A constant speed of light in all reference frames? Surely you can't be serious.
in [Relativity]
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From: Bruce Richmond on 12 Mar 2010 12:56 On Mar 11, 10:54 pm, "Inertial" <relativ...(a)rest.com> wrote: > "Paul Stowe" <theaether...(a)gmail.com> wrote in message > > news:722fe1d3-ba1d-4439-bffe-eda2ca668f82(a)p3g2000pra.googlegroups.com... > > > > > > > On Mar 10, 8:57 am, PD <thedraperfam...(a)gmail.com> wrote: > >> On Mar 9, 9:41 pm, PaulStowe<theaether...(a)gmail.com> wrote: > > >> > On Mar 8, 8:05 pm, "Inertial" <relativ...(a)rest.com> wrote: > > >> > > "PaulStowe" <theaether...(a)gmail.com> wrote in message > > >> > >news:1132a230-92d9-484a-b0c1-d3a97532cad9(a)z10g2000prh.googlegroups.com... > > >> > > >> >> SR explains it as having to be c due to the geometry of > >> > > >> >> spacetime > > >> > > >> > That's simply a silly idea... > > >> > > >> That you think it is silly is your problem, not that of SR > > >> > > > Something physical may be represented by a geometric description.. > > >> > > And our universe is represented by Minkowski geometry. > > >> > Yes, you can descibe localized behavior with that format. BUT! to do > >> > so you must depend on finite light speed and its physical > >> > independence. Geometry neither predicts. explains, or has a basis for > >> > that. > > >> That's incorrect, Paul. The geometric structure of spacetime imposes > >> both a finite speed of light AND makes it frame-independent. > > >> The geometric structure of spacetime *necessarily* divides pairs of > >> events into three categories: spacelike-separated, timelike-separated, > >> and nullcone-separated. This structure also immediately leads to the > >> result that any wordline that could be traversed by something between > >> timelike-separated events will, in any other inertial reference frame, > >> still be between timelike-separated events. What this means explicitly > >> is that this object can never span two spacelike-separated events. > >> Thus, the universe of events is strictly divided into two completely > >> separated causal domains. The boundary of these domains is the null > >> cone. Since the null cone has a definite slope of space vs time, this > >> imposes a causal speed limit. (This limit does not exist in Euclidean > >> 3D+1D space -- it is a unique feature of the 4D space and its > >> geometry.) > > >> Furthermore, while transformations between inertial frames will shift > >> the slopes between pairs of timelike events (that is, the speed of an > >> object traveling between the two events), the same transformation > >> between pairs of events on the null cone do not change slope. What > >> this means is that any object that can travel between two events on > >> null cone will have the same speed regardless of inertial reference > >> frame. > > >> So you see, the geometric structure DOES imply both a causal speed > >> limit and the invariance of that causal speed limit with choice of > >> inertial reference frame. It just so happens that light appears to be > >> one of the candidate objects that can travel between nullcone- > >> separated events. > > >> If you need to see how the structure does impose those limits > >> formally, I could point you to a reference book or two that derives > >> this unambiguously. > > >> At the time that Einstein proposed special relativity, he did not > >> understand how such a geometric structure could produce those two > >> conclusions as necessary consequences. And so he just posited the > >> invariance of the speed of light as a postulate (or equivalently, > >> demanded that Maxwell's equations obey the principle of relativity). > >> It was only later that the geometric structure was uncovered and it > >> was understood how the light postulate follows directly from this > >> structure. > > >> PD > > > I wasn't going to bother with a reply since we have gone round & round > > on this very point. I find your argument without merit and I'm > > certain that you mind is made up. Why act like kid and continuously > > and say no it ain't, yes it is??? > > > In minkowski math c can be any finite value. > > Indeed it can. But we observe it to have a particular value in our > universe. Would that be the value in meters per second, miles per second, miles per hour.... I could go on. > > As Tom Roberts would > > argue the are nearly a infinite number of variations which fit this > > form. > > All equivalent as long as c is finite > > > Thus it's dependent upon c being a 'physical' constant. > > Yes .. it just doesn't really matter that much what particular value it has. > But it does have a particular value in our universe > > > And, > > as GR shows, it not even global. Now why might that be??? The logic > > (actually lack thereof) and thought process is 'in my opinion' silly > > and no one, not in print nor herein has provided any argument that is > > convincing that the math and geometry is NOT! a resultant of physical > > processes rather some magical geometry... > > The geometry models what we find happens physically. Why you insist there > be some physical cause for why space and time is as modeled by Minkowski > geometry, but do not similarly require a physical cause for why it would be > modeled by Euclidean geometry (especially when experimental evidence points > to it NOT being so modeled) sounds rather hypocritical to me.- Hide quoted text - > > - Show quoted text -
