The Symmetric Twin Paradox
in [Relativity]
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From: BURT on 17 Jun 2010 22:41 On Jun 17, 7:08 pm, colp <c...(a)solder.ath.cx> wrote: > On Jun 18, 11:24 am, "Inertial" <relativ...(a)rest.com> wrote: > > > > > > > "colp" <c...(a)solder.ath.cx> wrote in message > > >news:bd7d4a85-d7b3-40e3-884c-720b9255f608(a)11g2000prv.googlegroups.com... > > > > On Jun 18, 8:14 am, PD <thedraperfam...(a)gmail.com> wrote: > > >> On Jun 16, 1:25 am, colp <c...(a)solder.ath.cx> wrote: > > > >> > 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. > > > >> No. This is a basic misunderstanding due to oversimplification, and it > > >> is exactly the kind of thing that the original puzzle was intended to > > >> highlight for learners of relativity. > > > > It is true that I haven't discussed what happens at turnaround, but > > > only for the reason that turnaround cannot possibly compensate for the > > > SR time dilation. > > > So you just don't bother doing the math and just ASSUME that it isn't > > important and then wonder why you get stupid results > > Maths is consistent with logic. Your snipped my argument as to why the > turnaround cannot logically compensate for the SR time dilation.- Hide quoted text - > > - Show quoted text - Einstein's theory of time difference between one twin and the other was lost time. But you can show that there are cases where lost time does not apply. In those cases both clocks cannot be goping slower than the other. Without lost time only one clock is slow and the others is fast and it is always seen that way. Even as they pass each other in space. Mitch Raemsch
From: rotchm on 17 Jun 2010 23:03 On Jun 17, 10:33 pm, colp <c...(a)solder.ath.cx> wrote: > On Jun 18, 2:13 pm, "Inertial" <relativ...(a)rest.com> wrote: > Haha. To continue *our* discussion that you are unable to point out major error in the article. > Here's the relevant text from the article. The previous version being > discussed was the classic twin paradox (Taurai and Tauwi are the names > of the twins). > > B. Twin Paradox (Symmetric) > We shall set forth a new version of the twin paradox which is > truly symmetric and this will introduce a true paradox and we > shall provide a solution. Suppose Taurai unlike in the previous > version, decided to be adventurous too. He decides to rocket > into space and travels not with his twin brother but all by himself > and instead of Alpha-Centauri he travels at the same constant > relativistic speed as Taurwi [this speed is measured by > the Earth bound observers] to an imaginary constellation (call > it Constellation Alpha-Christina) which is equidistant and directly > opposite to Alpha Centauri along the line of sight joining > the Earth and Alpha Centauri. In that paragraph that you transcribed, there is a major error; something is completely false. Can you figure out what?
From: Daryl McCullough on 18 Jun 2010 00:18 colp says... >B. Twin Paradox (Symmetric) >We shall set forth a new version of the twin paradox which is >truly symmetric and this will introduce a true paradox and we >shall provide a solution. Suppose Taurai unlike in the previous >version, decided to be adventurous too. He decides to rocket >into space and travels not with his twin brother but all by himself >and instead of Alpha-Centauri he travels at the same constant >relativistic speed as Taurwi [this speed is measured by >the Earth bound observers] to an imaginary constellation (call >it Constellation Alpha-Christina) which is equidistant and directly >opposite to Alpha Centauri along the line of sight joining >the Earth and Alpha Centauri. > >On their day of departure, their family and friends bid them >farewell and wish thema safe travel. Withoutmuch say, on the >day of reunion, the family and friends [who all have studied >physics at university and understand very well the STR] have >no doubt that they [the Twins] will all have aged the same. >The big question is, will the twins agree with their family and >friends that they have aged the same? The truth is that, each >of the twins will see the other as having aged less than they so >they would not agree with their family and friends that they >must be the same age. Herein we have a paradox! Who is >older than who here? 