Quantum Inf Process (2016) 15:3005–3034
Effects of a scalar scaling ﬁeld on quantum mechanics
Received: 18 December 2015 / Accepted: 1 April 2016 / Published online: 18 April 2016
© Springer Science+Business Media New York (outside the USA) 2016
Abstract This paper describes the effects of a complex scalar scaling ﬁeld on quantum
mechanics. The ﬁeld origin is an extension of the gauge freedom for basis choice in
gauge theories to the underlying scalar ﬁeld. The extension is based on the idea that
the value of a number at one space time point does not determine the value at another
point. This, combined with the description of mathematical systems as structures of
different types, results in the presence of separate number ﬁelds and vector spaces as
structures, at different space time locations. Complex number structures and vector
spaces at each location are scaled by a complex space time dependent scaling factor.
The effect of this scaling factor on several physical and geometric quantities has been
described in other work. Here the emphasis is on quantum mechanics of one and two
particles, their states and properties. Multiparticle states are also brieﬂy described.
The effect shows as a complex, nonunitary, scalar ﬁeld connection on a ﬁber bundle
description of nonrelativistic quantum mechanics. The lack of physical evidence for
the presence of this ﬁeld so far means that the coupling constant of this ﬁeld to fermions
is very small. It also means that the gradient of the ﬁeld must be very small in a local
region of cosmological space and time. Outside this region, there are no restrictions
on the ﬁeld gradient.
Keywords Scalar scaling ﬁelds· Entangled quantum states· Mathematical structures·
Physics Division, Argonne National Laboratory, Argonne, IL 60439, USA