Relativity Example
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From: harald on 10 Jul 2010 07:08 On Jul 9, 3:16 pm, "Inertial" <relativ...(a)rest.com> wrote: > "Daryl McCullough" wrote in messagenews: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] Yes nice presentation - easy to understand! > 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 I have given similar examples in the past, but not as simple as this. And yes, they will be equally misunderstood or ignored by the hardened cranks; but they can just make the difference for some people (incl. silent onlookers) to suddenly "get it". Harald
From: kenseto on 10 Jul 2010 08:39
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. OK this is an assumption. > e2: D2 shows 11:30, C2 shows 12:30 How do you use the LT to get these different times? Besides, D2 cannot show less time than 12:00. It must agree with D1 which shows 12:30 at e2. > e3: D1 shows 12:30, C2 shows 1:00. Wrong when D2 passes C2: D1 ahows 12:00 and C2 shows 12:00 The rest of your post is based on your wrong assumptions as shown above. Ken Seto > > 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 |