Pentcho Valev

2017-06-11 08:28:21 UTC

According to Newton's theory, in a gravitational field light falls with the same acceleration as ordinary falling bodies (on the Earth, the acceleration of falling photons is g). Gravitational lensing (light bending) is, essentially, a temporary fall of light towards some massive object, so the following conditional is obviously valid:

If light does fall with the same acceleration as ordinary falling bodies, calculations of gravitational lensing based on Newton's theory are correct.

The consequent of the above conditional, "calculations of gravitational lensing based on Newton's theory are correct", could be the end of the story but we still don't know whether the antecedent, "light does fall with the same acceleration as ordinary falling bodies", is true. According even to some Einsteinians, it is:

"If we accept the principle of equivalence, we must also accept that light falls in a gravitational field with the same acceleration as material bodies." http://sethi.lamar.edu/bahrim-cristian/Courses/PHYS4480/4480-PROBLEMS/optics-gravit-lens_PPT.pdf

The antecedent, "light does fall with the same acceleration as ordinary falling bodies", has been confirmed experimentally:

https://courses.physics.illinois.edu/phys419/sp2011/lectures/Lecture13/L13r.html

University of Illinois at Urbana-Champaign: "Consider a falling object. ITS SPEED INCREASES AS IT IS FALLING. Hence, if we were to associate a frequency with that object the frequency should increase accordingly as it falls to earth. Because of the equivalence between gravitational and inertial mass, WE SHOULD OBSERVE THE SAME EFFECT FOR LIGHT. So lets shine a light beam from the top of a very tall building. If we can measure the frequency shift as the light beam descends the building, we should be able to discern how gravity affects a falling light beam. This was done by Pound and Rebka in 1960. They shone a light from the top of the Jefferson tower at Harvard and measured the frequency shift. The frequency shift was tiny but in agreement with the theoretical prediction. Consider a light beam that is travelling away from a gravitational field. Its frequency should shift to lower values. This is known as the gravitational red shift of light."

http://www.einstein-online.info/spotlights/redshift_white_dwarfs

Albert Einstein Institute: "One of the three classical tests for general relativity is the gravitational redshift of light or other forms of electromagnetic radiation. However, in contrast to the other two tests - the gravitational deflection of light and the relativistic perihelion shift -, you do not need general relativity to derive the correct prediction for the gravitational redshift. A combination of Newtonian gravity, a particle theory of light, and the weak equivalence principle (gravitating mass equals inertial mass) suffices. [...] The gravitational redshift was first measured on earth in 1960-65 by Pound, Rebka, and Snider at Harvard University..."

Einstein initially plagiarized the Newtonian prediction for gravitational lensing - he derived it from his miraculous gravitational time dilation. However this made the theory incompatible with the gravitational redshift, and Einstein had to modify the prediction a few years later:

http://en.wikipedia.org/wiki/Johann_Georg_von_Soldner

"Soldner is now mostly remembered for having concluded - based on Newton's Corpuscular theory of light - that light would be diverted by heavenly bodies. In a paper written in 1801 and published in 1804, he calculated the amount of deflection of a light ray by a star... [...] Albert Einstein calculated and published a value for the amount of gravitational light-bending in light skimming the Sun in 1911, leading Phillip Lenard to accuse Einstein of plagiarising Soldner's result. Lenard's accusation against Einstein is usually considered to have been at least partly motivated by Lenard's Nazi sympathies and his enthusiasm for the Deutsche Physik movement. At the time, Einstein may well have been genuinely unaware of Soldner's work, or he may have considered his own calculations to be independent and free-standing, requiring no references to earlier research. Einstein's 1911 calculation was based on the idea of gravitational time dilation. In any case, Einstein's subsequent 1915 general theory of relativity argued that all these calculations had been incomplete, and that the "classic" Newtonian arguments, combined with light-bending effects due to gravitational time dilation, gave a combined prediction that was twice as high as the earlier predictions."

It can be shown that the miraculous gravitational time dilation fabricated by Einstein in 1911 and the gravitational redshift are only compatible if light in a gravitational field behaves in an idiotic way: Its speed DECREASES as the light falls towards the source of gravity - in the gravitational field of the Earth the acceleration of falling photons is NEGATIVE, -2g. In 1915 Einstein and his mathematical friends introduced the idiotic fudge factor, negative acceleration of photons, without any remorse:

https://archive.is/wn4PV

Albert Einstein: "Second, this consequence shows that the law of the constancy of the speed of light no longer holds, according to the general theory of relativity, in spaces that have gravitational fields. As a simple geometric consideration shows, the curvature of light rays occurs only in spaces where the speed of light is spatially variable."

"The change in speed of light with change in height is dc/dh=g/c."

http://www.physlink.com/Education/AskExperts/ae13.cfm

"Contrary to intuition, the speed of light (properly defined) decreases as the black hole is approached."

http://www.speed-light.info/speed_of_light_variable.htm

"Einstein wrote this paper in 1911 in German. (...) ...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+φ/c^2) where φ is the gravitational potential relative to the point where the speed of light c0 is measured. Simply put: Light appears to travel slower in stronger gravitational fields (near bigger mass). (...) You can find a more sophisticated derivation later by Einstein (1955) from the full theory of general relativity in the weak field approximation. (...) Namely the 1955 approximation shows a variation in km/sec twice as much as first predicted in 1911."

http://www.mathpages.com/rr/s6-01/6-01.htm

"Specifically, Einstein wrote in 1911 that the speed of light at a place with the gravitational potential φ would be c(1+φ/c^2), where c is the nominal speed of light in the absence of gravity. In geometrical units we define c=1, so Einstein's 1911 formula can be written simply as c'=1+φ. 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. (...) ...we have c_r =1+2φ, which corresponds to Einstein's 1911 equation, except that we have a factor of 2 instead of 1 on the potential term."

