Stars as Laboratories for Fundamental Physics - MPP Theory Group

Miscellaneous Exotica 555
A violation of the equivalence principle could also manifest itself by
a relative shift of the energies of different neutrino flavors in a gravitational
field. For a given momentum p the matrix of energies in flavor
space (relativistic limit) is E = p + M 2 /2p + 2pϕ(r)(1 + F ) where M 2
is the squared matrix of neutrino masses, ϕ(r) is the Newtonian gravitational
potential, and F is a matrix of dimensionless constants which
parametrize the violation of the equivalence principle; in general relativity
F = 0. A nontrivial matrix F can lead to neutrino oscillations in
analogy to the standard vacuum oscillations which are caused by the
matrix M 2 (Gasperini 1988, 1989; Halprin and Leung 1991; Pantaleone,
Halprin, and Leung 1993; Iida, Minakata, and Yasuda 1993; Minakata
and Nunokawa 1995; Bahcall, Krastev, and Leung 1995). Values for
F ij in the general 10 −14 −10 −17 range could account for the solar neutrino
problem and perhaps could be probed with future long-baseline
oscillation experiments.
15.4 Photon Mass and Charge
Even though in classical electrodynamics gauge invariance implies that
photons must be massless, quantum electrodynamics (QED) can be
formulated consistently with the inclusion of a photon mass, and the
limit m γ → 0 takes the modified theory smoothly over to massless QED
(Stückelberg 1941). Therefore, the possibility of a small photon mass
cannot be excluded theoretically; limits must be set by laboratory and
astrophysical methods. A still up-to-date review of the laboratory limits
was given by Goldhaber and Nieto (1971); the best is m γ ∼ < 10 −14 eV
from a test of Coulomb’s law (a photon mass would modify the inversesquare
behavior). More recent experiments worked at low temperature
(Ryan, Accetta, and Austin 1985; Chernikov et al. 1992); the resulting
limits on m γ are relatively weak, however.
An astrophysical limit may be set by the absence of an anomalous
dispersion of photon signals from distant sources, notably the pulsed
signal from radiopulsars. This method is limited by the presence of the
ionized interstellar medium. It causes a dispersion relation for photons
which mimics the effect of a photon mass m γ = ω P where the plasma
frequency is given by ω 2 P = 4παn e /m e . With a typical electron density
n e of order 0.1 cm −3 the photon plasma mass is of order 10 −11 eV so
that a vacuum mass much smaller than this value cannot be probed.
In Sect. 13.3.3 a limit on a hypothetical ν e charge was derived from
the absence of a dispersion of the SN 1987A neutrino pulse. The path of