Twins Paradox doesn't add up with light
in [Relativity]
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From: DSeppala on 3 May 2010 18:17 The typical analysis of the twin's paradox does a switching of frame views in which the traveling twin simply disregards the measurements he makes on the first leg of his journey. If the twin's paradox is done with the traveling twin moving around the circumference of a circle, and with the traveling twin measuring the propagation of light throughout his journey, the traveling twin must come to the conclusion that his measurements of time and distance are wrong if the speed of light is independent of the velocity of the light source. Here's the scenario. Let there be a circle of extremely large radius. At the center of this circle let there be a light source that emits a flash of light in all directions once a second. On the circumference of this circle, let there be a stationary twin at 0 degrees and let the traveling twin start his journey around the circle when the first light pulse arrives at that position on the circumference of the circle. Let the traveling twin move around the circumference of the circle at a constant speed of V = 0.866c. During his trip around the circle, the traveling twin carries a rod in his frame which he measures to be a length of 0.25 light-seconds plus or minus some small delta in length. The rod has a light source at one end and a mirror at the other end. When light is emitted on this traveling twin's rod, the light travels down the rod to the end and reflects off the mirror to return to the traveling twin's position 0.5 seconds plus or minus some small delta later as measured by the traveling twin. Let the radius of the circle be extremely large so that the traveling twin is almost traveling in a straight line, or in other words, almost in an inertial reference frame that when the first pulse is received and the journey begins the traveling twin is almost in an inertial reference frame that is moving at V = 0.866c relative to the center of the circle and the stationary twin. Let N pulses from the center of the circle reach the stationary twin during the time the traveling twin travels one complete circumference around the circle returning back to the stationary twin's position. Let there be a mirror positioned above the stationary twin a distance of N/2 light-seconds from the stationary twin as measured perpendicular to the plane of the circle and the motion of the traveling twin. When the experiment starts, the first light pulse from the center of the circle reaches the zero degree point on the circumference of the circle when both the traveling twin and the stationary twin are at this same point in space. When this event occurs, the stationary twin sends a light pulse upward, perpendicular to the plane of the circle. This light travels for N/2 seconds, hits the mirror and returns to the position of the stationary twin N seconds after the start of the experiment and just as the traveling twin returns to the starting position. When the experiment starts, the moving twin also sends a pulse along his rod. It hits the return mirror at the end of the traveling twins rod and returns to the traveling twin's position 0.5 seconds later as measured by the traveling twin's clock (given information). Since the moving twin is almost moving in a straight line, we can use the Lorentz transformations to compute when the traveling twin will receive the second pulse that was emitted from the center of the circle. With V = 0.866c we find that the traveling twin receives this second pulse 0.5 seconds after receiving the first pulse. So during the first and second of N pulses that are received as the traveling twin moves around the circumference of the circle, when the first pulse is received by the traveling twin, the traveling twin's light source emits a pulse that reflects off the traveling twin's mirror and returns to the traveling twin just as the traveling twin receives the second pulse that was emitted from the center of the circle. Since the traveling twin is almost in an inertial reference frame (for very large R), he measures that his light has traveled 0.5 light-seconds (plus or minus some very small delta) between receiving the first and second pulses that were emitted from the center of the circle. Now, the traveling twin repeats this for each of subsequent pulses he receives. Sending a pulse along his rod and measuring that the return pulse arrives 0.5seconds later just as the next pulse emitted from the center of the circle arrives at the same location that the traveling twin is at. During each of the N pulses, he measures that the light traveled approximately 0.5 light-seconds (constant speed of light). Thus when he returns to the starting point where the stationary twin is at, he has measured that during each of the N pulses, light has traveled 0.5 light-seconds (plus or minus some small delta), and therefore during the entire trip, light as measured by the traveling twin has traveled a distance of N* 0.5 light-seconds. However, the traveling twin also measures that the light emitted from the stationary twin's position at the start of the journey returns just as the traveling twin returns, and that this emitted light traveled at least a distance of N * 1 light-second since it hit a mirror N/2 light-seconds above the stationary twin and returned back to the stationary twin. So since the traveling twin's light started at time t0 at the beginning of the experiment, and the stationary twin's light was emitted at that exact same time from the same position in space, and since the light returned to their common location at the same time the traveling twin returned, the traveling twin must either conclude that some of his measurements of length and time are incorrect or the speed of light is not constant and independent of the velocity of the light source. The traveling twin notes that each of the N measurements he made were done exactly the same, and that there is nothing special about any particular position in space. So if the traveling twin concludes that there is an error in his measurements of time and space, then each of the N measurements he made must share this common error. With the traveling twin moving in almost a straight line, and having almost the same measurements as a co-moving inertial reference frame as when the experiment starts, the traveling twin must also conclude that the co-moving reference frame must have made the same error as he did since their measurements were virtually identical during the first and second pulses of the experiment when their velocities were virtually zero. Of course the traveling twin could conclude that light traveled at different speeds during the experiment, but that is contrary to the hypothesis that the speed of light in a vacuum is independent of the velocity of the light source. If the speed of light depends on the velocity of the light source and Newtonian concepts of time and distance are used with the notion of absolute space, then just as in the Michelson-Morley experiment, no conflicts between measurements taken in different frames occur. 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? Thanks David Seppala Bastrop, TX
