CMBR's motion wrt the Earth
in [Relativity]
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From: Inertial on 25 Sep 2009 07:28 "mluttgens" <mluttgens(a)orange.fr> wrote in message news:605a1705-a78e-48c0-b409-bf64fbf7b411(a)o13g2000vbl.googlegroups.com... > On 23 sep, 14:23, PD <thedraperfam...(a)gmail.com> wrote: >> On Sep 22, 7:32 pm, mluttgens <mluttg...(a)orange.fr> wrote: >> >> >> >> >> >> > On 22 sep, 15:30, PD <thedraperfam...(a)gmail.com> wrote: >> >> > > On Sep 22, 7:33 am, mluttgens <mluttg...(a)orange.fr> wrote: >> >> > > > On 21 sep, 14:09, PD <thedraperfam...(a)gmail.com> wrote: >> >> > > > > On Sep 21, 5:59 am, mluttgens <mluttg...(a)orange.fr> wrote: >> >> > > > > > On 19 sep, 20:37, "G. L. Bradford" <glbra...(a)insightbb.com> >> > > > > > wrote: >> >> > > > > > > "Inertial" <relativ...(a)rest.com> wrote in message >> >> > > > > > >news:003e775f$0$2915$c3e8da3(a)news.astraweb.com... >> >> > > > > > > > "mluttgens" <mluttg...(a)orange.fr> wrote in message >> > > > > > > >news:41d5a838-7be2-4786-8820-32048a494322(a)o13g2000vbl.googlegroups.com... >> > > > > > > >> On 19 sep, 02:25, "Inertial" <relativ...(a)rest.com> wrote: >> > > > > > > >>> "mluttgens" <mluttg...(a)orange.fr> wrote in message >> >> > > > > > > >>>news:756d9890-f435-4e91-b813-48c6c697cbc4(a)h30g2000vbr.googlegroups.com... >> >> > > > > > > >>> > On 13 sep, 15:55, Sam Wormley <sworml...(a)mchsi.com> >> > > > > > > >>> > wrote: >> > > > > > > >>> >> mluttgens wrote: >> >> > > > > > > >>> >> > Special relativity theory should be called the >> > > > > > > >>> >> > Theory of Mutual >> > > > > > > >>> >> > Time Dilation. Clearly, mutual time dilation is >> > > > > > > >>> >> > nonsensical. >> > > > > > > >>> >> > SRists found a solution for the twin paradox, >> > > > > > > >>> >> > explaining why "both >> > > > > > > >>> >> > twins cannot be younger than each other", but >> > > > > > > >>> >> > consider normal >> > > > > > > >>> >> > that two clocks moving relative to each other, for >> > > > > > > >>> >> > instance on >> > > > > > > >>> >> > a road, show the same time dilation. Contradiction >> > > > > > > >>> >> > doesn't bother >> > > > > > > >>> >> > them. They don't even try to find a general solution >> > > > > > > >>> >> > for >> > > > > > > >>> >> > the nonsense, and modify SR accordingly. >> >> > > > > > > >>> >> > Marcel Luttgens >> >> > > > > > > >>> >> Marcel, you should take some time to learn what >> > > > > > > >>> >> special >> > > > > > > >>> >> relativity really says. One cannot have more than >> > > > > > > >>> >> one >> > > > > > > >>> >> perspective simultaneously. There has yet to be an >> > > > > > > >>> >> observation >> > > > > > > >>> >> that contradicts a prediction of special >> > > > > > > >>> >> relativity. >> >> > > > > > > >>> > Let's consider two objects A and B in uniform >> > > > > > > >>> > translatory motion. >> >> > > > > > > >>> Fine >> >> > > > > > > >>> > According to SR, if A moves at v toward B, >> > > > > > > >>> > reciprocally, B moves at -v toward A. >> >> > > > > > > >>> That's not just SR .. its been known physics for hundreds >> > > > > > > >>> of years. >> >> > > > > > > >>> > SR obviously doesn't take into consideration >> > > > > > > >>> > the velocities vA and vB of the objects relative >> > > > > > > >>> > to the CMBR (sometimes rightly called the rest >> > > > > > > >>> > frame of the universe). >> >> > > > > > > >>> Why the fvck should it? It makes ABSOLUTELY NO >> > > > > > > >>> DIFFERENCE to the >> > > > > > > >>> relative >> > > > > > > >>> speeds of A and B >> >> > > > > > > >>> > Let v be the velocity of A wrt B. >> > > > > > > >>> > From the dipole anisotropy it observes, B >> > > > > > > >>> > determines that its velocity relative to the >> > > > > > > >>> > CMBR is vB, whose direction is the same as v. >> >> > > > > > > >>> No .. it wouldn't necessarily be in the same directions >> > > > > > > >>> as v >> >> > > > > > > >> Sure, but it is what B (which could be the Earth) observed >> > > > > > > >> in this scenario. >> >> > > > > > > > Not that it makes any difference to the relationship >> > > > > > > > between A and B. >> > > > > > > > you're wasting time discussing irrelevant nonsense. >> >> > > > > > > >>> > According to the CMBR observer (using c=1), >> > > > > > > >>> > vA = (v-vB)/(1-vB*v) >> > > > > > > >>> > tB = tCMBR * sqrt(1-vB^2) >> > > > > > > >>> > tA = tCMBR * sqrt(1-((v-vB)/(1-vB*v))^2) >> > > > > > > >>> > = tCMBR * sqrt1-vB^2)*sqrt(1-v^2)/(1-vB*v) >> > > > > > > >>> > Hence, tA = tB * sqrt(1-v^2) / (1-vB*v). >> >> > > > > > > >>> > Clearly, the SR formula tA = tB * sqrt(1-v^2) >> > > > > > > >>> > is correct only when B is at rest in the CMBR >> > > > > > > >>> > (vB = 0). >> > > > > > > >>> > But even in this case, SRists falsely claim >> > > > > > > >>> > that B moves at -v relative to A, >> >> > > > > > > >>> It does. You just don't understand basic physics >> >> > > > > > > >> You are indirectly claiming that the CMBR moves relative >> > > > > > > >> to A. >> >> > > > > > > > Not indirectly .. Directly >> >> > > > > > > >> Only brainwashed SRists can be so stupid. >> >> > > > > > > > Only you are so stupid to think that if I walk closer to a >> > > > > > > > wall, that the >> > > > > > > > wall stays the same distance away. >> >> > > > > > > ================================ >> >> > > > > > > There are walls, and then there are walls. There are those >> > > > > > > who are 'so >> > > > > > > stupid' as to think if they walk long enough they will walk >> > > > > > > closer to the >> > > > > > > horizon of Earth....that it will not stay the same distance >> > > > > > > from the walking >> > > > > > > traveler as from the standing observer left behind. They are >> > > > > > > 'so stupid' as >> > > > > > > to think that they can close with it. There are those who are >> > > > > > > 'so