colp, why did AE use the word "relativity"?
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From: colp on 21 Jun 2010 06:40 On Jun 21, 4:00 pm, stevendaryl3...(a)yahoo.com (Daryl McCullough) wrote: > colp says... > > > > >On Jun 20, 5:57=A0pm, Uncle Ben <b...(a)greenba.com> wrote: > >> colp, you complain that SR implies a contradiction: each twin is > >> younger than the other, which is absurd. No one has yet explained to > >> you why, in SR, it is not absurd. > > >They haven't explained the symmetric twin paradox because it is > >actually absurd to thing that two contradictory predictions are both > >true. > > SR only makes one prediction: in the symmetric case, the twins > are the same age when they reunite. That smacks of political reasoning: Start with your conclusion (in this case that there is no paradox) and make your argument fit the facts of the day as necessary. According to you, SR says: 1. Light travels at constant velocity, at speed c, in all directions, independent of the motion of the source. 2. An ideal clock traveling at speed v for time period t will show an elapsed time of T = t square-root(1-(v/c)^2). 3. An extended object traveling at speed v will, after reaching its equilibrium shape, be contracted in the direction of motion by a factor of square-root(1-(v/c)^2). 4. An object not under the influence of any forces will move at constant speed. Those are all true in any inertial coordinate system. The final claim, which is actually derivable from the first 4, (alternatively, 2&3 can be derived from 5) is: 5. If C is an inertial coordinate system, and C' is obtained from C by a translation, rotation or Lorentz transformation, then C' is an inertial coordinate system. There is no apparent reason for your selective application of the single clock transform and the time coordinate transform from the second premise, and there is nothing from the premises that would suggest that frame-jumping is prohibited. What appears to be the case is that relativists apply a set of rules which are not derived from the actual premises of SR in order to avoid the paradoxes which arise from the premises, and that these rules implictly enforce a preferred frame of reference. With this in mind, the symmetric twin paradox is harder to avoid: 1: Premise 2 implies that the twins will see each other's time dilate on both the outgoing and the return legs. 2. There is nothing from the premises which would describe the time compression necessary to compensate for the dilation and avoid the paradox.
From: Daryl McCullough on 21 Jun 2010 08:34 colp says... >>1. Light travels at constant velocity, at speed c, in all directions, >>independent of the motion of the source. >>2. An ideal clock traveling at speed v for time period t will show >>an elapsed time of T = t square-root(1-(v/c)^2). >>3. An extended object traveling at speed v will, after reaching its >>equilibrium shape, be contracted in the direction of motion by a >>factor of square-root(1-(v/c)^2). >>4. An object not under the influence of any forces will move at >>constant speed. >>Those are all true in any inertial coordinate system. The final claim, >>which is actually derivable from the first 4, (alternatively, >>2&3 can be derived from 5) is: >>5. If C is an inertial coordinate system, and C' is obtained from C >>by a translation, rotation or Lorentz transformation, then C' is >>an inertial coordinate system. >There is no apparent reason for your selective application of the >single clock transform and the time coordinate transform from the >second premise, and there is nothing from the premises that would >suggest that frame-jumping is prohibited. I'm not sure what you are asking for, but let me ask: Do you believe that you can derive a contradiction from 1-5? If so, then show how. As far as disallowing frame-jumping, the point is that rules 1-4 say what happens as measured using an inertial coordinate system. That doesn't mean that you can't use a noninertial coordinate system, it just means that SR does not justify apply rules 1-4 to such a coordinate system. If you are dealing with noninertial coordinate systems, and you apply rules 1-4, then you are *not* doing a derivation from the rules of SR. If you reach a contradiction, that is *not* a contradiction of SR, it's a contradiction of your own making. >What appears to be the case is that relativists apply a set of rules >which are not derived from the actual premises of SR in order to avoid >the paradoxes which arise from the premises, and that these rules >implictly enforce a preferred frame of reference. Rules 1-4 are derivable from the principle of relativity, together with the assumption that light travels at the same speed c in all directions. Einstein did that derivation. As for "implicitly enforcing a preferred frame of reference", that's absolutely false. As I said, rules 1-4 apply in *any* inertial coordinate system. As I said (rule 5), if they hold in one frame, then they hold in another frame, provided that the coordinates of the two frames are related through the Lorentz transformations. >With this in mind, the symmetric twin paradox is harder to avoid: > >1: Premise 2 implies that the twins will see each other's time dilate >on both the outgoing and the return legs. No, it doesn't. Look at what it says: it says for any *inertial* coordinate system. The traveling twin is *not* in an inertial coordinate system. In the symmetric twin