TEACHING THE DISCOVERIES OF EINSTEIN
Generally, relativists are excellent teachers:
http://www.physlink.com/Education/AskExperts/ae13.cfm :
"So, it is absolutely true that the speed of light is _not_ constant
in a gravitational field [which, by the equivalence principle, applies
as well to accelerating (non-inertial) frames of reference]. If this
were not so, there would be no bending of light by the gravitational
field of stars. One can do a simple Huyghens reconstruction of a wave
front, taking into account the different speed of advance of the
wavefront at different distances from the star (variation of speed of
light), to derive the deflection of the light by the star.
Indeed, this is exactly how Einstein did the calculation in:
"On the Influence of Gravitation on the Propagation of Light," Annalen
der Physik, 35, 1911.
which predated the full formal development of general relativity by
about four years. This paper is widely available in English. You can
find a copy beginning on page 99 of the Dover book "The Principle of
Relativity." You will find in section 3 of that paper, Einstein's
derivation of the (variable) speed of light in a gravitational
potential, eqn (3). The result is,
c' = c0 ( 1 + V / c^2 )
where V is the gravitational potential relative to the point where the
speed of light c0 is measured."
However, if teachers want their students to understand the real
grandeur of Einstein's discoveries, they should set more problems. For
instance: A light source on the surface of a huge celestial body,
where the gravitational field is enormous, sends light towards a very
distant INERTIAL observer (where the field is zero). What speed of
light will the observer measure?
Students will learn that, according to Einstein, the speed of light
for inertial observers is not only constant but also variable. So
students will understand both the grandeur and the essence of
Einstein's discoveries.
Pentcho Valev
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