stupid' as >> > > > > > > to think if they speed up they will speed closer to the >> > > > > > > universal horizon >> > > > > > > constant of c (even getting closer to the distant Planck >> > > > > > > horizon of the >> > > > > > > Universe), that it will not stay the same distance from the >> > > > > > > walking....er, >> > > > > > > speeding....traveler as from the standing observer left >> > > > > > > behind. They are 'so >> > > > > > > stupid' as to think that they can close with it. >> >> > > > > > > There are those 'so stupid' as to never realize that >> > > > > > > differences exist >> > > > > > > between every constituent [local] universe and the overall >> > > > > > > entity that is >> > > > > > > the [non-local] Universe. Differences that can be >> > > > > > > manipulated. Differences >> > > > > > > that can't be manipulated. There are walls, and then there >> > > > > > > are walls. >> >> > > > > > > GL >> >> > > > > > They will not understand what you mean, being really >> > > > > > brainwashed. >> > > > > > Talking to them is like talking to a wall (no pun >> > > > > > intended!). >> > > > > > They will not realize that the CMBR must be taken >> > > > > > into consideration, >> >> > > > > Actually, no it doesn't NEED to be taken into consideration, any >> > > > > more >> > > > > than the Sun needs to be taken into consideration, or the center >> > > > > of >> > > > > the galaxy needs to be taken into consideration, or any other >> > > > > arbitrarily chosen artifact of the universe needs to be taken >> > > > > into >> > > > > consideration. >> >> > > > Even if the SR analysis of the twin paradox were >> > > > right, which it is not, because it doesn't take the >> > > > Earth's velocity relative to the CMBR, >> >> > > Relative motion is a motion between TWO bodies, and a THIRD entity >> > > (like the CMBR) does not NEED to be taken into account. I don't know >> > > why you think relative velocity DOES need to take into account a >> > > third >> > > body. >> >> > The TWO bodies are not isolated in the universe, which is ignored >> > by SRT. >> >> Of course they're not isolated. This doesn't change the fact that the >> relative motion only involves the two of them, and that the physics >> depends only on the relative motion. It adds nothing to insist that an >> arbitrarily chosen third reference point in the universe should be >> taken into account, other than adding unnecessary baggage. >> >> >> >> >> >> >> >> > > > Occam's >> > > > razor (http://en.wikipedia.org/wiki/Occam%27s_razor) >> > > > "recommends selection of the hypothesis that introduces >> > > > the fewest assumptions and postulates the fewest >> > > > entities while still sufficiently answering the >> > > > question". >> >> > > Sorry, but now you're grasping at straws. >> > > Note that YOUR idea involves more assumptions, including a dependence >> > > of relative velocity on an arbitrarily chosen third entity in the >> > > universe, the CMBR. >> >> > SR is based on a pure mathematical concept, and wholly neglects the >> > fact that its objects are physically linked to the whole universe. >> >> And the physics depends only on the pairwise linkages. But all the >> pairwise linkages are of equal standing, and there is no reference >> body whose linkages should be taken as special, preferred, or >> absolute. >> >> >> >> > > Just because you have a hard time understanding SR, does NOT mean >> > > that >> > > it involves more complicated assumptions or postulates. There are >> > > only >> > > two assumptions in SR. Two. >> >> > Only two, that's why SR is wrong. >> >> Well, gee, just a second ago you said that Occam's razor would drive >> toward the one with the fewest assumptions, if it accounts for what's >> observed. Now suddenly you're not so sure you'd want to go with >> Occam's razor on this one. >> > > Hereafter are a few quotes from the introduction: > http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_intro.html > > "SR does not declare that all frames of reference are equivalent, > only so-called inertial frames. Yeup. GR covers all of them. > It seems passing strange that Terence could age several years > just because Stella engages her thrusters. The Time Gap and > Distance Dependence Objections put a sharper edge on this > uneasy feeling. Yes .. it is strange .. that doesn't mean its wrong > These cast doubt on how relevant the acceleration is in the > usual version. The change in what reference frame one is at rest in is important. Acceleration is the usual way of doing that. > Finally, what about the Equivalence Principle? Doesn't that say > that Stella can still claim to be motionless the whole time, but > that a huge pseudo-gravitational field just happened to sweep > through the universe when she hit her "thrusters on" button? That might have the same effect (though then you'd have to explain how Terence didn't experience it) > The EP viewpoint is nearly mandatory for understanding some > of the twin paradox variations. > The time gap objection: > Here we have let the turnaround become instantaneous. > On the Outbound Leg Stella uses one frame of reference, > and one notion of simultaneity. On the Inbound Leg she switches > to another. The "gap" (the section of Terence's worldline devoid > of blue lines) is a consequence of this abrupt switch. Yeup > I hasten to add that there are some pitfalls for the unwary: see > Section 6.3 of Misner, Thorne, and Wheeler for the fine points." > > How can you prefer the simple explanation of the absence of > paradox by using the CMBR to the multiple tentatives made > by SRists in order to get rid of it? The CMBR doesn't do any such thing. And there is no paradox And it is easily explained in SR > Is it due to brainwashing? I have no other explanation for your > position. Your ignorance is clearly the explanation for yours.
