If this is your first visit, be sure to check out the FAQ by clicking the link above. You may have to register before you can post: click the register link above to proceed. To start viewing messages, select the forum that you want to visit from the selection below. 


Thread Tools  Display Modes 
#17




Simplified Twin Paradox Resolution.
On Jan 7, 6:41 am, Vilas Tamhane wrote:
Koobee Wublee wrote: Instead of v, lets say (B = v / c) for simplicity. The earth is Point #0, outbound spacecraft is Point #1, and inbound spacecraft is Point #2. According to the Lorentz transform, relative speeds a ** B_00^2 = 0, speed of #0 as observed by #0 ** B_01^2 = B^2, speed of #1 as observed by #0 ** B_02^2 = B^2, speed of #2 as observed by #0 ** B_10^2 = B^2, speed of #0 as observed by #1 ** B_11^2 = 0, speed of #1 as observed by #1 ** B_12^2 = 4 B^2 / (1 B^2), speed of #2 as observed by #1 ** B_20^2 = B^2, speed of #0 as observed by #2 ** B_21^2 = 4 B^2 / (1 B^2), speed of #1 as observed by #2 ** B_22^2 = 0, speed of #2 as observed by #2 When Point #0 is observed by all, the Minkowski spacetime (divided by c^2) is: ** dt_00^2 (1 B_00^2) = dt_10^2 (1 B_10^2) = dt_20^2 (1 B_20^2) When Point #1 is observed by all, the Minkowski spacetime (divided by c^2) is: ** dt_01^2 (1 B_01^2) = dt_11^2 (1 B_11^2) = dt_21^2 (1 B_21^2) When Point #2 is observed by all, the Minkowski spacetime (divided by c^2) is: ** dt_02^2 (1 B_02^2) = dt_12^2 (1 B_12^2) = dt_22^2 (1 B_22^2) Where ** dt_00 = Local rate of time flow at Point #0 ** dt_01 = Rate of time flow at #1 as observed by #0 ** dt_02 = Rate of time flow at #2 as observed by #0 ** dt_10 = Rate of time flow at #0 as observed by #1 ** dt_11 = Local rate of time flow at Point #1 ** dt_12 = Rate of time flow at #2 as observed by #1 ** dt_20 = Rate of time flow at #0 as observed by #2 ** dt_21 = Rate of time flow at #1 as observed by #2 ** dt_22 = Local rate of time flow at Point #2 So, with all the pertinent variables identified, the contradiction of the twins paradox is glaring right at anyone with a thinking brain. shrug    From the Lorentz transformations, you can write down the following equation per Minkowski spacetime. Points #1, #2, and #3 are observers. They are observing the same target. ** c^2 dt1^2 ds1^2 = c^2 dt2^2 ds2^2 = c^2 dt3^2 ds3^2 Where ** dt1 = Time flow at Point #1 ** dt2 = Time flow at Point #2 ** dt3 = Time flow at Point #3 ** ds1 = Observed target displacement segment by #1 ** ds2 = Observed target displacement segment by #2 ** ds3 = Observed target displacement segment by #3 The above spacetime equation can also be written as follows. ** dt1^2 (1 B1^2) = dt2^2 (1 B2^2) = dt3^2 (1 B3^2) Where ** B^2 = (ds/dt)^2 / c^2 When #1 is observing #2, the following equation can be deduced from the equation above. ** dt1^2 (1 B1^2) = dt2^2 . . . (1) Where ** B2^2 = 0, #2 is observing itself Similarly, when #2 is observing #1, the following equation can be deduced. ** dt1^2 = dt2^2 (1 B2^2) . . . (2) Where ** B1^2 = 0, #1 is observing itself According to relativity, the following must be true. ** B1^2 = B2^2 Thus, equations (1) and (2) become the following equations respectively. ** dt1^2 (1 B^2) = dt2^2 . . . (3) ** dt2^2 = dt1^2 (1 B^2) . . . (4) Where ** B^2 = B1^2 = B2^2 The only time the equations (3) and (4) can coexist is when B^2 = 0. Thus, the twins paradox is very real under the Lorentz transform. shrug Stuff is so simple that it is a big surprise when all the socalled bright minds in the scientific communities have so much trouble understanding. Stuff is simple and they dont have any trouble in understanding. But they cannot go against the politics of people belonging to one race and same people who happen to hold the strings of economy of great America. After all these years trying to talk sense out of the likes, Koobee Wublee would have to disagree with you. They are indeed fvcking morons who cannot understand basic algebra and basic concept of what science is all about. The strong language is indeed very appropriate. shrug Coming back to Paul, he will never consider the example you suggested, that, A and B both go away from C and come back to C. In this case, there is no way to show difference in time in the clocks of A and B, though, according to Einstein, each others clock was running slow and still their own were running at proper rate. This proposed reciprocity is exactly the foolishness that SR is based on. Koobee Wublee would tend to agree on this one. paul is so busy justifying why he has said the Doppler effect from GR needed to be corrected for the carrier frequencies of downlink signals. The recent excuse is that he did not meant what he said in the past. We will see what other excuses that he can come up with. In the meantime, try not to hold your breath for paul to modify his JAVA applet to allow for both twins to travel with identical acceleration profile and also an arbitrary time period for the twins to coast (with no acceleration). It would be interesting to see how paul copes with the mutual time dilation building up. If he had any brain at all, it would be like similar to Zed holding his hands to his forehead yelling no in the movie Zardoz after the Wizard of Oz was exposed to him. shrug http://en.wikipedia.org/wiki/Zardoz 
Thread Tools  
Display Modes  


Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
The twin paradox  Koobee Wublee  Astronomy Misc  22  May 11th 12 02:35 AM 
twin paradox experiment done in lab  Koobee Wublee  Astronomy Misc  21  July 26th 11 02:39 AM 
TWIN PARADOX OR TWIN ABSURDITY?  Pentcho Valev  Astronomy Misc  111  November 25th 10 12:41 PM 
TWIN PARADOX OR TWIN ABSURDITY?  Androcles[_33_]  Amateur Astronomy  5  November 2nd 10 04:12 PM 
THE SECRET OF THE TWIN PARADOX  Pentcho Valev  Astronomy Misc  0  November 9th 07 03:48 PM 