Twins Paradox doesn't add up with light
in [Relativity]
|
From: DSeppala on 5 May 2010 12:19 On May 4, 3:23 am, Mike_Fontenot <mlf...(a)comcast.net> wrote: > DSeppala wrote: > > [...] > > When the traveling twin moves in a circle at constant speed (with the > home twin at the center of the circle), it turns out that BOTH twins > will agree (at all times) that the traveling twin is ageing more > slowly...and they will EACH agree about their "current ages", at all times. > > This is quite different from the usual linear-motion scenario, where the > two twins agree ONLY at the beginning and at the end of the trip...at > other times, they disagree (about their ageing rates, AND about their > "current ages"). > > But in both scenarios, each twin's conclusion is the ONLY conclusion > that is consistent with their own elementary measurements. > > Mike Fontenot The question is why does the twin moving around the circumference of the circle measure that light that he emits only travels half the distance that light from the start of the experiment traveled? The light beams both started at the point in space and time and the beams both returned to a common point in space and time when the moving twin returned to that same spot. Both twins agree that the beam that traveled from the starting location upward and back to the end location must have traveled at least N light-seconds, since both twins agree that the upward beam hits a mirror that is positioned N/2 light- seconds above the plane of the circle. The moving twin however measures that his light beam traveled only 0.5 * N light-seconds during that same time. He must conclude that either the speed of light is not constant, or his measurements of time and distance are wrong. If you look at the hypothesis that the speed of light is not constant, one may say that Einstein's view only applies to inertial reference frames. So if our moving twin travels on a circle of extremely large radius, say for example his path deviates from a straight line by one micron every light-year of arc-length, then what is the explanation of why his measurement is off by a factor of 2 in this example while if he didn't deviate from a straight line by that micron he his measurements would have agreed with Einstein's theory and he would have measured light to travel at c instead of c/2 as he does when he completes the circle? How does this acceleration of one micron per one-light year result in the factor of two difference in the two speeds of light. David Bastrop, TX
From: BURT on 5 May 2010 14:27 On May 4, 5:18 am, artful <artful...(a)hotmail.com> wrote: > On May 4, 8:17 am, DSeppala <dsepp...(a)austin.rr.com> wrote: > > Oh dear .. not another one > > [snip] > > The travelling twin's frame is not inertial, so it is not supposed to > have to measure the speed of light as c. Weight causes original motion to be dectable at its onset. The creation of speed is detectable. Mitch Raemsch
From: Darwin123 on 5 May 2010 16:39 On May 3, 6:17 pm, DSeppala <dsepp...(a)austin.rr.com> wrote: > Can anyone explain how the moving twin explains why his emitted > light traveled only N/2 light-seconds during the same time interval > the light emitted at the same time and place traveled N light-seconds, > with both pulses traveling in a vacuum? The moving twin has to use some type of accelerometer. If he measures a nonzero acceleration, then he can use the acceleration to explain the anomalous time measurement. He can't measure his absolute velocity according to SR, but he can measure his acceleration according to SR. So the critical difference is in terms of an accelerometer. The acceleration caused by forces is the critical difference in relativity. I am just now trying to teach myself GR. I just got started working through problems in the book. However, I have only got through the first chapter. In GR, there is subtle difference between nongravitational forces and gravitational forces that I don't understand yet. Since I know SR better, I will stick to SR. To make it clear, I list three types of accelerometers that each twin can use. Three types of accelerometer are the weight scale, the Sagnac cavity and the Foucault spring-mass. Any of these three accelerometers can be used to measure his radial acceleration. It is the radial acceleration that is used as an explanation of the anomalies. The rules of the universe are simplest in a frame where the acceleration caused by nongravitational forces is zero. So to use the simplest rules, one needs to be in a frame where the acceleration caused by nongravitational forces is zero. For purposes of SR, this means the twin has to check if he is in an inertial frame. For purposes of GR, he has to know whether he is traveling on a geodesiac (straight line in 4-space). There is no centripetal force necessary to keep the stationary twin on the circle. A body that is stationary tends to remain stationary unless acted on by some outside force. The stationary twin does not feel such a force. Suppose he places a bathroom scale at a point closer to the center of the circle than his head. He places his feet on the circle, and weights himself. He measures zero weight. So in SR, he has a zero acceleration. This is a nonlocal measurement since we are assuming the head of the twin sticks high above the weight scale. However, it is a true measurement of weight. The stationary twin knows he is stationary because he measures a zero force on him. So he knows he can apply the Lorentz time dilation and the Lorentz length contraction. The twin could have used a Sagnac cavity to measure the centripetal acceleration. A Sagnac cavity that is stationary won't make any beats. So if the twin holds a large Sagnac cavity, he could determine his centripetal acceleration without a scale. If there is a zero acceleration as measured by the cavity, the twin is stationary. Because the Sagnac cavity has a nonzero radius, this is a nonlocal measurement. The twin could have also used a bob on spring system, to measure an analog to the Foucault pendulum. He would not see a precession of the weighted bob. So he knows he is in an inertial frame. Or in its GR analog, the geodesaic line. Because the oscillation has a nonzero amplitude, this is a nonlocal measurement. The moving twin does the same experiments. He places a scale farther from the center of the circle