An apology to Androcles
in [Relativity]
|
From: harald on 5 Aug 2010 14:34 On Aug 4, 3:14 pm, Uncle Ben <b...(a)greenba.com> wrote: > On Aug 4, 6:27 am, harald <h...(a)swissonline.ch> wrote: > > > > > [Correction, as I had overlooked a "phi":] > > > On Jul 30, 9:10 pm, Uncle Ben <b...(a)greenba.com> wrote: > > > > An apology to Androcles > > > I had thought that the Einstein Expansion, proclaimed by Androcles in > > > sci.physics.relativity, was an error of confusing > > > frames of reference. But I was wrong. > > > I had not followed that particular discussion, but it's about a known > > topic. See below, you may be surprised! > > > > In his 1905 relativity paper, Einstein showed that x' = xi/gamma, > > > where x' is the length of a moving rod with respect to a stationary > > > frame of reference K and xi is the length of the moving rod with > > > respect to a frame k comoving with it. > > > Note: In that paper, x' is a *value* that corresponds to a *point* co- > > moving with the moving system, as measured with the stationary > > coordinate system. However, that value x' also corresponds to a moving > > *distance* with respect to the stationary system, that has the > > endpoints O' and xi on the moving system. Similarly the value of xi > > corresponds to a length as measured with the moving system. > > > > My difference with Androcles > > > was that I claimed that xi is the proper length L of the rod and the > > > shorter x' is a contracted length L/gamma. > > > x' is a value that corresponds to a moving distance along X as > > measured in the stationary system K. Einstein does not designate a rod > > with length L to such a distance; instead he does designate a rod with > > length L/phi for a similar measurement along Y. > > > > I thought that Androcles had these two backward. But no, he has > > > persuaded me otherwise; He agrees that x' is shorter than xi, but he > > > insists that x' is L and xi is an expanded length Lgamma. > > > No, L is used by Einstein for the "proper" length of a stationary rod > > as measured in a co-moving system. That differs from common, modern > > practice in textbook derivations in which the proper, co-moving length > > is indicated with L0, and L is used for the moving length as measured > > in the stationary system. > > > > The proper > > > length of the rod in k increases because of the existence of another > > > frame of reference K moving with respect to it. > > > I beg you pardon? The proper length of a rod cannot be affected by > > another reference frame, but it is clear from what follows that you > > are joking. > > > > (This other frame K is > > > called the "stationary" frame in Einstein's paper, but it can be > > > considered moving the other way with respect to the > > > rest frame k of the rod.) > > > This startling fresh idea would never have occurred to > > > me without Androcles's guidance. > > > It seems strange that a nearby frame of reference K, by its relative > > > motion, can expand a rod with respect to the rod's own proper frame k, > > > while the rod maintains a constant length with respect to K itself. > > > With a contracted ruler you measure a length L as gamma*L; that can be > > confusing but there is nothing strange about it! > > > Textbooks such as by Alonso&Finn put L=L'/gamma, so that the co-moving > > length L'= L*gamma. Einstein did not use that notation, but there is > > nothing wrong with it (nor is it a "fresh" idea). > > > > Imagine me in a Concorde (k) flying over you on the ground (K) sucking > > > on my cigar that had length L when I bought it. It seems strange that > > > to you the cigar has length L, but because I am flying within your > > > frame of reference, my cigar is Lgamma long. In fact, because of your > > > frame of reference, the Concord is stretched by gamma for me but not > > > for you. I have no idea why my cigar is now longer, because I have no > > > idea that you are down there. > > > It seems odd, doesn't it. Perhaps Androcles will explain it to us. > > > Androcles doesn't need to explain what textbooks already explained > > (surprise!). > > > Regards, > > Harald > > Harald, turn on your satire detector. > > Cheers! > > Ben Ben, as I wrote, it is clear from what follows that you are joking! However, it was not entirely clear to me what you thought that Androcles misunderstood... - Surely Androcles agrees with you that the moving rod is measured as LONGER in the moving frame than it is measured in the rest frame. In other words, the moving rod is measured as SHORTER in the rest frame than it is measured in the moving frame - it MIGHT be that he had not realised that such an observation only informs us about the RATIO of the measured lengths. However, surely Androcles wouldn't claim that a ruler of a nominal length of for example "2 m" will indicate another length if something happens to it - right? - Thus he'll certainly agree that a ruler cannot indicate another length than its own measure of itself (= proper length); - Similarly, if all rulers deform equally - as SRT assumes - also no other ruler or coordinate system can show anything else. He would expose himself as an absolute nutcase if he disagrees with that! Cheers, Harald