From: Ste on 12 Mar 2010 13:00 On 11 Mar, 20:57, PD <thedraperfam...(a)gmail.com> wrote: > On Mar 11, 2:15 pm, Ste <ste_ro...(a)hotmail.com> wrote: > > > > > > > On 11 Mar, 15:12, PD <thedraperfam...(a)gmail.com> wrote: > > > > On Mar 11, 6:43 am, Ste <ste_ro...(a)hotmail.com> wrote: > > > > > On 11 Mar, 01:51, "Peter Webb" <webbfam...(a)DIESPAMDIEoptusnet.com.au> > > > > wrote: > > > > > > No, perhaps you didn't understand. As I say, this is *not* the twins > > > > > paradox, because in the twins paradox only *one* twin leaves Earth. > > > > > > ________________________ > > > > > Its functionally the same. It is exactly the twins paradox, but with two > > > > > twins apparently doing exactly the same thing. > > > > > > Even if you cannot see that, the explanation on the Wikipedia page of the > > > > > Twins Paradox is trivially adapted for two twins. > > > > > > I assume that you do not understand the Wikipedia twins paradox page, or > > > > > else you would know the answers to your questions already. Which parts don't > > > > > you understand? > > > > > Let's just go through it step by step Peter, as we have been doing. > > > > It's pointless spending 10 more postings arguing about how the > > > > Wikipedia page does or does not answer the question, or how it is or > > > > is not relevant. As I've just said in a post to Inertial, the only > > > > analogy between my scenario and the twins paradox is that, in my > > > > scenario, both twins leave Earth, and both return the same age as each > > > > other - hence no paradox, and hence bearing no resemblance at all to > > > > the twins paradox. > > > > First of all, let's establish what you think is paradoxical at all > > > about the description of the twins in the twin puzzle. Then let's see > > > whether this paradox is present in the case you mention. > > > As I understand it, the supposed "paradox" in the twins paradox was > > that one returned younger than the other. It was, of course, not a > > paradox at all, but that's besides the point. > > No, then you do not understand the paradox, because there is nothing > contradictory in that statement at all. It may be surprising, but it's > not contradictory, not paradoxical. Disagreement of clocks is not a > paradox. > > The paradox, which is what is perceived (normally) by freshmen when > first introduced to this statement, is embodied in their immediate > classroom question: "But in the frame of the traveling twin, it is the > earth twin that is moving away and returning. Since this is symmetric > to the case of the traveling twin moving away and returning, then > shouldn't the traveling twin expect the earth twin to be younger when > they meet again?" Now perhaps the paradox is more apparent to you. > > However, the puzzle is specifically designed to emphasize the danger > of oversimplifying. In fact, the two twins are NOT symmetric, because > one unambiguously experiences acceleration and the other unambiguously > experiences no acceleration. This then leads to a discussion of what > produces the asymmetry in the time. I know Paul. I know. > Perhaps if you had started out by asking, "Since I don't see any > obvious paradox here at all, perhaps someone could illuminate me as to > why this is called the twin paradox?" Then at least you would have > been on square one. Really I just wanted to avoid going off on a long tangent about the twins paradox. As I said, the scenario that were were addressing is different from the twins paradox, in that we have three clocks, and the two clocks with which we are now concerned (B and C) both return to the origin point *synchronised* (albeit both lagging behind A), whereas the twins' ages are not synchronised on the return of the astronaut twin. So let me say again. The twins paradox would be applicable if we were talking about A and B, or A and C. In the event, we are talking about what B and C observe of each other from their own reference frames. There is, therefore, no correspondence with the twins paradox, because unlike the twins, B and C return synchronised with each other.
