Papers by Daniel Shanahan
International Journal of Quantum Foundations, 2019
Various attempts at a thoroughly wave-theoretic explanation of matter have taken as their fundame... more Various attempts at a thoroughly wave-theoretic explanation of matter have taken as their fundamental ingredient the de Broglie or matter wave. But that wave is superluminal whereas it is implicit in the Lorentz transformation that influences propagate ultimately at the velocity c of light. It is shown that if the de Broglie wave is understood, not as a wave in its own right, but as the relativistically induced modulation of an underlying standing wave comprising counter-propagating influences of velocity c, the energy, momentum, mass and inertia of a massive particle can be explained from the manner in which the modulated wave structure must adapt to a change of inertial frame. With those properties of the particle explained entirely from wave structure, nothing then remains to be apportioned to anything discrete or "solid" within the wave. Consideration may thus be given to the possibility of wave-theoretic explanations of particle trajectories, and to a deeper understanding of the Klein-Gordon, Schrödinger and Dirac equations, all of which were conceived as equations for the de Broglie wave. It is argued that this wave-theoretic interpretation of matter favours a physically realistic, rather than inherently probabilistic, interpretation of quantum mechanics.
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International Journal of Quantum Foundations, 2019
Effects associated in quantum mechanics with a divisible probability wave are explained as physic... more Effects associated in quantum mechanics with a divisible probability wave are explained as physically real consequences of the equal but opposite reaction of the apparatus as a particle is measured. Taking as illustration a Mach-Zehnder interferometer operating by refraction, it is shown that this reaction must comprise a fluctuation in the reradiation field of complementary effect to the changes occurring in the photon as it is projected into one or other path. The evolution of this fluctuation through the experiment will explain the alternative states of the particle discerned in self interference, while the maintenance of equilibrium in the face of such fluctuations becomes the source of the Born probabilities. In this scheme, the probability wave is a mathematical artifact, epistemic rather than ontic, and akin in this respect to the simplifying constructions of geometrical optics.
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It has been argued by R. T. Cahill and others that a Michelson interferometer in "gas mode" - in ... more It has been argued by R. T. Cahill and others that a Michelson interferometer in "gas mode" - in which the light paths are through an included gaseous medium - are able to detect and have detected an absolute frame of reference. It is shown here that this argument supposes incorrectly that the reduced velocity of light in gas is an observer-independent invariant. This velocity is not invariant, but given in a frame with respect to which the interferometer moves with velocity v by the usual relativistic formula for the addition of velocities, these being in this case the velocity v and the reduced velocity of light in the inertial frame of the interferometer. It is suggested nonetheless that though the absolute frame urged by Cahill may be undetectable, there are persuasive grounds for considering the alternative Lorentzian Relativity that did suppose the existence of such a frame.
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It is argued that the de Broglie wave is not the wave usually supposed, but the relativistically ... more It is argued that the de Broglie wave is not the wave usually supposed, but the relativistically induced modulation of an underlying carrier wave that moves with the velocity of the particle. In the rest frame of the particle this underlying structure has the form of a standing wave. De Broglie too assumed the existence of this antecedent standing wave, but failed to notice its survival as a carrier wave in the Lorentz transformed wave structure. Identified as a modulation, the de Broglie wave acquires a physically reasonable ontology, evidencing a more natural unity between matter and radiation than might otherwise be contemplated, and avoiding the necessity of recovering the particle velocity from a superposition of such waves. Because the Schrödinger and other wave equations for massive particles were conceived as equations for the de Broglie wave, this interpretation of the wave is also relevant to such issues in quantum mechanics as the meaning of the wave function, the nature of wave-particle duality, and the possibility of well-defined particle trajectories
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Foundations of Physics, Jan 1, 2014
The Lorentz transformation (the LT) is explained by changes occurring in the wave characteristics... more The Lorentz transformation (the LT) is explained by changes occurring in the wave characteristics of matter as it changes inertial frame. This explanation is akin to that favoured by Lorentz, but informed by later insights, due primarily to de Broglie, regarding the underlying unity of matter and radiation. To show the nature of these changes, a massive particle is modelled as a standing wave in three dimensions. As the particle moves, the standing wave becomes a travelling wave having two factors. One is a carrier wave displaying the dilated frequency and contracted ellipsoidal form described by the LT, while the other (identified as the de Broglie wave) is a modulation defining the dephasing of the carrier wave (and thus the failure of simultaneity) in the direction of travel. The superluminality of the de Broglie wave is thus explained, as are several other mysterious features of the optical behaviour of matter, including the physical meaning of the Schrödinger Eqn. and the relevance to scattering processes of the de Broglie wave vector. Consideration is given to what this Lorentzian approach to relativity might mean for the possible existence of a preferred frame and the origin of the observed Minkowski metric.
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It is argued that RT Cahill's criticism of the Michelson-Morley experiment (in Australian Physics... more It is argued that RT Cahill's criticism of the Michelson-Morley experiment (in Australian Physics) fails to correctly apply the relativistic formula for composition of velocities.
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In his famous doctoral dissertation, de Broglie assumed that a massive particle is surrounded in ... more In his famous doctoral dissertation, de Broglie assumed that a massive particle is surrounded in its rest frame by a standing wave. He argued that as observed from another inertial frame this wave becomes the superluminal wave now known as the de Broglie wave. It is shown here that under a Lorentz transformation, such a standing wave becomes, not the de Broglie wave, but a modulated wave moving at the velocity of the particle. It is the modulation that has the superluminal velocity of the de Broglie wave and should be recognized as the true de Broglie wave. De Broglie's demonstrations relied, variously, on his "theorem of the harmony of phases", on a mechanical model, and on a spacetime diagram. It is shown that in each case the underlying wave was inadvertently suppressed. Identified as a modulation, the de Broglie wave acquires a physically reasonable ontology, avoiding the awkward device of recovering the particle velocity from a superposition of such waves. The deeper wave structure implied by this de Broglie wave must also impinge on such issues in quantum mechanics as the meaning of the wave function and the nature of wave-particle duality.
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Drafts by Daniel Shanahan
In support of their contention that it is the absence of a subsisting medium that imbues the spee... more 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 "…shbowl universes"in which physical in-‡uences 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 "super ‡uous", 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 Lorentz transformation would explain why all aspects of matter transform in like manner, thereby avoiding a di¢ culty that was a signi…cant reason for the demise of Lorentzian relativity after 1905. Importantly, these sonic universes also 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.
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Papers by Daniel Shanahan
Drafts by Daniel Shanahan