The real twin paradox.
in [Relativity]
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From: Sue... on 3 Dec 2007 09:38 On Dec 3, 8:10 am, bz <bz+...(a)ch100-5.chem.lsu.edu> wrote: [...] > >> So, why do busy muons live longer than those that retire from the > >> rat-race? BTW... Einstein wanted to exclude pendulum clocks from his 1905 paper because they use the system they are responding to as an intrinsic component. By the same standards, the muon is disqualified as a time standard. Sue... [...] >
From: Daryl McCullough on 3 Dec 2007 09:43 colp says... >When the ticks actually arrive isn't imporant to the paradox. The >paradox is based on the fact that according to SR the ticks of the >other twin are generated more slowly that the local ticks on both >legs. To solve the paradox a description of the other twin generating >ticks more quickly that the local clock is required. Hasn't this been explained to you numerous times? In the case where A and B start together, accelerate rapidly to speed v = .8c, travel for 100 seconds, turn around, and return, we can look at the problem from many different points of view, and they *all* agree. There is no contradiction: Frame 1: In this frame, A travels at speed 0.8c, turns around, and returns at speed v. B travels in the opposite direction at 0.8c, turns around and returns. The time dilations are the same for both twins, so the elapsed times for both twins are the same. Frame 2: In this frame, A is initially at rest, while B travels at speed .976c. After 60 seconds, A accelerates to .976c. After 213 more seconds, B decelerates to rest. After 60 more seconds, they reunite. During the first 60 seconds, A's clock advances 60 seconds, B's clock advances 13 seconds. During the next 213 seconds, both A's clock and B's clock advance 47 seconds. During the final 60 seconds, A's clock advances 13 seconds, while B's clock advances 60 seconds. At the end, both clocks have advanced a total of 120 seconds. Frame 3: Same as Frame 2, but the roles of A and B are switched. At the end, both clocks have advanced a total of 120 seconds. "Frankenstein's Monster Coordinate System": If A pieces together a coordinate system that uses Frame 1's coordinate system for the first 60 seconds and Frame 2's coordinate system for the last 60 seconds, then in this coordinate system, A's clock advances 60 seconds during the first part of the trip while B's clock advances 13 seconds. During acceleration (assumed to be very brief), A's clock advances negligibly, but B's clock advances 94 seconds. During the last part of the trip, A's clock advances 60 seconds, while B's clock advances 13 seconds. At the end, both clocks have advanced a total of 120 seconds. Counting signals: If we forget about coordinate systems, but just have each twin send a light signal, once per second, to the other twin, then from the point of view of A: He receives about 7 signals during the first 60 seconds (at the rate of 1 signal every 9 seconds). He receives about 53 signals during the next 53 seconds (at the rate of 1 signal per second). He receives about 60 signals during the last 7 seconds (at the rate of 9 signals per second). The total number of signals received by A from B = 7 + 53 + 60 = 120 signals. Any way you look at it, if you are careful, you get the same answer: A's clock advances 120 seconds, and so does B's. -- Daryl McCullough Ithaca, NY
From: Daryl McCullough on 3 Dec 2007 09:59 Sue... says... >My claims are: > >1 <<A Lorentz transformation or any other coordinate >transformation will convert electric or magnetic >fields into mixtures of electric and magnetic fields, >but no transformation mixes them with the >gravitational field. >> >http://www.aip.org/pt/vol-58/iss-11/p31.html Nobody is disagreeing with that. And why is that relevant to anything being discussed? >2 <<it is impossible to perform a physical experiment >which differentiates in any fundamental sense between >different inertial frames. >> >http://farside.ph.utexas.edu/teaching/jk1/lectures/node7.html Nobody is disagreeing with that. Why is that relevant to anything being discussed? >Are those considered heretical statements in the >cult of Einstein? In general, why are you such a crank? There is no "cult of Einstein". Relativity is a theory of physics. In discussing it, Einstein's reputation is *irrelevant* to its correctness. Nobody even brings him up except you anti-relativity crackpots. -- Daryl McCullough Ithaca, NY
From: Sue... on 3 Dec 2007 11:20 On Dec 3, 9:59 am, stevendaryl3...(a)yahoo.com (Daryl McCullough) wrote: > Sue... says... > > >My claims are: > > >1 <<A Lorentz transformation or any other coordinate > >transformation will convert electric or magnetic > >fields into mixtures of electric and magnetic fields, > >but no transformation mixes them with the > >gravitational field. >> > >http://www.aip.org/pt/vol-58/iss-11/p31.html > > Nobody is disagreeing with that. And why is that relevant > to anything being discussed? When the use of a Lorentz transform is assumed to have some relation to inertial interaction, (and that assumption appears frequently in this thread) it is worthwhile to consider that statement. > > >2 <<it is impossible to perform a physical experiment > >which differentiates in any fundamental sense between > >different inertial frames. >> > >http://farside.ph.utexas.edu/teaching/jk1/lectures/node7.html > > Nobody is disagreeing with that. Why is that relevant > to anything being discussed? Several posters and indeed one of the websites offered, indicates that an anomalously aged twin would be the result of the theory. Such an effect would seem to violate the principle of relativity and falsify the theory. > > >Are those considered heretical statements in the > >cult of Einstein? > > In general, why are you such a crank? There is no > "cult of Einstein". Relativity is a theory of physics. > In discussing it, Einstein's reputation is *irrelevant* > to its correctness. Nobody even brings him up except you > anti-relativity crackpots. Einstin's reputation was not mentioed. It is in fact highly regared in the Weinberg article above. I mentioned a cult, and the term seems appropriate for people that will consider a difference in hair growth as in some way exempt from the clear interpretation of the PoR above. Perhaps you wouldn't consider modern day seekers of Ponce de Leon's fountain cultists, but I most people would. Sue... > > -- > Daryl McCullough > Ithaca, NY
From: bz on 3 Dec 2007 11:52
"Sue..." <suzysewnshow(a)yahoo.com.au> wrote in news:20b4bed5-5a84-4708-bdd0-2107c8a153d1(a)r60g2000hsc.googlegroups.com: > On Dec 3, 8:10 am, bz <bz+...(a)ch100-5.chem.lsu.edu> wrote: > [...] >> >> So, why do busy muons live longer than those that retire from the >> >> rat-race? > > BTW... Einstein wanted to exclude pendulum clocks from his > 1905 paper because they use the system they are > responding to as an intrinsic component. > > By the same standards, the muon is disqualified > as a time standard. The coherence length of your postings approaches zero. Muons do NOT oscillate up and down along a path, exchanging KE with PE as do pendulum. Pendulum periods depend on the length of the pendulum and the strength of gravity at the particular location. Although muons are expected to be influenced by Sagnac effect, by the strength of the swartzchild metric, and by their relativistic velocity, this is no more than can be said of ANY clock. Muons are only part of the system being studied in the same way that any part of reality is part of reality. You have yet to show ANY _relevant_ quote that would exclude clocks other than light clocks from relativistic effects. -- bz please pardon my infinite ignorance, the set-of-things-I-do-not-know is an infinite set. bz+spr(a)ch100-5.chem.lsu.edu remove ch100-5 to avoid spam trap |