Twins Paradox doesn't add up with light
in [Relativity]
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From: DSeppala on 6 May 2010 16:46 On May 5, 8:09 pm, eric gisse <jowr.pi.nos...(a)gmail.com> wrote: > Darwin123 wrote: > > [....] > > There's always some poor sumbitch who thinks he'll be the one to teach the > Seppala. In the problem I posted there are N identical segments as the twin moves around the circumference of a circle. Two light beams leave the same point in space at the same time (start of twin's travel), and both beams meet again at the same time at the point where the traveling twin returns. When the traveling twin returns to the start position the traveling twin discovers that one beam traveled a far greater distance than the other beam. Why does the traveling twin say that one light beam traveled faster than the other light beam? And why does the traveling twin reverse his view on which beam travels faster? Or does he conclude that his measurements of time and distance don't add up. Bet you think you know the answer but of course you won't post it to demonstrate your knowledge and to enlighten all of us. Or maybe you don't have a clue. Your post will demonstrate your physics prowess or lack thereof. David Bastrop, TX
From: DSeppala on 6 May 2010 16:53 On May 5, 3:39 pm, Darwin123 <drosen0...(a)yahoo.com> wrote: > 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. The moving twin knows he is accelerating, albeit very slowly. In the problem I posted two light beams leave the same point in space at the same time and the two beams meet at the same point in space and time when the traveling twin returns. At that point the traveling twin discovers that one beam traveled a much longer distance than the other light beam. Why does he say light traveling in a vacuum can travel at different speeds depending on whether he accelerates or not, even when the acceleration is as low as one micron per light-year of arc length? Or does he simply say that his measurements of time and distance are wrong? David Bastrop, TX
From: PD on 6 May 2010 16:59 On May 6, 3:53 pm, DSeppala <dsepp...(a)austin.rr.com> wrote: > On May 5, 3:39 pm, Darwin123 <drosen0...(a)yahoo.com> wrote: > > > > > 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. > > The moving twin knows he is accelerating, albeit very slowly. Yes, indeed, and this makes all the difference. It's the shape of the worldline that determines how much slower the clock there runs. You may want to check out the very simple explanation of this in Penrose's book Road to Reality. > In the > problem I posted two light beams leave the same point in space at the > same time and the two beams meet at the same point in space and time > when the traveling twin returns. At that point the traveling twin > discovers that one beam traveled a much longer distance than the other > light beam. Why does he say light traveling in a vacuum can travel at > different speeds depending on whether he accelerates or not, even when > the acceleration is as low as one micron per light-year of arc > length? Or does he simply say that his measurements of time and > distance are wrong? > David > Bastrop, TX
From: BURT on 6 May 2010 17:34 On May 6, 1:59 pm, PD <thedraperfam...(a)gmail.com> wrote: > On May 6, 3:53 pm, DSeppala <dsepp...(a)austin.rr.com> wrote: > > > > > > > On May 5, 3:39 pm, Darwin123 <drosen0...(a)yahoo.com> wrote: > > > > 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.. > > > The moving twin knows he is accelerating, albeit very slowly. > > Yes, indeed, and this makes all the difference. It's the shape of the > worldline that determines how much slower the clock there runs. > > You may want to check out the very simple explanation of this in > Penrose's book Road to Reality. > > > > > In the > > problem I posted two light beams leave the same point in space at the > > same time and the two beams meet at the same point in space and time > > when the traveling twin returns. At that point the traveling twin > > discovers that one beam traveled a much longer distance than the other > > light beam. Why does he say light traveling in a vacuum can travel at > > different speeds depending on whether he accelerates or not, even when > > the acceleration is as low as one micron per light-year of arc > > length? Or does he simply say that his measurements of time and > > distance are wrong? > > David > > Bastrop, TX- Hide quoted text - > > - Show quoted text -- Hide quoted text - > > - Show quoted text - If the station is aging faster then how can the passing train see the station's clock running slower in every moment? Mitch Raemsch
From: Darwin123 on 6 May 2010 21:14
On May 6, 4:46 pm, DSeppala <dsepp...(a)austin.rr.com> wrote: > On May 5, 8:09 pm, eric gisse <jowr.pi.nos...(a)gmail.com> wrote: > > > Darwin123 wrote: > > > [....] > > > There's always some poor sumbitch who thinks he'll be the one to teach the > > Seppala. > > In the problem I posted there are N identical segments as the twin > moves around the circumference of a circ ..... I answered your question in good faith, and without sarcasm. Instead of addressing my answer, you are addressing Gisse's sarcastic remark. Apparently, he has had experience with you before. > Or does he conclude that his measurements of time and distance >don't add up. The above is a leading statement. Superficially, it appears that this is the answer you are looking for and you won't accept anything else. Since you are an adult with an inquiring mind, this can't be true. You will obviously look at all proposed solutions, and examine them in their own merits. You won't dismiss all suggestions on the basis of your omniscient physical instincts. > Bet you think you know the answer but of course you won't >post it to demonstrate your knowledge and to enlighten all of us. I posted your answer. I have enlightened you. The answer is acceleration. The moving observer is undergoing a nonzero acceleration, caused an unbalanced external force on some of his measuring devices. The force in this case is the centripetal force. The stationary twin is not undergoing an acceleration, caused by an unbalanced external force. One way to think of the accelerometer is in terms of a 3 dimensional bubble balance. Einstein defined his "inertial frame" as just that. It is a frame, where at every node there is a ruler and a clock. A hypothetical carpenter that builds such a frame has to use a bubble balance in all three dimensions. A bubble balance is placed at each node, in addition to the ruler and the clock. The device isn't part of the frame if all three orthogonal bubble balances aren't centered. If there is an outside force acting on the clock or ruler, it will show in by a shift of the bubble in one of the three balances. At each observer origin, place a set of three bubble balances. Assume that one bubble balance faces the radial direction, one bubble balance faces the direction of motion, and one bubble balance is orthogonal to the other three. Place the third in a direction orthogonal to the other two. The shift of the bubbles in these orthogonal bubble balances shows quite clearly what is happening. The moving twin has a bubble shift in the radial direction. Therefore, he can't validly use the Lorentz time dilation formula or the Lorentz length contraction formula that you used in calculating what he sees. The stationary has centered bubbles on all three components, including the bubble corresponding to the radial direction. Therefore, he can use the Lorentz time dilation formula that you used in calculating what he sees. Slightly more complicated analysis is necessary if the three bubble balances are exactly lined up with the the radial direction. However, the answer comes out nearly the same. The presence of an external force acting on a travelers measuring instruments negates the use of the simple formulas often taught to undergraduate physics students. A device that is basically analogous to a bubble balance, with maybe higher precision, is necessary to determine what instruments can be considered part of an "inertial frame." What was left out of your scenario was an accelerometer (i.e., the bubble balance). We will see how well you address a valid answer to your question. > Or maybe you don't have a clue. Gisse probably understands. I can't be sure, however (sorry, Eric). However, it doesn't matter. I am the next sucker. Presently, I am entertaining the idea that you were asking a question about something you don't know and which you still hope to get an answer. I will be very happy if you prove Gisse wrong. It doesn't look likely. |