Twins Paradox doesn't add up with light
in [Relativity]
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From: BURT on 7 May 2010 15:42 On May 7, 9:31 am, Darwin123 <drosen0...(a)yahoo.com> wrote: > 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.- Hide quoted text - > > - Show quoted text - If the twin on a train passes the station and its clock for an interval will he see the station's clock running slow? And if so how can it be aging faster if that is the case? Mitch Raemsch; there is no Lost Time
From: Darwin123 on 7 May 2010 21:42 > 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 You keep on repeating your question, making the same mistake with slight semantic variations. Therefore, I'll say this four different ways: 1) To the traveling twin, the speed of light varies with position in space. It does not vary with the speed of the source, but it does vary with position. 2) The assumption that the speed of light is constant is not true for the traveling twin. However, it is still true that the speed of light is independent of the velocity of the source. 3) For an observer who is not in an inertial frame, the speed of light is not constant. 4) c'=c(1+gx/c^2) where x is the distance from the traveling twin in the direction of acceleration, c' is the speed of light measured by the traveling twin at position x, c is the speed of light of the stationary twin at all positions, and g is the acceleration as measured by the accelerometer. What is not to understand?
From: DSeppala on 8 May 2010 09:30 On May 7, 8:42 pm, Darwin123 <drosen0...(a)yahoo.com> wrote: > > 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 > > You keep on repeating your question, making the same mistake with > slight semantic variations. Therefore, I'll say this four different > ways: > 1) To the traveling twin, the speed of light varies with position > in space. It does not vary with the speed of the source, but it does > vary with position. > 2) The assumption that the speed of light is constant is not true > for the traveling twin. However, it is still true that the speed of > light is independent of the velocity of the source. > 3) For an observer who is not in an inertial frame, the speed of > light is not constant. > 4) c'=c(1+gx/c^2) > where x is the distance from the traveling twin in the direction of > acceleration, c' is the speed of light measured by the traveling twin > at position x, c is the speed of light of the stationary twin at all > positions, and g is the acceleration as measured by the accelerometer. > What is not to understand? So when Einstein states "... light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body" he really means that it is not propagated at a definite velocity c? Or was something lost in the translation? What source did you use to come up with the hypothesis that the speed of light is not constant as it travels through empty space, other than the notion of constant c conflicts with the twin's paradox? Thanks, David
From: DSeppala on 8 May 2010 21:56 On May 7, 11:31 am, Darwin123 <drosen0...(a)yahoo.com> wrote: > 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.- Hide quoted text - > > - Show quoted text - Einstein's theory has two stated postulates, one is that the speed of light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body. The other is that unsuccessful attempts to discover any motion of the earth relatively to the "light medium" suggest that the phenomena of electrodynamics as well as of mechanics possess no properties corresponding to the idea of absolute rest. Einstein states that the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good. You seem to take the constant speed of light postulate to mean that it is only constant in inertial frames and not valid for all frames of reference as Einstein stated. Where did your concept come from? We should note that Einstein states that the velocity of light is independent of the motion of the emitting body. I don't know if that is an error in the translation or not, or whether the word velocity had a different meaning a hundred years ago, but we all know that the velocity of light is dependent on the motion of the emitting body, whereas the accurate phrasing is that the speed of light is independent of the motion of the emitting body, but not the light's velocity (speed and direction). David
From: BURT on 8 May 2010 22:12
On May 8, 6:56 pm, DSeppala <dsepp...(a)austin.rr.com> wrote: > On May 7, 11:31 am, Darwin123 <drosen0...(a)yahoo.com> wrote: > > > > > > > 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.- Hide quoted text - > > > - Show quoted text - > > Einstein's theory has two stated postulates, one is that the speed of > light is always propagated in empty space with a definite velocity c > which is independent of the state of motion of the emitting body. The > other is that unsuccessful attempts to discover any motion of the > earth relatively to the "light medium" suggest that the phenomena of > electrodynamics as well as of mechanics possess no properties > corresponding to the idea of absolute rest. Einstein states that the > same laws of electrodynamics and optics will be valid for all frames > of reference for which the equations of mechanics hold good. > You seem to take the constant speed of light postulate to mean that > it is only constant in inertial frames and not valid for all frames of > reference as Einstein stated. Where did your concept come from? > We should note that Einstein states that the velocity of light is > independent of the motion of the emitting body. I don't know if that > is an error in the translation or not, or whether the word velocity > had a different meaning a hundred years ago, but we all know that the > velocity of light is dependent on the motion of the emitting body, > whereas the accurate phrasing is that the speed of light is > independent of the motion of the emitting body, but not the light's > velocity (speed and direction). > David- Hide quoted text - > > - Show quoted text - A twin in a train passing the station is said to see its clock running slow. But how can it age more if it is running slow? Mitch Raemsch |