Relativity Example
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From: Daryl McCullough on 9 Jul 2010 09:01 This post has a completely worked out example of time dilation and length contraction, showing that it is perfectly consistent for each frame to view clocks in the other frame to be time-dilated. But the key fact is that relativity of simultaneity is an *essential* feature to make SR work. Without that, it really is inconsistent to believe in mutual time dilation. For colp: that's the sense in which he has an oversimplified (inconsistent) view of relativity: He takes into account time dilation, but does *not* take into account the relativity of simultaneity. He's assuming that clocks that are synchronized in one frame are also synchronized in another frame. The inconsistency that he therefore derives is not an inconsistency of SR, but of his own theory of relativity. Suppose you have two clocks C1 and C2 at rest in frame F, a distance of 52 light-minutes apart, with C1 to the left of C2. They are synchronized in that frame. Two other clocks, D1 and D2 are at rest in frame F', also at a distance of 52 light-minutes apart (as measured in F'), with D1 to the left of D2. They are synchronized in that frame. Each clock is moving at a speed of 0.866 c to the right, relative to frame F. Let's identify three different events: e1: clock D1 passes clock C1. e2: clock D1 passes clock C2. e3: clock D2 passes clock C2. Let's assume that at event e1, both D1 and C1 show time 12:00. Then the Lorentz transformations predict the following times for the events: e1: D1 shows 12:00, C1 shows 12:00. e2: D2 shows 11:30, C2 shows 12:30. e3: D1 shows 12:30, C2 shows 1:00. Now, if you just look at events e1 and e3, you could reason as follows: D1 advances by 30 minutes between e1 and e3, but clocks C1 and C2 advance by 1 hour. So D1 is running slow by a factor of 2. If you just look at events e2 and e3, you could reason as follows: C2 advances by 30 minutes between e2 and e3, but clocks D1 and D2 advance by 1 hour. So C2 is running slow by a factor of 2. These two analyses reach opposite conclusions. Does that mean that facts e1, e2 and e3 on which the analyses are based are contradictory? Absolutely not! To be contradictory means that it can't happen, and we can arrange the settings on clocks to make these three facts all true. Possibility 1: According to frame F At time 12:00 we have the following situation: C1=12:00........................C2=12:00 D1=12:00........D2=11:15 At time 12:30 we have the following situation: C1=12:30........................C2=12:30 .................D1=12:15........D2=11:30 At time 1:00 we have the following situation: C1=1:00.........................C2=1:00 .................................D1=12:30........D2=11:45 So the frame F explanation of what happened is: (1) Clocks D1 and D2 are running slow by a factor of 2. (2) The distance between them is only half as large as the distance between clocks C1 and C2. (3) Clocks D1 and D2 are not synchronized in frame F: D2 is running 45 minutes behind D1. So that's a consistent explanation of all three events, but it involves the principles of time dilation, length contraction and relativity of simultaneity (clocks that are synchronized in one frame may not be synchronized in another frame) Even though this is a consistent explanation, does it treat the frame of clocks C1 and C2 as a "preferred frame"? No, because we can just as well look at things from the point of view of frame F' Possibility 2: According to frame F' At time 11:30 we have the following situation: .................................C1=11:45........C2=12:30 .................D1=11:30........................D2=11:30 At time 12:00 we have the following situation: .................C1=12:00........C2=12:45 .................D1=12:00........................D2=12:00 At time 12:30 we have the following situation: C1=12:15........C2=1:00 .................D1=12:30........................D2=12:30 So the frame F' explanation of what happened is: (1) Clocks C1 and C2 are running slow by a factor of 2. (2) The distance between them is only half as large as the distance between clocks D1 and D2. (3) Clocks C1 and C2 are not synchronized in frame F: C1 is running 45 minutes behind C2. The facts about the three events are *consistent*, because we can come up a consistent situation that explains those facts. But time dilation and length contraction are *relative*, because each frame views the other frame as the one that is dilated/contracted. -- Daryl McCullough Ithaca, NY
From: Inertial on 9 Jul 2010 09:14 "Daryl McCullough" wrote in message news:i176j301d65(a)drn.newsguy.com... > >This post has a completely worked out example of time dilation and length >contraction, showing that it is perfectly consistent for each frame to view >clocks in the other frame to be time-dilated. But the key fact is that >relativity of simultaneity is an *essential* feature to make SR work. >Without >that, it really is inconsistent to believe in mutual time dilation. > >For colp: that's the sense in which he has an oversimplified (inconsistent) >view >of relativity: He takes into account time dilation, but does *not* take >into >account the relativity of simultaneity. He's assuming that clocks that are >synchronized in one frame are also synchronized in another frame. The >inconsistency that he therefore derives is not an inconsistency of SR, but >of >his own theory of relativity. Exactly what I've been telling him for post after post after post. Nice post Daryl.
