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New Theories / Re: EINSTEIN, PHOTONS AND GRAVITATIONAL FIELD
« on: 02/07/2006 08:57:21 »
DIFFICULTIES EINSTEIN'S ZOMBIES OVERCOME
http://www.amazon.com/gp/product/0691122016/002-1780808-4228868?v=glance&n=283155
"It's About Time : Understanding Einstein's Relativity"
by N. David Mermin
"The difficult, counterintuitive part is grasping the implications for moving frames of the absolute constancy of the speed of light."
Initially zombies feel somewhat sad as they juxtapose "absolute constancy of the speed of light" with the following texts written by relativity hypnotists:
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 / c2 )
where V is the gravitational potential relative to the point where the speed of light c0 is measured. "
http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/speed_of_light.html
" Einstein went on to discover a more general theory of relativity which explained gravity in terms of curved spacetime, and he talked about the speed of light changing in this new theory. In the 1920 book "Relativity: the special and general theory" he wrote: . . . according to the general theory of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity [. . .] cannot claim any unlimited validity. A curvature of rays of light can only take place when the velocity of propagation of light varies with position. Since Einstein talks of velocity (a vector quantity: speed with direction) rather than speed alone, it is not clear that he meant the speed will change, but the reference to special relativity suggests that he did mean so. "
Then the sadness disappears and the absolute happiness zombies have experienced since 1905 is restored.
Pentcho Valev
http://www.amazon.com/gp/product/0691122016/002-1780808-4228868?v=glance&n=283155
"It's About Time : Understanding Einstein's Relativity"
by N. David Mermin
"The difficult, counterintuitive part is grasping the implications for moving frames of the absolute constancy of the speed of light."
Initially zombies feel somewhat sad as they juxtapose "absolute constancy of the speed of light" with the following texts written by relativity hypnotists:
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 / c2 )
where V is the gravitational potential relative to the point where the speed of light c0 is measured. "
http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/speed_of_light.html
" Einstein went on to discover a more general theory of relativity which explained gravity in terms of curved spacetime, and he talked about the speed of light changing in this new theory. In the 1920 book "Relativity: the special and general theory" he wrote: . . . according to the general theory of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity [. . .] cannot claim any unlimited validity. A curvature of rays of light can only take place when the velocity of propagation of light varies with position. Since Einstein talks of velocity (a vector quantity: speed with direction) rather than speed alone, it is not clear that he meant the speed will change, but the reference to special relativity suggests that he did mean so. "
Then the sadness disappears and the absolute happiness zombies have experienced since 1905 is restored.
Pentcho Valev