GRAVITATIONAL MASS
are derivable from an action principle and the units of mass, length, and
time are defined by atomic standards, and that the equivalence principle
holds whenever gravitational self-energy can be neglected.
108
The fact that the status of the equivalence principle in the Brans-
Dicke theory still engages the attention of theoreticians today is shown
by the investigations by Daniel Barraco and Victor Hamity
109
or by
the essay of Hassan Randjbar Askari and Nematullah Riazi.
110
The
validity of this principle within the framework of nonmetric theories
of gravitation, such as the so-called “new general relativity,” based on
absolute parallelism and the tetrad formalism, originally introduced
by Christian Møller, is also an active field of research as is shown, for
instance, by the work of Takeshi Shirafugi, Gamal G. L. Nashed, and
Yoshinitsu Kobayashi
111
and by the essays contributed by C. Alvarez
and R. B. Mann.
112
For details the interested reader is referred to the
original papers and the references listed therein.
We continue our discussion of the status of the equivalence principle
within the framework of some alternatives to Einstein’s general theory of
relativity with some remarks on its status in quantum electrodynamics.
As noted in chapter 1, according to this theory part of the mass of a
charged particle, such as the electron, arises through quantum radiation
corrections. An equality of the inertial with the gravitational mass of
a charged particle would therefore require that these radiative correc-
tions also satisfy the equivalence principle. That this is indeed the case
in a relativistic quantum field theory follows from certain quantum-
gravitational investigations of the energy-momentum–tensor trace that
were carried out in 1977 by Stephen L. Adler, John C. Collins, and
A. Duncan, and at the same time by Lowell S. Brown.
113
108
H. Ohanian, “Scalar-Tensor Theories and the Principle of Equivalence,” International
Journal of Theoretical Physics 4, 273–280 (1971).
109
D. Barraco and V. Hamity, “The Energy Concept and the Binding Energy in a Class
of Scalar-Tensor Theories of Gravity,” Classical and Quantum Gravity 11, 2113–2126 (1994).
110
H. R. Askari and N. Riazi, “Mass of a Body in Brans-Dicke Theory,” International
Journal of Theoretical Physics 34, 417–428 (1995).
111
T. Shirufugi, G.G.L. Nashed, and Y. Kobayashi, “Equivalence Principle in the New
General Relativity,” Progress of Theoretical Physics 96, 933–947 (1996).
112
C. Alvarez and R. B. Mann, “Testing the Equivalence Principle by Lamb Shift Ener-
gies,” Physical Review D 54, 5954–5974 (1996); “Equivalence Principle in the Nonbaryonic
Regime,” Physical Review D 55, 1732–1740 (1997).
113
S. L. Adler, J. C. Collins, and A. Duncan, “Energy-Momentum-Tensor Trace Anomaly
in Spin-1/2 Quantum Electrodynamics,” Physical Review D 15, 1712–1721 (1977). L. S.
137