Simultaneity of Relativity
in [Math]
|
Prev: chrouc
Next: Synergetics coordinates and Wikipedia
From: glird on 10 Nov 2009 12:36 On Nov 9, 6:17 pm, mpc755 wrote: > > The problem with simultaneity in Einstein's > train thought experiment [snip] The real problem is that his gedanken experiment has little to do with how the equations of STR actually work. Therefore these interminable arguments, as to whether or not they are valid, are useless. glird
From: PD on 10 Nov 2009 12:51 On Nov 10, 10:33 am, glird <gl...(a)aol.com> wrote: > On Nov 9, 1:00 pm, PD wrote:> On Nov 9, 11:19 am, glird wrote: > > > On Oct 13, 6:36 pm, PD wrote: > > > > Do you know the definition of simultaneity for two spatially separated events? > > > > I do. Do You? If so, please write it out for us. > > > < Here: If events occur at two spatially separated points, and a signal is sent with equal speed from each event to a single observer positioned midway between the two events, and the signals arrive at the observer at the same time, then this is what we mean when we say the two events are simultaneous. > > On the other hand, if events occur at two spatially separated events, > and a signal is sent with equal speed from each event to a single > observer positioned midway between the two events, and the signals > arrive at the observer at different times, then this is what we mean > when we say the two events are not simultaneous. > > > Please try again; this time without using signals or observers or > clocks. Why? This is what we MEAN when we say two events are simultaneous. > > > This is in fact the definition that Einstein used. > > In his 1905 STR paper he wrote: > "If at the point A of space there is a clock, an observer at A can > determine the time values events in the immediate proximity of A by > finding the positions of the hands which are simultaneous with these > events. If there is at the point B of space another clock in all > respects resembling the one at A, it is possible for an observer at B > to determine the time values of events in the immediate neighborhood > of B. but it is not possible without further assumption to compare in > respect of time, an event at A with an event at B. We have so far > defined only an "A time" and a "B time". We have not defined a common > "time" for A and B, for the latter cannot be defined at all unless we > establish _by definition_ [his italics] that the "time" required for > light to travel from A to B equals the "time" it requires to travel > from B to A." > He then gave an example that is similar to yours, though not > identical: > "Let a ray of light start at the "A time" t_A from A toward B, let it > at the "B time" t_B be reflected at B in the direction of A, and > arrive again at A at the "A time" t_A'." > Temporarily ignoring the fact that A and B might be on an inertially > moving system, he then said, The definition applies whether this is the case or not. And in fact, it is presumed that it IS! > "In accordance with definition the two clocks synchronize if > t_B - t_A = t_A' - t_B." OK, yes, you're right, Einstein used this definition to define how clocks get synchronized, and then he used this as a presumption for determining simultaneity of two spatially separated events. Do you need to see that the two definitions are equivalent? > A few pages later, after treating a horizontal rod moving at v on X of > a stationary system, he wrote, > "We imagine further that at the two ends A and B of the [moving] rod, > clocks are placed which synchronize > with [have the same settings as] > the clocks of the stationary system, that is to say that their > indications correspond at any instant to the "time of the stationary > system" at the places where they happen to be. These clocks are > therefore "synchronous in the stationary system". > "We imagine further that with each clock there is a co-moving > observer, and that these observers apply to both clocks the criterion > established in §1 for the synchronization of two clocks. Let a ray of > light depart from A at the time tA, let it be reflected at B at the > time tB, and reach A again at the time tA'. Taking into consideration > the principle of the constancy of the velocity of light we find that > tB-tA = rAB/(c-v) and tA'-tB = rAB/(c+v) > where rAB denotes the length of the moving rod -- measured in the > stationary system. Observers moving with the moving rod would thus > find that the two clocks were not synchronous, while observers in the > stationary system would declare the clocks to be synchronous." > > > Notice that there are no synchronized clocks anywhere. > > Perhaps not in his book to the layman, written decades later, but in > his germinal paper there were. He said "at the two ends A and B of > the [moving] rod, clocks are placed which synchronize with the clocks > of the stationary system". > He had previously postulated how those > clocks were to be set, and had here said that the observers on the > moving rod "apply to both clocks the criterion established in §1 for > the synchronization of two clocks". However, instead of continuing on > to show the next step required by the moving observers in order to > "synchronize" clocks A and B - which would have been that observer B > turns his clock's setting back by vx/c^2 seconds, where x = rAB as > measured by them and v is the velocity of their rod in the "empty > space" in which light propagates with a velocity c - he completely > changed the subject, saying, > "So we see that we cannot attach any absolute signification to the > concept of simultaneity, but that two events which, viewed from a > system of co-ordinates, are simultaneous, can no longer be looked upon > as simultaneous