The Symmetric Twin Paradox
in [Relativity]
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From: Koobee Wublee on 18 Jun 2010 01:28 On Jun 17, 8:50 am, eric gisse <jowr.pi.nos...(a)gmail.com> wrote: > Would it kill you to use a newsreader that can properly quote? Thank you. You and I finally have agreed on a subject of importance. <shrug>
From: Koobee Wublee on 18 Jun 2010 01:35 On Jun 17, 7:50 am, stevendaryl3...(a)yahoo.com wrote: > Transfer Principle says... > >Still, I admit that I've once thought about this > >"symmetric twin paradox." I also once asked myself > >that if the universe is closed, the twins travelling > >in opposite directions might end up meeting at the > >other side of the universe -- then which twin would > >be older? (But then I always waved this off by saying, > >therefore, the universe _isn't_ closed...) > > No, a closed cylindrical universe is no more a problem for > Special Relativity than the existence of cylinders is for > Euclidean geometry. A closed cylindrical universe is no more a problem for any theory that does not satisfy the principle of relativity either. So? <shrug> > For a flat infinite sheet, all directions are equivalent, but > if you wrap that paper into a cylinder, then there is suddenly > a big difference between the direction around the circumference > and the direction parallel to the axis. Nonsense. There is still no difference. <shrug> > Similarly for a cylindrical universe in SR. For a flat > infinite universe, all inertial frames are equivalent. > But if you wrap the universe into a cylinder, there is > a difference between the inertial frame of an observer > traveling out the circumference and the inertial frame > of an observer traveling parallel to the axis of the > cylinder. DITTO. <shrug>
From: Koobee Wublee on 18 Jun 2010 01:41 On Jun 17, 7:14 am, stevendaryl3...(a)yahoo.com wrote: > colp says... > >The classic twin paradox is asymmetric in that one twin remains on > >Earth while the other leaves (i.e. only one of them accelerates and > >deaccelerates). In the symmetric twin paradox both twins leave Earth, > >setting out in opposite directions and returning to Earth at the same > >time. The conventional explanation for the classic twin paradox is > >since only one twin accelerates, the ages of the twins will be > >different. In the symmetric case this argument cannot be applied. > > >The paradox of the symmetric twins is that according to special > >relativity (SR) each twin observes the other twin to age more slowly > >both on the outgoing leg and the return leg, so SR paradoxically > >predicts that each twin will be younger than > >the other when they return to Earth. > > This is only a paradox to those incompetent at mathematics. Gee! It shows how ignorant you are with the mathematics of the Lorentz transform. <shrug> > Let's > look at an analogous "paradox" in Euclidean geometry: > > You have two cities, Startville and Endville. Endville lies 1000 miles > due west of Startville. There are two different routes to get from > Startville to Endville: One route goes straight west for 1000 miles. > The other route starts off traveling northwest then at the halfway > point turns to travel southwest the rest of the way. > > From the point of view of a traveler following the straight path, > the bent path looks longer: it travels away to the north for a > while, and then it travels south for a while, and the total length > is given by the Pythagorean theorem. > > From the point of view of a traveler following the bent path, > it might seem that it is the *first* traveler who travels away > to the *south* for the first half of the trip, and then travels > to the *north* for the second half of the trip. So is it right > for the second traveler to claim that the *other* traveler is > following the bent path? Clearly no. > > In Euclidean geometry there is a "relativity" of directions. > You pick any direction you like and call it your coordinate > axis. There is nothing special about traveling west: you can > let your axis travel to the northwest just as well. > > But there is *no* relativity when it comes to bent paths > versus straight paths. All observers, regardless of how > they set up their coordinate systems, can tell the difference > between a straight path and a bent path. > > In SR, the analogy of "straight path" is "unaccelerated path" > and the analogy of "bent path" is "accelerated path". Oh, where is the math that shows this? Want to apply GR to an SR problem? Go right ahead and show me. I call your bluff. <shrug> > Whether > an observer is at rest or not is a matter of relativity, but > whether an observer is accelerated or not is not relative: > all observers agree about who it is that accelerates. Handwaving is not physics. <shrug>
From: Peter Webb on 18 Jun 2010 01:58 "Koobee Wublee" <koobee.wublee(a)gmail.com> wrote in message news:2803143b-dad0-446a-a8a5-e5e8d4dbc1c5(a)z10g2000yqb.googlegroups.com... > On Jun 17, 6:21 am, Tom Roberts wrote: >> colp wrote: > >> > The symmetric twin thought experiment (as described in the OP) is such >> > an experiment. >> >> No. It is a GEDANKEN, not an experiment. There are no actual measurements >> of >> this situation. > > Of course not. I know you would agree that a paradox is not a > physical reality. So, please clarify with professor Drape aka PD who > thinks a paradox is still a possibility in real life. > >> > In the experiment SR predicts that the twins will both be younger than >> > each other when they return to Earth, which is of course impossible. >> >> This is just plain not true. You and that paper did not actually use SR. >> The >> comic book used does not describe the actual theory accurately enough to >> be useful. > > Oh, careful here. You are treading on thin ice while embracing the > principle of relativity. The time dilation in the Lorentz transform > must be mutual. <shrug> > > As a on-stage magician, I have called your mathemagical tricks. There > is a slight difference between Larmor's transform and the later > Lorentz transform, but this slight difference is going to determine > what is reality and what is fairy tale. Larmor's and the Lorentz > transforms are different only that Larmor's requires one of the two > observers to be the stationary background of the Aether while the > Lorentz does not. The Lorentz transform can only possibly valid if > and only if these two observers are moving in parallel to each other > against the stationary background of the Aether. Excellent. Then it must be possible to design an experiment which determines if SR is correct. According to you, SR will only make the correct prediction occur if the two objects are moving in parallel against the stationary background of the ether. How about an experiment with two clocks that take different paths - say one is put on an airplane and flies in a loop, and the other stays at home. Or, even better, you measure the decay rates of hot atomic nucleuses, which being hot are in rapid motion and should decay slower according to SR. These are obviously not in parallel paths to cold nucleuses. So, all we have to do to determine if you are correct is find an experiment where clocks are taken in non-parallel paths, and see if SR still predicts the relative ages correctly. Or measure the decay rates of extremely hot radioactive materials. Or even just compare the lifetime of stationary K mesons vs those generated in cyclotrons and which are clearly not on parallel paths. I wonder if somebody has ever done these types of experiments?
From: Koobee Wublee on 18 Jun 2010 02:06
On Jun 17, 9:18 pm, stevendaryl3...(a)yahoo.com wrote: > There is no paradox here! To say that SR leads to a paradox, > you need to show that there is some experiment that can be > performed such that SR gives two different ways to calculate > the results, which gives two different answers. You are indeed out of this world like my six-year-olds who would always come up with a good story explaining what they should have ice cream before any meals. Since a paradox can never be proven valid in which I would bet my life savings on, it is absolutely not possible to come up with an experiment to support any paradox. We have someone who does not understand the basic logic going absolutely wild and insane here. <shrug> > What SR predicts is this: For any trip, the elapsed time on a > clock will be given by: [snipped the rest of nonsense] That is a typical Einstein Dingleberry who cannot listen to any logic but gulping down mystic nonsense at any chance. How many times have you been wrong? <shrug> |