From: PD on 25 Sep 2009 09:44 On Sep 25, 5:55 am, mluttgens <mluttg...(a)orange.fr> wrote: > On 23 sep, 14:23, PD <thedraperfam...(a)gmail.com> wrote: > > > On Sep 22, 7:32 pm, mluttgens <mluttg...(a)orange.fr> wrote: > > > > On 22 sep, 15:30, PD <thedraperfam...(a)gmail.com> wrote: > > > > > On Sep 22, 7:33 am, mluttgens <mluttg...(a)orange.fr> wrote: > > > > > > On 21 sep, 14:09, PD <thedraperfam...(a)gmail.com> wrote: > > > > > > > On Sep 21, 5:59 am, mluttgens <mluttg...(a)orange.fr> wrote: > > > > > > > > On 19 sep, 20:37, "G. L. Bradford" <glbra...(a)insightbb.com> wrote: > > > > > > > > > "Inertial" <relativ...(a)rest.com> wrote in message > > > > > > > > >news:003e775f$0$2915$c3e8da3(a)news.astraweb.com... > > > > > > > > > > "mluttgens" <mluttg...(a)orange.fr> wrote in message > > > > > > > > >news:41d5a838-7be2-4786-8820-32048a494322(a)o13g2000vbl.googlegroups.com... > > > > > > > > >> On 19 sep, 02:25, "Inertial" <relativ...(a)rest.com> wrote: > > > > > > > > >>> "mluttgens" <mluttg...(a)orange.fr> wrote in message > > > > > > > > > >>>news:756d9890-f435-4e91-b813-48c6c697cbc4(a)h30g2000vbr.googlegroups.com... > > > > > > > > > >>> > On 13 sep, 15:55, Sam Wormley <sworml...(a)mchsi.com> wrote: > > > > > > > > >>> >> mluttgens wrote: > > > > > > > > > >>> >> > Special relativity theory should be called the Theory of Mutual > > > > > > > > >>> >> > Time Dilation. Clearly, mutual time dilation is nonsensical. > > > > > > > > >>> >> > SRists found a solution for the twin paradox, explaining why "both > > > > > > > > >>> >> > twins cannot be younger than each other", but consider normal > > > > > > > > >>> >> > that two clocks moving relative to each other, for instance on > > > > > > > > >>> >> > a road, show the same time dilation. Contradiction doesn't bother > > > > > > > > >>> >> > them. They don't even try to find a general solution for > > > > > > > > >>> >> > the nonsense, and modify SR accordingly. > > > > > > > > > >>> >> > Marcel Luttgens > > > > > > > > > >>> >> Marcel, you should take some time to learn what special > > > > > > > > >>> >> relativity really says. One cannot have more than one > > > > > > > > >>> >> perspective simultaneously. There has yet to be an observation > > > > > > > > >>> >> that contradicts a prediction of special relativity. > > > > > > > > > >>> > Let's consider two objects A and B in uniform > > > > > > > > >>> > translatory motion. > > > > > > > > > >>> Fine > > > > > > > > > >>> > According to SR, if A moves at v toward B, > > > > > > > > >>> > reciprocally, B moves at -v toward A. > > > > > > > > > >>> That's not just SR .. its been known physics for hundreds of years. > > > > > > > > > >>> > SR obviously doesn't take into consideration > > > > > > > > >>> > the velocities vA and vB of the objects relative > > > > > > > > >>> > to the CMBR (sometimes rightly called the rest > > > > > > > > >>> > frame of the universe). > > > > > > > > > >>> Why the fvck should it? It makes ABSOLUTELY NO DIFFERENCE to the > > > > > > > > >>> relative > > > > > > > > >>> speeds of A and B > > > > > > > > > >>> > Let v be the velocity of A wrt B. > > > > > > > > >>> > From the dipole anisotropy it observes, B > > > > > > > > >>> > determines that its velocity relative to the > > > > > > > > >>> > CMBR is vB, whose direction is the same as v. > > > > > > > > > >>> No .. it wouldn't necessarily be in the same directions as v > > > > > > > > > >> Sure, but it is what B (which could be the Earth) observed > > > > > > > > >> in this scenario. > > > > > > > > > > Not that it makes any difference to the relationship between A and B. > > > > > > > > > you're wasting time discussing irrelevant nonsense. > > > > > > > > > >>> > According to the CMBR observer (using c=1), > > > > > > > > >>> > vA = (v-vB)/(1-vB*v) > > > > > > > > >>> > tB = tCMBR * sqrt(1-vB^2) > > > > > > > > >>> > tA = tCMBR * sqrt(1-((v-vB)/(1-vB*v))^2) > > > > > > > > >>> > = tCMBR * sqrt1-vB^2)*sqrt(1-v^2)/(1-vB*v) > > > > > > > > >>> > Hence, tA = tB * sqrt(1-v^2) / (1-vB*v). > > > > > > > > > >>> > Clearly, the SR formula tA = tB * sqrt(1-v^2) > > > > > > > > >>> > is correct only when B is at rest in the CMBR > > > > > > > > >>> > (vB = 0). > > > > > > > > >>> > But even in this case, SRists falsely claim > > > > > > > > >>> > that B moves at -v relative to A, > > > > > > > > > >>> It does. You just don't understand basic physics > > > > > > > > > >> You are indirectly claiming that the CMBR moves relative > > > > > > > > >> to A. > > > > > > > > > > Not indirectly .. Directly > > > > > > > > > >> Only brainwashed SRists can be so stupid. > > > > > > > > > > Only you are so stupid to think that if I walk closer to a wall, that the > > > > > > > > > wall stays the same distance away. > > > > > > > > > ================================ > > > > > > > > > There are walls, and then there are walls. There are those who are 'so > > > > > > > > stupid' as to think if they walk long enough they will walk closer to the > > > > > > > > horizon of Earth....that it will not stay the same distance from the walking > > > > > > > > traveler as from the standing observer left behind. They are 'so stupid' as > > > > > > > > to think that they can close with it. There are those who are 'so stupid' as > > > > > > > > to think if they speed up they will speed closer to the universal horizon > > > > > > > > constant of c (even getting closer to the distant Planck horizon of the > > > > > > > > Universe), that it will not stay the same distance from the walking....er, > > > > > > > > speeding....traveler as from the standing observer left behind. They are 'so > > > > > > > > stupid' as to think that they can close with it. > > > > > > > > > There are those 'so stupid' as to never realize that differences exist > > > > > > > > between every constituent [local] universe and the overall entity that is > > > > > > > > the [non-local] Universe. Differences that can be manipulated. Differences > > > > > > > > that can't be manipulated. There are walls, and then there are walls. > > > > > > > > > GL > > > > > > > > They will not understand what you mean, being really > > > > > > > brainwashed. > > > > > > > Talking to them is like talking to a wall (no pun > > > > > > > intended!). > > > > > > > They will not realize that the CMBR must be taken > > > > > > > into consideration, > > > > > > > Actually, no it doesn't NEED to be taken into consideration, any more > > > > > > than the Sun needs to be taken into consideration, or the center of > > > > > > the galaxy needs to be taken into consideration, or any other > > > > > > arbitrarily chosen artifact of the universe needs to be taken into > > > > > > consideration. > > > > > > Even if the SR analysis of the twin paradox were > > > > > right, which it is not, because it doesn't take the > > > > > Earth's velocity relative to the CMBR, > > > > > Relative motion is a motion between TWO bodies, and a THIRD entity > > > > (like the