events when envisaged from a system which is in motion > relatively to that system." > "Synchonous" and "simultaneity" are two entirely different things! > Clocks are synchronous if they have identical settings. Events are > simultaneous if they occur at the same instant; regardless of whether > or not clocks even exist, or if they do, how they are set. > > For the record, PD and Inertial and mpc and Bruce, please be aware > that I respect your intelligence and know where you are > coming from. I too began my study of STR by reading Einstein and > Infeld's book written to the layman. I too found places where I > disagreed with their logic. On what basis? Disagreement should be on the basis of conflicting experimental data. > It took a year or so for me to learn that my arguments -- especially > those about his train-lightning gedanken -- though valid, had nothing > to do with STR; that in order to understand the theory one has to go > back to Einstein's actual 1905 paper. It took MANY years thereafter > to understand it well enough to find an actual error in it; and then > more, and more and then, one day, to suddenly discover that Einstein > had revised the proof copy of his paper (in the summer of 1905) in > order to include the Lorentz mathematics set forth in an earlier 1905 > paper by Poincare'. Once I realized THAT, the roof fell in as I found > place after place where his revisions contradicted themselves and/or > are mathematically false. > In the end I realized - and have written an article that PROVES it - > that Einstein didn't understand Poincare's "Lorentz Transformation > Equations" nor his own equations along the way to "deriving" them. > Although much of this is presented in "A Flower for Einstein", the > details are in a much shorter article called "The Missing Symbol", > which proves via the fact that the symbol IS missing that Einstein > really did revise his proof copy and, while doing so, didn't > understand his own mathematics. > > glird
From: mpc755 on 10 Nov 2009 13:14 On Nov 10, 12:36 pm, glird <gl...(a)aol.com> wrote: > On Nov 9, 6:17 pm, mpc755 wrote: > > > > > The problem with simultaneity in Einstein's > > train thought experiment [snip] > > The real problem is that his gedanken experiment has little to do > with how the equations of STR actually work. Therefore these > interminable arguments, as to whether or not they are valid, are > useless. > > glird Einstein's train thought experiment is fundamental to people's misunderstanding of how light behaves. It behaves as any other wave in a medium does and that is it travels relative to the medium it is propagating through. Einstein made the same mistake and that is why his train gedanken is so important. Light waves to not travel from the emission point and travel at 'c' from that point to the destination in the same frame of reference. In Einstein's train thought experiment, where the marks are made on the train and on the embankment are irrelevant as to how far the light travels to the Observers at M and M'. If the light travels from the marks made at A and B to M, then the aether is entrained and at rest relative to the embankment. If the light travels from the marks made at A' and B' to M', then the aether is entrained and at rest relative to the train. Since the embankment frame of reference and the train frame of reference both occupy the same space, and for this aether/space to be at rest for the train frame of reference and for the embankment frame of reference is physically impossible. This is what Einstein was trying to accomplish when he says the "idea of motion may not be applied to the [aether]." He is trying to have it both ways. Einstein needs the space/aether to be motionless relative to both frames of reference or his whole Relativity of Simultaneity is false. That is why he says: 'Ether and the Theory of Relativity by Albert Einstein' http://www-groups.dcs.st-and.ac.uk/~history/Extras/Einstein_ether.html "Now comes the anxious question:- Why must I in the theory distinguish the K system above all K' systems, which are physically equivalent to it in all respects, by assuming that the ether is at rest relatively to the K system? For the theoretician such an asymmetry in the theoretical structure, with no corresponding asymmetry in the system of experience, is intolerable. If we assume the ether to be at rest relatively to K, but in motion relatively to K', the physical equivalence of K and K' seems to me from the logical standpoint, not indeed downright incorrect, but nevertheless unacceptable." It is an anxious question because it requires Einstein to finish with "The idea of motion may not be applied to [aether]", which winds up undermining Relativity of Simultaneity and undermining measuring to the marks left by the lightning strikes and concluding anything about the simultaneity of the lightning strikes. Without knowing how the light travels from the lightning strikes to the Observers relative to the aether, you cannot conclude anything about when the lightning strike events occurred in either frame of reference. You can assume the light travels from A and B to M and the light from A' and B' to M', but since the idea of motion may not be applied to the aether/ space, that requires the shared three dimensional space to be at rest relative to train frame of reference and the embankment frame of reference, which is impossible. What you can conclude is due to the lightning strike events interaction with the aether and the fact the lightning strike event at A/A' is a single event, there is one light wave associated with the lightning strike and it is propagating outward at 'c' in all directions relative to the aether in the present.
