Tests of Special Relativity 47- Calculate whether the following space-time intervals from the origin are space-
like, timelike or lightlike: (1, 3, 0, 0); (3, 3, 0, 0); (3, -3, 0, 0); (0, 3, 0, 0); (3, 1, 0,
0) [1]. - The supernova 1987A explosion in the Large Magellanic Cloud 170000 light
years from Earth produced a burst of anti-neutrinos휈ewhich were observed
in terrestrial detectors. If the anti-neutrinos are massive, their velocity would
depend on their mass as well as their energy. What is the proper time interval
between the emission, assumed to be instantaneous, and the arrival on Earth?
Show that in the limit of vanishing mass the proper time interval is zero. What
information can be derived about the anti-neutrino mass from the observation
that the energies of the anti-neutrinos ranged from 7 to 11MeV, and the arrival
times showed a dispersion of 7s? - The theoretical resolving power of a telescope is given by훼= 1. 22 휆∕퐷,where휆is
the wavelength of the incoming light and퐷is the diameter of the mirror. Assum-
ing퐷=5mand휆= 8 × 10 −^7 m, determine the largest distance to a star that can
be measured by the parallax method. (In reality, atmospheric disturbances set
tighter limits.)
References
[1] Kenyon, I. R. 1990General relativity. Oxford University Press, Oxford.
[2] Pyykkö, P. 1988Chem. Rev. 88 , 563.
[3] Lynden-Bell, D.et al. 1988 Astrophys. J. 326 , 19.
[4] Freedman, W. L.et al. 1994 Nature 371 , 757.
[5] Peacock, J. A. 1999Cosmological physics. Cambridge University Press, Cambridge.
[6] Friedman, Y. and Scarr, T. 2013Physica Scripta 87 , 055004, and references therein.
[7] Gasiorowicz, S. 1979The structure of matter. Addison-Wesley, Reading, MA.