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The "Aarau Question" and the de Broglie Wave

G. Galeczki

Published Jan 1, 1995• 0 citations
OpenAlex

Abstract

The analogy between Einstein’s “Aarau Question” of riding on a light-wave and— nevertheless—“seeing” the light-wave running away with velocity “c” and Mugur-Schachter’s proposal to associate with every particle having non-zero proper mass a progressive plane wave moving with invariant velocity “V” with respect to the particle, is shown not to solve any difficulties in fundamental physics. The spinning ring model of charged particles, however, provides an “internal clock” with a frequency independent of the relative motion of possible “observers”.

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Proceedings of the Physico-Mathematical Society of Japan. 3rd Series•Jan 1, 1927•0 citations
The analogy between Einstein’s “Aarau Question” of riding on a light-wave and— nevertheless—“seeing” the light-wave running away with velocity “c” and Mugur-Schachter’s proposal to associate with every particle having non-zero proper mass a progressive plane wave moving with invariant velocity “V” with respect to the particle, is shown not to solve any difficulties in fundamental physics. The spinning ring model of charged particles, however, provides an “internal clock” with a frequency independent of the relative motion of possible “observers”.
The Gravitation–Matter–Wave Theory (GMWT) introduces an intrinsic wave charge qω(m) = (Gm)3/2/h5/2, expressed in the internal unit ars. The wave charge characterizes the source level of the particle-induced wave structure, whereas observable energy, frequency, and length require projection into SI units. The present article establishes a direct formal link between GMWTand de Broglie’s phase-wave relations. In the GMWT interpretation, a moving particle produces a dynamical distortion of space. During the same interval ∆t, the particle moves by v∆t, while the associated distortion propagates over the scale c∆t. Their ratio defines the dimensionless phase-projection factor K = c∆tv∆t = cv .Consequently, the GMWT phase velocity is vϕ = cK = c2/v, exactly the phase velocity obtained by de Broglie. Combining this result with the observable frequency νphys = E/h gives the spatial projection λphys = cK/νphys. For a free relativistic particle, E = γmc2, so that λphys = h/(γmv) = h/p. The de Broglie wavelength therefore emerges as the observable spatial projection of the GMWT wave structure. No independent arbitrary calibration to metres is required. The result establishes a definitive formal correspondence within the internal logic of the theory, while experimental validation remains a separate question.
The de~Broglie relation λ=h/p\lambda = h/pλ=h/p is among the most well-confirmed results in modern physics, yet the kinematic origin of the associated matter wave remains conceptually obscure. This paper presents a kinematic analysis leading to the de~Broglie relation. The only assumption is the existence of a globally defined phase field with uniform rest-frame oscillation, a structure known to occur in superfluids and Bose--Einstein condensates. Under a Lorentz boost, the scalar transformation of the phase field converts temporal periodicity directly into spatial periodicity, yielding a wave number k′=γω0v/cs2k' = \gamma\omega_0 v/c_s^2k′=γω0​v/cs2​ and a phase velocity vphase=cs2/vv_{\mathrm{phase}} = c_s^2/vvphase​=cs2​/v. No wave equation, dynamical model, or quantization procedure is required. The result follows solely from the relativity of simultaneity applied to a scalar phase field. When the characteristic frequency and invariant speed are identified as ω0=mc2/ℏ\omega_0 = mc^2/\hbarω0​=mc2/ℏ and cs=cc_s = ccs​=c, the resulting wavelength and phase velocity reproduce the standard de~Broglie relations. The logical architecture inverts that of de~Broglie's original construction: rather than postulating a separate clock and wave linked by phase harmony, the wave emerges as the Lorentz-transformed image of a single coherent phase clock. The phase harmony that de~Broglie introduced as an independent postulate becomes a consequence of Lorentz covariance. The analysis establishes a precise kinematic correspondence without asserting that the physical vacuum is a coherent medium. Whether this correspondence reflects a deeper physical principle or a mathematical analogy remains an open question.
The famous 1927 Solvay Conference was considered a turning point in the world of Physics. The scientific realists like Albert Einstein had lost and the instrumentalists like Niels Bohr had won the fundamental conflict. Since then Physics has followed the path of the instrumentalists in which Quantum Physics has been determined by the concept of Elementary Particles and Probability Waves. Until May 2013, when for the first time a photo had been made of the Probability Waves Inside the Hydrogen Atom . It should be impossible to make a photo of a non-existing complex probability wave with mass zero But the fact could not be denied anymore that scientists had succeeded to make the complex and non-existing visible. This will be the fundamental question in this article. Does an alternative theory exist in which the existence of this particular photo could be explained. And that the famous photo of the Hydrogen Atom can be explained in a logical and a simple way. To find the answer, we have to go back in time. Back 300 years in time to the moment when Isaac Newton discovered the beauty and one of the many secrets of the light. The moment when science walked away from light. And we return to the fundamental question: “Is it possible to build matter out of Light (confined electromagnetic waves)?” To answer this question we first have to answer the question how we have come to this world of Probability Waves and Elementary Particles and Quantum Physics.Louis de Broglie described in 1924 in his PhD thesis the wave properties of matter. Erwin Schrödinger published in 1926 the well-known Schrödinger wave equation with the characteristic spherical and elliptical wave solutions. To describe these material waves, the immediately and first explanation was: “There is only one possibility. These are “electromagnetic waves”. De Broglie waves are ” Light Waves”. Because these were the only waves, known in the world of Physics. But there was a fundamental problem. These material waves, discovered by Louis de Broglie and mathematically described by Erwin Schrödinger could never be solutions of the well-known 4 equations of James Clerk Maxwell. The material waves were spherical and elliptical solutions and that was impossible for the solutions of the Maxwell Equations. According to the Maxwell Equations, light always travels along a straight path. A second problem was that the model of the atom of Bohr could not hold. How could an electron be everywhere at the same time in a kind of a spherical shell surrounding the nucleus. And be a particle at the same time. And Bohr found a compromise to declare the “De Broglie” waves to be the probability waves. Two problems were solved. Bohr’s planetary model could hold. And there was a name for the unknown material waves, discovered by Louis de Broglie and mathematically described by Erwin Schrödinger. The theory of “Probability Waves, Elementary Particles and Quantum Physics” had been created. To find a possibility, to create matter out of light we have to go back to the Equations of James Clerk Maxwell. The only possibility to declare the probability waves, discovered by Louis de Broglie, to be electromagnetic waves, to be light, and to be the building element of our universe, is to find evidence that he Maxwell Equations are not complete and that it is possible to confine light (electromagnetic waves) in spherical and elliptical shapes. A new equation has to be found. In this article it has been claimed that this missing equation is equation (5). Because the Theory of General Relativity has been built on the Einstein-Maxwell Equation, a new equation has to be found that describes in a generalized way the interaction between light and matter. This missing equation is equation (5-a).