Abstracts Details

Special relativity theory employs two types of time, invariant proper time (different for each differently-moving particle) and non-invariant frame time. A return to the simplicity of a single invariant time parameter is offered by the GPS method of correcting clock running rates so as to compensate environmental effects due to motion and gravity. Parameterizing timekeeping in terms of a single time allows restoration of distant simultaneity and a surprising number of other amenities of pre-relativistic physics.

Many textbooks of electromagnetism give an example in which a current-carrying wire is alleged to be electrically neutral when at rest in the laboratory. They then show that the Lorentz contraction of moving charge, demanded by special relativity theory, causes a bunching of positive charge and a thinning of negative charge in the inertial system co-moving with the conduction electrons, with a resulting charge density imbalance and non-vanishing electric field measurable in that system. By a more careful application of special relativity theory, we show, on the contrary, that the wire cannot be strictly neutral in its rest system. Therefore the textbook calculations are in error.

It is generally thought that, when direct current flows in a stationary wire, no external electric field is produced. However, we show that if the Lorentz contraction of the assemblage of moving electrons is taken into account, special relativity theory predicts a nonzero electric field. Other theory also predicts nonzero electric fields through other mechanisms, and experimental works report confirmation of these mechanisms.

Maxwell?s equations are covariant under the Lorentz transformation, whereas Hertz?s equations are invariant under the Galilean transformation. At first order in v/c, both are (rival) candidates to describe electromagnetic physics. Hertz?s equations entail a law of force on charge or current inherent in the field theoretical formalism. Maxwell?s equations do not; hence they require postulational supplementation by a force law due to Lorentz. The Hertzian force law is similar to the Lorentz law, with an extra term unobservable in closed circuits. Both formalisms, considered at first order, describe radiation. But we show that only Hertz?s theory correctly describes the weak radiation (few photon) limit.

There are numerous theories of stellar aberration. All agree on Bradley aberration, which describes the phenomenon to first order in , where is the Earth?s orbital speed. Here three exemplary theories are considered and shown to differ at second order ( ). The Very Long Baseline Interferometry (VLBI) system claims accuracy adequate to measure small angles of this size and thus to provide an empirical resolution. In particular, Einstein?s formula of 1905 might be confirmed to order ? something that has never been achieved, or apparently even attempted.

Universal invariance is shown to offer a plausible alternative to special relativity's conceptions of universal covariance, four-vectors, spacetime symmetry, etc. This alternative, supported by a conception of time similar to Newton's (here termed ?Collective Time? and patterned on GPS time) provides a mathematical basis particularly helpful in analyzing the many-body problem. Both particle mechanics and electromagnetism fit with this radically new way of formulating a relativistic description. A crucial experiment is advocated, requiring accurate measurement of stellar aberration to second order by means of the VLBI system.

Definitions of invariance and covariance are offered and a non-Einsteinian variety of physics (developed in Ref. 12) is sketched. This employs an invariant covering theory of Maxwell's equations due to Hertz, as well as a ?collective time' patterned upon the clock running-rate correction methods of the Global Positioning System. In this alternative physics invariance plays the same central role that covariance plays in Einstein's physics. Because of its fundamental importance in all relativity criticism, the twin paradox is also discussed.

An alternative approach to relativistic physics is reviewed, based on an invariant formulation of electromagnetic field theory due to Hertz. Both electromagnetism and mechanics are shown to be subject to reformulation whereby true invariance replaces ?universal covariance.? The invariant feature of Einstein's theory, proper time, is retained, but is supplemented for convenience in describing many-body motions by a generalized form of frame time termed ?collective time? (CT), patterned on Global Positioning System (GPS) time. CT resembles Newton's absolute time in regard to environmental independence, but is shown to satisfy a form of relativity principle. A crucial experiment is described involving accurate measurement of stellar aberration at second order by means of the Very Long-Based Interferometry (VLBI) system. This would decide definitively between the Hertz and Maxwell-Einstein formulations of electromagnetism. Another experiment that I proposed earlier,^{3} involving in-orbit light speed measurement, is disavowed, since I now recognize it as not crucial. This paper sums up a half-century of my dissident thinking in physics and forms a concluding testament.

The Fibonacci sequence is used as a ?hook? to direct interest toward generalizations.

A test theory is described for special relativity theory, based on universal invariance rather than universal covariance. A feature of the theory is its use of ?collective time,? similar to that told by GPS clocks, from which all environmental effects are compensated out. A second-order crucial experiment employing the VLBI system is proposed, involving the precise measurement of stellar aberration.

