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Revista Mexicana de Física

Diffraction in time

O. Costa de Beauregard

Published May 10, 2009• 0 citations
OpenAlex

Abstract

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.

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Revista Mexicana de Física•May 10, 2009•0 citations
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.
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.
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.
THIS WORK CONTAINSAN ANALYSIS OF SOME OF THE FUNDAMENTAL PRINCIPLES UNDERLAYING THE CONSTRUTION OF OPERATORS IN QUANTUM MECHANICS. FACH OPERATOR IS ASSOCIATED TO A PROJECTION OPERATOR AND THESE PROJECTION OPERATORS ARE SHOWS TO FULFIL A SET OF PROPERTIES FORMALLY INDENTICAL TO THOSE OF A PROBABILITY FIELD.IT IS SHOWN THAT, BY THE INTRODUCTION OFA MEASURE IN CONFIGURATION SPACE IT IS POSSIBLE TO OBTAIN COMPLETE SETS OF COMMUTING OBSERVABLES HAVING, WITHIN LIMITS, PREASIGNED SPECTRA. THE INTRODUCTION OF NEW OPERATORS BY CONSIDERATION OF THE GROUPS EXPRESSING THE SYMMETRIES OF THE SYSTEM, IS DISCUSSED.