Wave-particle duality is often considered as the modern answer to the problem of the nature of light after more than 2000 years of questioning. It is also the answer given by quantum physics concerning the nature of matter particles and any other radiations. The main objective of this work is to analyze the relations that are existing between this concept of wave-particle duality, the uncertainty principle and the concepts of phase space and microstates considered in statistical mechanics. It is mainly highlighted that while the concepts of phase space and microstates were already introduced in classical physics before the discovery of the wave-particle duality, a correct understanding of them cannot be achieved without the use of the concept of quantum phase space and phase space representation of quantum mechanics which are directly related to the uncertainty principle. The possibility of using these concepts of quantum phase space and phase space representations of quantum mechanics to help in a deeper description of the wave-particle duality and in the study of some current issues related to foundational problems of quantum mechanics like quantum decoherence and the measurement problem is also discussed.
This paper starts with the transition from classical physics to quantum mechanics which was greatly aided by the concept of phase space. The role of canonical transformations in quantum mechanics is addressed. The Wigner phase-space distribution function is then defined which arises from the formulation of the density matrix, followed by the harmonic oscillator in phase space. Coherent and one- and two-mode squeezed states of light as well as the squeezed vacuum are discussed in the phase-space picture. Attention is also drawn to the fact that squeezed states naturally generate entanglement between the two-modes. Coupled harmonic oscillators are also elucidated in connection with the Wigner phase space. It will be noted that the phase-space picture of quantum mechanics has become an important scientific language for the rapidly expanding field of quantum optics. Here, we mainly focus on the simplest form of the Wigner function, which finds application in many branches of quantum mechanics. We make use of several symmetry groups such as Lorentz groups, the symplectic group in two and four dimensions, and the Euclidean group. The decoherence problem of an optical field is examined through a reformulation of the Poincaré sphere as a further illustration of the density matrix.
This updated preprint (v2) investigates the fundamental ontological contradiction between macroscopic chemical determinism and microscopic quantum uncertainty. Standard interpretations of quantum mechanics propose a micro-world governed by causeless randomness and probability waves. However, this study argues that the flawless precision observed in macroscopic chemistry and industrial systems necessitates an underlying, strictly deterministic physical reality operating at the hardware level of the universe. To resolve this paradox, the paper introduces the "Cosmic Texture" (Texton) Model, which redefines the universe not as an empty void, but as a continuous, highly elastic, and compressible fluid substratum. Within this framework, quantum uncertainty is not a fundamental law of nature, but the deterministic result of the unmapped hydrodynamic background noise of this texton sea and the inherently destructive nature of measurement methods. Key concepts explored and expanded in this version include: Hydrodynamic Phase Transitions & Baroclinic Vorticity: Rejecting mass-energy duality, the model defines particles as varying physical phases of the texton fluid. Linear compression waves (energy) transition into highly dense, stable, rigid vortices (matter) via baroclinic torque (
∇ρ×∇P) during high-energy collisions. Charge as Pressure Gradients: Electric charge and attractive forces are redefined mechanically as hydrostatic pressure and central vacuum gradients within the continuous fluid network. Mechanical Wave Collapse (The Observer Effect): The "collapse" of probability waves is explained via classical fluid dynamics. A measurement shockwave causes a diffuse electron cloud to implode into a constricted state. Exceeding its structural carrying capacity, the vortex reflexively expels excess energy (photon emission) and returns to its stable limit cycle. Non-Local Determinism: Bell's non-locality is preserved through the De Broglie-Bohm pilot-wave theory, where the abstract "quantum potential" is physically identified as real hydrostatic pressure and tension gradients within the texton sea. Spin Quantization: The discrete nature of quantum spin is mathematically grounded in Kelvin's Circulation Theorem, demonstrating that topological fluid knots must exist in integer multiples. Empirical & Phenomenological Validation: Moving beyond theoretical frameworks, this study supports its deterministic model with discrete lattice simulations and macroscopic analogs. Crucially, the hydrodynamic behavior of the Cosmic Texture is corroborated by established laboratory evidence, including: Madelung's hydrodynamic formulation of the Schrödinger equation (1927). Yves Couder's macroscopic walking droplet experiments (2006). The Dynamic Casimir Effect (DCE): Demonstrating the mechanical excitation of the fluid substratum. The SLAC E144 Experiment: Providing evidence for wave-to-vortex phase transitions. The Aharonov-Bohm Effect & Superfluid Vortices: Validating vector potentials as physical momentum flow and confirming the macroscopic quantization of limit cycles. This study presents a testable, causal, and purely mechanical alternative to the Copenhagen interpretation, re-establishing absolute causality in theoretical physics.