Physics Essays has been established as an international journal dedicated to theoretical and experimental aspects of fundamental problems in Physics and, generally, to the advancement of basic knowledge of Physics. The Journal?s mandate is to publish rigorous and methodological examinations of past, current, and advanced concepts, methods and results in physics research. Physics Essays dedicates itself to the publication of stimulating exploratory, and original papers in a variety of physics disciplines, such as spectroscopy, quantum mechanics, particle physics, electromagnetic theory, astrophysics, space physics, mathematical methods in physics, plasma physics, philosophical aspects of physics, chemical physics, and relativity.

The Journal will endeavour to reflect the environment in which best research is carried out by providing a stimulating publication outlet for both the expression of ideas and reporting of results, within the rigour of the scientific discipline with which the Journal is concerned, namely Physics. As a dynamic new journal, Physics Essays combines rigorous scientific reporting with freedom to express ideas based on logically sound and well balanced points of view.

Physics Essays, an international, peer-reviewed journal of impeccable quality, supported and advised by a renowned Editorial Board, has been established as the sole journal to act as the voice of the international physics community in a truly interdisciplinary fashion.

A gedanken experiment is described that exposes an apparent conflict between the treatment of proper timekeeping on geodesics according to general relativity theory, as customarily understood, and empirical evidence such as that of the Global Positioning System. The paradox is resolved by noting that there may be many geodesics between two spacetime events, only one of which represents a global maximum of proper time. The cardinality of such nonuniqueness (which may be that of the continuum) at first seems to violate the property that a geodesic between two events always incurs a (local) extremum of proper time. However, to first order (hence to observationally significant order), all free-fall orbits that have the same period have the same proper time, so no first variations of the orbits within our solution set change the proper time?a consistency check on the geodesic (extremum) interpretation of such orbits.

Two papers by Arunasalam in this issue are considered. These treat his views on the twin paradox and on the subject of covariance versus invariance. He proposes to resolve the twin paradox in terms of asymmetrical acceleration. An alternative not involving acceleration is provided in Taylor and Wheeler, Spacetime Physics (Freeman, San Francisco, CA, 1966) p. 94. I agree that an alternative resolution is desirable, but feel that those offered by special relativity theory leave much to be desired. Instead, it may prove necessary to acknowledge clock running-rate asymmetries as physically real. More significant is Arunasalam's championing of covariance. He provides definitions of Lorentz covariance and Lorentz invariance that are helpful in clarifying discussion, but gives no definition of the general concept of ?invariance? as I should like to see it understood. I offer my own definitions and on that basis sketch a variety of physics [developed in Old Physics for New (Apeiron, Montreal, 2006)] that employs an invariant covering theory of Maxwell's equations due to Hertz, as well as a ?collective time? patterned upon the clock running-rate correction methods of the global positioning system. In this alternative physics, invariance plays the same central role that covariance plays in Einstein's physics.

Several paradoxical aspects of the twin problem of special relativity theory are reviewed, with the conclusion that none has been permanently resolved.

Ampere believed longitudinal forces exist between electrical current elements, but relativity theory indicates that this is not possible. Now empirical evidence exists in support of Ampere?s logically-derivable conclusions. In Part II of a three-part article, Peter Graneau?s replication of the classical Robson and Sethian experiment is reported. Robson and Sethian failed to detect longitudinal forces because their apparatus did not incorporate the asymmetry necessary to achieve an unbalanced (net) force.

Part I of this three-part article discussed how absurdities are built into theories of electrodynamics by ignoring longitudinal forces between current elements. These forces were first postulated by Andre-Marie Ampere, and have since been demonstrated in the lab. Part II described Neal Graneau?s demonstration of Ampere?s law through the introduction of spark gap asymmetries to the classical Robson and Sethian experiment. In the third and final part of this article, an experiment is described wherein a tuned electric current, applied perpendicularly across the tines of a tuning fork, exerts longitudinal forces that cause the fork to resonate.

This paper discusses two quite different experiments thqat have independent verified existence of longitudinal electrodynamic forces (denied by the accepted Lorents force law) associated with currents flowing in closed circuits. Both employ versions of a simple 'inertial modulation' method, whereby current flowing within circuit portions of low effective mass exerts reduced observable force actions of those low-mass portions acting upon a separate test portion of greater mass - this effective physical force reduction resulting from *recoil energy* taken up by the low-mass portions. By suitable design, such variations of force-application effectiveness around a circuit can be exploited to spoil the exactness of differentials of force action between current elements, allowing violations of those classical theorems that assert indistinguishability of the Lorentz law from alternatives proposed by Ampere and others. the differences (described by the exact differentials) between these proposed laws are traditionally supposed to integrate to zero around any closed circuit; but that will not be the case if the integrands lose exactness through containing also 'Green's functions' describing inertial (or other) modulations of the *observable* force. In effect, the classical theorems strictly apply only to immobilized (non-recoiling) circuits; e.g., to those of infinite mass in all their parts. The force modulation approach offers a powerful and practical observational method of violating theorems of classical electrodynamics that assert the impossibility of distinguishing force laws differing by exact differentials. We discuss experimental confirmations of this concept and its successful use to verify semi-quantitatively the Ampere law, and empirically disqualify the Lorentz force law.

