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EINSTEINIANA: SPEED OF LIGHT IN A GRAVITATIONAL FIELD
Divine Albert 1911: If clocks OF IDENTICAL CONSTITUTION are used, the
speed of light will not be measured to vary with the gravitational potential: http://www.relativitybook.com/resour...n_gravity.html Albert Einstein 1911: "For if we measure the velocity of light at different places in the accelerated, gravitation-free system K', employing clocks U of identical constitution we obtain the same magnitude at all these places. The same holds good, by our fundamental assumption, for the system K [a stationary system in a homogeneous gravitational field] as well." Divine Albert 1915: If clocks OF IDENTICAL CONSTITUTION are used, the speed of light will be measured to vary with the gravitational potential two times faster than the speed of cannonballs: http://www.speed-light.info/speed_of_light_variable.htm "Einstein wrote this paper in 1911 in German. 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.mathpages.com/rr/s6-01/6-01.htm "Around 1911 Einstein proposed to incorporate gravitation into a modified version of special relativity by allowing the speed of light to vary as a scalar from place to place in Euclidean space as a function of the gravitational potential. This "scalar c field" is remarkably similar to a simple refractive medium, in which the speed of light varies as a function of the density. Fermat's principle of least time can then be applied to define the paths of light rays as geodesics in the spacetime manifold (as discussed in Section 8.4). Specifically, Einstein wrote in 1911 that the speed of light at a place with the gravitational potential phi would be c(1+phi/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+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. (...) ...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." The truth: If clocks OF IDENTICAL CONSTITUTION are used, the speed of light will be measured to vary with the gravitational potential exactly as the speed of cannonballs does. The variation obeys the equation c'=c(1+phi/c^2) given by Newton's emission theory of light. Pentcho Valev |
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EINSTEINIANA: SPEED OF LIGHT IN A GRAVITATIONAL FIELD
The Feynman Lectures on Physics, Volume 2, Chapter 42-6:
"Suppose we put a clock at the "head" of the rocket ship - that is, at the front end - and we put another identical clock at the "tail," as in fig. 42-16. Let's call the two clocks A and B. If we compare these two clocks when the ship is accelerating, the clock at the head seems to run fast relative to the one at the tail. To see that, imagine that the front clock emits a flash of light each second, and that you are sitting at the tail comparing the arival of the light flashes with the ticks of clock B. (...) The first flash travels the distance L1 and the second flash travels the shorter distance L2. It is a shorter distance because the ship is acelerating and has a higher speed at the time of the second flash. You can see, then, that if the two flashes were emitted from clock A one second apart, they would arrive at clock B with a separation somewhat less than one second, since the second flash doesn't spend as much time on the way." Einsteiniana's idiocies can confuse any mind, even Richard Feynman's one! If the acceleration is uniform, it is obvious that L1=L2. The problem has an easy solution. The observer (sitting at the tail) measures the frequency of light to have increased. Then, by taking into account the formula: (frequency) = (speed of light)/(wavelength) he concludes that either the speed of light (relative to the observer) has increased (then Einstein's 1905 light postulate is false) or the wavelength has decreased. Einsteinians believe that the wavelength somehow varies with the speed of the observer: http://www.pitt.edu/~jdnorton/teachi...ang/index.html John Norton: "Here's a light wave and an observer. If the observer were to hurry towards the source of the light, the observer would now pass wavecrests more frequently than the resting observer. That would mean that moving observer would find the frequency of the light to have increased (AND CORRESPONDINGLY FOR THE WAVELENGTH - THE DISTANCE BETWEEN CRESTS - TO HAVE DECREASED)." Pentcho Valev |
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EINSTEINIANA: SPEED OF LIGHT IN A GRAVITATIONAL FIELD
The Feynman Lectures on Physics, Volume 1, Chapter 15-1:
