Broglie Waves Research Articles

Theory of Relativity – Biggest Mistake of the 20th Century?

According to the thesis presented here, the correct model of reality should be based on two major discoveries of the 20th century: Einstein's discovery that reality is four-dimensional (1905) and de Broglie's wave structure of matter (1924). In 1905, Einstein did not have all the information necessary to construct the proper model of relativity; therefore, by publishing the Theory of Relativity without knowledge of the wave structure of matter, he made a kind of a false start, which resulted in the excessive complexity and unintuitive nature of the Theory of Relativity. Including the wave nature of matter in the basic assumptions of the model of reality allows to greatly simplify the model, expand its capabilities compared to the model currently in force, and remove many problems specific to the Theory of Relativity. In this work, using the trivial example of waves on the surface of water, I derive relativistic relationships and give an unambiguous and precise interpretation of basic concepts like time, space, relativity of motion, and simultaneity of events. The new definition of time- and space dimensions also allows to define the proper time of particles directly as the number of de Broglie’s wave periods for both relativistic physics and Quantum Mechanics.

English

In the framework of Special Relativity and in agreement with the electromagnetic approach used to connect Quantum and Relativistic effects in Bridge Theory, a first order wave-equation able to emulate the wave-particle duality in terms of local electromagnetic interactions is proposed. The equation is able to describe the propagation of a fermion as a de Broglie's wave and simultaneously to characterise the wave in motion with a mass energy as a particle. The solution of the wave-equation proposed is compatible with the de Broglie's idea of an empty pilot wave, carrying information about the dynamical properties of a particle materialising during each local interaction with the observers.

Interfering Quantum Trajectories Without Which-Way Information

Quantum trajectory-based descriptions of interference between two coherent stationary waves in a double-slit experiment are presented, as given by the de Broglie-Bohm (dBB) and modified de Broglie-Bohm (MdBB) formulations of quantum mechanics. In the dBB trajectory representation, interference between two spreading wave packets can be shown also as resulting from motion of particles. But a trajectory explanation for interference between stationary states is so far not available in this scheme. We show that both the dBB and MdBB trajectories are capable of producing the interference pattern for stationary as well as wave packet states. However, the dBB representation is found to provide the `which-way' information that helps to identify the hole through which the particle emanates. On the other hand, the MdBB representation does not provide any which-way information while giving a satisfactory explanation of interference phenomenon in tune with the de Broglie's wave particle duality. By counting the trajectories reaching the screen, we have numerically evaluated the intensity distribution of the fringes and found very good agreement with the standard results.

The dispersion relation for matter waves in a two-phase vacuum

The cosmological constant Λ of general relativity is a natural consequence of embedding Einstein's theory in a five-dimensional (5D) theory of the type needed for unification. The exact 5D solution for Λ<0 shows waves in ordinary three-dimensional (3D) space with properties similar to those of de Broglie or matter waves. Here the dispersion relation is derived for matter waves in a toy two-phase model, where regions with Λ<0 and Λ>0 average on the large scale to Λ≃0, thus providing in principle a resolution of the cosmological-constant problem. A striking result of the analysis is that the dispersion relation is bimodal, with a well-defined window of high-frequency transmission which effectively defines the speed of light.