CMBR) does not NEED to be taken into account. I don't know > > > > why you think relative velocity DOES need to take into account a third > > > > body. > > > > The TWO bodies are not isolated in the universe, which is ignored > > > by SRT. > > > Of course they're not isolated. This doesn't change the fact that the > > relative motion only involves the two of them, and that the physics > > depends only on the relative motion. It adds nothing to insist that an > > arbitrarily chosen third reference point in the universe should be > > taken into account, other than adding unnecessary baggage. > > > > > > Occam's > > > > > razor (http://en.wikipedia.org/wiki/Occam%27s_razor) > > > > > "recommends selection of the hypothesis that introduces > > > > > the fewest assumptions and postulates the fewest > > > > > entities while still sufficiently answering the > > > > > question". > > > > > Sorry, but now you're grasping at straws. > > > > Note that YOUR idea involves more assumptions, including a dependence > > > > of relative velocity on an arbitrarily chosen third entity in the > > > > universe, the CMBR. > > > > SR is based on a pure mathematical concept, and wholly neglects the > > > fact that its objects are physically linked to the whole universe. > > > And the physics depends only on the pairwise linkages. But all the > > pairwise linkages are of equal standing, and there is no reference > > body whose linkages should be taken as special, preferred, or > > absolute. > > > > > Just because you have a hard time understanding SR, does NOT mean that > > > > it involves more complicated assumptions or postulates. There are only > > > > two assumptions in SR. Two. > > > > Only two, that's why SR is wrong. > > > Well, gee, just a second ago you said that Occam's razor would drive > > toward the one with the fewest assumptions, if it accounts for what's > > observed. Now suddenly you're not so sure you'd want to go with > > Occam's razor on this one. > > Hereafter are a few quotes from the introduction:http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_... > > "SR does not declare that all frames of reference are equivalent, > only so-called inertial frames. That's correct. And the CMBR does not distinguish itself by being different here. > It seems passing strange that Terence could age several years > just because Stella engages her thrusters. Note here that the author is tracing through the mental errors that a naive student will make. Stella sees Terence's clock leap forward when she engages her thrusters. This does NOT mean that she was able to reach across space and impinge some physical interaction on Terence to make him suddenly grow gray hair while he ate breakfast. You have the common misconception that the change in a physical parameter (like clock rate) implies some physical interaction with the clock to affect it. It couldn't be further from the truth. When I look at a car and see that is moving at 60 mph relative to me, and then I press my accelerator and look at the same car and see that it is moving at 35 mph relative to me, I have done NOTHING to push the car or physically impinge on it in any way. > The Time Gap and > Distance Dependence Objections put a sharper edge on this > uneasy feeling. > These cast doubt on how relevant the acceleration is in the > usual version. Again note that the author is tracing through some of the mental baggage that a naive student drags along with -- that acceleration here somehow must mean touching or physically altering a clock over there. > Finally, what about the Equivalence Principle? Doesn't that say > that Stella can still claim to be motionless the whole time, but > that a huge pseudo-gravitational field just happened to sweep > through the universe when she hit her "thrusters on" button? And again, the author is tracing through some of the misunderstandings of a naive student. That's the whole point of the twin puzzle. It is the naive student who says, "But I should just be able to look at it from Stella's point of view and see the Earth receding then accelerating back toward her." There's where the lesson of the puzzle is. There's a difference. Stella KNOWS she's accelerating. She can feel it. Terrance KNOWS he's NOT accelerating, otherwise he'd feel it. The two observers are NOT equivalent, NOT symmetric. And it's a misapplication of the Equivalence Principle to say that they should be. > The EP viewpoint is nearly mandatory for understanding some > of the twin paradox variations. > The time gap objection: > Here we have let the turnaround become instantaneous. > On the Outbound Leg Stella uses one frame of reference, > and one notion of simultaneity. On the Inbound Leg she switches > to another. The "gap" (the section of Terence's worldline devoid > of blue lines) is a consequence of this abrupt switch. > I hasten to add that there are some pitfalls for the unwary: see > Section 6.3 of Misner, Thorne, and Wheeler for the fine points." > > How can you prefer the simple explanation of the absence of > paradox by using the CMBR to the multiple tentatives made > by SRists in order to get rid of it? Not tentatives at all. It just points out some of the common misconceptions about relativity that can be cleared up by looking at the problem several different ways. > Is it due to brainwashing? I have no other explanation for your > position. I'm sorry you're still confused. You seem to think that the pedagogical lessons to be learned from the puzzle are in fact real confusions in the theory, and that the shallow misconceptions are to be retained as indicators of a real paradox -- rather than removing the misconceptions pointed out. And so to avoid dealing with that, you flee to the CMBR. > > Marcel Luttgens > > > > > > Whereas there is no paradox at all when the CMBR > > > > > is taken into consideration > > > > > (cf.http://pagesperso-orange.fr/mluttgens/twinpdx1.htm), > > > > > SRists have a lot of different explanations, > > > > > Yes, they are all different ways of saying the same thing. This is not > > > > unusual in physics. Take a look at the classical Atwood machine, for > > > > example. You can explain the behavior of that system by using Newton's > > > > 2nd law. You can also explain the behavior of that system using energy > > > > conservation. You can also explain the behavior of that system using > > > > momentum conservation. They all work, and all freshman students become > > > > familiar with that. There does not have to be one and only one way to > > > > analyze a physical system. > > > > A false analogy! > > > The fact is that nothing can be considered independently of the > > > rest of the universe. You seem to have a "hard time" realizing this. > > > I didn't say the objects were isolated. > > What is still true, though, is that there is nothing special about any > > of the objects involved in those interactions. They are all pairwise, > > with equal standing. And the physics only depends on relative motion. > > > > Marcel Luttgens > > > > > > see > > > > > >http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_... > > > > > > "*The *acceleration analysis* of the twin paradox. > > > > > > *The Doppler Shift Analysis* > > > > > Suppose Stella and Terence each film the other's > > > > > clock through a telescope throughout the trip; > > > > > when does Stella see Terence's clock run fast? > > > > > > *The Spacetime Diagram Analysis* > > > > > Where we take an Olympian view, and gaze with > > > > > the Fates upon the world lines of Terence and Stella. > > > > > > *The Equivalence > > > plus de détails » > >