Classical or Bradley stellar aberration is correctly described by special relativity theory, which predicts also a second-order departure that has never been verified. We point out that the Very Long-Based Interferometry system appears now to offer sufficient resolution to allow confirmation of this truly "relativistic" aspect of starlight. The one-way nature of starlight propagation, in conjunction with the fact that most existing verifications of the special theory rest implicitly on two-way light-speed averaging, suggests the desirability of such measurements as a further independent verification of the theory.

The existence of longitudinal forces between elements of electrical current was claimed by the earliest investigator, Ampere, but has been denied by modern relativistic theory. Until recently, experimental difficulties have prevented an empirical resolution of the issue. In the last decade, however, applications of a method, termed ?inertial modulation? of force, have made it possible to circumvent the difficulties, and clear resolution has emerged in favor of Ampere. It thus appears that electrodynamic forces violate the universal covariance of relativity.

Treatments of the invariant total time derivative by Mocanu [4] and by Post [3] are compared and found to be in substantial agreement, despite their different mathematical appearances. It is argued that the line integral approach is better adapted to electrodynamics and the surface integral approach to hydrodynamics. The line integral seems to yield a physically satisfactory invariant form of the electrodynamic force law based on the total time derivative.

Review of J.P. Wesley, *Selected Topics in Scientific Physics* (Benjamin Wesley, Weiherdammstrasse 24, 78176 Blumberg, Germany, 2002), ISBN 3-9800942-9-4, 402 pp. + XXVI, 35 figures, 219 references, US$50.

A first-order Galilean-invariant covering theory of Maxwell?s equations of vacuum electromagnetism, first proposed by Heinrich Hertz, is reappraised in modern context. Physically, when properly formulated and interpreted for electromagnetic description, Hertz? theory is found to be both necessary, and ? insofar as the empirical facts are presently known ? sufficient. Mathematically, its use of the total time derivative instead of the Maxwellian partial time derivative is shown to be logically necessary under broadly applicable conditions. The physical superiority of the Hertzian formulation in the weak-field limit is emphasized.

It is argued that definitions may be chosen a posteriori to reflect mathematical existence?the opposite of the usual approach by which definitions are chosen a priori and used to prove existence. This inverted view is applied to the question of ?divergence.? It is shown that a definition employing approximations to process remainders known as ?terminal summation? allows ?values? of divergent series to exist.

Force measurements by means of an analytic balance have been made to determine the interaction of two toroidal permanent magnets, of a type to which we have given the name ?Virtual Amp?rian Current Element? (VACE). We justify this name by showing that when kept at a fixed separation distance the toroids interact by the same law of angular dependence as Amp?re proposed for two ?current elements.?

Empiricism indicates that the Lorentz force is in need of additional terms. Phipps suggests that the force law could be generalized simply by redefining electric intensity as ?[grad][phi] ? dA/dt, where d/dt is defined as the total time derivative. The difference from the Lorentz force law would have escaped observation because it integrates to zero in closed circuits. Phipps presents the current status of his research and invites interested parties to help resolve remaining anomalies, either experimentally or theoretically.

Review of Paul Marmet, *Einstein's Theory of Relativity Versus Classical Mechanics* (Newton Physics Books, 2401 Ogilvie Road, Gloucester, ON, K1J 7N4 Canada, ISBN 0-921272-18-9), U.S. $30.00.

The projection postulate has recently been invoked to explain a new class of optical observations, the so-called interaction-free measurements. We reexamine the status of this postulate in light of a generalized reformulation of mechanics and point out several advantages of the modified formalism. Our principal theme is that enhanced parametrization of equations of motion can accomplish in a logically economical way what extra postulation and other accepted ?quantum measurement theory? approaches have never been able to do, to rid factual history of ensemble attributes having no basis in experience. The treatment of interaction-free measurements follows naturally, as well as a much-needed capacity of quantum theory to describe classical chaos.

Maxwell?s equations of electrodynamics are only special-case formulae of more generalized equations published in 1892 by Heinrich Hertz. Maxwell?s equations were derived for scenarios involving a stationary detector. Consequently, only a partial time derivative was taken, and so the measured current density was equal to the current density measured at the source. An important implication of Hertz? invariant, general equations of electrodynamics is that there is no space-time symmetry.