A Novel Hypothesis for Quantum Physics, Model with Telegraphs Equation

The article describes numerical model of basic structures in quantum physics. It was tested on the basic conflguration of the electron beam and it was verifled in Institute of Scientiflc Instruments Academy of Sciences of the Czech Republic experimentally. We had prepare the numerical model which was based on the particle theory. We prepared model which respects classical Electrodynamics. Numerical results were evaluated. The second model was prepared in respect to theory of wave packet (Louis de Broglie and Material Wave Theory (MWT)) and solved again. Results of both models were the similar, same in their quality, we evaluated electric fleld intensity E on the electron impact area, and they corresponded with results from experiments. In order to attempt | in modeling the H2O elementary molecule and the subsequent high quan- tity of H2O in the electric fleld | to obviate the problems resulting from quantum mechanics (1), a simple task was created and solved using the flnite element method (2). The main reason consists in the fact that, using the above hypothesis (1), it is not possible to formulate the problem with a flnite number of the degrees of freedom (the problem of a variable quantity of particles) or the problem of relation between the electric fleld and the particles (a Lorentz force efiect and tran- sitory stages of elementary particles, dynamic behaviour of particles and other items). Referring now back to the main task, the flrst step consisted in creating a numerical model based on the quantum mechanics hypothesis with an elementary model in the form of a difiusion equation | the Schrodinger equation. The numerical model simulated the reality that had been experimentally verifled in the 1960s. Then, we created a numerical model that is rather more complicated in terms of formulation: the formulation in question is realized using the telegraph equation, therefore it is a difiusion equation complemented with an element with second partial derivative. This model | based on the Material Wave Theory (MWT) flrst published by de Broglie | is however capable of solving transient conditions and the dynamics of the elementary structure of matter. The testing (1) has proved that the model is applicable. Nevertheless, there were certain variations in the testing due to the failure to simulate for identical conditions the task formulated with the help of quantum mechanics and the telegraph equation. Here, the conditions were merely approximate. Yet, based on the surprisingly proximate results, these models are being reflned and they are expected to reach a substantially higher degree of conformity. At this point we would like to attempt to brie∞y describe the formulated hypothesis, the model of the basic elements of matter behaviour, which is based on solving partial difierential equations of a dimension higher than the difiusion equation | the Schrodinger equation. 2. HYPOTHESIS The working hypothesis for quantum mechanics, based on the reduced difiusion equation

On the Extinction Paradox

The extinction paradox, the difference of classical and quantum scattering cross-sections for the scattering of particles by a rigid sphere (σ Q = 2πa 2 = 2σ C for ka » 1), is analyzed in a simpler 2D model of a rigid cylindrical potential. Rigorous solutions of the Schrodinger equation for particle beams, including also finite width beams, are derived and employed in the description of the scattering process. The scattering particle fluxes, with a thorough treatment of the forward directions, are being studied. It is pointed out that for wide beams (w > a) the scattered flux can reach the value determined by the quantum theory, provided that it is measured at distances R > waλ. Moderately narrow beams (1 < w « a) behave as classical trajectories, and their scattering can be described in classical terms. Thus, the classical limit of quantum scattering requires not only that the de Broglie wavelength λ B is much smaller than the size of the scatterer (a » λ B ), but also that the transverse width of beams of de Broglie's waves is small, w « a.

On the Relationship between Fluid Velocity and de Broglie's Wave Function and the Implications to the Navier - Stokes Equation

By exploring the relationship between the group velocity of the de Broglie's waves and a particle velocity we can demonstrate the existence of a close relationship between the continuity equation and the Schrodinger's equation. This relationship leads to the proportionality between the fluid velocity v and the corresponding de Broglie's wave's phase at the same location. That is, the existence of a scalar function q proportional to the phase of the de Broglie's wave, such that v = Сq can be proven without reference to the flow being inviscid. We then proceed to show that the Navier-Stokes equation in the case of constant viscosity incompressible fluid is equivalent to a reaction-diffusion equation for the wave function of the de Broglie's wave associated to the moving fluid element. A general solution to this equation, written in terms of the Green's functions, and the criterion for the solution to be stable is presented. Finally, in order to provide an example, the procedure is applied to obtain the solution for the simplest case of the Burgers' equation.

The Photon as a Soliton

Recently J. P. Vigier showed [1] that the photon can be reperesented as a solitary electromagnetic wave – a soliton. As a consequence one can ascribe to such a soliton effective volume, amplitude and frequency which coincide with the frequency of de Broglie's wave (measured by interference phenomena). In this paper we propose a soliton-like model for the photon. We show that the electromagnetic amplitude, the volume, the classical cross section and the photoeffect cross section of the photon-soliton can be estimated in an empirical as well as in an analytical way. In the framework of our model the relation between the electromagnetic amplitude of the soliton and its frequency that we found seams to be an universal one, in sense that it may not depend on the specific quantum system considered. We show that there are no essential contradictions between our photon-soliton and some well-known facts such as the interactions in the case of photoeffect and Compton effect.

