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Revista Mexicana de Física

Sobre la posibilidad de observar experimentalmente el efecto de difracción en el tiempo

José Goldemberg

Published May 10, 2009• 0 citations
OpenAlex

Abstract

MOSHINSKY´S RESULTS ON ”DIFFRACTION IN TIME” ARE EXTENDED TO THE CASE OF A RECTANGULAR PULSE.BESIDES INTERFERENCE EFFECTS OF THE TYPE STUDIED BY MOSHINSKY, THERE APPEARS ALSO THE WELL KNOWN QUANTUM MECHANICAL SPREADING EFFECT. RISE TIME AND MONOCHROMATICITY REQUIREMENTS SEEM TO PRECLUDE THE POSSIBILITY OF EXPERIMENTAL OBSEVATION OF THE INTERFERENCE EFFECTS, SO THAT THEY NEED NOT BE TAKEN ACCOUNT IN NEUTRON VELOCITY SELECTORS. THE DETECTION OF THE SPREADING, WICH IS SUBJECT TO WEAKER REQUIREMENTS WOULD PROVIDE A DIRECT TEST OF THE UNCERTAINTY RELATION.

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MOSHINSKY´S RESULTS ON ”DIFFRACTION IN TIME” ARE EXTENDED TO THE CASE OF A RECTANGULAR PULSE. BESIDES INTERFERENCE EFFECTS OF THE TYPE STUDIED BY MOSHINSKY THERE APPEARS ALSO THE WELL KNOWN QUANTUM MECHANICAL SPREADING EFFECT. RISE TIME AND MONOCHROMATICITY REQUIREMENTS SEEM TO PRECLUDE THE POSSIBILITY OF EXPERIMENTAL OBSERVATION OF THE INTERFERENCE EFFECTS, SO THAT THEY NEED NOT BE TAKEN INTO ACCOUNT IN NEUTRON VELOCITY SELECTORS. THE DETECTION OF THE SPREADING, WICH IS SUBJECT TO WEAKER REQUIREMENTS, WOULD PROVIDE A DIRECT TEST OF THE UNCERTAINTY RELATION.

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MOSHINSKY´S RESULTS ON ”DIFFRACTION IN TIME” ARE EXTENDED TO THE CASE OF A RECTANGULAR PULSE.BESIDES INTERFERENCE EFFECTS OF THE TYPE STUDIED BY MOSHINSKY, THERE APPEARS ALSO THE WELL KNOWN QUANTUM MECHANICAL SPREADING EFFECT. RISE TIME AND MONOCHROMATICITY REQUIREMENTS SEEM TO PRECLUDE THE POSSIBILITY OF EXPERIMENTAL OBSEVATION OF THE INTERFERENCE EFFECTS, SO THAT THEY NEED NOT BE TAKEN ACCOUNT IN NEUTRON VELOCITY SELECTORS. THE DETECTION OF THE SPREADING, WICH IS SUBJECT TO WEAKER REQUIREMENTS WOULD PROVIDE A DIRECT TEST OF THE UNCERTAINTY RELATION.
MOSHINSKY´S RESULTS ON ”DIFFRACTION IN TIME” ARE EXTENDED TO THE CASE OF A RECTANGULAR PULSE. BESIDES INTERFERENCE EFFECTS OF THE TYPE STUDIED BY MOSHINSKY THERE APPEARS ALSO THE WELL KNOWN QUANTUM MECHANICAL SPREADING EFFECT. RISE TIME AND MONOCHROMATICITY REQUIREMENTS SEEM TO PRECLUDE THE POSSIBILITY OF EXPERIMENTAL OBSERVATION OF THE INTERFERENCE EFFECTS, SO THAT THEY NEED NOT BE TAKEN INTO ACCOUNT IN NEUTRON VELOCITY SELECTORS. THE DETECTION OF THE SPREADING, WICH IS SUBJECT TO WEAKER REQUIREMENTS, WOULD PROVIDE A DIRECT TEST OF THE UNCERTAINTY RELATION.
EL TEMA DEL PRESENTE TRABAJO HA SIDO INVESTIGADO INDEPENDIENTEMENTE POR M. MOSHINSKY Y POR EL AUTOR. RECIENTEMENTE M. MOSHINSKY HA MOSTRADO LA EQUIVALENCIA ENTRE SU PUNTO DE VISTA Y EL DEL AUTOR. NUESTRO METODO EN ESTE PROBLEMA ESTA BASADO ESENCIALMENTE SOBRE LA GEOMETRIA DEL ESPACIO - TIEMPO DE MINKOWSKI Y EN EL ANALISIS INTUITIVO QUE FRESNEL HA DADO PARA LA DIFRACCION. EN ESTA FORMA, LAS FORMULAS FUNDAMENTALES DE LA MECANICA ONDULATORIA SE OBTIENEN EN FORMA SIMETRICA EN LO QUE SE REFIERE A ESPACIO Y TIEMPO, LA INTERPRETACION DE FEYNMAN DE LOS ESTADOS DE ENERGIA NEGATIVA, SE VE CLARAMENTE ILUSTRADA.
DOCTOR MARCOS MOSHINSKY AND THE AUTHOR HAVE BEEN INDEPENDETLY INTERESTED IN THE SUBJECT. RECENTLY, DOCTOR MOSHINSKY HAS SHOWN THE EQUIVALENCE BETWEEN HIS OWN TREATMENT AND THE AUTHORS.OUR METHOD IN THIS PROBLEM IS ESSENTIALLY BASED ON MINKOWSKIS SPACE- TIME GEOMETRY ANDE FRESNELS INTUITIVE TREATMENT OF DIFFRACTION. IN THIS WAY, THE FUNDAMENTAL FORMULAS OF WAVE MECHANICS COME OUT WITH A COMPLETE SYMMETRY BETWEEN SPACE AND TIME, AND FEYNMANS INTERPRETATION OF NEGATIVE ENERGY STATES IS VERY CLEARLY ILLUSTRATED.
THE MEASURABILITY OF THE GRAVITATIONAL FIELD IS DISCUSSED FROM BOTH THE CLASSICALLY SUCH A MEASUREMENT CAN BE PERFORMED IF ONE USES TEST BODIES WITH VANISHING SMALL MASS. ON THE OTHER HAND, DUE TO THE HEISENBERG UNCERTAINTY PRINCIPLE, IT IS FOUND THAT ONE MUST USE TEST BODIES OF EXTREMELY LARGE MASS IN ORDER TO OBTAIN ACCURATE RESULTS. THUS IT APPEARS THAT AN ACCURATE DETERMINATION OF THE GRAVITATIONAL FIELD IS NOT POSSIBLE IF ONE TAKES INTO ACCOUNT THE QUANTUM RESTRICTIONS. CONSEQUENCES OF THIS RESULT WILL BE DISCUSSED.
Moshinsky's work on diffraction in time is recognized as a particular case of monoenergetic, quantum dispersion process. Diffraction in time is extended to include new initial conditions, which under free evolution exhibit temporal quantum interference patterns in close analogy to spatial diffraction patterns found in optics. We show that free propagation of states, which initially are stationary states of infinite potential wells, diffract in time similarly as a plane wave by a double slit. We introduce the concepts of mass transport by transient Fraunhofer and Fresnel dispersion currents.