Many equations have been derived to describe the force caused by two current elements acting on each other. Only Lorentz? equation is conventionally accepted, but only Ampere?s equation is empirically supported. In this article, Phipps describes in detail his experiment that demonstrates Ampere?s force equation. His results are worthy of careful attention and consideration.

It is shown from Newton's second law and the conservation of linear momentum, for arbitrary types of force, that the full ?formula force? used in the second law is effective in exerting observable ponderomotive action on a test element only if the force-exerting element is infinitely massive or is otherwise immobilized in an inertial system to preclude its recoil. In the more realistic case of finite mass m of a force-exerting element free to recoil under mutual action-reaction, the recoil motion ?steals? energy from the observable force action, so that the physically effective force exerted on a test element of mass M can be represented as the product of formula force and an inertial modulation factor = m/(M + m)1. Application of this elementary result to classical electrodynamics shows that it can invalidate (as physics) many of the theorems universally taken for granted since the nineteenth century. For instance, the well-established mathematical theorem that a closed current loop external to a straight current-carrying test element necessarily exerts zero longitudinal ponderomotive force on the latter (for the Lorentz force law, the original Amp?re force law, and all others differing from these only by an additive exact differential quantity) need not be valid physically. The reason is that the inertial factor has been overlooked. Its presence as an extra factor (Green's function) multiplying the force differential can spoil the exact differential nature of the loop integrand. For instance, if the external loop is physically configured with a ?weak link,? namely, an ?unanchored? section of conductor of relatively low mass mM and high mobility (freedom to recoil), then along this portion of the circuit 0, whereas for the remainder of the circuit, if anchored in the laboratory, 1. Hence an integral around the whole circuit treats the low-mass portion of the circuit much as if it were an open gap despite the presence of current in it. This proposition is easily put to observational test. By using an electromagnetically driven tuning fork bearing straight segments of current-carrying conductor as sensor (test element), so arranged as to respond to longitudinal force, it has been confirmed through an observed alteration of fork resonance response under ac excitation that a suitably configured weak link in an external closed electrical circuit can, indeed, cause a readily detectable violation of the closed-loop-no- longitudinal-force theorem. In sum, we have exhibited ?cross talk? between electromagnetic and inertial properties of conducting circuits that can limit the applicability of many of the classical electrodynamic theorems concerning ?closed loops.? Such theorems are assuredly valid only in the special case of completely immobilized force-exerting circuits, or circuits all parts of which are constrained to prescribed states of motion (not free to recoil). The ability to violate classical theorems that for a century have made empirical choices among candidate force laws ?impossible? implies that now experiments can be designed to allow such choices to be made unambiguously.

A recent Special Issue on fundamental problems of quantum physics (Barut et al. 1995) confirmed widespread recognition of the persistent difficulties of quantum measurement theory and its canonical 'Copenhagen interpretation.' The measurement theory problems were faced with ingenuity, fortitude, and a shared hope for 'hidden variables.' What they were not faced with in respect to the latter was consensus.

That being the case, there remains room for consideration of still other approaches to hidden variables than those favored by the particular authorities chosen. I shall confine attention here to my own penchant on this subject, which will be summarized in the same spirit of "science criticism" as my previous essay (Phipps 1995), in which I touted the advantages of a Galilean invariant covering theory of Maxwell-Einstein electromagnetism first propounded by Hertz (1892).

It is demonstrated, first by a specific example related to Einstein's "train" and then by a more general argument, that absolute synchronicity of clocks permanently at rest is various inertial systems is attainable without any transport of the clocks or use of light signals, provided that a method is agreed upon for synchronizing clocks in a single inertial system. The assumption on which this rests is that relative *clock rates* are determined by their relative *states of motion, *not by their locations in space (either absolute or relative to an observer or coordinate origin). It is then shown that the same result, absoluteness of simultaneity, together with related results such an length invariance, can be attained by use of light signals, compatibly with a relativity principle, provided these signals are described by neo-Hertzian, rathen than by Maxwellian, electromagnetism.

Although art criticism is a recognized profession, the same is not true of science criticism. This is odd, in view of the convergent tendency of both fields to be ruled by aesthetic criteria. It might be thought that those who define an area of human endeavor in terms of their personal responses to inner voices should expect and even welcome the sound of other voices criticizing. But the science of physics, which took its most wrenching turn beautywards as recently as 1905 "soon after the blossoming of Oscar Wilde (post hoc ergo propter hoc?)" is too immature to have evolved career patterns, tenure, and retirement plans for such other voices. The latter are as yet recognized only as bespeaking heresy, treason, or lese majesty. So it is with something of the reckless spirit of the pioneer that I venture the following commentary on the current scene: By using brick and mortar to build a latrine one can make of it a very solid and enduring structure; and by decorating its interior with French wallpaper one can make of it a thing of beauty, admired of generations. But it is still a latrine, as can be verified by invoking the sense of smell. This observation begs application throughout the more pretentious parts of all modern theoretical science. But here we confine its illustration to Maxwell-Einstein electrodynamics, the rock on which much of the more loftily towering superstructure of contemporary "beauty" is founded. Without any expectation that our love of either truth or beauty will be requited, let us see what stimulus can be lent to the restoration of critical faculties.