From: mpc755 on 11 Nov 2009 00:14 On Nov 10, 1:14 pm, mpc755 <mpc...(a)gmail.com> wrote: > On Nov 10, 12:36 pm, glird <gl...(a)aol.com> wrote: > > > On Nov 9, 6:17 pm, mpc755 wrote: > > > > The problem with simultaneity in Einstein's > > > train thought experiment [snip] > > > The real problem is that his gedanken experiment has little to do > > with how the equations of STR actually work. Therefore these > > interminable arguments, as to whether or not they are valid, are > > useless. > > > glird > > Einstein's train thought experiment is fundamental to people's > misunderstanding of how light behaves. It behaves as any other wave in > a medium does and that is it travels relative to the medium it is > propagating through. > > Einstein made the same mistake and that is why his train gedanken is > so important. Light waves to not travel from the emission point and > travel at 'c' from that point to the destination in the same frame of > reference. In Einstein's train thought experiment, where the marks are > made on the train and on the embankment are irrelevant as to how far > the light travels to the Observers at M and M'. > > If the light travels from the marks made at A and B to M, then the > aether is entrained and at rest relative to the embankment. If the > light travels from the marks made at A' and B' to M', then the aether > is entrained and at rest relative to the train. Since the embankment > frame of reference and the train frame of reference both occupy the > same space, and for this aether/space to be at rest for the train > frame of reference and for the embankment frame of reference is > physically impossible. > > This is what Einstein was trying to accomplish when he says the "idea > of motion may not be applied to the [aether]." He is trying to have it > both ways. Einstein needs the space/aether to be motionless relative > to both frames of reference or his whole Relativity of Simultaneity is > false. That is why he says: > > 'Ether and the Theory of Relativity by Albert Einstein'http://www-groups.dcs.st-and.ac.uk/~history/Extras/Einstein_ether.html > > "Now comes the anxious question:- Why must I in the theory distinguish > the K system above all K' systems, which are physically equivalent to > it in all respects, by assuming that the ether is at rest relatively > to the K system? For the theoretician such an asymmetry in the > theoretical structure, with no corresponding asymmetry in the system > of experience, is intolerable. If we assume the ether to be at rest > relatively to K, but in motion relatively to K', the physical > equivalence of K and K' seems to me from the logical standpoint, not > indeed downright incorrect, but nevertheless unacceptable." > > It is an anxious question because it requires Einstein to finish with > "The idea of motion may not be applied to [aether]", which winds up > undermining Relativity of Simultaneity and undermining measuring to > the marks left by the lightning strikes and concluding anything about > the simultaneity of the lightning strikes. Without knowing how the > light travels from the lightning strikes to the Observers relative to > the aether, you cannot conclude anything about when the lightning > strike events occurred in either frame of reference. You can assume > the light travels from A and B to M and the light from A' and B' to > M', but since the idea of motion may not be applied to the aether/ > space, that requires the shared three dimensional space to be at rest > relative to train frame of reference and the embankment frame of > reference, which is impossible. > > What you can conclude is due to the lightning strike events > interaction with the aether and the fact the lightning strike event at > A/A' is a single event, there is one light wave associated with the > lightning strike and it is propagating outward at 'c' in all > directions relative to the aether in the present. There is a wall on the embankment. The lightning strike on the embankment occurs between the wall and the steel I bar. When the Observer C' on the train sticks out an arm and puts it in front of the Observer at M to take a picture of the I bar which is illuminated by the lightning strike, the light traveling from B' is blocked from reaching the outstretched arm of the by the wall on the embankment. The light from the lightning strike at B' does not reach the outstretched arm of the observer. If an image appears on the camera from the picture taken from the Observer at C's outstretched arm, then it must be of the light coming from the lightning strike at B. This means the image taken by the camera held at the Observer's chest and the image taken by the camera held in the outstretched arm will contain two different sized images of the I bar. If no image appears in the camera in the Observer at C's outstretched arm, what happened to the light waves that were traveling from B to M? Either way, Einstein's train thought experiment is incorrect. Either the images of the I bar are different sizes which means the light traveled from two different locations in three dimensional space and traveled two different distances to the Observer on the train, or no image appears in the picture taken from the outstretched arm of the Observer which means the light waves from B do not exist for the Observer at C'.