From: PD on 12 Mar 2010 13:12 On Mar 12, 11:56 am, Bruce Richmond <bsr3...(a)my-deja.com> wrote: > On Mar 11, 10:54 pm, "Inertial" <relativ...(a)rest.com> wrote: > > > > > "Paul Stowe" <theaether...(a)gmail.com> wrote in message > > >news:722fe1d3-ba1d-4439-bffe-eda2ca668f82(a)p3g2000pra.googlegroups.com... > > > > On Mar 10, 8:57 am, PD <thedraperfam...(a)gmail.com> wrote: > > >> On Mar 9, 9:41 pm, PaulStowe<theaether...(a)gmail.com> wrote: > > > >> > On Mar 8, 8:05 pm, "Inertial" <relativ...(a)rest.com> wrote: > > > >> > > "PaulStowe" <theaether...(a)gmail.com> wrote in message > > > >> > >news:1132a230-92d9-484a-b0c1-d3a97532cad9(a)z10g2000prh.googlegroups.com... > > > >> > > >> >> SR explains it as having to be c due to the geometry of > > >> > > >> >> spacetime > > > >> > > >> > That's simply a silly idea... > > > >> > > >> That you think it is silly is your problem, not that of SR > > > >> > > > Something physical may be represented by a geometric description. > > > >> > > And our universe is represented by Minkowski geometry. > > > >> > Yes, you can descibe localized behavior with that format. BUT! to do > > >> > so you must depend on finite light speed and its physical > > >> > independence. Geometry neither predicts. explains, or has a basis for > > >> > that. > > > >> That's incorrect, Paul. The geometric structure of spacetime imposes > > >> both a finite speed of light AND makes it frame-independent. > > > >> The geometric structure of spacetime *necessarily* divides pairs of > > >> events into three categories: spacelike-separated, timelike-separated, > > >> and nullcone-separated. This structure also immediately leads to the > > >> result that any wordline that could be traversed by something between > > >> timelike-separated events will, in any other inertial reference frame, > > >> still be between timelike-separated events. What this means explicitly > > >> is that this object can never span two spacelike-separated events. > > >> Thus, the universe of events is strictly divided into two completely > > >> separated causal domains. The boundary of these domains is the null > > >> cone. Since the null cone has a definite slope of space vs time, this > > >> imposes a causal speed limit. (This limit does not exist in Euclidean > > >> 3D+1D space -- it is a unique feature of the 4D space and its > > >> geometry.) > > > >> Furthermore, while transformations between inertial frames will shift > > >> the slopes between pairs of timelike events (that is, the speed of an > > >> object traveling between the two events), the same transformation > > >> between pairs of events on the null cone do not change slope. What > > >> this means is that any object that can travel between two events on > > >> null cone will have the same speed regardless of inertial reference > > >> frame. > > > >> So you see, the geometric structure DOES imply both a causal speed > > >> limit and the invariance of that causal speed limit with choice of > > >> inertial reference frame. It just so happens that light appears to be > > >> one of the candidate objects that can travel between nullcone- > > >> separated events. > > > >> If you need to see how the structure does impose those limits > > >> formally, I could point you to a reference book or two that derives > > >> this unambiguously. > > > >> At the time that Einstein proposed special relativity, he did not > > >> understand how such a geometric structure could produce those two > > >> conclusions as necessary consequences. And so he just posited the > > >> invariance of the speed of light as a postulate (or equivalently, > > >> demanded that Maxwell's equations obey the principle of relativity). > > >> It was only later that the geometric structure was uncovered and it > > >> was understood how the light postulate follows directly from this > > >> structure. > > > >> PD > > > > I wasn't going to bother with a reply since we have gone round & round > > > on this very point. I find your argument without merit and I'm > > > certain that you mind is made up. Why act like kid and continuously > > > and say no it ain't, yes it is??? > > > > In minkowski math c can be any finite value. > > > Indeed it can. But we observe it to have a particular value in our > > universe. > > Would that be the value in meters per second, miles per second, miles > per