Stars as Laboratories for Fundamental Physics - MPP Theory Group

498 Chapter 13
so that the speed of light and that of neutrinos are equal to within
(Longo 1987; Stodolsky 1988)
∣ c ν − c ∣∣∣∣ γ
∣ c < ∼ 2×10 −9 , (13.3)
γ
assuming an uncertainty of ±3 h in the relative duration of the transit
times from the LMC to us. This was interpreted as the most stringent
test of special relativity to date in the sense that it proves with high
precision the universality of a relativistic limiting velocity. 82
This result can also be interpreted as testing the weak equivalence
principle of general relativity (Krauss and Tremaine 1988). In the post-
Newtonian approximation one predicts that a gravitational potential
V (r) delays a light signal (Shapiro time delay) by an amount
∫ A
∆t = −2 V [r(t)] dt, (13.4)
E
where the integral is taken along the trajectory r(t) of the beam between
the points of emission (E) and absorption (A). This delay is the same
for neutrinos and photons to within
∣ ∆t ν − ∆t ∣∣∣∣ γ
< 0.7−4×10 −3 , (13.5)
∣ ∆t γ
where the uncertainty reflects the uncertain modelling of the gravitational
potential between Earth and SN 1987A. 83 This result has been
used to constrain the parameters of a specific model of C- and P-
violating gravitational forces (Almeida, Matsas, and Natale 1989), and
to constrain the parameters of a class of nonmetric theories of gravity
(Coley and Tremaine 1988).
13.3.2 Neutrinos vs. Antineutrinos
Assuming that the first event at Kamiokande represents the prompt ν e
burst one may also constrain the difference in transit time between ν e
and ν e and thus confirm the equivalence principle between matter and
antimatter (LoSecco 1988; Pakvasa, Simmons, and Weiler 1989). Of
course, in order to make such results reliable one would need to observe
the prompt burst from a future SN with greater statistical significance.
82 For a recent laboratory experiment which addresses the Lorentz limiting velocity,
see Greene et al. (1991), and references there to earlier works. See also the book
by Will (1993).
83 See Will (1993) for a review of many other empirical tests of general relativity.