Hestenes - Spin And Uncertainty In The Interpretation Of Quantum Mechanics (1979).pdf

In: Am. J. Phys., 47 (5), May 1979, 399–415.
Spin and uncertainty in the interpretation of quantum mechanics
David Hestenes
A rigorous derivation of the Schr
odinger theory from the Pauli (or Dirac)
theory implies that the Schr
odinger equation describes an electron in an
eigenstate of spin. Furthermore, the ground-state ic energy -
pletely determined by the electron spin density. This can be explained
by interpreting the spin as an orbital angular momentum, which is nec-
essarily panied by a ic energy. Thus, the spin is a zero-point
angular momentum associated with the zero-point energy of the electron.
Since the dispersion in electron momentum is determined by the zero-
point energy, the Heisenberg uncertainty relations for an electron can be
interpreted as a property of the electron spin motion. The ic inter-
pretation of spin and the statistical interpretation of quantum mechanics
can be jointly sustained by regarding the electron as a point particle. It
follows that stationary electron states are sources of
uctuating electric

elds. There is reason to believe that these
uctuating
elds are responsi-
ble for the Van der Waals force and can be identi
ed with ic
vacuum
eld
uctuations. The ic interpretation of spin then implies
that the Van der Waals forces are spin dependent. These ideas are not
only consistent with the conventional mathematical formalism of quantum
mechanics, they provide a plete and coherent interpretation of
many details in the formalism than does the alternative Copenhagen in-
terpretation. They present some di
culties, however, which, if the ic
interpretation of spin is correct, probably require some modi
cation of
quantum electrodynamics to be resolved.
1. INTRODUCTION
The longstanding debate and discussion about the interpretation of quantum mechanics
has been strongly focused on the meaning of Heisenberg’s Uncertainty Relations for the
position and momentum of an electron. However,