paradox, there are three relevant inertial frames: (1) The frame of the Earth. (2) The frame of the one twin as he travels outward (which is the same as the frame of the other twin as he travels back). (3) The frame of the second twin as he travels outward (which is the same as the frame of the first twin as he travels back). In every one of these frames, the two twins have the same age when they get back together. Frame 1: According to this frame, each twin ages at a rate of square-root(1-(v/c)^2) throughout. So they end up the same age. Frame 2: According to this frame, the first twin ages faster during the outward leg, and the second twin ages faster during the return leg. So they end up the same age. Frame 3: According to this frame, the second twin ages faster during the outward leg, and the first twin ages faster during the return leg. So they end up the same age. >2. There is nothing from the premises which would describe the time >compression necessary to compensate for the dilation and avoid the >paradox. You haven't shown any paradox, so there is no paradox to avoid. In every inertial coordinate system, in the symmetric case, the two twins are the same age when they get back together. What you want to do is to apply rule number (2), "an ideal clock traveling at speed v for time period t will show an elapsed time of T = t square-root(1-(v/c)^2)", to the *noninertial* frame of each traveling twin. Well, SR doesn't allow you to do that. If you want to go ahead and do it, anyway, you certainly may, but then you are not using SR, you are using a theory of your own invention, which is loosely based on SR. If you end up with a contradiction, that's your fault, not SR's. Now, maybe you really want to know is, philosophically, why is the derivation of the Lorentz transformations dependent on inertial frames? I don't know of a deep answer, but if you actually look at the derivation, you will see that it is. The derivation does *not* work unless you assume that the coordinate system is inertial. The Lorentz transformations can only be derived for inertial coordinate systems, and it doesn't apply to any other coordinate systems. If you want to consider that a *limitation* of SR, that's fine. But it's not *inconsistent* to say that the equations only work for inertial coordinate systems. -- Daryl McCullough Ithaca, NY
From: Inertial on 21 Jun 2010 09:48 "colp" <colp(a)solder.ath.cx> wrote in message news:61dff2bc-2261-4b00-bd44-02bbfc212db6(a)y6g2000pra.googlegroups.com... > On Jun 21, 4:00 pm, stevendaryl3...(a)yahoo.com (Daryl McCullough) > wrote: >> colp says... >> >> >> >> >On Jun 20, 5:57=A0pm, Uncle Ben <b...(a)greenba.com> wrote: >> >> colp, you complain that SR implies a contradiction: each twin is >> >> younger than the other, which is absurd. No one has yet explained to >> >> you why, in SR, it is not absurd. >> >> >They haven't explained the symmetric twin paradox because it is >> >actually absurd to thing that two contradictory predictions are both >> >true. >> >> SR only makes one prediction: in the symmetric case, the twins >> are the same age when they reunite. > > That smacks of political reasoning: Start with your conclusion (in > this case that there is no paradox) and make your argument fit the > facts of the day as necessary. No .. it is the truth .. something with which you are unfamiliar > > According to you, SR says: > > 1. Light travels at constant velocity, at speed c, in all directions, > independent of the motion of the source. Yeup .. it sas that > 2. An ideal clock traveling at speed v for time period t will show > an elapsed time of T = t square-root(1-(v/c)^2). Yeup .. thats what an at-rest observer would measure > 3. An extended object traveling at speed v will, after reaching its > equilibrium shape, be contracted in the direction of motion by a > factor > of square-root(1-(v/c)^2). Yeup .. thats what an at-rest observer would measure > 4. An object not under the influence of any forces will move at > constant speed. Yeup > Those are all true in any inertial coordinate system. The final claim, > which is actually derivable from the first 4, (alternatively, > 2&3 can be derived from 5) is: > > 5. If C is an inertial coordinate system, and C' is obtained from C > by a translation, rotation or Lorentz transformation, then C' is > an inertial coordinate system. Fine > There is no apparent reason for your selective application of the > single clock transform and the time coordinate transform from the > second premise, and there is nothing from the premises that would > suggest that frame-jumping is prohibited. > > What appears to be the case is that relativists apply a set of rules > which are not derived from the actual premises of SR in order to avoid > the paradoxes which arise from the premises, and that these rules > implictly enforce a preferred frame of reference. WRONG .. they don't > With this in mind, the symmetric twin paradox is harder to avoid: There is no paradox. > 1: Premise 2 implies that the twins will see each other's time dilate > on both the outgoing and the return legs. Yeup > 2. There is nothing from the premises which would describe the time > compression necessary to compensate for the dilation and avoid the > paradox. It happens at the turn around How many time does this need to be told to you? I've asked you repeatedly if you want to see an analysis .. and you ignore it. Seems like you just want to remain ignorant.