hour.... I could go on. A quantity can be thought of being something that is independent of the units used to measure it. A basketful of wheat contains the same quantity of wheat whether you choose to measure that quantity in bushels, quarts, tablespoons, cubic decimeters, ziploc bags, or kiloliters. In a sensible system of units (one where the units of space are the same as the units of time, rather than the artificially separate ones imposed by historical convenience), the value of c is 1, which is about the most obvious nonzero number you can imagine. > > > > As Tom Roberts would > > > argue the are nearly a infinite number of variations which fit this > > > form. > > > All equivalent as long as c is finite > > > > Thus it's dependent upon c being a 'physical' constant. > > > Yes .. it just doesn't really matter that much what particular value it has. > > But it does have a particular value in our universe > > > > And, > > > as GR shows, it not even global. Now why might that be??? The logic > > > (actually lack thereof) and thought process is 'in my opinion' silly > > > and no one, not in print nor herein has provided any argument that is > > > convincing that the math and geometry is NOT! a resultant of physical > > > processes rather some magical geometry... > > > The geometry models what we find happens physically. Why you insist there > > be some physical cause for why space and time is as modeled by Minkowski > > geometry, but do not similarly require a physical cause for why it would be > > modeled by Euclidean geometry (especially when experimental evidence points > > to it NOT being so modeled) sounds rather hypocritical to me.- Hide quoted text - > > > - Show quoted text - > >
From: PD on 12 Mar 2010 13:16 On Mar 12, 12:00 pm, Ste <ste_ro...(a)hotmail.com> wrote: > On 11 Mar, 20:57, PD <thedraperfam...(a)gmail.com> wrote: > > > > > On Mar 11, 2:15 pm, Ste <ste_ro...(a)hotmail.com> wrote: > > > > On 11 Mar, 15:12, PD <thedraperfam...(a)gmail.com> wrote: > > > > > On Mar 11, 6:43 am, Ste <ste_ro...(a)hotmail.com> wrote: > > > > > > On 11 Mar, 01:51, "Peter Webb" <webbfam...(a)DIESPAMDIEoptusnet.com..au> > > > > > wrote: > > > > > > > No, perhaps you didn't understand. As I say, this is *not* the twins > > > > > > paradox, because in the twins paradox only *one* twin leaves Earth. > > > > > > > ________________________ > > > > > > Its functionally the same. It is exactly the twins paradox, but with two > > > > > > twins apparently doing exactly the same thing. > > > > > > > Even if you cannot see that, the explanation on the Wikipedia page of the > > > > > > Twins Paradox is trivially adapted for two twins. > > > > > > > I assume that you do not understand the Wikipedia twins paradox page, or > > > > > > else you would know the answers to your questions already. Which parts don't > > > > > > you understand? > > > > > > Let's just go through it step by step Peter, as we have been doing. > > > > > It's pointless spending 10 more postings arguing about how the > > > > > Wikipedia page does or does not answer the question, or how it is or > > > > > is not relevant. As I've just said in a post to Inertial, the only > > > > > analogy between my scenario and the twins paradox is that, in my > > > > > scenario, both twins leave Earth, and both return the same age as each > > > > > other - hence no paradox, and hence bearing no resemblance at all to > > > > > the twins paradox. > > > > > First of all, let's establish what you think is paradoxical at all > > > > about the description of the twins in the twin puzzle. Then let's see > > > > whether this paradox is present in the case you mention. > > > > As I understand it, the supposed "paradox" in the twins paradox was > > > that one returned younger than the other. It was, of course, not a > > > paradox at all, but that's besides the point. > > > No, then you do not understand the paradox, because there is nothing > > contradictory in that statement at all. It may be surprising, but it's > > not contradictory, not paradoxical. Disagreement of clocks is not a > > paradox. > > > The paradox, which is what is perceived (normally) by freshmen when > > first introduced to this statement, is embodied in their immediate > > classroom question: "But in the frame of the traveling twin, it is the > > earth twin that is moving away and