It is difficult to find critical work about Einstein's Theory of Relativity in most standard physics journals. Galilean Electrodynamics, founded by the late Dr. Petr Beckmann in 1989, is a notable exception. Since Einstein's 1905 paper, Relativity has had many critics and although it is widely accepted today, there is still a minority who question the central tenets of Relativity Theory. Galilean Electrodynamics is devoted to publishing high quality scientific papers, refereed by professional scientists, that are critical of Special Relativity, General Relativity, Quantum Mechanics, Big Bang theory and other establishment doctrines.

The traditional definition of entropy employed in statistical mechanics and in Shannon's information theory, −npn ln (pn), may be viewed as a noninvariant special case (associated with an implicit uniform prior) of an invariant covering theory based on −npn ln (pn/p), where pn refers to a posterior probability distribution, as affected by the arrival of ?new data,? and p refers to a Bayesian prior probability distribution. This generalized or explicitly Bayesian form of ?entropy? thus quantifies the transition between two states of knowledge, prior and posterior, exactly as does Bayes' theorem, and may be considered to have the same scope and information content as that theorem. Constrained extremalization of this form of entropy is demonstrated to be useful in solving three types of classical probability problems: (1) those for which the availability or presumption of single-parameter information allows a Poisson distribution to serve as ?universal prior,? (2) those for which additional prior information justifies a known departure from the Poisson law, and (3) those for which statistical sampling provides arbitrary nonuniform prior information; that is, prior to additional data input. In all cases the ?new data? must be of the aggregated or summed type expressible as Lagrange constraints. By reference to an example taken from Denting and by extension of the proof of Shannon's ?composition law? (hitherto thought to be valid only for the traditional form of entropy), it is shown that use of Bayesian entropy can broaden the scope of information theory, with interpretation of ?information? as that which quantifies a transition between states of knowledge. Shannon's ?monotonicity law? becomes superfluous and can be eliminated. This generalized form of entropy also promises a more powerful means of treating nonequilibrium thermodynamics, by freeing statistical-mechanical entropy from implicit connection to the equilibrium (uniform prior) or thermostatic state.

A way of looking at the topics of stellar and planetary aberration is suggested that enables them to be viewed as closely related?both being conceived as dependent on source-detector relative velocity. We show that the long-range limiting case, stellar aberration, has certain uniquely subtle aspects, as well as some hypothesized characteristics that lend themselves to empirical testing.

Heinrich Hertz developed a covering theory of Maxwell's equations that was Galilean invariant - i.e., first-order invariant, not covariant. This was accomplished by replacing Maxwell's partial time derivatives with total (complete) time derivatives, while leaving the spatial partial derivatives unaltered. To proceed to high-order approximations, frame time is replaced by field detector proper time. The resulting "neo-Hertzian" wave equation is solved in three dimensions by the method of d'Alembert. The solution is shown to give an account of aberration, based on a 3-vector invariance, that is simpler and less beset with equivocations than that offered by the established 4-vector covariant formalism. The 4-vectors seem to be fighting the physics every step of the way - and, were it not for their friends, losing.

An experiment claiming to have resolved a long-standing controversy regarding the existence of so-called Ampere forces (longitudinal forces between electric current elements) is shown to have been in fact indecisive. A slight modification of the experiment, proposed here, should enable it to be crucial.

It is shown that an alternative kinematics in which the Lorentz contraction does not occur is compatible with the familiar "two postulates" of relativity theory. This implies that possible breaking of spacetime symmetry, inasmuch as such symmetry is not a logical consequence of those postulates.

The failure of Maxwell's equations to exhibit invariance under the Galilean transformation was corrected by Hertz through a simple, but today largely forgotten, mathematical trick. This involves substituting total (convective) time derivatives for partial time derivatives wherever the latter appear in Maxwell's equations. By this means Hertz derived a formally Galilean-invariant covering theory of Maxwell's vacuum electrodynamics - which, however, was not space-time symmetrical (in view of his tampering with the time but not space derivatives). Had Hertz's mathematical accom-plishment received wider recognition, his invariant covering theory of Maxwell's could have furnished the formal key (almost two decades before Minkowski's "covariance") to unification of the "relativistic" properties of electrodynamics and Newtonian mechanics, explanation of the Michelson-Morley result, etc. The task of finding a viable physical interpretation of the Hertzian convective velocity parameter - which Hertz himself did not live to accomplish - remains for continuing research. We discuss this and related matters and give an explicit proof of invariance.