From: BURT on 3 May 2010 19:05 On May 3, 3:17 pm, DSeppala <dsepp...(a)austin.rr.com> wrote: > The typical analysis of the twin's paradox does a switching of frame > views in which the traveling twin simply disregards the measurements > he makes on the first leg of his journey. If the twin's paradox is > done with the traveling twin moving around the circumference of a > circle, and with the traveling twin measuring the propagation of light > throughout his journey, the traveling twin must come to the conclusion > that his measurements of time and distance are wrong if the speed of > light is independent of the velocity of the light source. Here's the > scenario. > Let there be a circle of extremely large radius. At the center of > this circle let there be a light source that emits a flash of light in > all directions once a second. On the circumference of this circle, > let there be a stationary twin at 0 degrees and let the traveling twin > start his journey around the circle when the first light pulse arrives > at that position on the circumference of the circle. Let the > traveling twin move around the circumference of the circle at a > constant speed of V = 0.866c. During his trip around the circle, the > traveling twin carries a rod in his frame which he measures to be a > length of 0.25 light-seconds plus or minus some small delta in length. > The rod has a light source at one end and a mirror at the other end. > When light is emitted on this traveling twin's rod, the light travels > down the rod to the end and reflects off the mirror to return to the > traveling twin's position 0.5 seconds plus or minus some small delta > later as measured by the traveling twin. Let the radius of the circle > be extremely large so that the traveling twin is almost traveling in a > straight line, or in other words, almost in an inertial reference > frame that when the first pulse is received and the journey begins the > traveling twin is almost in an inertial reference frame that is moving > at V = 0.866c relative to the center of the circle and the stationary > twin. > Let N pulses from the center of the circle reach the stationary > twin during the time the traveling twin travels one complete > circumference around the circle returning back to the stationary > twin's position. Let there be a mirror positioned above the > stationary twin a distance of N/2 light-seconds from the stationary > twin as measured perpendicular to the plane of the circle and the > motion of the traveling twin. When the experiment starts, the first > light pulse from the center of the circle reaches the zero degree > point on the circumference of the circle when both the traveling twin > and the stationary twin are at this same point in space. When this > event occurs, the stationary twin sends a light pulse upward, > perpendicular to the plane of the circle. This light travels for N/2 > seconds, hits the mirror and returns to the position of the stationary > twin N seconds after the start of the experiment and just as the > traveling twin returns to the starting position. > When the experiment starts, the moving twin also sends a pulse > along his rod. It hits the return mirror at the end of the traveling > twins rod and returns to the traveling twin's position 0.5 seconds > later as measured by the traveling twin's clock (given information). > Since the moving twin is almost moving in a straight line, we can use > the Lorentz transformations to compute when the traveling twin will > receive the second pulse that was emitted from the center of the > circle. With V = 0.866c we find that the traveling twin receives this > second pulse 0.5 seconds after receiving the first pulse. So during > the first and second of N pulses that are received as the traveling > twin moves around the circumference of the circle, when the first > pulse is received by the traveling twin, the traveling twin's light > source emits a pulse that reflects off the traveling twin's mirror and > returns to the traveling twin just as the traveling twin receives the > second pulse that was emitted from the center of the circle. Since > the traveling twin is almost in an inertial reference frame (for very > large R), he measures that his light has traveled 0.5 light-seconds > (plus or minus some very small delta) between receiving the first and > second pulses that were emitted from the center of the circle. > Now, the traveling twin repeats this for each of subsequent pulses > he receives. Sending a pulse along his rod and measuring that the > return pulse arrives 0.5seconds later just as the next pulse emitted > from the center of the circle arrives at the same location that the > traveling twin is at. During each of the N pulses, he measures that > the light traveled approximately 0.5 light-seconds (constant speed of > light). Thus when he returns to the starting point where the > stationary twin is at, he has measured that during each of the N > pulses, light has traveled 0.5 light-seconds (plus or minus some small > delta), and therefore during the entire trip, light as measured by the > traveling twin has traveled a distance of N* 0.5 light-seconds. > However, the traveling twin also measures that the light emitted > from the stationary twin's position at the start of the journey > returns just as the traveling twin returns, and that this emitted > light traveled at least a distance of N * 1 light-second since it hit > a mirror N/2 light-seconds above the stationary twin and returned back > to the stationary twin. So since the traveling twin's light started > at time t0 at the beginning of the experiment, and the stationary > twin's light was emitted at that exact same time from the same > position in space, and since the light returned to their common > location at the same time the traveling twin returned, the traveling > twin must either conclude that some of his measurements of length and > time are incorrect or the speed of light is not constant and > independent of the velocity of the light source. > The traveling twin notes that each of the N measurements he made > were done exactly the same, and that there is nothing special about > any particular position in space. So if the traveling twin concludes > that there is an error in his measurements of time and space, then > each of the N measurements he made must share this common error. With > the traveling twin moving in almost a straight line, and having almost > the same measurements as a co-moving inertial reference frame as when > the experiment starts, the traveling twin must also conclude that the > co-moving reference frame must have made the same error as he did > since their measurements were virtually identical during the first and > second pulses of the experiment when their velocities were virtually > zero. > Of course the traveling twin could conclude that light traveled at > different speeds during the experiment, but that is contrary to the > hypothesis that the speed of light in a vacuum is independent of the > velocity of the light source. > If the speed of light depends on the velocity of the light source > and Newtonian concepts of time and distance are used with the notion > of absolute space, then just as in the Michelson-Morley experiment, no > conflicts between measurements taken in different frames occur. > 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? > Thanks > David Seppala > Bastrop, TX When the train passes the station and sees its clock running slow how is the station going to age more than the train is if that's the case? Mitch Raemsch
From: artful on 4 May 2010 08:18 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.
From: Mike_Fontenot on 4 May 2010 04:23 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
From: BURT on 4 May 2010 15:41
On May 4, 1:23 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 A fast moving twin can move behind light with it inching ahead. Also he could travel ahead of light leaving light behind in space creating a temporary motion black hole behind it. Light and matter move in the absolute space frame that has a speed limit. Mitch Raemsch |