returning. Since this is symmetric > > to the case of the traveling twin moving away and returning, then > > shouldn't the traveling twin expect the earth twin to be younger when > > they meet again?" Now perhaps the paradox is more apparent to you. > > > However, the puzzle is specifically designed to emphasize the danger > > of oversimplifying. In fact, the two twins are NOT symmetric, because > > one unambiguously experiences acceleration and the other unambiguously > > experiences no acceleration. This then leads to a discussion of what > > produces the asymmetry in the time. > > I know Paul. I know. You can imagine my surprise, since what you said explicitly above was that the paradox was that the twins aged differently. > > > Perhaps if you had started out by asking, "Since I don't see any > > obvious paradox here at all, perhaps someone could illuminate me as to > > why this is called the twin paradox?" Then at least you would have > > been on square one. > > Really I just wanted to avoid going off on a long tangent about the > twins paradox. As I said, the scenario that were were addressing is > different from the twins paradox, in that we have three clocks, and > the two clocks with which we are now concerned (B and C) both return > to the origin point *synchronised* (albeit both lagging behind A), > whereas the twins' ages are not synchronised on the return of the > astronaut twin. Well, yes, it is a different result from the application of the same principle. If I calculate the angle that I can tip a TV tray before the coffee cup on it starts to slide, I find that I'm using the same principle (equilibrium of forces) that I would use to determine the tension in picture-hanger wire when mounting a photo on the wall. Different situation. Very same principle. Fine example of losing the forest for the trees. As you've done here. > > So let me say again. The twins paradox would be applicable if we were > talking about A and B, or A and C. In the event, we are talking about > what B and C observe of each other from their own reference frames. > There is, therefore, no correspondence with the twins paradox, because > unlike the twins, B and C return synchronised with each other.
From: ben6993 on 12 Mar 2010 14:13
On Mar 12, 6:16 pm, PD <thedraperfam...(a)gmail.com> wrote: > On Mar 12, 12:00 pm, Ste <ste_ro...(a)hotmail.com> wrote: > > > > > > > On 11 Mar, 20:57, PD <thedraperfam...(a)gmail.com> wrote: > > > > On Mar 11, 2:15 pm, Ste <ste_ro...(a)hotmail.com> wrote: > > > > > On 11 Mar, 15:12, PD <thedraperfam...(a)gmail.com> wrote: > > > > > > On Mar 11, 6:43 am, Ste <ste_ro...(a)hotmail.com> wrote: > > > > > > > On 11 Mar, 01:51, "Peter Webb" <webbfam...(a)DIESPAMDIEoptusnet.com.au> > > > > > > wrote: > > > > > > > > No, perhaps you didn't understand. As I say, this is *not* the twins > > > > > > > paradox, because in the twins paradox only *one* twin leaves Earth. > > > > > > > > ________________________ > > > > > > > Its functionally the same. It is exactly the twins paradox, but with two > > > > > > > twins apparently doing exactly the same thing. > > > > > > > > Even if you cannot see that, the explanation on the Wikipedia page of the > > > > > > > Twins Paradox is trivially adapted for two twins. > > > > > > > > I assume that you do not understand the Wikipedia twins paradox page, or > > > > > > > else you would know the answers to your questions already. Which parts don't > > > > > > > you understand? > > > > > > > Let's just go through it step by step Peter, as we have been doing. > > > > > > It's pointless spending 10 more postings arguing about how the > > > > > > Wikipedia page does or does not answer the question, or how it is or > > > > > > is not relevant. As I've just said in a post to Inertial, the only > > > > > > analogy between my scenario and the twins paradox is that, in my > > > > > > scenario, both twins leave Earth, and both return the same age as each > > > > > > other - hence no paradox, and hence bearing no resemblance at all to > > > > > > the twins paradox. > > > > > > First of all, let's establish what you think is paradoxical at all > > > > > about the description of the twins in the twin puzzle. Then let's see > > > > > whether this paradox is present in the case you mention. > > > > > As I understand it, the supposed "paradox" in the twins