Quantum-to-Classical Coexistence: Wavefunction Decay   Kinetics, Photon Entanglement, and Q-Bits

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The SQHM presents a framework for characterizing the behavior of quantum systems in a physical vacuum, incorporating a fluctuating metric. This model posits that the spa-tial noise spectrum is non-white, featuring a correlation function defined by the de Broglie characteristic length. Consequently, effective quantum entanglement emerges, persisting in systems where the physical length is significantly smaller than this characteristic length. Nonlocal quantum interactions may extend beyond the de Broglie length, reaching a finite distance in nonlinear weakly bonded systems. The dynamics of such systems can be described by the Schrodinger-Langevin equation, deviating from the deterministic bounds of quantum mechanics. As the physical length of the system increases, classical physics may predominate when the scale surpasses the range of interaction of the quantum potential. The long-distance characteristics of the quantum potential govern the existence of a coarse-grained classical large-scale description. The SQHM further elucidates that the minimum uncertainty during the measurement process tends to approach the quantum uncertainty relations in the absence of noise. The principle of minimum uncertainty holds when interactions and information propagate no faster than the speed of light, aligning with the relativistic macroscopic locality and non-local quantum interactions at the microscale. The SQHM posits that the interaction between a quantum system and the gravita-tional background induces a gradual loss of coherence, resulting in classical-like behavior and outcomes nearly identical to those predicted by the decoherence approach. A key dis-tinction lies in the self-generation of fluctuations in the SQHM, intrinsic to the spacetime characteristics originating at the Big Bang, without the reliance on an external environ-ment. Within the SQHM framework, weak quantum potentials fail to sustain coherence in the presence of fluctuations as a drag force emerges, leading to decoherence. This phenomenon is observable in macroscopic systems, such as those comprised of molecules and atoms interacting through long-range weak potentials, as seen in the Len-nard-Jones gas phase. In such scenarios, the impacts of decoherence become more pro-nounced, and the quantum characteristics of the system become increasingly challenging to discern as the system’s size and complexity grow. The SQHM offers a valuable frame-work for comprehending the intricate interplay between quantum mechanics and classical behavior in such systems. The stochastic quantum hydrodynamic model proposes that classical mechanics can manifest in a quantum system when the physical length of the system far exceeds the range of interaction of the quantum potential . When the eigenstates of a quantum system experience fluctuations, their stationary configurations undergo slight perturbations but persist as stationary and are closely aligned with those predicted by quantum mechanics. However, when the system evolves in a superposition of states, fluctuations induce the relaxation of the superposition to the stationary configuration of one of the eigenstates composing the superposition. This re-sults in the emergence of classical mechanics on a large scale, influenced by the tempera-ture dependence of the de Broglie length, as observed in phenomena like the fluid–superfluid transition. Additionally, this classical emergence is influenced by the extension of the quantum potential range of interactions, as seen in events such as the solid–fluid transition occurring at the melting point of the crystal lattice. The model offers a comprehensive path integral solution that can be derived in a re-cursive manner. Additionally, it encompasses conventional quantum mechanics as the deterministic limit of the theory. In accordance with the stochastic quantum hydrodynamic model, decoherence is deemed essential for a quantum measurement to transpire within finite time intervals, playing a role in the execution, data collection and management of the measuring appa-ratus. The model posits that the wavefunction collapse phenomenon in the Copenhagen interpretation of quantum mechanics may align with the concept of wavefunction decay. This decay process is characterized by unique kinetics and occurs within a finite timespan. With the premise that wavefunction decay occurs within a finite timeframe during the measurement process, a thought experiment is conducted to scrutinize the measurement of the photon entanglement. The SQHM posits the existence of an underlying wave state pri-or to the polarizer measurements. This preexisting wave state consists of two entangled photons, which give rise to an aggregate quantum potential. When a measurement takes place, the polarizers modify this preexisting wave state, resulting in the emergence of po-larized states as the outcome. According to the SQHM framework, the process of polariza-tion detection for two quantum-entangled photons occurs over two distinct steps. During the first one, only a portion of the quantum system is affected. However, during the first part of the measurement, the “two-photon system” transitions into the measured state as it interacts with the polarizer. Consequently, when the second photon is detected on Mars, its quantum state is found to be coherent with the state measured for the first photon. The quantum hydrodynamic approach posits that the information encoded within the quan-tum potential can effectively transfer from the first photon to the second one, resulting in a delay of the second photon’s detection due to its prolonged wavefunction decay time. The model reveals that canonical quantum mechanics is applicable only in a perfectly static universal spacetime. In real-world scenarios, due to fluctuations in the spacetime background caused by the Big Bang and other cosmological sources, the quantum evolu-tion of mass densities encounters a resistance force while traveling through spacetime with oscillating metrics. This phenomenon shows some analogy to the effect observed with the Higgs Boson, where its field imparts inertia to elementary particles as they move through it. The description offered by the stochastic quantum hydrodynamic theory envisions a situation where classical mechanics emerges on a macroscopic scale within a spacetime characterized by fluctuations in the curvature. This portrayal seamlessly aligns with the quantum gravitational representation of the cosmos, where gravity serves as the catalyst for universal decoherence. The model shows that, if reversible quantum mechanics are realized in a static vac-uum, the measurement process cannot take a finite time to occur.

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