than his head. He tries to weigh himself. The moving twin succeeds. He sees he has a nonzero weight. He sees the laser beam that comes out of the Sagnac cavity blink. So he knows he is accelerating. He sees the Foucault bob precess. So he know he is accelerating. He has a nonzero acceleration, as determined by three types of nonlocal measurements. Thus, the moving twin knows he is not in an inertial frame. He is subject to some nonzero force. Therefore, the laws of the universe are not in their simplest form in his frame. The moving twin can not apply the Lorentz time dilation to his brother. The moving twin is not in an inertial frame. There are at least three nonlocal experiments that can demonstrate it. He is accelerating, and he can measure it. He can use this nonzero acceleration to explain why his life is so complicated. The moving twin can not apply the Lorentz time dilation or the Lorentz length contraction to his brother. These are no simple laws for the accelerating twin. He has to use laws more complicated than those used by the stationary twin. The moving twin can use the nonzero acceleration as a reason (excuse?) as to why the laws of SR don't seem to apply to him. So the answer has to be the centripetal acceleration of the moving twin. The stationary twin has no measurable centripetal acceleration. The stationary twin can use the simple laws of time dilation and length contraction. The moving twin can not. An observer can not justify using SR directly unless he uses an accelerometer, and the accelerometer says zero acceleration. Therefore, hidden in all these so called "paradoxes" is an accelerometer measurement that has to be performed. Although SR doesn't permit a measurement of absolute velocity, it does permit a measurement of absolute acceleration. The moving twin can use a complicated set of laws appropriate to an accelerated observer. The stationary twin can use the Lorentz transformation on the separate gears in the moving twins clock to get those complicated rules. However, these rules have to be consistent with what the stationary twin observes. Anyone who counters me with a GR argument may very well be right. I have just complete one chapter in a book on GR. However, I am enough along to suggest that the answer in GR comes down to the acceleration that is caused by nongravitational forces. In whatever relativity you want to use, the moving twin uses a nonzero acceleration to explain the anomalous ways his clocks and rulers work.
From: Darwin123 on 5 May 2010 17:04 On May 5, 12:19 pm, DSeppala <dsepp...(a)austin.rr.com> wrote: > On May 4, 3:23 am, Mike_Fontenot <mlf...(a)comcast.net> wrote: > > > > > DSeppala wrote: > > > [...] > > > When the traveling twin moves in a circle at constant speed (with the > > home twin at the center of the circle), it turns out that BOTH twins > > will agree (at all times) that the traveling twin is ageing more > > slowly...and they will EACH agree about their "current ages", at all times. > > He must conclude that either the speed of light is not constant, > or his measurements of time and distance are wrong. I know SR fairly well, and am just starting to learn GR. I can give a somewhat authoritative rebuttal to this given my background in SR. An observer who is not in an inertial frame will not observe that the speed of light is constant over the entire universe. In your case, the moving observer is not in an inertial frame. So he will not observe a constant speed of light. The observer must use some type of accelerometer to determine if he is in an inertial frame. The observer is in an inertial frame only if his accelerometer says zero in all directions. If the accelerometer is does not say zero in all directions, then he is not in an inertial frame. If the observer is in an inertial frame, then he will find that the speed of light is constant all over the universe and for all time that he remains in the inertial frame. I have done several problems for the special case of linear acceleration in one direction. I do not know how applicable it is in your circular motion case. I suspect the answer is the same. However, I will know when I am further along in GR. I think it may be helpful to you for me to explain the linear acceleration case, which I have studied exhaustively. If the observer is in a state of constant acceleration in one direction, then the speed of light increases in the direction of his acceleration and decreases in the direction opposite his acceleration. That is, time speeds up for large distances in the direction he is accelerating and slows down for large distances opposite the direction he is accelerating. The observer can determine his acceleration using an accelerometer. I went through this in another post. However, review time. Three types of accelerometer are a weight scale, a Sagnac cavity and a Foucault spring-bob. If the observer measures a nonzero acceleration using any accelerometer, he should not be surprised to see the speed of light change at large distances from him. For local measurements, the speed of light is constant. However, the distances over which a measurement can be local decrease with acceleration. An observer that is accelerating means an observer that is under the influence of a nongravitational force. If there is a nongravitational force in the situation, then it has to be measured for each proposed observer. Only the observer that is subject to a zero total force can see the speed of light as exactly constant. The observers in noninertial frames will observe phenomena consistent with a changing speed of light. The postulates of special relativity, as described by Einstein, only apply to an observer in an inertial frame. The speed of light relative to the any point on an inertial frame is zero. Einstein was extremely explicit about it. The mirrors in the Michaelson-Morley experiment were not fixed on the points of the inertial frame, as Einstein defined them. That explains some of the "paradoxes" some people like to discuss, here. The tricky part of many SR problems is to determine which devices in the problem are nailed to the points of an inertial frame. That is the situation in SR. Ask someone else about GR.
From: eric gisse on 5 May 2010 21:09
Darwin123 wrote: [....] There's always some poor sumbitch who thinks he'll be the one to teach the Seppala. |