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EINSTEINIANA: GRAVITATIONAL TIME DILATION
http://student.fizika.org/~jsisko/Kn...Morin/CH13.PDF
David Morin (pp. 2-4): "The equivalence principle has a striking consequence concerning the behavior of clocks in a gravitational field. It implies that higher clocks run faster than lower clocks. If you put a watch on top of a tower, and then stand on the ground, you will see the watch on the tower tick faster than an identical watch on your wrist. When you take the watch down and compare it to the one on your wrist, it will show more time elapsed. (...) As seen in frame S, when the receiver and a particular pulse meet, the next pulse is a distance ct_s behind. The receiver and this next pulse then travel toward each other at relative speed c+v (as measured by someone in S). (...) 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." Question: What is the relative speed of the receiver and "the next pulse" as measured BY THE RECEIVER? Answer given by Newton's emission theory of light: c+v Answer given by Einstein's general relativity: c+2v Neither answer is compatible with the prediction that "when you take the watch down and compare it to the one on your wrist, it will show more time elapsed". Moreover, it can be shown that both answers contradict Einstein's 1905 constant-speed-of-light postulate. Given the formula: (frequency) = (speed of light)/(wavelength) the Pound-Rebka experiment confirms the answer c+v given by Newton's emission theory of light and refutes the answer c+2v given by Einstein's general relativity. 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: GRAVITATIONAL TIME DILATION
The top of a tower emits light towards the ground. The photons either
accelerate exactly like cannonballs in the gravitational field (Newton's emission theory of light and Einstein in the period 1907-1915), or accelerate two times faster than cannonballs (Einstein's general relativity after 1915), or do not accelerate at all (Stephen Hawking), or both accelerate and do not accelerate (Steve Carlip): http://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.d1heidorn.homepage.t-onli...k/VSL/VSL.html "In two works from 1907 and 1911 Einstein introduces a variable speed of light. Sometimes this is taken as a contradiction to the constancy of the speed of light, which was postulated in the foundation of Special Relativity in 1905. However there is no contradiction at all - even if in the fully developed GR from 1916 there is a variable speed of light." 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 "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.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.hawking.org.uk/index.php?...64&It emid=66 Stephen Hawking: "Interestingly enough, Laplace himself wrote a paper in 1799 on how some stars could have a gravitational field so strong that light could not escape, but would be dragged back onto the star. He even calculated that a star of the same density as the Sun, but two hundred and fifty times the size, would have this property. But although Laplace may not have realised it, the same idea had been put forward 16 years earlier by a Cambridge man, John Mitchell, in a paper in the Philosophical Transactions of the Royal Society. Both Mitchell and Laplace thought of light as consisting of particles, rather like cannon balls, that could be slowed down by gravity, and made to fall back on the star. But a famous experiment, carried out by two Americans, Michelson and Morley in 1887, showed that light always travelled at a speed of one hundred and eighty six thousand miles a second, no matter where it came from. How then could gravity slow down light, and make it fall back." 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." Einsteiniana's priests teach anything about the speed of light in a gravitational field in the hope that the dismal confusion will repel potential clever critics and Einstein's 1905 false constant-speed-of- light postulate will continue to be "the linchpin that holds the whole range of modern physics theories together": http://www.ekkehard-friebe.de/wallace.htm Bryan Wallace: "There is a popular argument that the world's oldest profession is sexual prostitution. I think that it is far more likely that the oldest profession is scientific prostitution, and that it is still alive and well, and thriving in the 20th century. I suspect that long before sex had any commercial value, the prehistoric shamans used their primitive knowledge to acquire status, wealth, and political power, in much the same way as the dominant scientific and religious