From: mluttgens on 26 Sep 2009 07:27 On 25 sep, 15:44, PD <thedraperfam...(a)gmail.com> wrote: > On Sep 25, 5:55 am, mluttgens <mluttg...(a)orange.fr> wrote: > > > > > > > On 23 sep, 14:23, PD <thedraperfam...(a)gmail.com> wrote: > > > > On Sep 22, 7:32 pm, mluttgens <mluttg...(a)orange.fr> wrote: > > > > > On 22 sep, 15:30, PD <thedraperfam...(a)gmail.com> wrote: > > > > > > On Sep 22, 7:33 am, mluttgens <mluttg...(a)orange.fr> wrote: > > > > > > > On 21 sep, 14:09, PD <thedraperfam...(a)gmail.com> wrote: > > > > > > > > On Sep 21, 5:59 am, mluttgens <mluttg...(a)orange.fr> wrote: > > > > > > > > > On 19 sep, 20:37, "G. L. Bradford" <glbra...(a)insightbb.com> wrote: > > > > > > > > > > "Inertial" <relativ...(a)rest.com> wrote in message > > > > > > > > > >news:003e775f$0$2915$c3e8da3(a)news.astraweb.com... > > > > > > > > > > > "mluttgens" <mluttg...(a)orange.fr> wrote in message > > > > > > > > > >news:41d5a838-7be2-4786-8820-32048a494322(a)o13g2000vbl.googlegroups.com... > > > > > > > > > >> On 19 sep, 02:25, "Inertial" <relativ...(a)rest.com> wrote: > > > > > > > > > >>> "mluttgens" <mluttg...(a)orange.fr> wrote in message > > > > > > > > > > >>>news:756d9890-f435-4e91-b813-48c6c697cbc4(a)h30g2000vbr.googlegroups.com... > > > > > > > > > > >>> > On 13 sep, 15:55, Sam Wormley <sworml...(a)mchsi.com> wrote: > > > > > > > > > >>> >> mluttgens wrote: > > > > > > > > > > >>> >> > Special relativity theory should be called the Theory of Mutual > > > > > > > > > >>> >> > Time Dilation. Clearly, mutual time dilation is nonsensical. > > > > > > > > > >>> >> > SRists found a solution for the twin paradox, explaining why "both > > > > > > > > > >>> >> > twins cannot be younger than each other", but consider normal > > > > > > > > > >>> >> > that two clocks moving relative to each other, for instance on > > > > > > > > > >>> >> > a road, show the same time dilation. Contradiction doesn't bother > > > > > > > > > >>> >> > them. They don't even try to find a general solution for > > > > > > > > > >>> >> > the nonsense, and modify SR accordingly. > > > > > > > > > > >>> >> > Marcel Luttgens > > > > > > > > > > >>> >> Marcel, you should take some time to learn what special > > > > > > > > > >>> >> relativity really says. One cannot have more than one > > > > > > > > > >>> >> perspective simultaneously. There has yet to be an observation > > > > > > > > > >>> >> that contradicts a prediction of special relativity. > > > > > > > > > > >>> > Let's consider two objects A and B in uniform > > > > > > > > > >>> > translatory motion. > > > > > > > > > > >>> Fine > > > > > > > > > > >>> > According to SR, if A moves at v toward B, > > > > > > > > > >>> > reciprocally, B moves at -v toward A. > > > > > > > > > > >>> That's not just SR .. its been known physics for hundreds of years. > > > > > > > > > > >>> > SR obviously doesn't take into consideration > > > > > > > > > >>> > the velocities vA and vB of the objects relative > > > > > > > > > >>> > to the CMBR (sometimes rightly called the rest > > > > > > > > > >>> > frame of the universe). > > > > > > > > > > >>> Why the fvck should it? It makes ABSOLUTELY NO DIFFERENCE to the > > > > > > > > > >>> relative > > > > > > > > > >>> speeds of A and B > > > > > > > > > > >>> > Let v be the velocity of A wrt B. > > > > > > > > > >>> > From the dipole anisotropy it observes, B > > > > > > > > > >>> > determines that its velocity relative to the > > > > > > > > > >>> > CMBR is vB, whose direction is the same as v. > > > > > > > > > > >>> No .. it wouldn't necessarily be in the same directions as v > > > > > > > > > > >> Sure, but it is what B (which could be the Earth) observed > > > > > > > > > >> in this scenario. > > > > > > > > > > > Not that it makes any difference to the relationship between A and B. > > > > > > > > > > you're wasting time discussing irrelevant nonsense. > > > > > > > > > > >>> > According to the CMBR observer (using c=1), > > > > > > > > > >>> > vA = (v-vB)/(1-vB*v) > > > > > > > > > >>> > tB = tCMBR * sqrt(1-vB^2) > > > > > > > > > >>> > tA = tCMBR * sqrt(1-((v-vB)/(1-vB*v))^2) > > > > > > > > > >>> > = tCMBR * sqrt1-vB^2)*sqrt(1-v^2)/(1-vB*v) > > > > > > > > > >>> > Hence, tA = tB * sqrt(1-v^2) / (1-vB*v). > > > > > > > > > > >>> > Clearly, the SR formula tA = tB * sqrt(1-v^2) > > > > > > > > > >>> > is correct only when B is at rest in the CMBR > > > > > > > > > >>> > (vB = 0). > > > > > > > > > >>> > But even in this case, SRists falsely claim > > > > > > > > > >>> > that B moves at -v relative to A, > > > > > > > > > > >>> It does. You just don't understand basic physics > > > > > > > > > > >> You are indirectly claiming that the CMBR moves relative > > > > > > > > > >> to A. > > > > > > > > > > > Not indirectly .. Directly > > > > > > > > > > >> Only brainwashed SRists can be so stupid. > > > > > > > > > > > Only you are so stupid to think that if I walk closer to a wall, that the > > > > > > > > > > wall stays the same distance away. > > > > > > > > > > ================================ > > > > > > > > > > There are walls, and then there are walls. There are those who are 'so > > > > > > > > > stupid' as to think if they walk long enough they will walk closer to the > > > > > > > > > horizon of Earth....that it will not stay the same distance from the walking > > > > > > > > > traveler as from the standing observer left behind. They are 'so stupid' as > > > > > > > > > to think that they can close with it. There are those who are 'so stupid' as > > > > > > > > > to think if they speed up they will speed closer to the universal horizon > > > > > > > > > constant of c (even getting closer to the distant Planck horizon of the > > > > > > > > > Universe), that it will not stay the same distance from the walking....er, > > > > > > > > > speeding....traveler as from the standing observer left behind. They are 'so > > > > > > > > > stupid' as to think that they can close with it. > > > > > > > > > > There are those 'so stupid' as to never realize that differences exist > > > > > > > > > between every constituent [local] universe and the overall entity that is > > > > > > > > > the [non-local] Universe. Differences that can be manipulated. Differences > > > > > > > > > that can't be manipulated. There are walls, and then there are walls. > > > > > > > > > > GL > > > > > > > > > They will not understand what you mean, being really > > > > > > > > brainwashed. > > > > > > > > Talking to them is like talking to a wall (no pun > > > > > > > > intended!). > > > > > > > > They will not realize that the CMBR must be taken > > > > > > > > into consideration, > > > > > > > > Actually, no it doesn't NEED to be taken into consideration, any more > > > > > > > than the Sun needs to be taken into consideration, or the center of > > > > > > > the galaxy needs to be taken into consideration, or any other > > > > > > > arbitrarily chosen artifact of the universe needs to be taken into > > > > > > > consideration. > > > > > > > Even if the SR analysis of the twin paradox were > > > > > > right, which it is not, because it doesn't take the > > > > > > Earth's velocity relative to the CMBR, > > > > > > Relative motion is a motion between TWO bodies, and a THIRD entity > > > > > (like the CMBR) does not NEED to be taken into account. I don't know > > > > > why you think relative velocity DOES need to take into account a third > > > > > body. > > > > > The TWO bodies are not isolated in the universe, which is ignored > > > > by SRT. > > > > Of course they're not isolated. This doesn't change the fact that the > > > relative motion only involves the two of them, and that the physics > > > depends only on the relative motion. It adds nothing to insist that an > > > arbitrarily chosen third reference point in the universe should be > > > taken into account, other than adding unnecessary baggage. > > > > > > > Occam's > > > > > > razor (http://en.wikipedia.org/wiki/Occam%27s_razor) > > > > > > "recommends selection of the hypothesis that introduces > > > > > > the fewest assumptions and postulates the fewest > > > > > > entities while still sufficiently answering the > > > > > > question". > > > > > > Sorry, but now you're grasping at straws. > > > > > Note that YOUR idea involves more assumptions, including a dependence > > > > > of relative velocity on an arbitrarily chosen third entity in the > > > > > universe, the CMBR. > > > > > SR is based on a pure mathematical concept, and wholly neglects the > > > > fact that its objects are physically linked to the whole universe. > > > > And the physics depends only on the pairwise linkages. But all the > > > pairwise linkages are of equal standing, and there is no reference > > > body whose linkages should be taken as special, preferred, or > > > absolute. > > > > > > Just because you have a hard time understanding SR, does NOT mean that > > > > > it involves more complicated assumptions or postulates. There are only > > > > > two assumptions in SR. Two. > > > > > Only two, that's why SR is wrong. > > > > Well, gee, just a second ago you said that Occam's razor would drive > > > toward the one with the fewest assumptions, if it accounts for what's > > > observed. Now suddenly you're not so sure you'd want to go with > > > Occam's razor on this one. > > > Hereafter are a few quotes from the introduction:http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_... > > > "SR does not declare that all frames of reference are equivalent, > > only so-called inertial frames. > > That's correct. And the CMBR does not distinguish itself by being > different here. How muddled up are the analyses of the twin paradox in terms. of relativity theory! , see for instance http://www.physicsforums.com/showthread.php?s=12dddfc2f78c05c783324da355c4780a&t=209625&page=2 Anyhow, a simple analysis uses SR + acceleration. But the simplest one would use SR + cmbr, which straightforwardly shows the absence of the paradox. Note that the applicability of SR(cmbr) is wholly general: When a clock A moves at V relative to the CMBR, and a clock B moves at v relative to clock A, it can be shown that tB = tA * sqrt(1-v^2)/(1+Vv) (see http://pagesperso-orange.fr/mluttgens/twinpdx1.htm for more insight). Let's note that V and v can have identical or opposite signs. Let's also note that claiming that the CMBR can be moving wrt an object is physically nonsensical. So, in SR(cmbr), one is left with tB = tA * sqrt(1-v^2)/(1+Vv) tA = tB * (1+Vv)/sqrt(1-v^2) Clearly, the time dilation effect is not reciprocal. Marcel Luttgens > > > It seems passing strange that Terence could age several years > > just because Stella engages her thrusters. > > Note here that the author is tracing through the mental errors that a > naive student will make. > > Stella sees Terence's clock leap forward when she engages her > thrusters. > This does NOT mean that she was able to reach across space and impinge > some physical interaction on Terence to make him suddenly grow gray > hair while he ate breakfast. You have the common misconception that > the change in a physical parameter (like clock rate) implies some > physical interaction with the clock to affect it. It couldn't be > further from the truth. > > When I look at a car and see that is moving at 60 mph relative to me, > and then I press my accelerator and look at the same > > plus de détails »- Masquer le texte des messages précédents - > > - Afficher le texte des messages précédents -...
From: PD on 26 Sep 2009 09:38 On Sep 26, 6:27 am, mluttgens <mluttg...(a)orange.fr> wrote: > On 25 sep, 15:44, PD <thedraperfam...(a)gmail.com> wrote: > > > > > On Sep 25, 5:55 am, mluttgens <mluttg...(a)orange.fr> wrote: > > > > On 23 sep, 14:23, PD <thedraperfam...(a)gmail.com> wrote: > > > > > On Sep 22, 7:32 pm, mluttgens <mluttg...(a)orange.fr> wrote: > > > > > > On 22 sep, 15:30, PD <thedraperfam...(a)gmail.com> wrote: > > > > > > > On Sep 22, 7:33 am, mluttgens <mluttg...(a)orange.fr> wrote: > > > > > > > > On 21 sep, 14:09, PD <thedraperfam...(a)gmail.com> wrote: > > > > > > > > > On Sep 21, 5:59 am, mluttgens <mluttg...(a)orange.fr> wrote: > > > > > > > > > > On 19 sep, 20:37, "G. L. Bradford" <glbra...(a)insightbb.com> wrote: > > > > > > > > > > > "Inertial" <relativ...(a)rest.com> wrote in message > > > > > > > > > > >news:003e775f$0$2915$c3e8da3(a)news.astraweb.com... > > > > > > > > > > > > "mluttgens" <mluttg...(a)orange.fr> wrote in message > > > > > > > > > > >news:41d5a838-7be2-4786-8820-32048a494322(a)o13g2000vbl.googlegroups.com... > > > > > > > > > > >> On 19 sep, 02:25, "Inertial" <relativ...(a)rest.com> wrote: > > > > > > > > > > >>> "mluttgens" <mluttg...(a)orange.fr> wrote in message > > > > > > > > > > > >>>news:756d9890-f435-4e91-b813-48c6c697cbc4(a)h30g2000vbr.googlegroups.com... > > > > > > > > > > > >>> > On 13 sep, 15:55, Sam Wormley <sworml...