Neutron interferometry can prove (or refute) the existence of de Broglie's waves

An experimental apparatus based on neutron interferometry is is presented which can in principle decide the question whether the empty waves of de Broglie really exist or not.

On universal fields and de Broglie's waves

Some properties of the universal gravitational field are derived by using the supposed observational equivalence with the apparent universal velocity field. It is found that de Broglie's hypothesis about the wave nature of matter indicates that there exist two different kinds of fundamental waves in Nature, to be named de Broglie's waves of first and second order, respectively. Of these waves the first one is a universal wave travelling at the constant velocityc0, while the second can be reflected and travels at the velocity of light which depends on the aether density. It is conjectured that de Broglie's waves of second order reflect on the knots of de Broglie's waves of first order. The Larmos slowing down of clocks and the Fitzgerald-Lorentz contraction of bodies are considered as caused by the universal action of the homogeneous aether field. A formula for the aether density around a point mass is derived.

De Broglie's wave particle duality in the stochastic interpretation of quantum mechanics: A testable physical assumption

If one starts from de Broglie's basic relativistic assumptions, i.e., that all particles have an intrinsic real internal vibration in their rest frame, i.e., hv0=m0c2; that when they are at any one point in space-time the phase of this vibration cannot depend on the choice of the reference frame, then, one can show (following Mackinnon(1)) that there exists a nondispersive wave packet of de Broglie's waves which can be assimilated to the nonlinear soliton wave U0 introduced by him in his double solution model of wave mechanics.(2) Since de Broglie's linear pilot waves can be considered to be real waves propagating as collective motions on a covariant subquantum chaotic “aether,”(3) these new solition waves can be considered as describing the particle's immediate neighborhood, i.e., the aether's reaction to the particle's motion in the stochastic interpretation of quantum mechanics. The existence of such a physical aether (which provides a perfectly causal interpretation of the action-a-distance implied by the Einstein-Podolsky-Rosen experiments) can now be proved by establishing the reality of de Broglie's waves in realizable experiments.

De Broglie's wave revisited

The concept of the de Broglie wave as an electromagnetic wave of a special kind is examined. Natural and ensemble coherence lengths are defined. Using these concepts, two experiments with neutrons are considered. The first experiment(22) is concerned with interferences of the neutron de Broglie waves for neutrons propagating in moving matter. The second experiment(23) is a diffraction experiment on neutron optical test of nonlinear wave mechanics. Finally, a short description of a proposed Young's experiment with ultra cold neutrons is given.

Deflexion of Light in the Gravitational Field of the Sun

ACCORDING to the whirl theory of light and matter1, the whole physical world is the manifestation of Maxwell's electromagnetic waves. The fundamental particles of matter, and the photons, are represented by integral solutions of Maxwell's equations in vacuo, in cylindrical co-ordinates. For the former the integral is taken from a very low limit of the variable parameter of the integrant solution to infinity, while in the latter the interval of integration is much smaller. The forces are determined from the standard equations of classical dynamics as the derivatives of the exchange integrals of electromagnetic fields of interacting entities with respect to parameters defining their mutual position. The necessary condition of physical validity of these forces is the synchronism between the fundamental frequencies of the entities or their sub-harmonics. In the case of gravitation the sub-harmonics are due to the ‘micro-precessions’ of the entities, of about 8.3 × 10−7 sec.−1, caused by their inherent eccentricity of about 10−10 h/mc. In this very slow motion the wave-length of de Broglie's waves (which are inherent in these solutions of Maxwell's equations) is about 1012 cm. They are called the ‘macrowaves’ The macrowaves produce the mutual synchronization of micro-precessions. The resultant macrowaves of thus synchronized particles constituting large axially symmetrical bodies, such as the Sun or the planets, form co-axially revolving wave systems with radial standing waves. The orbits of planets are situated in the troughs of the latter.