I show that the classical Hamilton-Jacobi (H-J) equation can be used as a technique to study quantum mechanical problems. I first show that the the Schrödinger equation is just the classical H-J equation, constrained by a condition that forces the solutions of the H-J equation to be everywhere
C2. That is, quantum mechanics is just classical mechanics constrained to ensure that ``God does not play dice with the universe.'' I show that this condition, which imposes global determinism, strongly suggests that
ψ∗ψ measures the density of universes in a multiverse. I show that this interpretation implies the Born Interpretation, and that the function space for
ψ is larger than a Hilbert space, with plane waves automatically included. Finally, I use H-J theory to derive the momentum-position uncertainty relation, thus proving that in quantum mechanics, uncertainty arises from the interference of the other universes of the multiverse, not from some intrinsic indeterminism in nature.
It is our science governs the mathematics and it is “not” our mathematics governs our science. One of the very important aspects is that every science has to comply with the boundary condition of our universe; dimensionality and temporal (t > 0) or causality. In which I have shown that time is real and it is not an illusion, since every aspect within our universe is coexisted with time. Since our universe is a temporal (t > 0) subspace, everything within our universe is temporal. Science is mathematics but mathematics is not science, we have shown that any analytic solution has to be temporal (t > 0); otherwise, it cannot be implemented within our universe. Which includes all the laws, principles, and theories have to be temporal? Uncertainty principle is one of the most fascinated principles in quantum mechanics, yet Heisenberg principle was based on diffraction limited observation, it is not due to the nature of time. We have shown it is the temporal (t > 0) uncertainty that changes with time. We have introduced a certainty principle as in contrast with uncertainty principle. Of which certainty subspace can be created within our universe; which can be exploited for application. Overall of this chapter is to show that; it is not how rigorous the mathematics is, it is the physical realizable paradigm that we embrace.
Several theories of quantum gravity propose the existence of a minimal measurable length and maximum measurable momentum near the Planck scale. When integrated into the framework of quantum mechanics, such restrictions lead to the generalization of the Heisenberg uncertainty principle, which is commonly referred to as the generalized uncertainty principle (GUP). The GUP has been applied to a plethora of physical models in order to provide further insights on our understanding of the Universe, both in the macroscopic and the microscopic regime. Nevertheless, the corrections related to GUP are expected to be extremely small, which thus renders experimental verification a difficult task. Therefore, phenomenological approaches on a qualitative level are typically addressed with the aim of enhancing our possibility of detecting these tiny effects. Motivated by a recent work on a universal decoherence mechanism stemming from the standard formulation of GUP, we extend the ideas contained therein by considering a more general form of GUP which includes linear and quadratic momentum terms to examine its implications. To achieve such a picture, we equip the deformation parameter appearing in front of all momentum terms with a stochastic nature, so that the effective decoherence mechanism emerges by taking the average over fluctuations. We find that, despite the apparently small differences among the two generalizations of the Heisenberg uncertainty principle, the consequences at the level of the universal decoherence mechanism they entail is significant, as they predict decoherence times that are completely uncorrelated and distinct.