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An excerpt from COSMIC HORIZONS: ASTRONOMY AT THE CUTTING EDGE, edited
by Steven Soter and Neil deGrasse Tyson, a publication of the New Press. © 2000 American Museum of Natural History. To order the book, call 1-800-233-4830, or go to http://www.amnh.org/education/resour...l/web/buybook/ http://www.amnh.org/education/resour...s_michell.html "Michell accepted Newton's theory that light consists of small material particles. He reasoned that such particles, emerging from the surface of a star, would have their speed reduced by the star's gravitational pull, just like projectiles fired upward from the Earth. (...) Michell got the right answer, although he was wrong about one point. We now know, from Einstein's relativity theory of 1905, that light moves through space at a constant speed, regardless of the local strength of gravity." Needless to say, in 1905 Einstein did not say anything like "light moves through space at a constant speed, regardless of the local strength of gravity". Rather, from 1907 on, he claimed that, in a gravitational field, the speed of light is VARIABLE, not constant. In 1911 Einstein was explicitly using Newton's emission theory of light in order to show how the speed of light varies with the gravitational potential: ttp://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....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." http://www.blazelabs.com/f-g-gcont.asp "So, faced with this evidence most readers must be wondering why we learn about the importance of the constancy of speed of light. Did Einstein miss this? Sometimes I find out that what's written in our textbooks is just a biased version taken from the original work, so after searching within the original text of the theory of GR by Einstein, I found this quote: "In the second place our result shows that, 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 and to which we have already frequently referred, 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. Now we might think that as a consequence of this, the special theory of relativity and with it the whole theory of relativity would be laid in the dust. But in reality this is not the case. We can only conclude that the special theory of relativity cannot claim an unlimited domain of validity ; its results hold only so long as we are able to disregard the influences of gravitational fields on the phenomena (e.g. of light)." - Albert Einstein (1879-1955) - The General Theory of Relativity: Chapter 22 - A Few Inferences from the General Principle of Relativity-. Today we find that since the Special Theory of Relativity unfortunately became part of the so called mainstream science, it is considered a sacrilege to even suggest that the speed of light be anything other than a constant. This is somewhat surprising since even Einstein himself suggested in a paper "On the Influence of Gravitation on the Propagation of Light," Annalen der Physik, 35, 1911, that the speed of light might vary with the gravitational potential. Indeed, the variation of the speed of light in a vacuum or space is explicitly shown in Einstein's calculation for the angle at which light should bend upon the influence of gravity. One can find his calculation in his paper. The result is c'=c(1+V/c^2) where V is the gravitational potential relative to the point where the measurement is taken. 1+V/c^2 is also known as the GRAVITATIONAL REDSHIFT FACTOR." In 1915 Einstein managed to get rid of Newton's emission theory of light by replacing the equation c'=c(1+V/c^2) with c'=c(1+2V/c^2), which is tantamount to replacing 2+2=4 with 2+2=5: http://www.mathpages.com/rr/s6-01/6-01.htm "In geometrical units we define c_0 = 1, so Einstein's 1911 formula can be written simply as c=1+phi. However, this formula for the speed of light (not to mention this whole approach to gravity) turned out to be incorrect, as Einstein realized during the years leading up to 1915 and the completion of the general theory. In fact, the general theory of relativity doesn't give any equation for the speed of light at a particular location, because the effect of gravity cannot be represented by a simple scalar field of c values. Instead, the "speed of light" at a each point depends on the direction of the light ray through that point, as well as on the choice of coordinate systems, so we can't generally talk about the value of c at a given point in a non- vanishing gravitational field. However, if we consider just radial light rays near a spherically symmetrical (and non- rotating) mass, and if we agree to use a specific set of coordinates, namely those in which the metric coefficients are independent of t, then we can read a formula analogous to Einstein's 1911 formula directly from the Schwarzschild metric. (...) In the Newtonian limit the classical gravitational potential at a distance r from mass m is phi=-m/r, so if we let c_r = dr/dt denote the radial speed of light in Schwarzschild coordinates, we have c_r =1+2phi, which corresponds to Einstein's 1911 equation, except that we have a factor of 2 instead of 1 on the potential term." http://www.speed-light.info/speed_of_light_variable.htm "Einstein wrote this paper in 1911 in German (download from: http://www.physik.uni-augsburg.de/an...35_898-908.pdf ). It predated the full formal development of general relativity by about four years. You can find an English translation of this paper in the Dover book 'The Principle of Relativity' beginning on page 99; 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+phi/c^2) where phi is the gravitational potential relative to the point where the speed of light co is measured......You can find a more sophisticated derivation later by Einstein (1955) from the full theory of general relativity in the weak field approximation....For the 1955 results but not in coordinates see page 93, eqn (6.28): c(r)=[1+2phi(r)/c^2]c. Namely the 1955 approximation shows a variation in km/sec twice as much as first predicted in 1911." http://www.online-literature.com/orwell/1984/ George Orwell "1984": "In the end the Party would announce that two and two made five, and you would have to believe it. It was inevitable that they should make that claim sooner or later: the logic of their position demanded it. Not merely the validity of experience, but the very existence of external reality, was tacitly denied by their philosophy. The heresy of heresies was common sense. And what was terrifying was not that they would kill you for thinking otherwise, but that they might be right. For, after all, how do we know that two and two make four? Or that the force of gravity works? Or that the past is unchangeable? If both the past and the external world exist only in the mind, and if the mind itself is controllable what then?" Pentcho Valev |
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