From: Uncle Ben on 5 Aug 2010 15:30 On Aug 5, 2:34 pm, harald <h...(a)swissonline.ch> wrote: > On Aug 4, 3:14 pm, Uncle Ben <b...(a)greenba.com> wrote: > > > > > > > On Aug 4, 6:27 am, harald <h...(a)swissonline.ch> wrote: > > > > [Correction, as I had overlooked a "phi":] > > > > On Jul 30, 9:10 pm, Uncle Ben <b...(a)greenba.com> wrote: > > > > > An apology to Androcles > > > > I had thought that the Einstein Expansion, proclaimed by Androcles in > > > > sci.physics.relativity, was an error of confusing > > > > frames of reference. But I was wrong. > > > > I had not followed that particular discussion, but it's about a known > > > topic. See below, you may be surprised! > > > > > In his 1905 relativity paper, Einstein showed that x' = xi/gamma, > > > > where x' is the length of a moving rod with respect to a stationary > > > > frame of reference K and xi is the length of the moving rod with > > > > respect to a frame k comoving with it. > > > > Note: In that paper, x' is a *value* that corresponds to a *point* co- > > > moving with the moving system, as measured with the stationary > > > coordinate system. However, that value x' also corresponds to a moving > > > *distance* with respect to the stationary system, that has the > > > endpoints O' and xi on the moving system. Similarly the value of xi > > > corresponds to a length as measured with the moving system. > > > > > My difference with Androcles > > > > was that I claimed that xi is the proper length L of the rod and the > > > > shorter x' is a contracted length L/gamma. > > > > x' is a value that corresponds to a moving distance along X as > > > measured in the stationary system K. Einstein does not designate a rod > > > with length L to such a distance; instead he does designate a rod with > > > length L/phi for a similar measurement along Y. > > > > > I thought that Androcles had these two backward. But no, he has > > > > persuaded me otherwise; He agrees that x' is shorter than xi, but he > > > > insists that x' is L and xi is an expanded length Lgamma. > > > > No, L is used by Einstein for the "proper" length of a stationary rod > > > as measured in a co-moving system. That differs from common, modern > > > practice in textbook derivations in which the proper, co-moving length > > > is indicated with L0, and L is used for the moving length as measured > > > in the stationary system. > > > > > The proper > > > > length of the rod in k increases because of the existence of another > > > > frame of reference K moving with respect to it. > > > > I beg you pardon? The proper length of a rod cannot be affected by > > > another reference frame, but it is clear from what follows that you > > > are joking. > > > > > (This other frame K is > > > > called the "stationary" frame in Einstein's paper, but it can be > > > > considered moving the other way with respect to the > > > > rest frame k of the rod.) > > > > This startling fresh idea would never have occurred to > > > > me without Androcles's guidance. > > > > It seems strange that a nearby frame of reference K, by its relative > > > > motion, can expand a rod with respect to the rod's own proper frame k, > > > > while the rod maintains a constant length with respect to K itself. > > > > With a contracted ruler you measure a length L as gamma*L; that can be > > > confusing but there is nothing strange about it! > > > > Textbooks such as by Alonso&Finn put L=L'/gamma, so that the co-moving > > > length L'= L*gamma. Einstein did not use that notation, but there is > > > nothing wrong with it (nor is it a "fresh" idea). > > > > > Imagine me in a Concorde (k) flying over you on the ground (K) sucking > > > > on my cigar that had length L when I bought it. It seems strange that > > > > to you the cigar has length L, but because I am flying within your > > > > frame of reference, my cigar is Lgamma long. In fact, because of your > > > > frame of reference, the Concord is stretched by gamma for me but not > > > > for you. I have no idea why my cigar is now longer, because I have no > > > > idea that you are down there. > > > > It seems odd, doesn't it. Perhaps Androcles will explain it to us. > > > > Androcles doesn't need to explain what textbooks already explained > > > (surprise!). > > > > Regards, > > > Harald > > > Harald, turn on your satire detector. > > > Cheers! > > > Ben > > Ben, as I wrote, it is clear from what follows that you are joking! > However, it was not entirely clear to me what you thought that > Androcles misunderstood... > > - Surely Androcles agrees with you