Foundations of Physics, Vol. 7, Nos. 5/6, 1977
Momentum Conservation Decides Heisenberg's
Interpretation of the Uncertainty Formulas
Th. D. Angelidis 1
Received March 24, 1975
The present thesis considers, in the light of Heisenberg's interpretation of the
uncertainty formulas, the conditions necessary for the derivation of the quanti-
tative statement or law of momentum conservation. The result of such con-
siderations is a contradiction between the formalism of quantum physics and the
asserted consequenees of Heisenberg's interpretation. This contradiction decides
against Heisenberg's interpretation of the uncertainty formulas on upholding
that the formalism of quantum physics is both consistent and complete, at
least insofar as the statement of momentum conservation can be proved within
this formalism. A few comments are also included on Bohr's "complementarity
interpretation" of the formalism of quantum physics. A suggestion, based on a
statistical mode of empirical test#~g of the "uncerta#~ty" formulas, does not
give rise to any such contradiction.
1. INTRODUCTION
A deductive theory is consistent a) if of any two contradictory statements at
least one cannot be derived or proved in this theory; two statements of which
one is the negation of the other are called contradictory. A deductive theory
is complete if of any two contradictory statements formulated in the terms of
this theory at least one statement can be derived or proved in this theory.
Hence, a deductive theory is inconsistent if there are two contradictory
statements which can both be proved within this theory. A deductive theory
is incomplete if there are two contradictory statements formulated in the
terms of this theory neither of which can be proved within this theory.
Momentum conservation is an empirical fact. The quantitative statement
or formula whose physical reference is the empirical fact of momentum con-
o
University College London, London, England.
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