Justifying Born’s Rule Pα = |Ψα|2 Using Deterministic Chaos, Decoherence, and the de Broglie-Bohm Quantum Theory

In this work, we derive Born’s rule from the pilot-wave theory of de Broglie and Bohm. Based on a toy model involving a particle coupled to an environment made of “qubits” (i.e., Bohmian pointers), we show that entanglement together with deterministic chaos leads to a fast relaxation from any statistical distribution ρ(x) of finding a particle at point x to the Born probability law |Ψ(x)|2. Our model is discussed in the context of Boltzmann’s kinetic theory, and we demonstrate a kind of H theorem for the relaxation to the quantum equilibrium regime.

Quantum and Electromagnetic Fields in Our Universe and Brain: A New Perspective to Comprehend Brain Function

The concept of wholeness or oneness refers to not only humans, but also all of creation. Similarly, consciousness may not wholly exist inside the human brain. One consciousness could permeate the whole universe as limitless energy; thus, human consciousness can be regarded as limited or partial in character. According to the limited consciousness concept, humans perceive projected waves or wave-vortices as a waveless item. Therefore, human limited consciousness collapses the wave function or energy of particles; accordingly, we are only able to perceive them as particles. With this “limited concept”, the wave-vortex or wave movement comes into review, which also seems to have a limited concept, i.e., the limited projected wave concept. Notably, this wave-vortex seems to embrace photonic light, as well as electricity and anything in between them, which gives a sense of dimension to our brain. These elements of limited projected wave-vortex and limitless energy (consciousness) may coexist inside our brain as electric (directional pilot wave) and quantum (diffused oneness of waves) brainwaves, respectively, with both of them giving rise to one brain field. Abnormality in either the electrical or the quantum field or their fusion may lead to abnormal brain function.

Quantum relaxation in a system of harmonic oscillators with time-dependent coupling

In the context of the de Broglie–Bohm pilot-wave theory, numerical simulations for simple systems have shown that states that are initially out of quantum equilibrium—thus violating the Born rule—usually relax over time to the expected | ψ | 2 distribution on a coarse-grained level. We analyse the relaxation of non-equilibrium initial distributions for a system of coupled one-dimensional harmonic oscillators in which the coupling depends explicitly on time through numerical simulations, focusing on the influence of different parameters such as the number of modes, the coarse-graining length and the coupling constant. We show that in general the system studied here tends to equilibrium, but the relaxation can be retarded depending on the values of the parameters, particularly to the one related to the strength of the interaction. Possible implications on the detection of relic non-equilibrium systems are discussed.

Kuramoto-Like Synchronization Mediated through Faraday Surface Waves

A new class of problems in free surface hydrodynamics appeared after the groundbreaking discovery by Yves Couder and Emmanuel Fort. A bouncing droplet in association with Faraday surface waves gives rise to new nonlinear dynamics, in analogy with the pilot-wave proposed by de Broglie. The droplet and the underlying vibrating bath are of silicon oil. A weakly viscous potential theory model should be used. Numerical simulations are presented with one and two bouncing droplets oscillating while confined to their cavities. These oscillators are implicitly coupled by the underlying surface wave field. In certain regimes, the oscillators can spontaneously synchronize, even when placed at a distance. Cavity parameters are varied in order to highlight the sensitive wave-mediated coupling. The present nonlinear wave-mediated oscillator synchronization is more general than that displayed by the celebrated Kuramoto model and therefore of general interest.

A complex nonlinear approach for understanding quantum physics

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.