"Suppose we are riding in a car that is going at a speed u, and light from the rear is going past the car with speed c. Differentiating the first equation in (15.2) gives dx'/dt=dx/dt-u, which means that according to the Galilean transformation the apparent speed of the passing light, as we measure it in the car, should not be c but should be c-u." Needless to say, Feynman rejects the equation c'=c-u (it is incompatible with Einstein's special relativity) but: 1. According to Maxwell's theory, the equation c'=c-u is correct (u is the speed of the car relative to the ether). 2. According to Newton's emission theory of light, the equation c'=c-u is correct (u is the speed of the car relative to the emitter). 3. In the absence of ad hoc auxiliary hypotheses (Lorentz-FitzGerald's length contraction), the Michelson-Morley experiment unequivocally confirms the equation c'=c-u and refutes the alternative equation c'=c compatible with Einstein's special relativity. Pentcho Valev |
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EINSTEINIANA: SPEED OF LIGHT IN A GRAVITATIONAL FIELD
Einsteinians compelled to stick to Newton's emission theory of light:
A light source on top of a tower of height h emits light with frequency f and speed c (relative to the source). The light reaches an observer on the ground with frequency f' and speed c' (relative to the observer). Equivalently, a light source at the front end of an accelerating rocket of length h and accelaration g emits light with frequency f and speed c (relative to the source). The light reaches an observer at the back end with frequency f' and speed c' (relative to the observer). Consider equations (13.2) on p. 3 in David Morin's text: http://student.fizika.org/~jsisko/Kn...Morin/CH13.PDF f' = f(1 + v/c) = f(1 + gh/c^2) (13.2) where v is the relative speed of the light source (at the moment of emission) and the observer (at the moment of reception) in the rocket scenario. By combining these equations with: (frequency) = (speed of light)/(wavelength) one obtains the fundamental equations of Newton's emission theory of light: c' = c + v = c(1 + gh/c^2) In the absence of ad hoc auxiliary hypotheses the Pound-Rebka experiment, just like the Michelson-Morley experiment, unequivocally confirms the fundamental equations of Newton's emission theory of light and refutes the principle of constancy of the speed of light: http://student.fizika.org/~jsisko/Kn...Morin/CH13.PDF David Morin (p. 4): "This GR time-dilation effect was first measured at Harvard by Pound and Rebka in 1960. They sent gamma rays up a 20m tower and measured the redshift (that is, the decrease in frequency) at the top. This was a notable feat indeed, considering that they were able to measure a frequency shift of gh/c^2 (which is only a few parts in 10^15) to within 1% accuracy." David Morin's text referred to above reappears as Chapter 14 in: http://www.people.fas.harvard.edu/~djmorin/book.html Introduction to Classical Mechanics With Problems and Solutions, David Morin, Cambridge University Press Pentcho Valev |
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EINSTEINIANA: SPEED OF LIGHT IN A GRAVITATIONAL FIELD
Einsteiniana's priests shock believers:
http://www.logosjournal.com/issue_4.3/smolin.htm Lee Smolin: "Special relativity was the result of 10 years of intellectual struggle, yet Einstein had convinced himself it was wrong within two years of publishing it." Believers are baffled. What could have happened in 1907? "Wrong" is a wrong word perhaps? Did Smolin mean "incomplete"? An hour of silence but then again the wind carries the tunes of "Divine Einstein" and "Yes we all believe in relativity, relativity, relativity" all over the world. Then John Norton shocks believers by providing the second moiety of the story: http://www.pitt.edu/~jdnorton/papers...UP_TimesNR.pdf John Norton: "Already in 1907, a mere two years after the completion of the special theory, he [Einstein] had concluded that the speed of light is variable in the presence of a gravitational field." Believers are baffled again. Variable?!?! This is more serious and the silence lasts for two days. On the third day Steve Carlip restores the serenity in Einsteiniana's schizophrenic world by explaining to believers that, even though the speed of light may have been variable in 1907, now it is constant and that's it: http://math.ucr.edu/home/baez/physic..._of_light.html Steve Carlip: "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. This interpretation is perfectly valid and makes good physical sense, but a more modern interpretation is that the speed of light is constant in general relativity." Pentcho Valev |
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EINSTEINIANA: SPEED OF LIGHT IN A GRAVITATIONAL FIELD
Implicit references to Halton Arp's "intrinsic redshift" in
