By expressing the Schrödinger wave function in the form $\psi =R{e}^{iS/\hslash }$ , where R and S are real functions, we have shown that the expectation value of S is conserved. The amplitude of the wave (R) is found to satisfy the Schrödinger equation while the phase (S) is related to the energy conservation. Besides the quantum potential that depends on R, viz., $V_Q=-\frac{{\hslash }^2}{2m}\frac{{\nabla }^{2}R}{R}$ , we have obtained a spin potential $V_S=-\frac{S{\nabla }^{2}S}{m}$ that depends on S which is attributed to the particle spin. The spin force is found to give rise to dissipative viscous force. The quantum potential may be attributed to the interaction between the two subfields S and R comprising the quantum particle. This results in splitting (creation/annihilation) of these subfields, each having a mass $m{c}^2$ with an internal frequency of $2m{c}^2/\hslash$ , satisfying the original wave equation and endowing the particle its quantum nature. The mass of one subfield reflects the interaction with the other subfield. If in Bohmian ansatz R satisfies the Klein-Gordon equation, then S must satisfies the wave equation. Conversely, if R satisfies the wave equation, then S yields the Einstein relativistic energy momentum equation.

It is shown that quantum entanglement is the only force able to maintain the fourth state of matter, possessing fixed shape at an arbitrary volume. Accordingly, a new relativistic Schrödinger equation is derived and transformed further to the relativistic Bohmian mechanics via the Madelung transformation. Three dissipative models are proposed as extensions of the quantum relativistic Hamilton-Jacobi equation. The corresponding dispersion relations are obtained.

We describe results from a Monte-Carlo simulation of Bell-CHSH type correlations in hydrodynamic walkers. We study feasibility of a real life walker test with relevant hydrodynamic parametric ranges. We observe the generic formation of pairs of walkers strongly anti-correlated both in position and momentum. With this source of entangled walkers, we model the insertion of 2 pins in the bath as a notion of measure, akin to the polarizers of photonic Bell tests. This insertion of pins, either static or dynamic, introduces 2 weak field signals. Each field has the physical form of a standing wave Bessel hat, representing the non-local (field mediated) influences of the measure on the walkers. With this representation of the measure, we develop protocol for a Bell game with actual hydrodynamic walkers. We model both static and dynamic insertion of pins in the walker bath. Static pins give us numerical S > 2, as a permissible Bell violation for a non-local (field based) effect. Dynamic insertion of the pins, however, leads to causal space separation of the two arms. We observe the again expected S ≤ 2. We argue for the hydrodynamic implementation and observation of these effects as a walker visualization of Bell inequalities.

For more than eighty years the standard interpretation (SI) has dominated quantum physics. Perspectives that have tried to challenge this domination have been remarkably unsuccessful. As a result, quantum theory (QT) has remained remarkably stagnant. The article offers a critical examination of SI and provides an explanation for its continued domination. It also uses Bohmian mechanics—a theoretical perspective advanced by American physicist David Bohm—as a case study for why alternative interpretations have failed to displace SI. The article sees the main reason for the failure to achieve much progress beyond SI in the unresolved philosophical problem of subject-object relation that continues to plague our study of physics. The article sketches a path to a possible solution and outlines a new science practice that this solution will require.

The diffraction-like process displayed by a spatially localized matter wave is here analyzed in a case where the free evolution is frustrated by the presence of hard-wall-type boundaries (beyond the initial localization region). The phenomenon is investigated in the context of a nonrelativistic, spinless particle with mass m confined in a one-dimensional box, combining the spectral decomposition of the initially localized wave function (treated as a coherent superposition of energy eigenfunctions) with a dynamical analysis based on the hydrodynamic or Bohmian formulation of quantum mechanics. Actually, such a decomposition has been used to devise a simple and efficient analytical algorithm that simplifies the computation of velocity fields (flows) and trajectories. As it is shown, the development of space-time patters inside the cavity depends on three key elements: the shape of the initial wave function, the mass of the particle considered, and the relative extension of the initial state with respect to the total length spanned by the cavity. From the spectral decomposition it is possible to identify how each one of these elements contribute to the localized matter wave and its evolution; the Bohmian analysis, on the other hand, reveals aspects connected to the diffraction dynamics and the subsequent appearance of interference traits, particularly recurrences and full revivals of the initial state, which constitute the source of the characteristic symmetries displayed by these patterns. It is also found that, because of the presence of confining boundaries, even in cases of increasingly large box lengths, no Fraunhofer-like diffraction features can be observed, as happens when the same wave evolves in free space. Although the analysis here is applied to matter waves, its methodology and conclusions are also applicable to confined modes of electromagnetic radiation (e.g., light propagating through optical fibers).

In quantum approaches to consciousness, the authors try to propose a model and mechanism for the mind-brain interaction using modern physics and some quantum concepts which do not exist in the classical physics. The independent effect of mind on the brain has been one of the challenging issues in the history of science and philosophy. In some recent mind-brain interaction models, the direct influence of mind on matter is either not accepted (as in Stapp’s model) or not clear, and there have not been any clear mechanism for it (as in Penrose-Hameroff’s model or in Eccles’s model). In this manuscript we propose a model and mechanism for mind’s effect on the matter using an extended Bohmian quantum mechanics and Avicenna’s ideas. We show that mind and mental states can affect brain’s activity without any violation of physical laws. This is a mathematical and descriptive model which shows the possibility of providing a causal model for mind’s effect on matter. It is shown that this model guarantees the realistic philosophical constraints and respects the laws of nature. In addition, it is shown that it is in agreement with the Libet style experimental results and parapsychological data. To propose this model, we obtained a modified (non-unitary) Schrödinger equation via second quantization method which affects the particle through a modified quantum potential and a new term in the continuity equation. At the second quantized level, which is equivalent to quantum field theory level (QFT), we can use the path integral formalism of Feynman. We show that there are three methods to extend Bohmian QM via path integral formalism, which has different interpretations. By numerical simulation of trajectories in the two-slits experiment, we show their differences and choose one of these methods for our mind-brain model which can be the basis for explaining some phenomena which are not possible to explain in the standard Bohmian QM.