From: Inertial on 9 Jul 2010 09:16 "Daryl McCullough" wrote in message news:i176j301d65(a)drn.newsguy.com... >Suppose you have two clocks C1 and C2 at rest in frame F, a distance of 52 >light-minutes apart, with C1 to the left of C2. They are synchronized in >that >frame. [snip good stuff] All this is pretty much the same example I've given previously (to Colp and others), showing how RoS can give you mutual time dilation:):) Unfortunately, I'm sure it will be equally misunderstood or ignored by them
From: kenseto on 9 Jul 2010 20:38 On Jul 9, 9:01 am, stevendaryl3...(a)yahoo.com (Daryl McCullough) wrote: > This post has a completely worked out example of time dilation and length > contraction, showing that it is perfectly consistent for each frame to view > clocks in the other frame to be time-dilated. But the key fact is that > relativity of simultaneity is an *essential* feature to make SR work. Without > that, it really is inconsistent to believe in mutual time dilation. > > For colp: that's the sense in which he has an oversimplified (inconsistent) view > of relativity: He takes into account time dilation, but does *not* take into > account the relativity of simultaneity. He's assuming that clocks that are > synchronized in one frame are also synchronized in another frame. The > inconsistency that he therefore derives is not an inconsistency of SR, but of > his own theory of relativity. > > Suppose you have two clocks C1 and C2 at rest in frame F, a distance of 52 > light-minutes apart, with C1 to the left of C2. They are synchronized in that > frame. > > Two other clocks, D1 and D2 are at rest in frame F', also at a distance of 52 > light-minutes apart (as measured in F'), with D1 to the left of D2. They are > synchronized in that frame. Each clock is moving at a speed of 0.866 c to the > right, relative to frame F. > > Let's identify three different events: > > e1: clock D1 passes clock C1. > e2: clock D1 passes clock C2. > e3: clock D2 passes clock C2. > > Let's assume that at event e1, both D1 and C1 show time 12:00. Then the Lorentz > transformations predict the following times for the events: > > e1: D1 shows 12:00, C1 shows 12:00. > e2: D2 shows 11:30, C2 shows 12:30. > e3: D1 shows 12:30, C2 shows 1:00. > > Now, if you just look at events e1 and e3, you could reason as follows: > D1 advances by 30 minutes between e1 and e3, but clocks C1 and C2 advance by 1 > hour. So D1 is running slow by a factor of 2. > > If you just look at events e2 and e3, you could reason as follows: > C2 advances by 30 minutes between e2 and e3, but clocks D1 and D2 advance by 1 > hour. So C2 is running slow by a factor of 2. > > These two analyses reach opposite conclusions. Does that mean that facts e1, e2 > and e3 on which the analyses are based are contradictory? Absolutely not! To be > contradictory means that it can't happen, and we can arrange the settings on > clocks to make these three facts all true. > > Possibility 1: According to frame F > At time 12:00 we have the following situation: > > C1=12:00........................C2=12:00 > D1=12:00........D2=11:15 > > At time 12:30 we have the following situation: > > C1=12:30........................C2=12:30 > ................D1=12:15........D2=11:30 > > At time 1:00 we have the following situation: > > C1=1:00.........................C2=1:00 > ................................D1=12:30........D2=11:45 > > So the frame F explanation of what happened is: > (1) Clocks D1 and D2 are running slow by a factor of 2. > (2) The distance between them is only half as large as the distance between > clocks C1 and C2. > (3) Clocks D1 and D2 are not synchronized in frame F: D2 is running 45 minutes > behind D1. > > So that's a consistent explanation of all three events, but it involves the > principles of time dilation, length contraction and relativity of simultaneity > (clocks that are synchronized in one frame may not be synchronized in another > frame) > > Even though this is a consistent explanation, does it treat the frame of clocks > C1 and C2 as a "preferred frame"? No, because we can just as well look at things > from the point of view of frame F' > > Possibility 2: According to frame F' > At time 11:30 we have the following situation: > > ................................C1=11:45........C2=12:30 > ................D1=11:30........................D2=11:30 > > At time 12:00 we have the following situation: > > ................C1=12:00........C2=12:45 > ................D1=12:00........................D2=12:00 > > At time 12:30 we have the following situation: > > C1=12:15........C2=1:00 > ................D1=12:30........................D2=12:30 > > So the frame F' explanation of what happened is: > (1) Clocks C1 and C2 are running slow by a factor of 2. > (2) The distance between them is only half as large as the distance between > clocks D1 and D2. > (3) Clocks C1 and C2 are not synchronized in frame F: C1 is running 45 minutes > behind C2. > > The facts about the three events are *consistent*, because we can come up a > consistent situation that explains those facts. But time dilation and length > contraction are *relative*, because each frame views the other frame as the one > that is dilated/contracted. No this is wrong....you ignoreds the fact that the clocks in F and F' are running at different rates as follows: 1. If the clocks in F is truly running at a faster rate than the F' clocks then the F' clock is truly running slower than the F clocks. 2. If the clocks in F' frame is truly running at a faster rate than the F clocks then the F clocks are truly running slower than the F' clock. You can choose one of the above possibilities but not both at the same time. What this means is that the SR concept of relativity of simultaneity is bogus and besides it violates the SR postulate: the isotropy of the speed of light in all frames. Ken Seto > > -- > Daryl McCullough > Ithaca, NY
From: Inertial on 9 Jul 2010 22:08
"kenseto" wrote in message news:7b1ddc11-90eb-4505-b421-a544b1526a23(a)k39g2000yqb.googlegroups.com... > No this is wrong.... Nope >you ignoreds the fact that the clocks in F and F' > are running at different rates as follows: No he didn't [snip nonsense and lies] Nothing left. Really Ken .. you are WAY out of your depth . .Why do continue to embarrass yourself like this? |