Uncertainties and an interpretation of nonrelativistic quantum theory

Bernard H. Lavenda, Enrico Santamato

Emilio Santos

Arthur S. Wightman

From the very beginning of quantum mechanics, the notion of the position of a particle has been much discussed. In the nonrelativistic case, the proof of the equivalence of matrix and wave mechanics, the discovery of the uncertainty relations, and the development of the statistical interpretation of the theory led to an understanding which, within the inevitable limitations of the nonrelativistic theory, may be regarded as completely satisfactory.

John Maddox

シロウ イシカワ, Shiro Ishikawa, 史郎 石川

In this note, we shall propose a new measurement-axiom in nonrelativistic quantum theory, which can be considered a kind of generalized Copenhagen interpretation. This interpretation can assert rather radical statements, which may irritate our minds familiar with Copenhagen interpretation. We shall, under this interpretation, assert the following two statements: (i) the uncertainties (i.e. Δq and Δp) in Heisenberg's uncertainty relation "Δq・Δp≥■/2" can be characterized as (average) errors in the approximates simultaneous measurement, and so, Heisenberg's uncertainty relation can be clarified as the statement in physics for the first time, (ii) the (discrete) trajectory of a particle is enough significant (though this, of course, includes errors). Furthermore, concerning (ii) we shall show the numerical results of the trajectory of a particle in two slit experiment. (Though almost all parts of this note are composed of summaries of references [11], [12], [13] and [14], we add some discussions from other angles.)

史郎 石川

In this note, we shall propose a new measurement-axiom in nonrelativistic quantum theory, which can be considered a kind of generalized Copenhagen interpretation.This interpretation can assert rather radical statements, which may irritate our minds familiar with Copenhagen interpretation.We shall, under this interpretation, assert the following two statements: (i) the uncertainties (i.e.Δq and Δp) in Heisenberg's uncertainty relation "Δq・Δp≥■/2" can be characterized as (average) errors in the approximates simultaneous measurement, and so, Heisenberg's uncertainty relation can be clarified as the statement in physics for the first time, (ii) the (discrete) trajectory of a particle is enough significant (though this, of course, includes errors).Furthermore, concerning (ii) we shall show the numerical results of the trajectory of a particle in two slit experiment.(Though almost all parts of this note are composed of summaries of references [11], [12], [13] and [14], we add some discussions from other angles.)