politicians of our time do. (...) Because many of the dominant theories of our time do not follow the rules of science, they should more properly be labeled pseudoscience. The people who tend to believe more in theories than in the scientific method of testing theories, and who ignore the evidence against the theories they believe in, should be considered pseudoscientists and not true scientists. To the extent that the professed beliefs are based on the desire for status, wealth, or political reasons, these people are scientific prostitutes. (...) Einstein's special relativity theory with his second postulate that the speed of light in space is constant is the linchpin that holds the whole range of modern physics theories together. Shatter this postulate, and modern physics becomes an elaborate farce! (...) The speed of light is c+v. (...) I expect that the scientists of the future will consider the dominant abstract physics theories of our time in much the same light as we now consider the Medieval theories of how many angels can dance on the head of a pin or that the Earth stands still and the Universe moves around it." [Bryan Wallace wrote "The Farce of Physics" on his deathbed hence some imperfections in the text!] Pentcho Valev |
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EINSTEINIANA: GRAVITATIONAL TIME DILATION
The top of a tower of height h emits light towards the ground. An
observer on the ground measures the frequency to be shifted in accordance with the equation f'=f(1+gh/c^2), an equation confirmed by the Pound-Rebka experiment. Given the formula: (frequency) = (speed of light)/(wavelength) two implications are conceivable: (A) The speed of light is shifted in accordance with the equation c'=c(1+gh/c^2), an equation given by Newton's emission theory of light. The wavelength remains unchanged. (B) The wavelength is shifted in accordance with the equation L'=L/ (1+gh/c^2). The speed of light remains unchanged. (A) is too dangerous for Einsteinana while (B) is too silly. So references to the behaviour of the speed of light in a gravitational field usually evoke crimestop: http://www.liferesearchuniversal.com...html#seventeen George Orwell: "Crimestop means the faculty of stopping short, as though by instinct, at the threshold of any dangerous thought. It includes the power of not grasping analogies, of failing to perceive logical errors, of misunderstanding the simplest arguments if they are inimical to Ingsoc, and of being bored or repelled by any train of thought which is capable of leading in a heretical direction. Crimestop, in short, means protective stupidity." Pentcho Valev |
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EINSTEINIANA: GRAVITATIONAL TIME DILATION
On Apr 30 Pentcho Valev wrote:
The top of a tower of height h emits light towards the ground. An observer on the ground measures the frequency to be shifted in accordance with the equation f'=f(1+gh/c^2), an equation confirmed by the Pound-Rebka experiment. Given the formula: (frequency) = (speed of light)/(wavelength) two implications are conceivable: (A) The speed of light is shifted in accordance with the equation c'=c(1+gh/c^2), an equation given by Newton's emission theory of light. The wavelength remains unchanged. (B) The wavelength is shifted in accordance with the equation L'=L/ (1+gh/c^2). The speed of light remains unchanged. (A) is too dangerous for Einsteinana while (B) is too silly. Why is (B) "too silly"? Because, if the wavelength varies with the gravitational potential, then, in an equivalent scenario, it must vary with the speed of the observer: http://student.fizika.org/~jsisko/Kn...Morin/CH13.PDF Scenario 1: "A light source on top of a tower of height h emits flashes at time intervals t_s. A receiver on the ground receives the flashes at time intervals t_r. What is t_r in terms of t_s?" Scenario 2: "A rocket of length h accelerates with acceleration g. A light source at the front end emits flashes at time intervals t_s. A receiver at the back end receives the flashes at time intervals t_r. What is t_r in terms of t_s?" The variation of the wavelength with the speed of the observer is so absurd that only "the subtlest practitioners of doublethink" in Einsteiniana refer to it explicitly: 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)." http://www.liferesearchuniversal.com...html#seventeen George Orwell: "Doublethink means the power of holding two contradictory beliefs in one's mind simultaneously, and accepting both of them. The Party intellectual knows in which direction his memories must be altered; he therefore knows that he is playing