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| Tags: annotated, clock, einstein |
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Annotated Exerpt from: XII. The Behaviour of Measuring-Rods and Clocks in Motion Albert Einstein (1879-1955). Relativity: The Special and General Theory. 1920 http://www.bartleby.com/173/12.html ============================================ [Begin non-clock fluff] A priori it is quite clear that we must be able to learn something about the physical behaviour of measuring-rods and clocks from the equations of transformation, for the magnitudes x, y, z, t, are nothing more nor less than the results of measurements obtainable by means of measuring-rods and clocks. If we had based our considerations on the Galilei transformation we should not have obtained a contraction of the rod as a consequence of its motion. 4 Let us now consider a seconds-clock which is permanently situated at the origin (x' = 0) of K'. t' = 0 and t' = 1 are two successive ticks of this clock. The first and fourth equations of the Lorentz transformation give for these two ticks: t = 0 and (eqution for interval t) [End non-clock fluff] As judged from K, the clock is moving with the velocity v; as judged [ note that judgement over a non zero length path is the only mechanism stated to cause a variation in local and remote clocks] from this reference-body, the time which elapses between two strokes of the clock is not one second, but http://www.bartleby.com/173/M5.GIF (equation for interval) seconds, i.e. a somewhat larger time. [here we must make the assumtion that the clock is moving away from the observer. if it was moving toward the observer, he would say "a somewhat smaller time" ] As a consequence of its motion [away from the observer] [Doppler effect] the clock goes more slowly than when at rest. Here also the velocity c plays the part of an unattainable limiting velocity. [the result of Coulomb coupling to matter in the local FoR] ======================== Comments The clock described, in order to slow with motion, depends on the *inclusion* of an optical path delay, which increases with the motion. The clock is not characterized for motion which would decrease the path length. Absent is any inversse form of equation http://www.bartleby.com/173/M5.GIF further absent is a rigorous demonstration that such inverse application will conserve all clock strokes emitted as images. Sue... |
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#2
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"sue jahn" wrote in message ... Annotated Exerpt from: XII. The Behaviour of Measuring-Rods and Clocks in Motion Albert Einstein (1879-1955). Relativity: The Special and General Theory. 1920 http://www.bartleby.com/173/12.html ============================================ [Begin non-clock fluff] A priori it is quite clear that we must be able to learn something about the physical behaviour of measuring-rods and clocks from the equations of transformation, for the magnitudes x, y, z, t, are nothing more nor less than the results of measurements obtainable by means of measuring-rods and clocks. If we had based our considerations on the Galilei transformation we should not have obtained a contraction of the rod as a consequence of its motion. 4 Let us now consider a seconds-clock which is permanently situated at the origin (x' = 0) of K'. t' = 0 and t' = 1 are two successive ticks of this clock. The first and fourth equations of the Lorentz transformation give for these two ticks: t = 0 and (eqution for interval t) [End non-clock fluff] As judged from K, the clock is moving with the velocity v; as judged [ note that judgement over a non zero length path is the only mechanism stated to cause a variation in local and remote clocks] from this reference-body, the time which elapses between two strokes of the clock is not one second, but http://www.bartleby.com/173/M5.GIF (equation for interval) seconds, i.e. a somewhat larger time. [here we must make the assumtion that the clock is moving away from the observer. if it was moving toward the observer, he would say "a somewhat smaller time" ] As a consequence of its motion [away from the observer] [Doppler effect] the clock goes more slowly than when at rest. Here also the velocity c plays the part of an unattainable limiting velocity. [the result of Coulomb coupling to matter in the local FoR] ======================== Comments The clock described, in order to slow with motion, depends on the *inclusion* of an optical path delay, which increases with the motion. The clock is not characterized for motion which would decrease the path length. Absent is any inversse form of equation http://www.bartleby.com/173/M5.GIF further absent is a rigorous demonstration that such inverse application will conserve all clock strokes emitted as images. Sue... ---Conclusion--- The clock's operation is not defined by the theorist for motion that our real world experience shows should produce positive doppler shifts. http://www.srh.noaa.gov/mfl/newpage/...ado_radar.html We can accept no form of a "twins paradox" or "differential aging", real or imaginary, on the basis of a clock, whose operation is undefined for the condition where the variable element, the path to the observer, is undefined. Sue... |
