Twins Paradox doesn't add up with light
in [Relativity]
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From: Darwin123 on 6 May 2010 21:29 On May 6, 4:53 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. 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? As his acceleration decreases, the time he needs to turn around increases in both frames. So even if he accelerates as slowly as you claim he does, the time needed to reverse direction becomes extremely long. The two effects cancel each other out. A small acceleration has to be exerted over a longer time. Therefore, the small acceleration has a much longer time over which to act. So the affect of a small change in the speed of light acts over a longer time, as seen by the traveling twin. Another way to put it: The twin can go very slowly, or the radius of the circle be very big. If either is true, the length of the round trip will be very big. What matters is not the affect of the acceleration at any one point in time. What matters is the accumulated affect of the acceleration over the time necessary to complete the round trip. In the equivalent textbook problem, the answers come out as integrals over the total round trip. The integrals end up canceling each other out to first order. What I mean by first order is the a priori assumption that the moving traveler isn't squashed by the horrific force needed in the case of a very fast moving traveler. If you want a quantitative calculation of the possible error caused by the squish factor, you have to go through the entire calculation. However, the squish factor doesn't matter for your initial question. What makes the traveling twin different from the stationary twin is the acceleration. Less acceleration, longer round trip time. The two factors cancel each other out, other that what I call the squish factor. I should have copyrighted the phrase "squish factor" before I posted it <sigh> >Or does he simply say that his measurements of time and > distance are wrong? Apparently, you won't accept any other answer. Reality: The traveling twin does not have to "simply" say his measurements of time and distance are wrong. If he thought to bring an accelerometer with him, he can state with authority that his measurements of time and distance are wrong. Or at least that they were not made with instruments fixed in an inertial frame. Being a true inquiring mind, you will consider this possible answer.
From: DSeppala on 6 May 2010 22:05 On May 6, 8:29 pm, Darwin123 <drosen0...(a)yahoo.com> wrote: > On May 6, 4:53 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. 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? > > As his acceleration decreases, the time he needs to turn around > increases in both frames. So even if he accelerates as slowly as you > claim he does, the time needed to reverse direction becomes extremely > long. The two effects cancel each other out. > A small acceleration has to be exerted over a longer time. > Therefore, the small acceleration has a much longer time over which to > act. So the affect of a small change in the speed of light acts over a > longer time, as seen by the traveling twin. > Another way to put it: > The twin can go very slowly, or the radius of the circle be very > big. If either is true, the length of the round trip will be very big. > What matters is not the affect of the acceleration at any one point in > time. What matters is the accumulated affect of the acceleration over > the time necessary to complete the round trip. > In the equivalent textbook problem, the answers come out as > integrals over the total round trip. The integrals end up canceling > each other out to first order. What I mean by first order is the a > priori assumption that the moving traveler isn't squashed by the > horrific force needed in the case of a very fast moving traveler. If > you want a quantitative calculation of the possible error caused by > the squish factor, you have to go through the entire calculation. > However, the squish factor doesn't matter for your initial > question. What makes the traveling twin different from the stationary > twin is the acceleration. Less acceleration, longer round trip time. > The two factors cancel each other out, other that what I call the > squish factor. > I should have copyrighted the phrase "squish factor" before I > posted it <sigh>>Or does he simply say that his measurements of time and > > distance are wrong? > > Apparently, you won't accept any other answer. Reality: > The traveling twin does not have to "simply" say his measurements > of time and distance are wrong. If he thought to bring an > accelerometer with him, he can state with authority that his > measurements of time and distance are wrong. Or at least that they > were not made with instruments fixed in an inertial frame. > Being a true inquiring mind, you will consider this possible > answer.- Hide quoted text - > > - Show quoted text - Let's say he has every piece of measuring equipment there is. Why does the traveling twin say that if the speed of light is constant and independent of the velocity of the light source in a vacumm that light travels two different distances during the same time interval? In the problem two beams leave a common point in space at the same time, and they return to a common point at the same time, yet the traveling twin says that one beam travels a different distance than the other beam, and that the speed of light is independent of the velocity of the light source. David That's what I don't understand.
From: BURT on 6 May 2010 22:09 On May 6, 7:05 pm, DSeppala <dsepp...(a)austin.rr.com> wrote: > On May 6, 8:29 pm, Darwin123 <drosen0...(a)yahoo.com> wrote: > > > > > > > On May 6, 4:53 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. 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? > > > As his acceleration decreases, the time he needs to turn around > > increases in both frames. So even if he accelerates as slowly as you > > claim he does, the time needed to reverse direction becomes extremely > > long. The two effects cancel each other out. > > A small acceleration has to be exerted over a longer time. > > Therefore, the small acceleration has a much longer time over which to > > act. So the affect of a small change in the speed of light acts over a > > longer time, as seen by the traveling twin. > > Another way to put it: > > The twin can go very slowly, or the radius of the circle be very > > big. If either is true, the length of the round trip will be very big. > > What matters is not the affect of the acceleration at any one point in > > time. What matters is the accumulated affect of the acceleration over > > the time necessary to complete the round trip. > > In the equivalent textbook problem, the answers come out as > > integrals over the total round trip. The integrals end up canceling > > each other out to first order. What I mean by first order is the a > > priori assumption that the moving traveler isn't squashed by the > > horrific force needed in the case of a very fast moving traveler. If > > you want a quantitative calculation of the possible error caused by > > the squish factor, you have to go through the entire calculation. > > However, the squish factor doesn't matter for your initial > > question. What makes the traveling twin different from the stationary > > twin is the acceleration. Less acceleration, longer round trip time. > > The two factors cancel each other out, other that what I call the > > squish factor. > > I should have copyrighted the phrase "squish factor" before I > > posted it <sigh>>Or does he simply say that his measurements of time and > > > distance are wrong? > > > Apparently, you won't accept any other answer. Reality: > > The traveling twin does not have to "simply" say his measurements > > of time and distance are wrong. If he thought to bring an > > accelerometer with him, he can state with authority that his > > measurements of time and distance are wrong. Or at least that they > > were not made with instruments fixed in an inertial frame. > > Being a true inquiring mind, you will consider this possible > > answer.- Hide quoted text - > > > - Show quoted text - > > Let's say he has every piece of measuring equipment there is. Why > does the traveling twin say that if the speed of light is constant and > independent of the velocity of the light source in a vacumm that light > travels two different distances during the- Hide quoted text - > > - Show quoted text -... > > read more » You can leave light behind in space. You can get behind it. In both these cases it is not moving much at all. Mitch Raemsch
From: eric gisse on 7 May 2010 06:05 DSeppala 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 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 The "I dare you to solve this problem" gambit works a few times, but when you repost the same class of problem time after time year after year for close to 15 years straight it gets a bit ooold. Riddle me this - why are you incapable of solving these problems yourself?