The ?difference equation viewpoint? previously applied to speeding the convergence of infinite series convergent in the Cauchy sense [Phys. Essays 6, 135 (1993)] and to forcing the convergence of series divergent in that sense [Phys. Essays 6, 440 (1993)] is here applied to continued fractions. The difference equation equivalent to a continued fraction is of second order, whereas that equivalent to an infinite series is of first order. The order of its equivalent difference equation is equal to the root multiplicity of any discrete infinite process, an nth-order process being capable of assuming (in the absence of root confluence) up to n distinct ?values.? This means that continued fractions are rightly conceived at the definitional level as bivalued. We give examples to support this claim.

In our first essay on infinite process convergence [Phys. Essays 6, 135 (1993)] a method of ?terminal summation? of infinite series was introduced, which employed at each stage of the limiting process an asymptotic approximation to the remainder term at that stage. In application to two rapidly convergent (in the Cauchy sense) infinite series for , the method was shown to speed convergence. We now pass to the opposite extreme and apply the same method to a nowhere-convergent (in the Cauchy sense) series proposed by Brown [Phys. Essays 2, 270 (1989)]. As he conjectured, computable values of this function are found throughout the range of its real variable x. The evaluation proves to be highly computation-intensive. As previously claimed [Heretical Verities: Mathematical Themes in Physical Description (Classic Non-fiction Library, Urbana, IL, 1987)], the method accomplishes convergence-forcing as readily as it does convergence-speeding. A relationship of the function represented by the Brown series to the exponential integral along the real axis is shown ? on the basis of which a simplification of the definition of the latter, free of ?cuts,? is proposed. We offer Brown's series as a challenge to established ?summability? methods and flatly assert that none can match the convergence-forcing capabilities of terminal summation.

The idea of ?renormalization,? used by physicists for overcoming series divergences by ?subtracting them out,? is generalized here through a reconceptualization of the meaning of discrete infinite process (redefinition of ?value?). The standard mathematical conception, due to Cauchy, approaches ?the infinite? one-sidedly, discarding at the nth stage (n = 1, 2, ?) of a limiting process the whole of whatever may be ?at infinity.? The new concept proposes to treat the process two-sidedly, retaining at each stage of the limiting process an asymptotic approximation to any remainder term ?at infinity.? This accomplishes the same goal as ?summability,? but without modification of finite summands at any stage. Application is made in this paper to speeding convergence of the fast Ramanujan series for pi, and of a still faster-converging series for pi recently discovered. In addition to convergence speeding, the method accomplishes (like summability methods, but in general more powerfully) convergence forcing of ?divergent? processes. As will be shown in later parts, it is applicable not only to series but to continued fractions and all other discrete infinite processes whose ?summands? are known functions of n, required to be asymptotically expandable.

Despite a number of attempts, the Lorentz contraction has never been directly observed, the worldline-relational or metric "structural" statements of special relativity remain therefore empiricallly unsupported, and the metric nature of spacetime retains an inferential or speculative character. In these circumstances any direct evidence would be of value. It is suggested that a much more easily observable phenomenon than the Lorentz contraction of a material structure be exploited; namely, the contraction of the Coulomb field accompanying a high-speed electron pulse. A proposal is made for a simple laboratory experiment to measure this effect. To lend interest, a modernized version of an alternative electrodynamics due to W. Weber (propounded in the nineteenth century and never observationally refuted), based upon action-at-a-distance, is described and its predictions in the proposed experimental situation are contrasted with those of Lorentz-Einstein. The same is done for the original Weber theory and for a neo-Hertzian version of electromagnetism. The experiment should be "crucial" for deciding among such alternative theories

A national way to express an hypothesized first-order departure from light-speed constancy is by addition to *c *of a scalar product of some convective velocity and the normalized light propagation vector. This is the form proposed in a recent paper by Hill [4] in this journal. It is shown here that a principle discovered by Potier [2] during the last century, based on Fermat's principle, denies the theoretical possibility of any simple optical testing (proof and disproof) of such a presumed first-order effect. It was Potier's principle, joined to physical interpretation of the convective velocity as ether velocity, that established motional "relativity" as a first-order empirical fact before the advent of either Michelson-Morley (second-order empiricism) or Poincare-Einstein (higher-order theory).