(a)mchsi.com> wrote: > > > > > > > > > > >>> >> mluttgens wrote: > > > > > > > > > > > >>> >> > Special relativity theory should be called the Theory of Mutual > > > > > > > > > > >>> >> > Time Dilation. Clearly, mutual time dilation is nonsensical. > > > > > > > > > > >>> >> > SRists found a solution for the twin paradox, explaining why "both > > > > > > > > > > >>> >> > twins cannot be younger than each other", but consider normal > > > > > > > > > > >>> >> > that two clocks moving relative to each other, for instance on > > > > > > > > > > >>> >> > a road, show the same time dilation. Contradiction doesn't bother > > > > > > > > > > >>> >> > them. They don't even try to find a general solution for > > > > > > > > > > >>> >> > the nonsense, and modify SR accordingly. > > > > > > > > > > > >>> >> > Marcel Luttgens > > > > > > > > > > > >>> >> Marcel, you should take some time to learn what special > > > > > > > > > > >>> >> relativity really says. One cannot have more than one > > > > > > > > > > >>> >> perspective simultaneously. There has yet to be an observation > > > > > > > > > > >>> >> that contradicts a prediction of special relativity. > > > > > > > > > > > >>> > Let's consider two objects A and B in uniform > > > > > > > > > > >>> > translatory motion. > > > > > > > > > > > >>> Fine > > > > > > > > > > > >>> > According to SR, if A moves at v toward B, > > > > > > > > > > >>> > reciprocally, B moves at -v toward A. > > > > > > > > > > > >>> That's not just SR .. its been known physics for hundreds of years. > > > > > > > > > > > >>> > SR obviously doesn't take into consideration > > > > > > > > > > >>> > the velocities vA and vB of the objects relative > > > > > > > > > > >>> > to the CMBR (sometimes rightly called the rest > > > > > > > > > > >>> > frame of the universe). > > > > > > > > > > > >>> Why the fvck should it? It makes ABSOLUTELY NO DIFFERENCE to the > > > > > > > > > > >>> relative > > > > > > > > > > >>> speeds of A and B > > > > > > > > > > > >>> > Let v be the velocity of A wrt B. > > > > > > > > > > >>> > From the dipole anisotropy it observes, B > > > > > > > > > > >>> > determines that its velocity relative to the > > > > > > > > > > >>> > CMBR is vB, whose direction is the same as v. > > > > > > > > > > > >>> No .. it wouldn't necessarily be in the same directions as v > > > > > > > > > > > >> Sure, but it is what B (which could be the Earth) observed > > > > > > > > > > >> in this scenario. > > > > > > > > > > > > Not that it makes any difference to the relationship between A and B. > > > > > > > > > > > you're wasting time discussing irrelevant nonsense. > > > > > > > > > > > >>> > According to the CMBR observer (using c=1), > > > > > > > > > > >>> > vA = (v-vB)/(1-vB*v) > > > > > > > > > > >>> > tB = tCMBR * sqrt(1-vB^2) > > > > > > > > > > >>> > tA = tCMBR * sqrt(1-((v-vB)/(1-vB*v))^2) > > > > > > > > > > >>> > = tCMBR * sqrt1-vB^2)*sqrt(1-v^2)/(1-vB*v) > > > > > > > > > > >>> > Hence, tA = tB * sqrt(1-v^2) / (1-vB*v). > > > > > > > > > > > >>> > Clearly, the SR formula tA = tB * sqrt(1-v^2) > > > > > > > > > > >>> > is correct only when B is at rest in the CMBR > > > > > > > > > > >>> > (vB = 0). > > > > > > > > > > >>> > But even in this case, SRists falsely claim > > > > > > > > > > >>> > that B moves at -v relative to A, > > > > > > > > > > > >>> It does. You just don't understand basic physics > > > > > > > > > > > >> You are indirectly claiming that the CMBR moves relative > > > > > > > > > > >> to A. > > > > > > > > > > > > Not indirectly .. Directly > > > > > > > > > > > >> Only brainwashed SRists can be so stupid. > > > > > > > > > > > > Only you are so stupid to think that if I walk closer to a wall, that the > > > > > > > > > > > wall stays the same distance away. > > > > > > > > > > > ================================ > > > > > > > > > > > There are walls, and then there are walls. There are those who are 'so > > > > > > > > > > stupid' as to think if they walk long enough they will walk closer to the > > > > > > > > > > horizon of Earth....that it will not stay the same distance from the walking > > > > > > > > > > traveler as from the standing observer left behind. They are 'so stupid' as > > > > > > > > > > to think that they can close with it. There are those who are 'so stupid' as > > > > > > > > > > to think if they speed up they will speed closer to the universal horizon > > > > > > > > > > constant of c (even getting closer to the distant Planck horizon of the > > > > > > > > > > Universe), that it will not stay the same distance from the walking....er, > > > > > > > > > > speeding....traveler as from the standing observer left behind. They are 'so > > > > > > > > > > stupid' as to think that they can close with it. > > > > > > > > > > > There are those 'so stupid' as to never realize that differences exist > > > > > > > > > > between every constituent [local] universe and the overall entity that is > > > > > > > > > > the [non-local] Universe. Differences that can be manipulated. Differences > > > > > > > > > > that can't be manipulated. There are walls, and then there are walls. > > > > > > > > > > > GL > > > > > > > > > > They will not understand what you mean, being really > > > > > > > > > brainwashed. > > > > > > > > > Talking to them is like talking to a wall (no pun > > > > > > > > > intended!). > > > > > > > > > They will not realize that the CMBR must be taken > > > > > > > > > into consideration, > > > > > > > > > Actually, no it doesn't NEED to be taken into consideration, any more > > > > > > > > than the Sun needs to be taken into consideration, or the center of > > > > > > > > the galaxy needs to be taken into consideration, or any other > > > > > > > > arbitrarily chosen artifact of the universe needs to be taken into > > > > > > > > consideration. > > > > > > > > Even if the SR analysis of the twin paradox were > > > > > > > right, which it is not, because it doesn't take the > > > > > > > Earth's velocity relative to the CMBR, > > > > > > > Relative motion is a motion between TWO bodies, and a THIRD entity > > > > > > (like the CMBR) does not NEED to be taken into account. I don't know > > > > > > why you think relative velocity DOES need to take into account a third > > > > > > body. > > > > > > The TWO bodies are not isolated in the universe, which is ignored > > > > > by SRT. > > > > > Of course they're not isolated. This doesn't change the fact that the > > > > relative motion only involves the two of them, and that the physics > > > > depends only on the relative motion. It adds nothing to insist that an > > > > arbitrarily chosen third reference point in the universe should be > > > > taken into account, other than adding unnecessary baggage. > > > > > > > > Occam's > > > > > > > razor (http://en.wikipedia.org/wiki/Occam%27s_razor) > > > > > > > "recommends selection of the hypothesis that introduces > > > > > > > the fewest assumptions and postulates the fewest > > > > > > > entities while still sufficiently answering the > > > > > > > question". > > > > > > > Sorry, but now you're grasping at straws. > > > > > > Note that YOUR idea involves more assumptions, including a dependence > > > > > > of relative velocity on an arbitrarily chosen third entity in the > > > > > > universe, the CMBR. > > > > > > SR is based on a pure mathematical concept, and wholly neglects the > > > > > fact