Einsteiniana's schizophrenic world: http://www.wired.com/wiredscience/20...in-relativity/ "The researchers, led by Radek Wojtak of the Niels Bohr Institute at the University of Copenhagen, set out to test a classic prediction of general relativity: that light will lose energy as it is escaping a gravitational field. The stronger the field, the greater the energy loss suffered by the light. As a result, photons emitted from the center of a galaxy cluster - a massive object containing thousands of galaxies - should lose more energy than photons coming from the edge of the cluster because gravity is strongest in the center." "Light will lose energy as it is escaping a gravitational field" is a euphemism. In fact, general relativity predicts that light will lose SPEED. The speed of light varies with the gravitational potential, phi, either in accordance with the equation c'=c(1+phi/c^2) given by Newton's emission theory of light or in accordance with the equation c'=c(1+2phi/c^2) given by general relativity: http://www.speed-light.info/speed_of_light_variable.htm "Einstein wrote this paper in 1911 in German. 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." Pentcho Valev |
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EINSTEINIANA: SPEED OF LIGHT IN A GRAVITATIONAL FIELD
Truth in Einsteiniana's schizophrenic world: Einsteinians show that
the speed of light varies with gh, the gravitational potential, in accordance with the equation c'=c(1+gh/c^2) (an equation given by Newton's emission theory of light): http://www.youtube.com/watch?v=FJ2SVPahBzg Relativity 3 - gravity and light Of course, this truth is unnoticeable since two blatant lies are officially taught: that the speed of light is constant in a gravitational field (for beginners) and that it varies with the gravitational potential in accordance with the equation c'=c(1+2gh/ c^2) (for advanced Einsteinians): http://www.amazon.com/Brief-History-.../dp/0553380168 Stephen Hawking, "A Brief History of Time", Chapter 6: "Under the theory that light is made up of waves, it was not clear how it would respond to gravity. But if light is composed of particles, one might expect them to be affected by gravity in the same way that cannonballs, rockets, and planets are.....In fact, it is not really consistent to treat light like cannonballs in Newton's theory of gravity because the speed of light is fixed. (A cannonball fired upward from the earth will be slowed down by gravity and will eventually stop and fall back; a photon, however, must continue upward at a constant speed...)" http://www.mathpages.com/rr/s6-01/6-01.htm "Around 1911 Einstein proposed to incorporate gravitation into a modified version of special relativity by allowing the speed of light to vary as a scalar from place to place in Euclidean space as a function of the gravitational potential. This "scalar c field" is remarkably similar to a simple refractive medium, in which the speed of light varies as a function of the density. Fermat's principle of least time can then be applied to define the paths of light rays as geodesics in the spacetime manifold (as discussed in Section 8.4). Specifically, Einstein wrote in 1911 that the speed of light at a place with the gravitational potential phi would be c(1+phi/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+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. (...) ...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." Pentcho Valev |
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EINSTEINIANA: SPEED OF LIGHT IN A GRAVITATIONAL FIELD
Irwin Shapiro incidentally hears "something about the speed depending
on the gravitational potential" and realizes that the speed of light is obviously variable: http://www.hep.yorku.ca/menary/cours...relativity.pdf Irwin Shapiro: "...I attended an afternoon of presentations c. 1961-1962 by MIT staff on their progress on various research projects, conducted under joint services (DOD) sponsorship. One was on speed-of- light measurements by George Stroke who mentioned something about the speed depending on the gravitational potential. This remark surprised me and I pursued it via "brushing up" on my knowledge of general relativity and realized the obvious: whereas the speed of light measured locally in an inertial frame will have the same value everywhere, save for measurement errors, the propagation time of light along some path will depend on the gravitational potential along that path." Of course, although Shapiro and Stroke are free to discuss anything, even the variation of the speed of light, believers are not. They should just sing, as fiercely as possible, "Divine Einstein" and "Yes we all believe in relativity, relativity, relativity". Pentcho Valev |
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