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"sue jahn" wrote in message ... Annotated Exerpt from: XII. The Behaviour of Measuring-Rods and Clocks in Motion Albert Einstein (1879-1955). Relativity: The Special and General Theory. 1920 http://www.bartleby.com/173/12.html ============================================ [Begin non-clock fluff] A priori it is quite clear that we must be able to learn something about the physical behaviour of measuring-rods and clocks from the equations of transformation, for the magnitudes x, y, z, t, are nothing more nor less than the results of measurements obtainable by means of measuring-rods and clocks. If we had based our considerations on the Galilei transformation we should not have obtained a contraction of the rod as a consequence of its motion. 4 Let us now consider a seconds-clock which is permanently situated at the origin (x' = 0) of K'. t' = 0 and t' = 1 are two successive ticks of this clock. The first and fourth equations of the Lorentz transformation give for these two ticks: t = 0 and (eqution for interval t) [End non-clock fluff] As judged from K, the clock is moving with the velocity v; as judged [ note that judgement over a non zero length path is the only mechanism stated to cause a variation in local and remote clocks] from this reference-body, the time which elapses between two strokes of the clock is not one second, but http://www.bartleby.com/173/M5.GIF (equation for interval) = gamma seconds, i.e. a somewhat larger time. [here we must make the assumtion that the clock is moving away from the observer. if it was moving toward the observer, he would say "a somewhat smaller time" ] Certainly not! As judged from K, the observer corrects for the (classical) Dopper effect, assuming that light speed = c , homogeneously wrt K. As a consequence of its motion [away from the observer] [Doppler effect] the clock goes more slowly than when at rest. Completely erroneous, as I explained above. Doppler effect and time dilation are fully independent, and the Doppler effect is not taken into account in the above discussion. However, due to the fact that in observation the two effects are combined, the combined equation is often used and it's called "Relativistic Doppler". Perhaps that is the cause of your confusion. Here also the velocity c plays the part of an unattainable limiting velocity. [the result of Coulomb coupling to matter in the local FoR] Did you mean the unattainable infinite magnetic field energy? ======================== Comments You already gave a completely erroneous comment as "entree"... I can't wait to see where you are heading! ;-) The clock described, in order to slow with motion, depends on the *inclusion* of an optical path delay, which increases with the motion. No it does not. You may use local detectors anywhere along K. The clock is not characterized for motion which would decrease the path length. ?? Absent is any inversse form of equation http://www.bartleby.com/173/M5.GIF Why would you want that? further absent is a rigorous demonstration that such inverse application will conserve all clock strokes emitted as images. Hmm, I once did that for myself (with a spreadsheet) and it was enlightening. I can recommend it, nothing better than to do such an exercise yourself! BTW, there have been papers with full descriptions, for example Builder's 1957 paper on the Twin paradox and I think you can also find such description on internet. Cheers, Harald |
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"Harry" wrote in message ... "sue jahn" wrote in message ... Annotated Exerpt from: XII. The Behaviour of Measuring-Rods and Clocks in Motion Albert Einstein (1879-1955). Relativity: The Special and General Theory. 1920 http://www.bartleby.com/173/12.html ============================================ [Begin non-clock fluff] A priori it is quite clear that we must be able to learn something about the physical behaviour of measuring-rods and clocks from the equations of transformation, for the magnitudes x, y, z, t, are nothing more nor less than the results of measurements obtainable by means of measuring-rods and clocks. If we had based our considerations on the Galilei transformation we should not have obtained a contraction of the rod as a consequence of its motion. 4 Let us now consider a seconds-clock which is permanently situated at the origin (x' = 0) of K'. t' = 0 and t' = 1 are two successive ticks of this clock. The first and fourth equations of the Lorentz transformation give for these two ticks: t = 0 and (eqution for interval t) [End non-clock fluff] As judged from K, the clock is moving with the velocity v; as judged [ note that judgement over a non zero length path is the only mechanism stated to cause a variation in local and remote clocks] from this reference-body, the time which elapses between two strokes of the clock is not one second, but http://www.bartleby.com/173/M5.GIF (equation for interval) = gamma seconds, i.e. a somewhat larger time. [here we must make the assumtion that the clock is moving away from the observer. if it was moving toward the observer, he would say "a somewhat smaller time" ] Certainly not! As judged from K, the observer corrects for the (classical) Dopper effect, assuming that light speed = c , homogeneously wrt K. As a consequence of its motion [away from the observer] [Doppler effect] the clock goes more slowly than when at rest. Completely erroneous, as I explained above. Doppler effect and time dilation Your argument is circular. This clock IS the only basis for "time dilation" Sue... are fully independent, and the Doppler effect is not taken into account in the above discussion. However, due to the fact that in observation the two effects are combined, the combined equation