Pentcho Valev

If light does fall with the same acceleration as ordinary falling bodies, calculations of gravitational lensing based on Newton's theory are correct.

The consequent of the above conditional, "calculations of gravitational lensing based on Newton's theory are correct", could be the end of the story but we still don't know whether the antecedent, "light does fall with the same acceleration as ordinary falling bodies", is true. According even to some Einsteinians, it is:

"If we accept the principle of equivalence, we must also accept that light falls in a gravitational field with the same acceleration as material bodies." http://sethi.lamar.edu/bahrim-cristian/Courses/PHYS4480/4480-PROBLEMS/optics-gravit-lens_PPT.pdf

The antecedent, "light does fall with the same acceleration as ordinary falling bodies", has been confirmed experimentally:

https://courses.physics.illinois.edu/phys419/sp2011/lectures/Lecture13/L13r.html

University of Illinois at Urbana-Champaign: "Consider a falling object. ITS SPEED INCREASES AS IT IS FALLING. Hence, if we were to associate a frequency with that object the frequency should increase accordingly as it falls to earth. Because of the equivalence between gravitational and inertial mass, WE SHOULD OBSERVE THE SAME EFFECT FOR LIGHT. So lets shine a light beam from the top of a very tall building. If we can measure the frequency shift as the light beam descends the building, we should be able to discern how gravity affects a falling light beam. This was done by Pound and Rebka in 1960. They shone a light from the top of the Jefferson tower at Harvard and measured the frequency shift. The frequency shift was tiny but in agreement with the theoretical prediction. Consider a light beam that is travelling away from a gravitational field. Its frequency should shift to lower values. This is known as the gravitational red shift of light."

http://www.einstein-online.info/spotlights/redshift_white_dwarfs

Albert Einstein Institute: "One of the three classical tests for general relativity is the gravitational redshift of light or other forms of electromagnetic radiation. However, in contrast to the other two tests - the gravitational deflection of light and the relativistic perihelion shift -, you do not need general relativity to derive the correct prediction for the gravitational redshift. A combination of Newtonian gravity, a particle theory of light, and the weak equivalence principle (gravitating mass equals inertial mass) suffices. [...] The gravitational redshift was first measured on earth in 1960-65 by Pound, Rebka, and Snider at Harvard University..."

Einstein initially plagiarized the Newtonian prediction for gravitational lensing - he derived it from his miraculous gravitational time dilation. However this made the theory incompatible with the gravitational redshift, and Einstein had to modify the prediction a few years later:

http://en.wikipedia.org/wiki/Johann_Georg_von_Soldner

"Soldner is now mostly remembered for having concluded - based on Newton's Corpuscular theory of light - that light would be diverted by heavenly bodies. In a paper written in 1801 and published in 1804, he calculated the amount of deflection of a light ray by a star... [...] Albert Einstein calculated and published a value for the amount of gravitational light-bending in light skimming the Sun in 1911, leading Phillip Lenard to accuse Einstein of plagiarising Soldner's result. Lenard's accusation against Einstein is usually considered to have been at least partly motivated by Lenard's Nazi sympathies and his enthusiasm for the Deutsche Physik movement. At the time, Einstein may well have been genuinely unaware of Soldner's work, or he may have considered his own calculations to be independent and free-standing, requiring no references to earlier research. Einstein's 1911 calculation was based on the idea of gravitational time dilation. In any case, Einstein's subsequent 1915 general theory of relativity argued that all these calculations had been incomplete, and that the "classic" Newtonian arguments, combined with light-bending effects due to gravitational time dilation, gave a combined prediction that was twice as high as the earlier predictions."

It can be shown that the miraculous gravitational time dilation fabricated by Einstein in 1911 and the gravitational redshift are only compatible if light in a gravitational field behaves in an idiotic way: Its speed DECREASES as the light falls towards the source of gravity - in the gravitational field of the Earth the acceleration of falling photons is NEGATIVE, -2g. In 1915 Einstein and his mathematical friends introduced the idiotic fudge factor, negative acceleration of photons, without any remorse:

https://archive.is/wn4PV

Albert Einstein: "Second, this consequence shows that the law of the constancy of the speed of light no longer holds, according to the general theory of relativity, in spaces that have gravitational fields. As a simple geometric consideration shows, the curvature of light rays occurs only in spaces where the speed of light is spatially variable."

"The change in speed of light with change in height is dc/dh=g/c."

http://www.physlink.com/Education/AskExperts/ae13.cfm

"Contrary to intuition, the speed of light (properly defined) decreases as the black hole is approached."

http://www.speed-light.info/speed_of_light_variable.htm

"Einstein wrote this paper in 1911 in German. (...) ...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+φ/c^2) where φ is the gravitational potential relative to the point where the speed of light c0 is measured. Simply put: Light appears to travel slower in stronger gravitational fields (near bigger mass). (...) You can find a more sophisticated derivation later by Einstein (1955) from the full theory of general relativity in the weak field approximation. (...) Namely the 1955 approximation shows a variation in km/sec twice as much as first predicted in 1911."

http://www.mathpages.com/rr/s6-01/6-01.htm

"Specifically, Einstein wrote in 1911 that the speed of light at a place with the gravitational potential φ would be c(1+φ/c^2), where c is the nominal speed of light in the absence of gravity. In geometrical units we define c=1, so Einstein's 1911 formula can be written simply as c'=1+φ. 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. (...) ...we have c_r =1+2φ, which corresponds to Einstein's 1911 equation, except that we have a factor of 2 instead of 1 on the potential term."

Pentcho Valev