A derivation from first principles is given of a modernized form, recently proposed in this journal [Phys. Essays 3, 414 (1990)], of the Weber action-at-a-distance law of force between point electrical charges. The modernization invokes the existence of a limiting relative particle speed in nature. Like Weber's original (1848) law, our result amounts to a Coulomb law describing static interaction, modified at higher orders to describe instant action-at-a-distance through a simple dependence of potential energy on charged-particle relative velocity. Weber's law appears as a low-speed limiting case.

A previously advanced hypothesis of radiation convection by the absorber, deduced from the so-called neo-Hertzian electomagnetism, is tested for its ability to account for the facts of stellar aberration. The test is passed at first order. Satellite astronomy may in the future offer some hope of observationally distinguishing this theory from special relativity.

Recent data indicate that the law of action between electric current elements proposed by Ampere is notably superior to the Lorentz (Biot-Savart) law in its ability to describe laboratory observations of currents flowing in single circuits. Ampere?s law conforms to Newton?s third law and thus cannot be covariantly expressed. Since all field theories of retarded action violate Newton?s third law in describing nonstatic situations, it appears that the observational evidence in question weighs against all field theories as applied to the description of force actions. A reexamination of force instant action-at-a-distance modes of description is therefore indicated. We investigate here the possible revival of such a formulation proposed by W. Weber before 1850. The virtues of this approach are (a) mathematical simplicity, (b) rigorous conformity to Newton?s third law, and (c) agreement with Ampere?s law of action between current elements hence with the observations just mentioned. Two different "modernizations" of Weber?s approach are examined, dependent on whether energy or force methods are viewed as more fundamental in mechanics. Implications for plasma physics are touched upon.

Editor's note: Richard A.Waldron passed away in Northern Ireland on May 24 of this year, shortly before he was to retire from the University of Ulster. Just prior to his death, Professor Waldron had agreed to join the editorial board of APEIRON, and contributed an article on stellar collapse which he eagerly looked forward to seeing published in this journal (see page 4). Richard A. Waldron's youthful enthusiasm for physics and his compulsive desire to discover nature's secrets were at once endearing and inspirational. Thomas E. Phipps Jr. has generously agreed to produce an account of his work, and offers this appraisal of the debt owed by science to an extraordinary human being.

Weber's electrodynamics based on a velocity-dependent potential with instantaneous action-at-a-distance reproduced the observational agreements of Amp?re's force law. Critics such as Heimholt pointed out that Weber's law implied nonphysical negative mass effects. A modernization of Weber's formulation is suggested that overcomes Helmholtz's objection. The consequences offer possibilities of experimental testing and revival of the action-at-a-distance mode of description. A method of clock synchronization based on proper time, which confirms the feasibility of such a development, is reviewed in an appendix. Another appendix examines the possibility of higher-order modifications of the force law.

This article was reviewed by Harold Milnes, *V8, N4, pp. 4273-4276*.

An experiment proposed by J. P. Wesley has been carried out to test for the existence of longitudinal ponderomotive forces between current-carrying conductive elements within a single circuit, as predicted by Amp?re but denied by the Lorentz force law. The experiment performed consists in passing a low-frequency alternating current I of a few amperes through a mercury cell of varying cross section and observing the resulting internal pressure (Amp?re tension) differences by measuring height changes of vertical mercury columns situated at positions of different current density. The resulting I2 ponderomotive forces predicted by Amp?re-Wesley are observed (at twice the frequency of electrical excitation) to produce a mechanical resonance corresponding to the natural oscillation frequency of a portion of the total mercury mass. Alternative explanations based on the Lorentz (Biot-Savart) force law are sought but not found. It is concluded that

- Amp?re appears to have been correct in demanding compatibility between the inter-current-element force law and Newton's third law, and
- the action of a noncovariant force may have been observed in nature.

A proposed alternative to Einstein's kinematics, based on the postulated invariance 1) of particle proper time and 2) of object length (i.e., nonoccurrence of the Lorentz contraction), is tested for its ability to exhibit consistency between the aging rates of an accelerated 'light clock' and its comoving observer. The problem is nontrivial because the altered kinematics requires employment of an altered electromagnetism, the so-called 'neo-Hertzian' generalization of Maxwell's theory, which is invariant under inertial transformations. Difficulties of crucial experimentation are touched upon.

Big-bang cosmology rests mainly on accepted interpretations of two empirical facts: the Hubble redshift, interpreted as a Doppler effect, and the 2.7?K cosmic background radiation, interpreted as a direct echo of the hypothesized primordial event. Recent findings of Marmet, providing both a plausible non-Doppler redshift mechanism and a brilliant new resolution of Olbers' paradox, are reviewed and shown to support altered interpretations of the empirical evidence. These appear to justify renewed interest in steady-state and related cosmological models. Numerous other considerations, including the quasar data of Arp, lend support to this conclusion.