From: Darwin123 on 7 May 2010 12:31
On May 6, 10:05 pm, DSeppala <dsepp...(a)austin.rr.com> wrote: > On May 6, 8:29 pm, Darwin123 <drosen0...(a)yahoo.com> wrote: > > > On May 6, 4:53 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 > Let's say he has every piece of measuring equipment there is. Why > does the traveling twin say that if the speed of light is constant and > independent of the velocity of the light source in a vacumm that light > travels two different distances during the same time interval? I already addressed that. However, to repeat the obvious: The traveling twin does not say that the speed of light is constant in every region of space. The traveling twin is not in an inertial frame, so the postulates of special relativity do not apply to him. He knows he is not in an inertial frame because his accelerometer, whatever form it is in, shows a nonzero acceleration. The traveling twin can observe the speed of light as constant only over a small spacial region near him. At large distances from him, he observes the speed of light as different than that in that small region of space. Suppose both twins have a clock that is based on a pulse of light bouncing between two mirrors. Every time it hits a detector, it blips. The traveling twin sees the rate of blip of his traveling clock being at a certain rate near him. If stationary twin is within the small region of space that surrounds the traveling twin, the blip rate will be the same for both clocks. However, in your scenario, the two twins are at times very far apart. At the time that both twins are on opposite sides of the circle, the speed of light is very different for the two clocks. The traveling twin observes the blip rate of the stationary twin as much faster than his own blip rate. Thus, he concludes that the speed of light is bigger for the stationary twin while on the opposite side of the circle. The faster blip rate doesn't bother the traveling twin because his accelerometer says he has a nonzero acceleration. The Lorentz time dilation shouldn't apply to a distant object when the accelerometer says nonzero. The stationary twin sees the blip rate of the stationary twin as slower than his own. However, his accelerometer says zero. So he expects that the Lorentz time dilation to apply over all space and time. For the stationary twin, the speed of light is constant everywhere. The speed of light is constant over all space only when the accelerometer says zero. The traveling twin spends a lot of time at the far point of the circle. The smaller the acceleration, the longer he spends at distances far from the stationary twin. I'll give you an estimate of the region over which the traveling twin can expect the speed of light to be constant to first order. Let "L" be the radius of a sphere around the traveling twin where the speed of light determined by the traveling twin is nonzero. Then, gL/c^2<<1 where g is the acceleration measured by the traveling twin, and c is the speed of light. Of course, the above equation is an approximation. "First order" means that assuming the speed of light is constant will cause fractional errors on the order of "gL/c^2". Please note that one only has to to be concerned with acceleration if "L<<R", where "R" is the radius of the circle traveled. If the velocity of the traveling twin relative to the center of the circle is "v", and "v<<c", then g=v^2/R, just as in Newtonian theory. Also note that I am ignoring the "squish". If "g" is too big, the measuring instruments will be warped by the centripetal force. Unmentioned in your scenario is the reason the traveling twin is traveling in a circle. He has to be using some type of rocket, or maybe a rope, to force his trajectory in a circle. He and his instruments feel "g" forces, which we both are ignoring for now. If g is too big, the clocks and rulers don't work. The traveling twin is dead. So there are pragmatic limits on "g". "g" has to be fairly small. So the time that the round trip takes has to be fairly big. So you can't let the round trip time go to the limit of zero. The traveling twin is going to take a long time to meet his stationary brother again. Unless we are talking about small people. These "pragmatic limits" can be addressed by using instruments that are very small, or by using certain mechanical corrections in the calculations. However, you implied that the instruments were suitably small by ignoring the centripetal "squish." So I am also reasonably that all your instruments are small enough to fit in the small region where the speed of light is constant. In my analysis, I am assuming that the effect of gravitational mass is negligible. As long as gravitational can be ignored, we are in the realm of special relativity. The precise way to analyze the effect of acceleration and gravity involves general relativity. Our discussion hasn't left special relativity. However, we are just on the border to general relativity. Since I admit to not fully understanding general relativity yet, you will kindly refrain from dragging gravity in the discussion. I am sure of what I am saying up to now, in terms of special relativity. In SR, acceleration is important. No matter what anybody else says |:-) In the > problem two beams leave a common point in space at the same time, and > they return to a common point at the same time, yet the traveling twin > says that one beam travels a different distance than the other beam, > and that the speed of light is independent of the velocity of the > light source. > David > That's what I don't understand. |