutionsand the following substitutions for the field variablesThen, if terms depending on second and higher powers of (v/c) are dropped, the resulting equations have the same form as the original homogeneous Maxwell equations, i.e.