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Speed of light is variable says Einstein
On 10 Aug, 17:52, Tom Roberts wrote:
qbit wrote: To see the steps how Einstein theorized that the speed of light in a gravitational field is actually not a constant, but rather a variable depending upon the reference frame of the observer: 'On the Influence of Gravitation on the Propagation of Light', Annalen der Physik, 35, 1911. Einstein wrote this paper in 1911 in German 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' = c * (1 + phi / c^2) Where phi is the gravitational potential relative to the point where the speed of light c is measured. Simply put: Light appears to travel slower in stronger gravitational fields (near bigger mass). [...] [Bewa Pentcho Valev obsesses about that equation, and posts endless articles about it around here, ALL WRONG.] That 1911 article was documenting a portion of Einstein's arduous trek from SR to GR. The above formula does not hold in GR, except in certain approximations for specific physical situations; it is not a general formula at all. In GR, the speed of light (in vacuum) is c in EVERY locally inertial frame (when measured with standard clocks and rulers). But due to the curvature of spacetime, when measured over a non-local distance one can obtain other values. The above formula purports to describe the speed of light "there" when measured by an observer "here" -- in GR that in general makes no sense; in the small-field APPROXIMATION to GR it does make sense, and that formula holds APPROXIMATELY for certain specific measurements (even in the small-field approximation it is not a general formula). So yes, there are cases where the speed of light is not c (in vacuum). But it is considerably more subtle than you seem to think. Tom Roberts Bravo Roberts bravo Tom bravo Albert Einstein of our generation (Hawking is no longer the Albert Einstein of our generation etc.). From now on your zombies will know everything about Einstein's 1911 formula c' = c * (1 + phi / c^2) and what is even more important Roberts Roberts, your explanation is so clear and unambiguous that even other hypnotists' zombies will be able to learn something from it (you used to say Einstein's formula was wrong but now you do not wish to be so rude). Yet there is a small detail you forgot to explain clearly and unambiguously: there is an equivalent formula proved experimentally by Pound and Rebka and showing how the frequency varies with the gravitational potential: f' = f * (1 + phi / c^2) I say the two formulas are "equivalent" because they are related by the textbook equation frequency = (speed of light)/(wavelength) So Roberts Roberts the danger is not over: unless you offer more clear and unambiguous explanations, even your zombies will find that the two formulas are JUST TRUE, confirmed by experiment, and will also find, by applying Einstein's equivalence principle, that c' = c * (1 + phi / c^2) is equivalent to c' = c + v where c is the initial speed of photons relative to the light source and v is the relative speed of the light source and the observer, in the absence of a gravitational field. Pentcho Valev |
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Speed of light is variable says Einstein
On Aug 10, 10:14 pm, Pentcho Valev wrote:
On 10 Aug, 17:52, Tom Roberts wrote: qbit wrote: To see the steps how Einstein theorized that the speed of light in a gravitational field is actually not a constant, but rather a variable depending upon the reference frame of the observer: 'On the Influence of Gravitation on the Propagation of Light', Annalen der Physik, 35, 1911. Einstein wrote this paper in 1911 in German http://www.physik.uni-augsburg.de/an...s/1911_35_898-... 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' = c * (1 + phi / c^2) Where phi is the gravitational potential relative to the point where the speed of light c is measured. Simply put: Light appears to travel slower in stronger gravitational fields (near bigger mass). [...] [Bewa Pentcho Valev obsesses about that equation, and posts endless articles about it around here, ALL WRONG.] That 1911 article was documenting a portion of Einstein's arduous trek from SR to GR. The above formula does not hold in GR, except in certain approximations for specific physical situations; it is not a general formula at all. In GR, the speed of light (in vacuum) is c in EVERY locally inertial frame (when measured with standard clocks and rulers). But due to the curvature of spacetime, when measured over a non-local distance one can obtain other values. The above formula purports to describe the speed of light "there" when measured by an observer "here" -- in GR that in general makes no sense; in the small-field APPROXIMATION to GR it does make sense, and that formula holds APPROXIMATELY for certain specific measurements (even in the small-field approximation it is not a general formula). So yes, there are cases where the speed of light is not c (in vacuum). But it is considerably more subtle than you seem to think. Tom Roberts Bravo Roberts bravo Tom bravo Albert Einstein of our generation (Hawking is no longer the Albert Einstein of our generation etc.).From now on your zombies will know everything about Einstein's 1911 formula c' = c * (1 + phi / c^2) and what is even more important Roberts Roberts, your explanation is so clear and unambiguous that even other hypnotists' zombies will be able to learn something from it (you used to say Einstein's formula was wrong but now you do not wish to be so rude). Yet there is a small detail you forgot to explain clearly and unambiguously: there is an equivalent formula proved experimentally by Pound and Rebka and showing how the frequency varies with the gravitational potential: f' = f * (1 + phi / c^2) I say the two formulas are "equivalent" because they are related by the textbook equation frequency = (speed of light)/(wavelength) So Roberts Roberts the danger is not over: unless you offer more clear and unambiguous explanations, even your zombies will find that the two formulas are JUST TRUE, confirmed by experiment, and will also find, by applying Einstein's equivalence principle, that c' = c * (1 + phi / c^2) is equivalent to c' = c + v where c is the initial speed of photons relative to the light source and v is the relative speed of the light source and the observer, in the absence of a gravitational field. Really? Explain how phi = 0 equates to c' = c+v. Then once your finished explaining that, explain why anyone should care about Einstein's defunct attempt at gravitation. http://bip.cnrs-mrs.fr/bip10/valevfaq.htm Pentcho Valev |
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Speed of light is variable says Einstein
On 11 Aug, 09:24, Eric Gisse wrote:
On Aug 10, 10:14 pm, Pentcho Valev wrote: Bravo Roberts bravo Tom bravo Albert Einstein of our generation (Hawking is no longer the Albert Einstein of our generation etc.).From now on your zombies will know everything about Einstein's 1911 formula c' = c * (1 + phi / c^2) and what is even more important Roberts Roberts, your explanation is so clear and unambiguous that even other hypnotists' zombies will be able to learn something from it (you used to say Einstein's formula was wrong but now you do not wish to be so rude). Yet there is a small detail you forgot to explain clearly and unambiguously: there is an equivalent formula proved experimentally by Pound and Rebka and showing how the frequency varies with the gravitational potential: f' = f * (1 + phi / c^2) I say the two formulas are "equivalent" because they are related by the textbook equation frequency = (speed of light)/(wavelength) So Roberts Roberts the danger is not over: unless you offer more clear and unambiguous explanations, even your zombies will find that the two formulas are JUST TRUE, confirmed by experiment, and will also find, by applying Einstein's equivalence principle, that c' = c * (1 + phi / c^2) is equivalent to c' = c + v where c is the initial speed of photons relative to the light source and v is the relative speed of the light source and the observer, in the absence of a gravitational field. Really? Explain how phi = 0 equates to c' = c+v. Then once your finished explaining that, explain why anyone should care about Einstein's defunct attempt at gravitation. http://bip.cnrs-mrs.fr/bip10/valevfaq.htm Gisse Gisse your statement: "Explain how phi = 0 equates to c' = c+v" is EXTREMELY silly. Never do so again! One more statement of this kind and you will never become Master Tom Roberts' PhD student. Master Tom Roberts loves silly zombies but not SO silly. Consider: http://www.courses.fas.harvard.edu/~...tbook/ch13.pdf pp.2-4 Note that phi = gh = cv. Substitute this in Einstein's 1911 equation c' = c * (1 + phi / c^2) and you obtain c'=c+v. Pentcho Valev |
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