paradox was > > > > that one returned younger than the other. It was, of course, not a > > > > paradox at all, but that's besides the point. > > > > No, then you do not understand the paradox, because there is nothing > > > contradictory in that statement at all. It may be surprising, but it's > > > not contradictory, not paradoxical. Disagreement of clocks is not a > > > paradox. > > > > The paradox, which is what is perceived (normally) by freshmen when > > > first introduced to this statement, is embodied in their immediate > > > classroom question: "But in the frame of the traveling twin, it is the > > > earth twin that is moving away and returning. Since this is symmetric > > > to the case of the traveling twin moving away and returning, then > > > shouldn't the traveling twin expect the earth twin to be younger when > > > they meet again?" Now perhaps the paradox is more apparent to you. > > > > However, the puzzle is specifically designed to emphasize the danger > > > of oversimplifying. In fact, the two twins are NOT symmetric, because > > > one unambiguously experiences acceleration and the other unambiguously > > > experiences no acceleration. This then leads to a discussion of what > > > produces the asymmetry in the time. > > > I know Paul. I know. > > You can imagine my surprise, since what you said explicitly above was > that the paradox was that the twins aged differently. > > > > > > Perhaps if you had started out by asking, "Since I don't see any > > > obvious paradox here at all, perhaps someone could illuminate me as to > > > why this is called the twin paradox?" Then at least you would have > > > been on square one. > > > Really I just wanted to avoid going off on a long tangent about the > > twins paradox. As I said, the scenario that were were addressing is > > different from the twins paradox, in that we have three clocks, and > > the two clocks with which we are now concerned (B and C) both return > > to the origin point *synchronised* (albeit both lagging behind A), > > whereas the twins' ages are not synchronised on the return of the > > astronaut twin. > > Well, yes, it is a different result from the application of the same > principle. > > If I calculate the angle that I can tip a TV tray before the coffee > cup on it starts to slide, I find that I'm using the same principle > (equilibrium of forces) that I would use to determine the tension in > picture-hanger wire when mounting a photo on the wall. > > Different situation. Very same principle. > > Fine example of losing the forest for the trees. As you've done here. > > > > > > > So let me say again. The twins paradox would be applicable if we were > > talking about A and B, or A and C. In the event, we are talking about > > what B and C observe of each other from their own reference frames. > > There is, therefore, no correspondence with the twins paradox, because > > unlike the twins, B and C return synchronised with each other.- Hide quoted text - > > - Show quoted text -- Hide quoted text - > > - Show quoted text - I have written below a twin plank paradox of length. I know the explanation must really be very straightforward, but I don't see it yet. This is not a time paradox, but it looks to be a similar issue. A plank has four units of length (----) in its own frame and a garage has two units of length (--) in its own frame. There are two similar planks and garages in relative motion such that plank P and garage G are moving fast towards the other plank p and garage g. The relative speed is such that lengths are approximately halved in relativistic contraction. <--- direction of motion p ---- G' - g -- P' -- Where ' sign indicates motion in the other twins' frame. Here, p does not fit within G', but P' fits approx. within g. Looked at from the other frame, below, a similar result occurs: p' fits approx. within G, but P does not fit within g'. ----> p' -- G -- g' - P ---- As the same two events are looked at twice, i.e. from two frameworks, there are four outcomes in total. The shed doors are destroyed in two outcomes and the planks fit into the sheds in the other two outcomes. So it looks like one of the two sheds is damaged and the other is safe. But that cannot be true as the motion is relative not absolute, and the planks and garages are twins, and so the two outcomes should be identical. |