To understand quantum phenomena, namely, the particle-wave duality, in a causal relational way, a complex nonlinear process, in which a minor action may, under adequate conditions, give rise to a huge reaction, was proposed by de Broglie. The nonlinear process is mediated by the guiding or pilot wave principle, or as is now named by the principle of eurhythmy. This process rejects the ontic status of the Cartesian linear method in which the whole is assumed to be the simple linear combination of the parts and the action is always presumed to be equal and opposite to the reaction. The constituent parts of the whole are supposed to be naturally expected to maintain their own identity in every conceivable interacting situation.
To understand quantum phenomena, namely, the particle-wave duality, in a causal relational way, a complex nonlinear process, in which a minor action may, under adequate conditions, give rise to a huge reaction, was proposed by de Broglie. The nonlinear process is mediated by the guiding or pilot wave principle, or as is now named by the principle of eurhythmy. This process rejects the ontic status of the Cartesian linear method in which the whole is assumed to be the simple linear combination of the parts and the action is always presumed to be equal and opposite to the reaction. The constituent parts of the whole are supposed to be naturally expected to maintain their own identity in every conceivable interacting situation.
The de Broglie-Bohm “pilot-wave” theory replaces the paradoxical wave-particle duality of ordinary quantum theory with a more mundane and literal kind of duality: each individual photon or electron comprises a quantum wave (evolving in accordance with the usual quantum mechanical wave equation) and a particle that, under the influence of the wave, traces out a definite trajectory. The definite particle trajectory allows the theory to account for the results of experiments without the usual recourse to additional dynamical axioms about measurements. Instead, one need simply assume that particle detectors click when particles arrive at them. This alternative understanding of quantum phenomena is illustrated here for two elementary textbook examples of one-dimensional scattering and tunneling. We introduce a novel approach to reconcile standard textbook calculations (made using unphysical plane-wave states) with the need to treat such phenomena in terms of normalizable wave packets. This approach allows for a simple but illuminating analysis of the pilot-wave theory's particle trajectories and an explicit demonstration of the equivalence of the pilot-wave theory predictions with those of ordinary quantum theory.
The action reaction principle (ARP), a fundamental ingredient of Physics, is taken for granted, because it is automatically fulfilled along the ordinary Hamiltonian, classical or quantum, time evolution law. But in quantum mechanics, there is an extraordinary evolution law, the projection of state rule along quantum measurements, which is not Hamiltonian. Consequently, the ARP is not automatically fulfilled along quantum measurements, and it must be checked case by case. Surprisingly, very simple quantum measurements, both theoretical processes and experiments, show an apparent violation of the ARP, so that the hidden reaction must be found. In the analyzed experiment, the ARP is restored if some new system, the quantum or de Broglie wave, exists and locally interacts with the detector. There cannot be interaction at a spatial distance between the particle (photon or electron) and the obstacle‐detector.
We present the complete, ontically grounded wave mechanics derived from the de Broglie equation λp = h, interpreted literally as a real, physical wave. By treating ψ = 1/λ as a spatial compaction field and anchoring it on the Euler ComplexPlane (ECP)—a two-faced, rotating, compact topological surface—we derive the nonlinear wave equation, the soliton identity 1 = 1, the logarithmic spiral geodesic, the dual velocities and frequencies, the eigen-energy spectrum, and the photon asthe uncompacted reference state. We show that the Maxwell and d’Alembert equations are linear, uncompacted limits of the Prince nonlinear wave equation. The framework resolves the wave-particle duality, quantizes time and energy, and vindicatesde Broglie’s law of phase harmony as the foundational principle of quantum mechanics.
The Copenhagen interpretation has been the subject of much criticism, notably by De Broglie and Einstein, because it contradicts the principles of causality and realism. The aim of this essay is to study the wave mechanics as an alternative to traditional quantum mechanics, in the continuity of the ideas of Louis de Broglie: the pilot wave theory of De Broglie (where each particle is associated with a wave which guides it), De Broglie-Bohm theory, stochastic electrodynamics (where the stochastic character of particles is caused by the energy field of the fluctuating vacuum), and the analogies between quantum mechanics and hydrodynamics.
Of all basic principles of classical physics, realism should arguably be the last to be given up when seeking a better interpretation of quantum mechanics. We examine the de Broglie-Bohm pilot wave theory as a well-developed example of a realistic theory. We present three challenges to a naive reading of pilot wave theory, each based on a system of several entangled particles. With the help of a coarse graining of pilot wave theory into a discrete system, we show how these challenges can be answered. However, this comes with a cost. In the description of individual systems, particles appear to scatter off empty branches of the wave function as if they were particles and conversely travel through particles as if they were waves. More generally, the ``particles'' of pilot wave theory are led by the guidance equation to move in ways no classical particle would, involving apparent violations of the principles of inertia and momentum conservation. We next argue that the aforementioned cost can be avoided within a retrocausal model. In the proposed version of the pilot wave theory, the particle is guided by a combination of advanced and retarded waves. The resulting account for quantum physics seems to have greater heuristic power, demands less damage to intuition, and moreover provides some general hints regarding spacetime and causality. This is the first of two papers. In the second [E. Cohen, M. Cort\^es, A. C. Elitzur, and L. Smolin, Realism and causality. II. Retrocausality in energetic causal sets, Phys. Rev. D 102, 124028 (2020).], we show that, in the context of an explicit model, retrocausality, with respect to an effective, emergent spacetime metric, can coexist with a strict irreversibility of causal processes.
In some situations nonlinearity seems to pervade in nature.Indeed, in adequate conditions, a minor action may give origin to a very large reaction, only apparently providing a gain in output power from a lesser inputted value.Extending de Broglie seminal ideas to a more general pilot-wave theory, we describe the relation between nonlinearity and energy conservation, dismissing any apparent contradiction between the two.We also present what seems to be a possible way to harness energy from the pervading subquantum medium.