is often used and it's called "Relativistic Doppler". Perhaps that is the cause of your confusion. Here also the velocity c plays the part of an unattainable limiting velocity. [the result of Coulomb coupling to matter in the local FoR] Did you mean the unattainable infinite magnetic field energy? ======================== Comments You already gave a completely erroneous comment as "entree"... I can't wait to see where you are heading! ;-) The clock described, in order to slow with motion, depends on the *inclusion* of an optical path delay, which increases with the motion. No it does not. You may use local detectors anywhere along K. The clock is not characterized for motion which would decrease the path length. ?? Absent is any inversse form of equation http://www.bartleby.com/173/M5.GIF Why would you want that? further absent is a rigorous demonstration that such inverse application will conserve all clock strokes emitted as images. Hmm, I once did that for myself (with a spreadsheet) and it was enlightening. I can recommend it, nothing better than to do such an exercise yourself! BTW, there have been papers with full descriptions, for example Builder's 1957 paper on the Twin paradox and I think you can also find such description on internet. Cheers, Harald |
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Harry wrote: "sue jahn" wrote in message ... Annotated Exerpt from: XII. The Behaviour of Measuring-Rods and Clocks in Motion Albert Einstein (1879-1955). Relativity: The Special and General Theory. 1920 http://www.bartleby.com/173/12.html ============================================ [Begin non-clock fluff] A priori it is quite clear that we must be able to learn something about the physical behaviour of measuring-rods and clocks from the equations of transformation, for the magnitudes x, y, z, t, are nothing more nor less than the results of measurements obtainable by means of measuring-rods and clocks. If we had based our considerations on the Galilei transformation we should not have obtained a contraction of the rod as a consequence of its motion. 4 Let us now consider a seconds-clock which is permanently situated at the origin (x' = 0) of K'. t' = 0 and t' = 1 are two successive ticks of this clock. The first and fourth equations of the Lorentz transformation give for these two ticks: t = 0 and (eqution for interval t) [End non-clock fluff] As judged from K, the clock is moving with the velocity v; as judged [ note that judgement over a non zero length path is the only mechanism stated to cause a variation in local and remote clocks] from this reference-body, the time which elapses between two strokes of the clock is not one second, but http://www.bartleby.com/173/M5.GIF (equation for interval) = gamma seconds, i.e. a somewhat larger time. [here we must make the assumtion that the clock is moving away from the observer. if it was moving toward the observer, he would say "a somewhat smaller time" ] Certainly not! As judged from K, the observer corrects for the (classical) Dopper effect, assuming that light speed = c , homogeneously wrt K. As a consequence of its motion [away from the observer] [Doppler effect] the clock goes more slowly than when at rest. Completely erroneous, as I explained above. Doppler effect and time dilation are fully independent, and the Doppler effect is not taken into account in the above discussion. However, due to the fact that in observation the two effects are combined, the combined equation is often used and it's called "Relativistic Doppler". Perhaps that is the cause of your confusion. Here also the velocity c plays the part of an unattainable limiting velocity. [the result of Coulomb coupling to matter in the local FoR] Did you mean the unattainable infinite magnetic field energy? ======================== Comments You already gave a completely erroneous comment as "entree"... I can't wait to see where you are heading! ;-) The clock described, in order to slow with motion, depends on the *inclusion* of an optical path delay, which increases with the motion. No it does not. You may use local detectors anywhere along K. The clock is not characterized for motion which would decrease the path length. ?? Absent is any inversse form of equation http://www.bartleby.com/173/M5.GIF Why would you want that? further absent is a rigorous demonstration that such inverse application will conserve all clock strokes emitted as images. Hmm, I once did that for myself (with a spreadsheet) and it was enlightening. I can recommend it, nothing better than to do such an exercise yourself! BTW, there have been papers with full descriptions, for example Builder's 1957 paper on the Twin paradox and I think you can also find such description on internet. Cheers, Harald BTW Harald, I forgot my manners. Thank you for your thoughtful response and the suggestions for other sources. Kind regards, Sue... |
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sue jahn wrote:
