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 Classical Cosmology in the Brans–Dicke Theory

In this paper, we discuss classical and quantum aspects of cosmological models in the Brans–Dicke theory. First, we review cosmological bounce solutions in the Brans–Dicke theory that obeys energy conditions (without ghost) for a universe filled with radiative fluid. Then, we quantize this classical model in a canonical way, establishing the corresponding Wheeler–DeWitt equation in the minisuperspace, and analyze the quantum solutions. When the energy conditions are violated, corresponding to the case ω<−32, the energy is bounded from below and singularity-free solutions are found. However, in the case ω>−32, we cannot compute the evolution of the scale factor by evaluating the expectation values because the wave function is not finite (energy spectrum is not bounded from below). However, we can analyze this case using Bohmian mechanics and the de Broglie–Bohm interpretation of quantum mechanics. Using this approach, the classical and quantum results can be compared for any value of ω.

Could there be no wave-particle duality, but only waves?

Here, the concept of a wave-particle duality is questioned. First, the experimental proofs existing, respectively, for particles and waves are examined. In the case of particles, no experimental evidence can be found which establishes them; it seems that particles have always been taken for granted. In the case of waves, considerable evidence has accumulated with results on diffraction, interference, and self-interference of larger and larger objects. Then an important remark is made concerning the fact that unlike particles, waves are not observation-dependent: waves existed before observation otherwise the patterns of diffraction or interference would not have been appearing; the wave nature does not depend on the making of a measurement, there is no measurement problem for waves. Consequently, since waves are not observation-dependent, if the objects are demonstrated to be waves, they are only waves. This fact, along with some other evidence, disagrees with the current interpretation of the Wheeler-type delayed-choice experiments, where the absence of interference is interpreted as a particle behavior. Finally, recent works regarding the de Broglie‐Bohm theory are presented, which lead to suggest a new wave-only version of this theory. It is concluded that a wave-only view might be worth considering instead of the wave-particle duality view which has prevailed so far.

Minisuperspace Quantization of f(T, B) Cosmology

We discuss the quantization in the minisuperspace for the generalized fourth-order teleparallel cosmological theory known as fT,B. Specifically we focus on the case where the theory is linear on the torsion scalar, in that consideration we are able to write the cosmological field equations with the use of a scalar field different from the scalar tensor theories, but with the same dynamical constraints as that of scalar tensor theories. We use the minisuperspace description to write for the first time the Wheeler-DeWitt equation. With the use of the theory of similarity transformations we are able to find exact solutions for the Wheeler-DeWitt equations as also to investigate the classical and semiclassical limit in the de Broglie -Bohm representation of quantum mechanics.

The de Broglie–Bohm Quantum Theory and Its Application to Quantum Cosmology

We review the de Broglie–Bohm quantum theory. It is an alternative description of quantum phenomena in accordance with all the quantum experiments already performed. Essentially, it is a dynamical theory about objectively real trajectories in the configuration space of the physical system under investigation. Hence, it is not necessarily probabilistic, and it dispenses with the collapse postulate, making it suitable to be applied to cosmology. The emerging cosmological models are usually free of singularities, with a bounce connecting a contracting era with an expanding phase, which we are now observing. A theory of cosmological perturbations can also be constructed under this framework, which can be successfully confronted with current observations, and can complement inflation or even be an alternative to it.

Bouncing Quantum Cosmology

The goal of this contribution is to present the properties of a class of quantum bouncing models in which the quantum bounce originates from the Dirac canonical quantization of a midi-superspace model composed of a homogeneous and isotropic background, together with small inhomogeneous perturbations. The resulting Wheeler-DeWitt equation is interpreted in the framework of the de Broglie-Bohm quantum theory, enormously simplifying the calculations, conceptually and technically. It is shown that the resulting models are stable and they never get to close to the Planck energy, where another more involved quantization scheme would have to be evoked, and they are compatible with present observations. Some physical effects around the bounce are discussed, like baryogenesis and magnetogenesis, and the crucial role of dark matter and dark energy is also studied.

Testing Quantum Mechanics with an Ultra-Cold Particle Trap

It is possible to empirically discriminate between the predictions of orthodox (i.e., Copenhagen) quantum theory and the de Broglie−Bohm theory of quantum mechanics. A practical experiment is proposed in which a single, laser-cooled ion inside an ultra-cold particle trap is either found to be near the trap’s walls or not. Detections of the former kind would support the prediction of orthodox quantum theory and of the latter kind would support the de Broglie−Bohm theory. The outcome of this experiment would show which theory gives the more correct description and, consequently, would have far-reaching implications for our understanding of quantum mechanics.