From: mpc755 on 11 Nov 2009 00:21
On Nov 10, 1:14 pm, mpc755 <mpc...(a)gmail.com> wrote: > On Nov 10, 12:36 pm, glird <gl...(a)aol.com> wrote: > > > On Nov 9, 6:17 pm, mpc755 wrote: > > > > The problem with simultaneity in Einstein's > > > train thought experiment [snip] > > > The real problem is that his gedanken experiment has little to do > > with how the equations of STR actually work. Therefore these > > interminable arguments, as to whether or not they are valid, are > > useless. > > > glird > > Einstein's train thought experiment is fundamental to people's > misunderstanding of how light behaves. It behaves as any other wave in > a medium does and that is it travels relative to the medium it is > propagating through. > > Einstein made the same mistake and that is why his train gedanken is > so important. Light waves to not travel from the emission point and > travel at 'c' from that point to the destination in the same frame of > reference. In Einstein's train thought experiment, where the marks are > made on the train and on the embankment are irrelevant as to how far > the light travels to the Observers at M and M'. > > If the light travels from the marks made at A and B to M, then the > aether is entrained and at rest relative to the embankment. If the > light travels from the marks made at A' and B' to M', then the aether > is entrained and at rest relative to the train. Since the embankment > frame of reference and the train frame of reference both occupy the > same space, and for this aether/space to be at rest for the train > frame of reference and for the embankment frame of reference is > physically impossible. > > This is what Einstein was trying to accomplish when he says the "idea > of motion may not be applied to the [aether]." He is trying to have it > both ways. Einstein needs the space/aether to be motionless relative > to both frames of reference or his whole Relativity of Simultaneity is > false. That is why he says: > > 'Ether and the Theory of Relativity by Albert Einstein'http://www-groups.dcs.st-and.ac.uk/~history/Extras/Einstein_ether.html > > "Now comes the anxious question:- Why must I in the theory distinguish > the K system above all K' systems, which are physically equivalent to > it in all respects, by assuming that the ether is at rest relatively > to the K system? For the theoretician such an asymmetry in the > theoretical structure, with no corresponding asymmetry in the system > of experience, is intolerable. If we assume the ether to be at rest > relatively to K, but in motion relatively to K', the physical > equivalence of K and K' seems to me from the logical standpoint, not > indeed downright incorrect, but nevertheless unacceptable." > > It is an anxious question because it requires Einstein to finish with > "The idea of motion may not be applied to [aether]", which winds up > undermining Relativity of Simultaneity and undermining measuring to > the marks left by the lightning strikes and concluding anything about > the simultaneity of the lightning strikes. Without knowing how the > light travels from the lightning strikes to the Observers relative to > the aether, you cannot conclude anything about when the lightning > strike events occurred in either frame of reference. You can assume > the light travels from A and B to M and the light from A' and B' to > M', but since the idea of motion may not be applied to the aether/ > space, that requires the shared three dimensional space to be at rest > relative to train frame of reference and the embankment frame of > reference, which is impossible. > > What you can conclude is due to the lightning strike events > interaction with the aether and the fact the lightning strike event at > A/A' is a single event, there is one light wave associated with the > lightning strike and it is propagating outward at 'c' in all > directions relative to the aether in the present. There is a wall on the embankment. The lightning strike on the embankment occurs between the wall and the steel I bar. When the Observer C' on the train sticks out an arm and puts it in front of the Observer at M to take a picture of the I bar which is illuminated by the lightning strike, the light traveling from B' is blocked from reaching the outstretched arm by the wall on the embankment. The light from the lightning strike at B' does not reach the outstretched arm of the observer. If an image appears on the camera from the picture taken from the Observer at C's outstretched arm, then it must be of the light coming from the lightning strike at B. This means the image taken by the camera held at the Observer's chest and the image taken by the camera held in the outstretched arm will contain two different sized images of the I bar. If no image appears in the camera in the Observer at C's outstretched arm, what happened to the light waves that were traveling from B to M? Either way, Einstein's train thought experiment is incorrect. Either the images of the I bar are different sizes which means the light traveled from two different locations in three dimensional space and traveled two different distances to the Observer on the train, or no image appears in the picture taken from the outstretched arm of the Observer which means the light waves from B do not exist for the Observer at C'. |