that the moving rod is measured as > LONGER in the moving frame than it is measured in the rest frame. > > In other words, the moving rod is measured as SHORTER in the rest > frame than it is measured in the moving frame - it MIGHT be that he > had not realised that such an observation only informs us about the > RATIO of the measured lengths. > > However, surely Androcles wouldn't claim that a ruler of a nominal > length of for example "2 m" will indicate another length if something > happens to it - right? > > - Thus he'll certainly agree that a ruler cannot indicate another > length than its own measure of itself (= proper length); > > - Similarly, if all rulers deform equally - as SRT assumes - also no > other ruler or coordinate system can show anything else. > > He would expose himself as an absolute nutcase if he disagrees with > that! > > Cheers, > Harald- Hide quoted text - > > - Show quoted text - Harald, never presume that Androcles will choose the rational answer! I always read all your posts as I seek occasional sanity in this newsgroup. Ben
From: harald on 5 Aug 2010 15:46 On Aug 5, 9:30 pm, Uncle Ben <b...(a)greenba.com> wrote: > On Aug 5, 2:34 pm, harald <h...(a)swissonline.ch> wrote: > > > > > On Aug 4, 3:14 pm, Uncle Ben <b...(a)greenba.com> wrote: > > > > On Aug 4, 6:27 am, harald <h...(a)swissonline.ch> wrote: > > > > > [Correction, as I had overlooked a "phi":] > > > > > On Jul 30, 9:10 pm, Uncle Ben <b...(a)greenba.com> wrote: > > > > > > An apology to Androcles > > > > > I had thought that the Einstein Expansion, proclaimed by Androcles in > > > > > sci.physics.relativity, was an error of confusing > > > > > frames of reference. But I was wrong. > > > > > I had not followed that particular discussion, but it's about a known > > > > topic. See below, you may be surprised! > > > > > > In his 1905 relativity paper, Einstein showed that x' = xi/gamma, > > > > > where x' is the length of a moving rod with respect to a stationary > > > > > frame of reference K and xi is the length of the moving rod with > > > > > respect to a frame k comoving with it. > > > > > Note: In that paper, x' is a *value* that corresponds to a *point* co- > > > > moving with the moving system, as measured with the stationary > > > > coordinate system. However, that value x' also corresponds to a moving > > > > *distance* with respect to the stationary system, that has the > > > > endpoints O' and xi on the moving system. Similarly the value of xi > > > > corresponds to a length as measured with the moving system. > > > > > > My difference with Androcles > > > > > was that I claimed that xi is the proper length L of the rod and the > > > > > shorter x' is a contracted length L/gamma. > > > > > x' is a value that corresponds to a moving distance along X as > > > > measured in the stationary system K. Einstein does not designate a rod > > > > with length L to such a distance; instead he does designate a rod with > > > > length L/phi for a similar measurement along Y. > > > > > > I thought that Androcles had these two backward. But no, he has > > > > > persuaded me otherwise; He agrees that x' is shorter than xi, but he > > > > > insists that x' is L and xi is an expanded length Lgamma. > > > > > No, L is used by Einstein for the "proper" length of a stationary rod > > > > as measured in a co-moving system. That differs from common, modern > > > > practice in textbook derivations in which the proper, co-moving length > > > > is indicated with L0, and L is used for the moving length as measured > > > > in the stationary system. > > > > > > The proper > > > > > length of the rod in k increases because of the existence of another > > > > > frame of reference K moving with respect to it. > > > > > I beg you pardon? The proper length of a rod cannot be affected by > > > > another reference frame, but it is clear from what follows that you > > > > are joking. > > > > > > (This other frame K is > > > > > called the "stationary" frame in Einstein's paper, but it can be > > > > > considered moving the other way with respect to the > > > > > rest frame k of the rod.) > > > > > This startling fresh idea would never have occurred to > > > > > me without Androcles's guidance. > > > > > It seems strange that a nearby frame of reference K, by its relative > > > > > motion, can expand a rod with respect to the rod's own proper frame k, > > > > > while the rod maintains a constant length with respect to K itself. > > > > > With a contracted ruler you measure a length L as gamma*L; that can be > > > > confusing but there is nothing strange about it! > > > > > Textbooks such as by Alonso&Finn put L=L'/gamma, so that the co-moving > > > > length L'= L*gamma. Einstein did not use that notation, but there is > > > > nothing wrong with it (nor is it a "fresh" idea). > > > > > > Imagine me in a Concorde (k) flying over you on the ground (K) sucking > > > > > on my cigar that had length L when I bought it. It seems strange that > > > > > to you the cigar has length L, but because I am flying within your > > > > > frame of reference, my cigar is Lgamma long. In fact, because of your > > > > > frame of reference, the Concord is stretched by gamma for me but not > > > > > for you. I have no idea why my cigar is now longer, because I have no > > > > > idea that you are down there. > > > > > It seems odd, doesn't it. Perhaps Androcles will explain it to us. > > > > > Androcles doesn't need to explain what textbooks already explained > > > > (surprise!). > > > > > Regards, > > > > Harald > > > > Harald, turn on your satire detector. > > > > Cheers! > > > > Ben > > > Ben, as I wrote, it is clear from what follows that you are joking! > > However, it was not entirely clear to me what you thought that > > Androcles misunderstood... > > > - Surely Androcles agrees with you that the moving > > rod is measured as > > LONGER in the moving frame than it is measured in the > > rest frame. > > > In other words, the moving rod is measured as SHORTER > > in the rest > > frame than it is measured in the moving frame - it > > MIGHT be that he > > had not realised that such an observation only > > informs us about the > > RATIO of the measured lengths. > > > However, surely Androcles wouldn't claim that a > > ruler of a nominal > > length of for example "2 m" will indicate another > > length if something > > happens to it - right? > > > - Thus he'll certainly agree that a ruler cannot > > indicate another > > length than its own measure of itself > > (= proper length); [improve phrasing:] > > - Similarly, if all co-moving rulers deform > > equally --as SRT assumes-- no co-moving ruler > > or coordinate system can show anything else. > > He would expose himself as an absolute nutcase if he > > disagrees with that! > > > Cheers, > > Harald > > > Harald, never presume that Androcles will choose the > rational answer! > > I always read all your posts as I seek occasional > sanity in this newsgroup. > > Ben Thanks Ben, I also enjoy reading your posts. And occasionally Androcles surprises with a rational answer - let's see! Harald
From: ben6993 on 5 Aug 2010 16:30 On Aug 5, 7:34 pm, harald <h...(a)swissonline.ch> wrote: > On Aug 4, 3:14 pm, Uncle Ben <b...(a)greenba.com> wrote: > > > > > > > On Aug 4, 6:27 am, harald <h...(a)swissonline.ch> wrote: > > > > [Correction, as I had overlooked a "phi":] > > > > On Jul 30, 9:10 pm, Uncle Ben <b...(a)greenba.com> wrote: > > > > > An apology to Androcles > > > > I had thought that the Einstein Expansion, proclaimed by Androcles in > > > > sci.physics.relativity, was an error of confusing > > > > frames of reference. But I was wrong. > > > > I had not followed that particular discussion, but it's about a known > > > topic. See below, you may be surprised! > > > > > In his 1905 relativity paper, Einstein showed that x' = xi/gamma, > > > > where x' is the length of a moving rod with respect to a stationary > > > > frame of reference K and xi is the length of the moving rod with > > > > respect to a frame k comoving with it. > > > > Note: In that paper, x' is a *value* that corresponds to a *point* co- > > > moving with the moving system, as measured with the stationary > > > coordinate system. However, that value x' also corresponds to a moving > > > *distance* with respect to the stationary system, that has the > > > endpoints O' and xi on the moving system. Similarly the value of xi > > > corresponds to a length as measured with the moving system. > > > > > My difference with Androcles > > > > was that I claimed that xi is the proper length L of the rod and the > > > > shorter x' is a contracted length L/gamma. > > > > x' is a value that corresponds to a moving distance along X as > > > measured in the stationary system K. Einstein does not designate a rod > > > with length L to such a distance; instead he does designate a rod with > > > length L/phi for a similar measurement along Y. > > > > > I thought that Androcles had these two backward. But no, he has > > > > persuaded me otherwise; He agrees that x' is shorter than xi, but he > > > > insists that x' is L and xi is an expanded length Lgamma. > > > > No, L is used by Einstein for the "proper" length of a stationary rod > > > as measured in a co-moving system. That differs from common, modern > > > practice in textbook derivations in which the proper, co-moving length > > > is indicated with L0, and L is used for the moving length as measured > > > in the stationary system. > > > > > The proper > > > > length of the rod in k increases because of the existence of another > > > > frame of reference K moving with respect to it. > > > > I beg you pardon? The proper length of a rod cannot be affected by > > > another reference frame, but it is clear from what follows that you > > > are joking. > > > > > (This other frame K is > > > > called the "stationary" frame in Einstein's paper, but it can be > > > > considered moving the other way with respect to the > > > > rest frame k of the rod.) > > > > This startling fresh idea would never have occurred to > > > > me without Androcles's guidance. > > > > It seems strange that a nearby frame of reference K, by its relative > > > > motion, can expand a rod with respect to the rod's own proper frame k, > > > > while the rod maintains a constant length with respect to K itself. > > > > With a contracted ruler you measure a length L as gamma*L; that can be > > > confusing but there is nothing strange about it! > > > > Textbooks such as by Alonso&Finn put L=L'/gamma, so that the co-moving > > > length L'= L*gamma. Einstein did not use that notation, but there is > > > nothing wrong with it (nor is it a "fresh" idea). > > > > > Imagine me in a Concorde (k) flying over you on the ground (K) sucking > > > > on my cigar that had length L when I bought it. It seems strange that > > > > to you the cigar has length L, but because I am flying within your > > > > frame of reference, my cigar is Lgamma long. In fact, because of your > > > > frame of reference, the Concord is stretched by gamma for me but not > > > > for you. I have no idea why my cigar is now longer, because I have no > > > > idea that you are down there. > > > > It seems odd, doesn't it. Perhaps Androcles will explain it to us. > > > > Androcles doesn't need to explain what textbooks already explained > > > (surprise!). > > > > Regards, > > > Harald > > > Harald, turn on your satire detector. > > > Cheers! > > > Ben > > Ben, as I wrote, it is clear from what follows that you are joking! > However, it was not entirely clear to me what you thought that > Androcles misunderstood... > > - Surely Androcles agrees with you that the moving rod is measured as > LONGER in the moving frame than it is measured in the rest frame. > > In other words, the moving rod is measured as SHORTER in the rest > frame than it is measured in the moving frame - it MIGHT be that he > had not realised that such an observation only informs us about the > RATIO of the measured lengths. > > However, surely Androcles wouldn't claim that a ruler of a nominal > length of for example "2 m" will indicate another length if something > happens to it - right? > > - Thus he'll certainly agree that a ruler cannot indicate another > length than its own measure of itself (= proper length); > > - Similarly, if all rulers deform equally - as SRT assumes - also no > other ruler or coordinate system can show anything else. > > He would expose himself as an absolute nutcase if he disagrees with > that! > > Cheers, > Harald- Hide quoted text - > > - Show quoted text - http://en.wikipedia.org/wiki/Bell's_spaceship_paradox: Extract: "Bell pointed out that length contraction of objects as well as the lack of length contraction between objects in frame S can be explained physically, using Maxwell's laws. The distorted intermolecular fields cause moving objects to contract or to become stressed if hindered from doing so. In contrast, no such forces act in the space between rockets." I don't know about the supposed length contraction of objects and the suposed lack of length contraction between objects noted in the above extract. That seems to be a different thing from SR. In the derivation of the SR length contraction you could have two moving rods and the light emitted from the far end of the first rod and reflected back off the near end of the far rod after travelling through the gap. So L0 would instead now represent the gap between the two rods. SR should show that the gap contracted, just as much as a rod would have done. If there was a Bell-type contraction of a rod coupled with an SR contraction of the rod then wouldn't the effects be multiplicative and you would get a resultant L0/4 instead of L0/2? But why are the intermolecular fields distorted by constant relative velocity. I know that there are acceleration in Bell's spaceship paradox, maybe the answer lies there. I need to read the paradox again. In SR, the observer in frame K observes/calculated the apparent rod as length L0/2. The observer in frame k measures with a ruler the rod to be of length L0. I had previously assumed that the observer in K would, if he only could have the opportunity, measure the rest length of the rod as L0 too. But to get from rest to speed 0.886c the rod must at some point have been accelerated. Would any intermolecular field distortions still be affecting the rod once the acceleration is removed when limiting speed 0.886c has been achieved? Ie would the observer in k measure the rod as length L0 in his own frame, that being the same L0 as would have been measured in frame K were the rod to have started at rest pre-experment in frame K?