From: colp on 21 Jun 2010 16:14 On Jun 22, 12:34 am, stevendaryl3...(a)yahoo.com (Daryl McCullough) wrote: > colp says... > > > > >>1. Light travels at constant velocity, at speed c, in all directions, > >>independent of the motion of the source. > >>2. An ideal clock traveling at speed v for time period t will show > >>an elapsed time of T = t square-root(1-(v/c)^2). > >>3. An extended object traveling at speed v will, after reaching its > >>equilibrium shape, be contracted in the direction of motion by a > >>factor of square-root(1-(v/c)^2). > >>4. An object not under the influence of any forces will move at > >>constant speed. > >>Those are all true in any inertial coordinate system. The final claim, > >>which is actually derivable from the first 4, (alternatively, > >>2&3 can be derived from 5) is: > >>5. If C is an inertial coordinate system, and C' is obtained from C > >>by a translation, rotation or Lorentz transformation, then C' is > >>an inertial coordinate system. > >There is no apparent reason for your selective application of the > >single clock transform and the time coordinate transform from the > >second premise, and there is nothing from the premises that would > >suggest that frame-jumping is prohibited. > > I'm not sure what you are asking for, but let me ask: Do you > believe that you can derive a contradiction from 1-5? If so, > then show how. There is a maxim of law which states: Tout ce que la loi ne defend pas est permis. Everything is permitted, which is not forbidden by law. What this means in this context is that it is proper to make observations from any frame of reference and to make inferences based upon them, since there is no law, either natural or otherwise which forbids this. Since SR is a theory about natural physical laws, it follows that there is nothing which forbids those observations and inferences from taking place within SR, unless the premises of SR prohibit it, either explictly or by implication. So, if we start with the second premise that: 2. An ideal clock traveling at speed v for time period t will show an elapsed time of T = t square-root(1-(v/c)^2). .... then before we can say anything about what SR predicts that an ideal clock will show, we have to know what limitations are placed upon this (apparently universally applicable) premise by implication, since there are no explicit limitations in the theory. The first limitation is implied by the title of special relativity, meaning that the prediction only applies to inertial frames of reference. However, if there is no preferred frame of reference, as is implied by relativity, then an observation made in one inertial frame should be consistent with a similar observation made in another inertial frame. If observations made in different inertial frames are treated differently, then there is a contradiction with the principle of relativity implied by the title; i.e. that there is no preferred frame of reference. At this point I'll ask a question with respect to the second premise: What elapsed time will be shown by an clock travelling at constant speed of 0.866c when a stationary local clock shows an elapsed time of 1 second? The answer, it would seem, is "it depends". Apparently you can't actually apply the second premise directly, but rather that you must first determine if there are any other observations being made, and then adjust the prediction so it is compatible with those predictions. Thus rather than looking at the situation from the local frame of reference, you must adjust your prediction based on another frame of reference, which I will call the preferred frame of reference. The bottom line is that either the symmetric twin paradox is a real paradox, or that a preferred frame of reference exists.
From: colp on 21 Jun 2010 16:50
<quote> colp says... >O.K. What remains from my previous post is the question of how you get >from the original premises of SR to a determination on when you should >apply the transformation for a single clock, and when you should apply >the transformation for the time coordinate in the case of the twins. It depends on the question. If you have a clock moving around on some path from event E1 to event E2, and you want to know the elapsed time on that clock, then you compute it like this: Elapsed time on the clock = Integral from t1 to t2 of square-root(1-(v/c)^2) dt where t1 is the time of E1, t2 is the time of t2, and where v is the velocity of the clock at time t. You can use any inertial coordinate system that is convenient to measure t1, t2 and v, and you'll get the same answer. The other kind of question is this: How old is one twin when the other twin's clock shows 200 seconds? That question is *not* a question about elapsed times on a single clock. You have to *also* answer questions about simultaneity. To answer the question, you need to know which events involving one twin are simultaneous with which events involving the other twin. To know whether two events are simultaneous, you have to pick a coordinate system. -- Daryl McCullough Ithaca, NY </quote> Re: How old is one twin when the other twin's clock shows 200 seconds? You say that I have to answer questions about simultaneity, but isn't it clear that the twin's clocks are simultaneous as the start of the experiment? You say that to know whether two events are simultaneous, you have to pick a coordinate system, but if two events occur at the same time and the same place, then are they not simultaneous regardless of the coordinate system? |