that its objects are physically linked to the whole universe.. > > > > > And the physics depends only on the pairwise linkages. But all the > > > > pairwise linkages are of equal standing, and there is no reference > > > > body whose linkages should be taken as special, preferred, or > > > > absolute. > > > > > > > Just because you have a hard time understanding SR, does NOT mean that > > > > > > it involves more complicated assumptions or postulates. There are only > > > > > > two assumptions in SR. Two. > > > > > > Only two, that's why SR is wrong. > > > > > Well, gee, just a second ago you said that Occam's razor would drive > > > > toward the one with the fewest assumptions, if it accounts for what's > > > > observed. Now suddenly you're not so sure you'd want to go with > > > > Occam's razor on this one. > > > > Hereafter are a few quotes from the introduction:http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_... > > > > "SR does not declare that all frames of reference are equivalent, > > > only so-called inertial frames. > > > That's correct. And the CMBR does not distinguish itself by being > > different here. > > How muddled up are the analyses of the twin paradox in terms. > of relativity theory! , see for instancehttp://www.physicsforums.com/showthread.php?s=12dddfc2f78c05c783324da... Well, you get what you pay for, Marcel. If you're hoping for the same clarity about the twin paradox on an unmoderated newsgroup that you'd find in more carefully explained materials, then I think you're barking up the wrong tree. > > Anyhow, a simple analysis uses SR + acceleration. That's a matter of taste. The simplest one for me is the one that notes the signature of the metric, and then points out that because of that, the straightest worldline will obviously have the longest proper time, in complete and intuitive analogy with Euclidean distance. Penrose agrees in his book, to the point where he dismisses the twin puzzle as being obvious and trivial in a couple sentences by virtue of this simple fact. > > But the simplest one would use SR + cmbr, which > straightforwardly shows the absence of the paradox. The only problem with that of course, is that it is physically indefensible, flies in the face of the principle of relativity, and arbitrarily singles out a particular artifact of the universe as being special for no good reason. > Note that the applicability of SR(cmbr) is wholly general: > When a clock A moves at V relative to the CMBR, and > a clock B moves at v relative to clock A, it can be shown > that tB = tA * sqrt(1-v^2)/(1+Vv) > (seehttp://pagesperso-orange.fr/mluttgens/twinpdx1.htm > for more insight). > Let's note that V and v can have identical or opposite signs. > Let's also note that claiming that the CMBR can be moving > wrt an object is physically nonsensical. Why, no, it's not, as has been pointed out before -- no more than saying that the ocean can be said to be moving wrt to the boat is physically nonsensical, which it is not. > So, in SR(cmbr), one is left with > tB = tA * sqrt(1-v^2)/(1+Vv) > tA = tB * (1+Vv)/sqrt(1-v^2) > Clearly, the time dilation effect is not reciprocal. > > Marcel Luttgens > > > > > > It seems passing strange that Terence could age several years > > > just because Stella engages her thrusters. > > > Note here that the author is tracing through the mental errors that a > > naive student will make. > > > Stella sees Terence's clock leap forward when she engages her > > thrusters. > > This does NOT mean that she was able to reach across space and impinge > > some physical interaction on Terence to make him suddenly grow gray > > hair while he ate breakfast. You have the common misconception that > > the change in a physical parameter (like clock rate) implies some > > physical interaction with the clock to affect it. It couldn't be > > further from the truth. > > > When I look at a car and see that is moving at 60 mph relative to me, > > and then I press my accelerator and look at the same > > > plus de détails »- Masquer le texte des messages précédents - > > > - Afficher le texte des messages précédents -... > >
From: Dirk Van de moortel on 26 Sep 2009 13:16
mluttgens <mluttgens(a)orange.fr> wrote in message 0e036cc7-d090-4958-8c55-6d872544f3d3(a)o35g2000vbi.googlegroups.com [snip] >>>>>>>>>>>>>> According to the CMBR observer (using c=1), >>>>>>>>>>>>>> vA = (v-vB)/(1-vB*v) >>>>>>>>>>>>>> tB = tCMBR * sqrt(1-vB^2) >>>>>>>>>>>>>> tA = tCMBR * sqrt(1-((v-vB)/(1-vB*v))^2) >>>>>>>>>>>>>> = tCMBR * sqrt(1-vB^2)*sqrt(1-v^2)/(1-vB*v) >>>>>>>>>>>>>> Hence, tA = tB * sqrt(1-v^2) / (1-vB*v). [snip] > How muddled up are the analyses of the twin paradox in terms. > of relativity theory! , see for instance > http://www.physicsforums.com/showthread.php?s=12dddfc2f78c05c783324da355c4780a&t=209625&page=2 > > Anyhow, a simple analysis uses SR + acceleration. > > But the simplest one would use SR + cmbr, which > straightforwardly shows the absence of the paradox. > Note that the applicability of SR(cmbr) is wholly general: > When a clock A moves at V relative to the CMBR, and > a clock B moves at v relative to clock A, it can be shown > that tB = tA * sqrt(1-v^2)/(1+Vv) You obviously derived this formula as follows: You took the velocy of B w.r.t. CMBR as vB = (v+V) / (1+v V) so, using t for the CMBR-time you used tB = t sqrt (1-vB^2) = t sqrt( 1 - (v+V)^2 / (1+v V)^2 ) = t sqrt( (1+v V)^2 - (v+V)^2 ) / (1+v V) = t sqrt( 1-v^2 ) sqrt ( 1-V^2 ) / (1+v V ) and of course you also used tA = t sqrt( 1-V^2 ) so you took these together to find tB = tA sqrt( 1-v^2 ) / (1+ v V). Good, the algebra is correct. But note, Marcel, as always you fucked up where we take the meanings of the variables into account. In special relativity, the equation tA = t sqrt( 1-V^2 ) says something about two events occuring at the same place in A's frame, whereas the equation tB = t sqrt (1-vB^2) says something about two events occuring at the same place in B's frame. So, still in special relativity the combination tB = tA sqrt( 1-v^2 ) / (1+ v V) is only meaningful if it says something about two events that are simultaneous in A's frame AND in B's frame. That's only possible if v = 0, in other words words if tB = tA sqrt( 1-0 ) / (1+0) i.o.w. if tB = tA, but we already knew that, didn't we? > (see http://pagesperso-orange.fr/mluttgens/twinpdx1.htm > for more insight). Right. More insight in your failure to understand what the variables represent. > Let's note that V and v can have identical or opposite signs. > Let's also note that claiming that the CMBR can be moving > wrt an object is physically nonsensical. > So, in SR(cmbr), one is left with > tB = tA * sqrt(1-v^2)/(1+Vv) > tA = tB * (1+Vv)/sqrt(1-v^2) > Clearly, the time dilation effect is not reciprocal. Well, with the necessary condition that this can only happen when v = 0 , one is left with tB = tA tA = tB which looks quite reciprocal if you ask me. Quod Erat Debunkandum. Dirk Vdm |