From: harald on 6 Aug 2010 05:47
On Aug 5, 10:30 pm, ben6993 <ben6...(a)hotmail.com> wrote: > On Aug 5, 7:34 pm, harald <h...(a)swissonline.ch> wrote: > > > > > On Aug 4, 3:14 pm, Uncle Ben <b...(a)greenba.com> wrote: > > > > On Aug 4, 6:27 am, harald <h...(a)swissonline.ch> wrote: > > > > > [Correction, as I had overlooked a "phi":] > > > > > On Jul 30, 9:10 pm, Uncle Ben <b...(a)greenba.com> wrote: > > > > > > An apology to Androcles > > > > > I had thought that the Einstein Expansion, proclaimed by Androcles in > > > > > sci.physics.relativity, was an error of confusing > > > > > frames of reference. But I was wrong. > > > > > I had not followed that particular discussion, but it's about a known > > > > topic. See below, you may be surprised! > > > > > > In his 1905 relativity paper, Einstein showed that x' = xi/gamma, > > > > > where x' is the length of a moving rod with respect to a stationary > > > > > frame of reference K and xi is the length of the moving rod with > > > > > respect to a frame k comoving with it. > > > > > Note: In that paper, x' is a *value* that corresponds to a *point* co- > > > > moving with the moving system, as measured with the stationary > > > > coordinate system. However, that value x' also corresponds to a moving > > > > *distance* with respect to the stationary system, that has the > > > > endpoints O' and xi on the moving system. Similarly the value of xi > > > > corresponds to a length as measured with the moving system. > > > > > > My difference with Androcles > > > > > was that I claimed that xi is the proper length L of the rod and the > > > > > shorter x' is a contracted length L/gamma. > > > > > x' is a value that corresponds to a moving distance along X as > > > > measured in the stationary system K. Einstein does not designate a rod > > > > with length L to such a distance; instead he does designate a rod with > > > > length L/phi for a similar measurement along Y. > > > > > > I thought that Androcles had these two backward. But no, he has > > > > > persuaded me otherwise; He agrees that x' is shorter than xi, but he > > > > > insists that x' is L and xi is an expanded length Lgamma. > > > > > No, L is used by Einstein for the "proper" length of a stationary rod > > > > as measured in a co-moving system. That differs from common, modern > > > > practice in textbook derivations in which the proper, co-moving length > > > > is indicated with L0, and L is used for the moving length as measured > > > > in the stationary system. > > > > > > The proper > > > > > length of the rod in k increases because of the existence of another > > > > > frame of reference K moving with respect to it. > > > > > I beg you pardon? The proper length of a rod cannot be affected by > > > > another reference frame, but it is clear from what follows that you > > > > are joking. > > > > > > (This other frame K is > > > > > called the "stationary" frame in Einstein's paper, but it can be > > > > > considered moving the other way with respect to the > > > > > rest frame k of the rod.) > > > > > This startling fresh idea would never have occurred to > > > > > me without Androcles's guidance. > > > > > It seems strange that a nearby frame of reference K, by its relative > > > > > motion, can expand a rod with respect to the rod's own proper frame k, > > > > > while the rod maintains a constant length with respect to K itself. > > > > > With a contracted ruler you measure a length L as gamma*L; that can be > > > > confusing but there is nothing strange about it! > > > > > Textbooks such as by Alonso&Finn put L=L'/gamma, so that the co-moving > > > > length L'= L*gamma. Einstein did not use that notation, but there is > > > > nothing wrong with it (nor is it a "fresh" idea). > > > > > > Imagine me in a Concorde (k) flying over you on the ground (K) sucking > > > > > on my cigar that had length L when I bought it. It seems strange that > > > > > to you the cigar has length L, but because I am flying within your > > > > > frame of reference, my cigar is Lgamma long. In fact, because of your > > > > > frame of reference, the Concord is stretched by gamma for me but not > > > > > for you. I have no idea why my cigar is now longer, because I have no > > > > > idea that you are down there. > > > > > It seems odd, doesn't it. Perhaps Androcles will explain it to us. > > > > > Androcles doesn't need to explain what textbooks already explained > > > > (surprise!). > > > > > Regards, > > > > Harald > > > > Harald, turn on