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. That's not the case here. What SR predicts is this: For any trip, the elapsed time on a clock will be given by: T_elapsed = Integral of square-root(1-(v/c)^2) dt where v is the speed of the clock, and t is the coordinate time. The "relativity" of different inertial frames says that we can measure v and t in *any* inertial coordinate system at all, and you get the same result for T_elapsed. If a rocket travels at constant speed in one direction, turns around, and travels at the same speed back, then there are three inertial frames involved: (1) the initial rest frame of the rocket, before it takes off, (2) the outbound frame of the rocket, and (3) the inbound frame of the rocket. You can use any of these three frames to calculate elapsed times for a clock aboard the rocket, and you will get the same answer. You say that in the case of the two twins traveling in opposite directions, each one thinks the other is older on their outbound trips. That's true, but that's not a paradox. There is no way to measure the age now of a distant twin. The fact that two coordinate systems disagree on the coordinates of an event doesn't mean anything, physical, it just means that you are two different coordinate systems. That's what "different coordinate system" means---it gives different values for coordinates. Describe an experiment for measuring times or distances, and SR gives a unique prediction for the results of those measurements. There are no paradoxes in SR. If you believe that there are paradoxes in SR, then describe what sort of measurement you want to make for this symmetric twin paradox, and then show that there are two different ways to compute the result of the measurement that give different answers. You can't use "see which twin is older" as the measurement, unless you can give an experiment whose result would determine which twin was older. It's not enough to say what each twin *believes* about the question, you have to describe an experiment. -- Daryl McCullough Ithaca, NY
From: Koobee Wublee on 18 Jun 2010 00:59 On Jun 17, 6:13 am, Tom Roberts wrote: > Peter Webb wrote: Oh, good. The big guns like Professor Roberts has decided to come to the rescue of the pawns of the self-styled physicists like Peter Webb. I can now ignore these ignorant minions. Thanks for showing up. <TWO THUMBS UP> > > GPS will function without any GR effect applied if indeed exists. You > > can google the previous few posts by yours truly to understand how GPS > > works. > > This is just plain not true. The relativistic effects in the GPS are well known > and are MEASURED to agree with the predictions of GR to excellent accuracy. The algorithms in any GPS receivers do not require any relativistic corrections. <shrug> > The > GPS could not possibly work without applying the relativistic effects. Hmmm... That statement is a wishful thinking from the self-styled physicists. <shrug> > Note that the GPS is an ENGINEERED system, and consists of clocks > both in satellites and on the ground. Yes. <shrug> > It is true that a similar system without ground clocks could IN PRINCIPLE be > designed to work without relativistic corrections; I hope the Einstein Dingleberry Peter Webb is taking notes on this one. <shrug> > IN PRACTICE the engineering > of such a system would be impossible (e.g. any satellite that missed its orbit > by a small amount would be useless); It is funny that a physicists would try to be an engineer on this one. Please explain what this 'missing the orbit' thing. > the required perfection does not occur in > the real world. It is great that a physicist can put on an engineer's hat. > Fortunately, the designers of the GPS knew this and designed a > system that actually works; it requires BOTH relativistic corrections and daily > parameter updates (the largest corrections are to satellite orbits). According to the algorithms inside each GPS receiver, there is no relativistic effect, and no relativistic effect is necessary. Where is this relativistic effect applied? > Note that > the manufactured modification to the satellite clocks (due to relativistic > effects) completely dwarfs the daily updates. So, as long as all satellites exhibit the same clock rate that accumulates the chronological time, the system has to work. So, since they are all built on the surface of the earth, applying any relativistic effect whether if it is valid or not is a waste of effort. <shrug>
From: Koobee Wublee on 18 Jun 2010 01:25
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. Your mathemagical trick is to show the Lorentz transform in your hand while performing all calculations/applications with Larmor's transform. That may pass the Einstein Dingleberries, but you cannot fool the true scholars of physics since Larmor's transform does not satisfy the principle of relativity and thus supporting the absolute simultaneity in accordance with real-life observations in the coherencies of interferometers time after time. <shrug> > > Some solutions proposed by the relativists are: > > [...] > > Those are not the real solution. The REAL solution is to actually use SR in the > analysis of this gedanken. The Keating experiment did not show a mutual time dilation thus is a valid proof to SR. Remember that no experiment can possibly prove a paradox valid. <shrug> |