Simultaneity of Relativity
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From: PD on 9 Nov 2009 13:00 On Nov 9, 11:19 am, glird <gl...(a)aol.com> 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. > > Note: As used in Einstein's tor, it means > "If events occur at two spatially separated events, one at A and one > at B, their "simultaneity" requires that two clocks - one at A and the > other at B - that are set to mark rAB/c-v equal to rAB/c+v will mark > them as happening at the same time. Here: 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 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. This is in fact the definition that Einstein used. Notice that there are no synchronized clocks anywhere. > It is obvious that since the clocks are NOT synchronous (other than > via Einstein's novel definition of the word) the two events were NOT > simultaneous either. > > glird
From: Inertial on 9 Nov 2009 17:49 "glird" <glird(a)aol.com> wrote in message news:8259e389-8301-42f1-8e6b-5420c133303a(a)m38g2000yqd.googlegroups.com... > 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. > > Note: As used in Einstein's tor, it means > "If events occur at two spatially separated events, one at A and one > at B, their "simultaneity" requires that two clocks - one at A and the > other at B - that are set to mark rAB/c-v equal to rAB/c+v will mark > them as happening at the same time. Where did you get that from? In particular, what is v? > It is obvious that since the clocks are NOT synchronous (other than > via Einstein's novel definition of the word) the two events were NOT > simultaneous either. Why do you think they are not synchronous .. how would YOU synchronise two clocks?
From: mpc755 on 9 Nov 2009 18:17 On Nov 9, 12:19 pm, glird <gl...(a)aol.com> 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. > > Note: As used in Einstein's tor, it means > "If events occur at two spatially separated events, one at A and one > at B, their "simultaneity" requires that two clocks - one at A and the > other at B - that are set to mark rAB/c-v equal to rAB/c+v will mark > them as happening at the same time. > It is obvious that since the clocks are NOT synchronous (other than > via Einstein's novel definition of the word) the two events were NOT > simultaneous either. > > glird The problem with simultaneity in Einstein's train thought experiment is it only works with the idea of motion not being able to be applied to the aether, which means the aether is at rest relative to the train and at rest relative to the embankment. And if you don't even want to discuss aether, the three dimensional space the train frame of reference and the embankment frame of reference share cannot have the idea of motion applied to it which for both frames moving relative to one another is impossible. Measuring to the marks left by the lightning strikes in Einstein's train thought experiment is arbitrary. A platform is sitting above moving water and a pebble is dropped off the back of the platform and a mark is made into a sheet of paper as the pebble dropped into the water. The wave will ripple outward from where it hits the water at the same speed in all directions, relative to the water. If the center of this ripple is moving away from the platform the wave in the water will take longer to reach the platform than does a pebble dropped off the front of the platform which also goes through the sheet of paper. If the pebble is dropped off the back of the platform and later on a pebble is dropped off the front of the platform in such a way that the waves reach the platform simultaneously, when the Observer on the platform measures to the marks in the sheet of paper, which are equi- distant from the platform, the Observer will incorrectly conclude the pebbles were dropped simultaneously. In Einstein's train thought experiment the assumption is light travels at 'c' in all frames of reference from a point in three dimensional space related to the frame of reference. This is incorrect. In the above, when the waves reach the platform the waves have traveled from where the pebbles were dropped into the water, relative to the water. If the Observer on the platform had this information, the Observer would correctly conclude the pebble was dropped off the back of the platform prior to the pebble dropped off the front of the platform. Light waves travel at 'c' from the emission point in three dimensional space relative to the aether.
From: glird on 10 Nov 2009 11:33 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. > 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, "In accordance with definition the two clocks synchronize if t_B - t_A = t_A' - t_B." 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. 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: glird on 10 Nov 2009 12:24
On Nov 9, 5:49 pm, "Inertial" wrote: > "glird" wrote > << Note: As used in Einstein's tor, it means "If events occur at two spatially separated events, one at A and one at B, their "simultaneity" requires that two clocks - one at A and the other at B - that are set to mark rAB/c-v equal to rAB/c+v will mark them as happening at the same time. >> > > Where did you get that from? In particular, what is v? I got it from Einstein's 1905 paper, in which we find, x'/(c-v) + x'/(c+v), where x' = x-vt is the length of the moving rod as measured by the stationary system. In there, and as I used it, v is the speed of the moving rod wrt his "stationary system". > > It is obvious that since the clocks are NOT synchronous (other than via Einstein's novel definition of the word) the two events were NOT simultaneous either. > > > > Why do you think they are not synchronous? Let a rod moving at v = .6c be x' = rAB = .8 units long as measured by stationary system Z'. It is obvious that x'/(c-v) = .8/.4 = 2 is unequal to x'/(c+v)= .8/1.6 = .5. Since his moving clocks had been set to register the identical readings as those of this system, which have entirely different "times" than those required to measure the speed of light as the same in each direction, it is therefore obvious that clocks that are set to MEASURE 2 = .5 are not "synchronous" i.e. set to read the same "time" at the same instant. > How would YOU synchronise two clocks? I don't object to using Einstein's METHOD; I DO object to calling esynched clocks "synchronous" even if they aren't identically set per instant (i.e per "epoch"). glird |