Currently accepted explanations of the superluminal velocities reported by astronomers are characterized by a superunitary ratio of hypotheses to facts. This motivates a review of alternatives, beginning with doubts cast by investigations of Arp and Marmet on the distance scale of quasars and culminating in a reexamination of the foundations of kinematics. A simple analysis based on postulates of invariance of length and proper-time intervals leads to velocity nonreciprocity ? which explains the astronomical observations with logical economy. It also offers new perceptions concerning the well-known twin paradox.

Some recent experimental searches for a detectable ?ether wind,? including two reportedly successful, are described and analyzed It is concluded that no compelling evidence to date refutes the relativity principle.

Quantum measurement theory is subject to improvement through enhanced rigor of the formal Correspondence between c-number and q-number physics. Such rigor, based upon a covering theory of the Hamilton-Jacobi formalism, implies restoration on the q-number side of formal analogs of the classical ?new canonical variables? or constants of the motion, which in quantum description become ?hidden variables? appearing in a phase factor on the wave function. Though not subject to Bell's theorem, such hidden parameters (dynamical constants) are capable of severing phase connections through unpredictable ?phase jumps? descriptive in phase space of localized events (after the fact). Prediction thus remains probabilistic, but factual history loses all statistical attributes in a description asymmetrical between past and future.

A series of articles, eventually reprinted in Phipps' book *Heretical Verities*.

- V2, N1, pp. 509-523; N2, pp. 609-625; N3, pp. 801-814; N4, pp. 924-947
- V3, N1, pp. 1008-1031; N2, pp. 1205-1219; N3, pp. 1440-1457; N4, pp. 1467-1484
- V4, N1, pp. 1714-1725; N2, pp. 1874-1885; N3, pp. 2060-2065; N4, pp. 2235-2256
- V5, N1, pp. 2335-2341; N3, pp. 2629-2636

We show that if the Lorentz transformation equations are routinely applied to compute the expected arrival times of two photons simultaneously emitted from a star source, then a large time difference is predicted between the instants when the photons would be seen by observers moving in opposite directions at velocities equal to the surface velocity of Earth at its equator, or its orbital velocity. In the case of the binary star Rigel, located only 250pc from Earth, observers stationed on opposite sides of the equator should note a discrepancy of 11.05 hrs.; in the caseof observers at opposed points of the Earth's orbit, moving with the mean orbital velocity of Earth, it should be 29.59 days. Since no such anomalies occur, the principle that the velocity of light is c relatively to every observer is false, and the Lorentz transform equations cannot be validly applied to astronomical observations.

We also cast very serious doubt on the general validity of the reciprocity of inertial reference frames, as a consequence of Zeeman's experimental observations with moving quartz rods.

Attention is called to the remarkable fact that, relative to the observer, Maxwell's equations allow field-source motions but not field-sink motions. These equations thus implicitly refer to a "preferred observer." On correcting this unwarranted suppresssion of instrumental degrees of freedom, we obtain generalized equations for electromagnetism that (at first order in detector velocity) prove to be Galilean invariant. The extra parameters needed to describe filed-detector motions enter the wave equation and spoil the spherical symmetry of radiation propagation, so our previous "acausal" hypothesis of radiation convection by the absorber, in conjunction with physical non-occurrence of the Lorentz contraction, - receives independent confirmation. Higher-order correction to Maxwell's equations are also discussed. Experimental testing of the radiation convection hypothesis becomes imperative and should be feasible in view of the first-order nature of the effect. Convection is defined as something that occurs at the locus of each detector - a 'pulling along of the wave by the detectors.

**Physics Letters A**, Volume 65, Issue 2, 20 February 1978, Pages 83-84

Marinov's proposed experiment on light velocity and its dependence on source velocity is discussed in terms of the background synchrotron radiation. The angular distribution of this radiation is shown to support the Einstein second postulate.

The possibility of generalizing quantum mechanics in such a way as to retain its predictive results, while comprehending additional solutions, is examined. It is found that this can be done through a perfected formal correspondence with Hamilton-Jacobi mechanics, by which one is led to consider generalizations of the Heisenberg postulate of the form pk qj - qj pk = S (delta jk), where S is a quantum analog of Hamilton's principal function. The formalism is shown to be equivalent to a simple change in Hamiltonian, with transformed momentum operators satisfying conventional commutation relations, and with an additional relationship involving formal analogs of the classical "initial constants" adjoined. A particular choice of S (= h-bar/i) leads to a theory identical with wave mechanics apart from a constant (unobservable) phase factor on the wave function. The fact that S may possess other, nonconstant values, demonstrated by a specific example, suggests the ability of the mechanical equations to describe a broader class of physical states than has hitherto been investigated.