tricks with reality; but by the exercise of doublethink he also satisfies himself that reality is not violated. The process has to be conscious, or it would not be carried out with sufficient precision, but it also has to be unconscious, or it would bring with it a feeling of falsity and hence of guilt. Doublethink lies at the very heart of Ingsoc, since the essential act of the Party is to use conscious deception while retaining the firmness of purpose that goes with complete honesty. To tell deliberate lies while genuinely believing in them, to forget any fact that has become inconvenient, and then, when it becomes necessary again, to draw it back from oblivion for just so long as it is needed, to deny the existence of objective reality and all the while to take account of the reality which one denies - all this is indispensably necessary. Even in using the word doublethink it is necessary to exercise doublethink. For by using the word one admits that one is tampering with reality; by a fresh act of doublethink one erases this knowledge ; and so on indefinitely, with the lie always one leap ahead of the truth. (...) It need hardly be said that the subtlest practitioners of doublethink are those who invented doublethink and know that it is a vast system of mental cheating. In our society, those who have the best knowledge of what is happening are also those who are furthest from seeing the world as it is. In general, the greater the understanding, the greater the delusion ; the more intelligent, the less sane." Saner scientists are convinced that the wavelength remains unchanged as the speed of the observer changes; the frequency varies with the speed of the observer because the speed of light varies with the speed of the observer, in contradiction with Einstein's 1905 constant-speed- of-light postulate: http://www.hep.man.ac.uk/u/roger/PHY.../lecture18.pdf Roger Barlow: "Now suppose the source is fixed but the observer is moving towards the source, with speed v. In time t, ct/(lambda) waves pass a fixed point. A moving point adds another vt/(lambda). So f'=(c +v)/(lambda)." http://www-physics.ucsd.edu/students.../lecture16.pdf Convention we will choose: u = velocity of observer or source v = velocity of wave Moving Observer Observer approaching: f'=(1/T')=(v+u)/(lambda) Observer receding: f'=(1/T')=(v-u)/(lambda) http://www.expo-db.be/ExposPrecedent...%20Doppler.pdf 6. Source immobile - Observateur en mouvement La distance entre les crêtes, la longueur d'onde lambda ne change pas. Mais la vitesse des crêtes par rapport à l'observateur change ! L'observateur se rapproche de la source f' = V'/(lambda) f' = f (1 + Vo/V) L'observateur s'éloigne de la source f' = f (1 - Vo/V) http://www.eng.uwi.tt/depts/elec/sta...relativity.pdf The Invalidation of a Sacred Principle of Modern Physics Stephan J.G. Gift "For a stationary observer O, the stationary light source S emits light at speed c, wavelength Lo, and frequency Fo given by Fo=c/Lo. If the observer moves toward S at speed v, then again based on classical analysis, the speed of light relative to the moving observer is (c + v) and not c as required by Einstein's law of light propagation. Hence the observer intercepts wave-fronts of light at a frequency fA, which is higher than Fo, as is observed, and is given by fA = (c+v)/Lo Fo. (...) In light of this elementary result invalidating STR, it is difficult to understand why this invalid theory has been (and continues to be) accepted for the past 100 years." Pentcho Valev |
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EINSTEINIANA: GRAVITATIONAL TIME DILATION
The only text in Einsteiniana suggesting that the gravitational time
dilation is illusory and that the gravitational redshift arises from the variation of the speed of light in a gravitational field: http://www.amazon.com/Relativity-Its.../dp/0486406768 Banesh Hoffmann: "In an accelerated sky laboratory, and therefore also in the corresponding earth laboratory, the frequence of arrival of light pulses is lower than the ticking rate of the upper clocks EVEN THOUGH ALL THE CLOCKS GO AT THE SAME RATE. (...) As a result the experimenter at the ceiling of the sky laboratory will see with his own eyes that the floor clock is going at a slower rate than the ceiling clock - EVEN THOUGH, AS I HAVE STRESSED, BOTH ARE GOING AT THE SAME RATE. (...) THE GRAVITATIONAL RED SHIFT DOES NOT ARISE FROM CHANGES IN THE INTRINSIC RATES OF CLOCKS. It arises from WHAT BEFALLS LIGHT SIGNALS AS THEY TRAVERSE SPACE AND TIME IN THE PRESENCE OF GRAVITATION." Pentcho Valev |
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