arXiv subjects
Publications and source records attributed to Alberto C. de la Torre.
A simple locus model for the space-time fabric is presented and is compared with quantum foam and random walk models. The induced indeterminacies in momentum are calculated and it is shown that these space-time fabric indeterminacies are, in most cases, negligible compared with the quantum mechanical indeterminacies. This result restricts the possibilities of an experimental observation of the space-time fabric.
The ontology emerging from quantum field theory and the results following from Bell's theorems allowed the development of an intuitive picture of the microscopic world described by quantum mechanics, that is, we can say that we understand this theory. However there remain several aspects of it that are still mysterious and require more work on the foundations of quantum mechanics.
Several stochastic processes with virtual particles in two dimensional space-time are presented whose mean field equations coincide with Schrödinger, Dirac, Klein-Gordon and the quantum mechanic equation for a photon. These processes could be used to detect discrete space-time features at the Planck scale.
It is shown that adopting the \emph{Quantum Field} ---extended entity in space-time build by dynamic appearance propagation and annihilation of virtual particles--- as the primary ontology the astonishing features of quantum mechanics can be rendered intuitive. This interpretation of quantum mechanics follows from the formalism of the most successful theory in physics: quantum field theory.
It is shown that position-momentum correlation is never decreasing and therefore it is a good candidate as a quantum arrow of time devoid of shortcomings of other proposals.
It is shown that the Fourier transformation that relates position and momentum representations of quantum mechanics can be understood as a consequence of a symmetry principle that establishes the equivalence of being and becoming in the description of reality. There are however other transformation compatible with the same principle that could lead to different formalisms of quantum mechanics.
It is shown that quantum systems of identical particles can be treated as if they were different when they are in well differentiated states. This simplifying assumption allows the consideration of quantum systems isolated from the rest of the universe and justifies many intuitive statements about identical systems. However, it is shown that this simplification may lead to wrong results in the calculation of the entropy. Keywords: quantum mechanics, identical systems, entropy
An iterative algorithm for state determination is presented that uses as physical input the probability distributions for the eigenvalues of two or more observables in an unknown state $Φ$. Starting form an arbitrary state $Ψ_{0}$, a succession of states $Ψ_{n}$ is obtained that converges to $Φ$ or to a Pauli partner. This algorithm for state reconstruction is efficient and robust as is seen in the numerical tests presented and is a useful tool not only for state determination but also for the study of Pauli partners. Its main ingredient is the Physical Imposition Operator that changes any state to have the same physical properties, with respect to an observable, of another state.
The quantum mechanical probability densities are compared with the probability densities treated by the theory of random variables. The relevance of their difference for the interpretation of quantum mechanics is commented.
A very simple illustration of the Bell-Kochen-Specker contradiction is presented using continuous observables in infinite dimensional Hilbert space. It is shown that the assumption of the \emph{existence} of putative values for position and momentum observables for one single particle is incompatible with quantum mechanics.