your satire detector. > > > > Cheers! > > > > Ben > > > Ben, as I wrote, it is clear from what follows that you are joking! > > However, it was not entirely clear to me what you thought that > > Androcles misunderstood... > > > - Surely Androcles agrees with you that the moving rod is measured as > > LONGER in the moving frame than it is measured in the rest frame. > > > In other words, the moving rod is measured as SHORTER in the rest > > frame than it is measured in the moving frame - it MIGHT be that he > > had not realised that such an observation only informs us about the > > RATIO of the measured lengths. > > > However, surely Androcles wouldn't claim that a ruler of a nominal > > length of for example "2 m" will indicate another length if something > > happens to it - right? > > > - Thus he'll certainly agree that a ruler cannot indicate another > > length than its own measure of itself (= proper length); > > > - Similarly, if all rulers deform equally - as SRT assumes - also no > > other ruler or coordinate system can show anything else. > > > He would expose himself as an absolute nutcase if he disagrees with > > that! > > > Cheers, > > Harald- Hide quoted text - > > > - Show quoted text - > > http://en.wikipedia.org/wiki/Bell's_spaceship_paradox: > Extract: "Bell pointed out that length contraction of objects as well > as the lack of length contraction between objects in frame S can be > explained physically, using Maxwell's laws. The distorted > intermolecular fields cause moving objects to contract or to become > stressed if hindered from doing so. In contrast, no such forces act in > the space between rockets." > > I don't know about the supposed length contraction of objects and the > suposed lack of length contraction between objects noted in the above > extract. That seems to be a different thing from SR. In the > derivation of the SR length contraction you could have two moving rods > and the light emitted from the far end of the first rod and reflected > back off the near end of the far rod after travelling through the gap. > So L0 would instead now represent the gap between the two rods. If you stick with Einstein's derivation as you suggest, that distance is determined with co-moving "measuring-rods". > SR should show that the gap contracted, just as much as a rod would have > done. The result of a physical experiment depends on the experimental conditions. If you put two measuring rods a distance apart on a platform and bring the system in inertial motion, you have the conditions of Einstein's "moving system" derivation. From that kinematic derivation follows that the endpoints of the moving two rods should have a reduced distance between them; that implies that the rods did NOT exactly have the same acceleration in the "stationary" system. In contrast, the two identical and unconnected spaceships of Bells' example have the SAME acceleration as measured on earth. > If there was a Bell-type contraction of a rod coupled with an SR > contraction of the rod then wouldn't the effects be multiplicative and > you would get a resultant L0/4 instead of L0/2? But why are the > intermolecular fields distorted by constant relative velocity. I > know that there are acceleration in Bell's spaceship paradox, maybe > the answer lies there. I need to read the paradox again. > In SR, the observer in frame K observes/calculated the apparent rod as > length L0/2. The observer in frame k measures with a ruler the rod to > be of length L0. I had previously assumed that the observer in K > would, if he only could have the opportunity, measure the rest length > of the rod as L0 too. But to get from rest to speed 0.886c the rod > must at some point have been accelerated. Would any intermolecular > field distortions still be affecting the rod once the acceleration is > removed when limiting speed 0.886c has been achieved? Indeed, Heaviside calculated the electric and magnetic field distortions around 1888, based on Maxwell's theory. Based on that, Fitzgerald came with the hypothesis that molecular forces are electromagnetic, so that all moving objects will be contracted accordingly. Lorentz deduced the same. > Ie would the > observer in k measure the rod as length L0 in his own frame, The nominal length of a measuring rod does not change. ;-) > that > being the same L0 as would have been measured in frame K were the rod > to have started at rest pre-experment in frame K? Yes. Again, how could it be otherwise? Regards, Harald |