NEWTON WRONG IN EINSTEIN'S WORLD

J. Mulligan, INTRODUCTORY COLLEGE PHYSICS, McGraw-Hill, 1985, pp.631-632:

"Sir Isaac Newton had proposed a particle theory of light which explained the refraction of light by the difference in the forces exerted on the particles by the two media, the more dense medium exerting a larger force and causing light to move more rapidly. A measurement of the speed of light in water, made by Foucault in 1850, clearly showed that light has a lower speed in water than in air, and that Newton's theory must therefore be wrong."

If Newton's theory is wrong the more dense medium cannot cause light to move more rapidly (if it can Newton's theory is right). The educator should have stated clearly: Newton wrong means the speed of light is constant (does not vary with position) in either medium, only at the boundary it suddenly changes. However the educator knows Newton is right. Even Einstein knew Newton was right:

http://www.physlink.com/Education/AskExperts/ae13.cfm [nofollow] "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 [nofollow] "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."

As for the fact that light has a lower speed in water than in air, it is irrelevant. As the photon enters the more dense medium (water), its INITIAL speed is higher than the speed it had in the less dense medium (air) before the acceleration. So far Newton is right. If Newton thought this initial high speed in the more dense medium remained constant all along then he was mistaken but the mistake is immaterial. His theory of refraction based on the concept of variable speed of light remains correct.

Pentcho Valev

pvalev@yahoo.com