From Permanence to Total Availability: A Quantum Conceptual Upgrade

We consider the classical concept of time of permanence and observe that its quantum equivalent is described by a bona fide self-adjoint operator. Its interpretation, by means of the spectral theorem, reveals that we have to abandon not only the idea that quantum entities would be characterizable in terms of spatial trajectories but, more generally, that they would possess the very attribute of spatiality. Consequently, a permanence time shouldn’t be interpreted as a “time” in quantum mechanics, but as a measure of the total availability of a quantum entity in participating to a process of creation of a spatial localization.

[1]  Massimiliano Sassoli de Bianchi,et al.  Ephemeral Properties and the Illusion of Microscopic Particles , 2010, 1008.2450.

[2]  Z. Tao,et al.  Observables, maximal symmetric operators and POV measures in quantum mechanics , 1995 .

[3]  Elena Castellani.  Interpreting bodies : classical and quantum objects in modern physics , 1998 .

[4]  Ph. A. Martin.  Scattering theory with dissipative interactions and time delay , 1975 .

[5]  Jaworski,et al.  Sojourn time, sojourn time operators, and perturbation theory for one-dimensional scattering by a potential barrier. , 1989, Physical review. A, General physics.

[6]  R. Werner.  Screen observables in relativistic and nonrelativistic quantum mechanics , 1986 .

[7]  Massimiliano Sassoli de Bianchi,et al.  Time-delay of classical and quantum scattering processes: a conceptual overview and a general definition , 2010, 1010.5329.

[8]  H. Narnhofer.  Another definition for time delay , 1980 .

[9]  Ph. A. Martin,et al.  Time Delay of Quantum Scattering Processes , 1981 .

[10]  Complementary Descriptions (PART I): A Set of Ideas Regarding the Interpretation of Quantum Mechanics , 2005, quant-ph/0507105.

[11]  Asymptotic behavior of the probability density in one dimension , 2001, quant-ph/0109151.

[12]  W. Jaworski.  The concept of a time‐of‐sojourn operator and spreading of wave packets , 1989 .

[13]  Diederik Aerts.  The stuff the world is made of: physics and reality , 1999 .

[14]  P. Martin,et al.  On the theory of the Larmor clock and time delay , 1992 .

[15]  Jan Hilgevoord,et al.  Time in quantum mechanics , 2002 .

[16]  R. Lavine.  Absolute continuity of positive spectrum for Schrödinger operators with long-range potentials , 1973 .

[17]  G. R. Allcock,et al.  The time of arrival in quantum mechanics I , 1969 .