Annotated Exerpt from: XII. The Behaviour of Measuring-Rods and Clocks in Motion Albert Einstein (1879-1955). Relativity: The Special and General Theory. 1920 http://www.bartleby.com/173/12.html ============================================ [Begin non-clock fluff] A priori it is quite clear that we must be able to learn something about the physical behaviour of measuring-rods and clocks from the equations of transformation, for the magnitudes x, y, z, t, are nothing more nor less than the results of measurements obtainable by means of measuring-rods and clocks. If we had based our considerations on the Galilei transformation we should not have obtained a contraction of the rod as a consequence of its motion. 4 Let us now consider a seconds-clock which is permanently situated at the origin (x' = 0) of K'. t' = 0 and t' = 1 are two successive ticks of this clock. The first and fourth equations of the Lorentz transformation give for these two ticks: t = 0 and (eqution for interval t) [End non-clock fluff] As judged from K, the clock is moving with the velocity v; as judged [ note that judgement over a non zero length path is the only mechanism stated to cause a variation in local and remote clocks] from this reference-body, the time which elapses between two strokes of the clock is not one second, but http://www.bartleby.com/173/M5.GIF (equation for interval) seconds, i.e. a somewhat larger time. [here we must make the assumtion that the clock is moving away from the observer. if it was moving toward the observer, he would say "a somewhat smaller time" ] As a consequence of its motion [away from the observer] [Doppler effect] the clock goes more slowly than when at rest. You are indeed confused. Time dilation has nothing whatsoever with Doppler effect to do, and it is irrelevant in which direction the clock is moving. When measured in K, the moving clock is running slow. It doesn't matter where an optional observer might be. And a clock that is running slow has _longer_ seconds. That is why it is called time _dilation_. Here also the velocity c plays the part of an unattainable limiting velocity. [the result of Coulomb coupling to matter in the local FoR] ======================== Comments The clock described, in order to slow with motion, depends on the *inclusion* of an optical path delay, which increases with the motion. The clock is not characterized for motion which would decrease the path length. Utter nonsense. :-) Absent is any inversse form of equation http://www.bartleby.com/173/M5.GIF And why would you have an inverse form of said equation? The LT is: x' = (x - vt)/sqrt(1-v^2/c^2) t' = (t - vx/c^2)/sqrt(1-v^2/c^2) the inverse transform is: x = (x' + vt')/sqrt(1-v^2/c^2) t = (t' + vx'/c^2)/sqrt(1-v^2/c^2) further absent is a rigorous demonstration that such inverse application will conserve all clock strokes emitted as images. What is this? New-speek? :-) Paul |
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"Paul B. Andersen" wrote in message ... sue jahn wrote: Annotated Exerpt from: XII. The Behaviour of Measuring-Rods and Clocks in Motion Albert Einstein (1879-1955). Relativity: The Special and General Theory. 1920 http://www.bartleby.com/173/12.html ============================================ [Begin non-clock fluff] A priori it is quite clear that we must be able to learn something about the physical behaviour of measuring-rods and clocks from the equations of transformation, for the magnitudes x, y, z, t, are nothing more nor less than the results of measurements obtainable by means of measuring-rods and clocks. If we had based our considerations on the Galilei transformation we should not have obtained a contraction of the rod as a consequence of its motion. 4 Let us now consider a seconds-clock which is permanently situated at the origin (x' = 0) of K'. t' = 0 and t' = 1 are two successive ticks of this clock. The first and fourth equations of the Lorentz transformation give for these two ticks: t = 0 and (eqution for interval t) [End non-clock fluff] As judged from K, the clock is moving with the velocity v; as judged [ note that judgement over a non zero length path is the only mechanism stated to cause a variation in local and remote clocks] from this reference-body, the time which elapses between two strokes of the clock is not one second, but http://www.bartleby.com/173/M5.GIF (equation for interval) seconds, i.e. a somewhat larger time. [here we must make the assumtion that the clock is moving away from the observer. if it was moving toward the observer, he would say "a somewhat smaller time" ] As a consequence of its motion [away from the observer] [Doppler effect] the clock goes more slowly than when at rest. You are indeed confused. Time dilation has nothing whatsoever with Doppler effect to do, and it is irrelevant in which direction the clock is moving. When measured in K, the moving clock is running slow. It doesn't matter where an optional observer might be. And a clock that is running slow has _longer_ seconds. That is why it is called time _dilation_. Here also the velocity c plays the part of an unattainable limiting velocity. [the result of Coulomb coupling to matter in the local FoR] ======================== Comments The clock described, in order to slow with motion, depends on the *inclusion* of an optical path delay, which increases with the motion. The clock is not characterized for motion which would decrease the path length. Utter nonsense. :-) Absent is any inversse form of equation http://www.bartleby.com/173/M5.GIF And why would you have an inverse form of said equation? So the twin can get home. The LT is: x' = (x - vt)/sqrt(1-v^2/c^2) t' = (t - vx/c^2)/sqrt(1-v^2/c^2) the inverse transform is: x = (x' + vt')/sqrt(1-v^2/c^2) t = (t' + vx'/c^2)/sqrt(1-v^2/c^2) further absent is a rigorous demonstration that such inverse application will conserve all clock strokes emitted as images. What is this? Satisfy the condition and the twins will agree on what was on the screen at the Jupiter Drive-in Theatre. Don't satify it and you have a fairy tale. New-speek? :-) Paul Thank you for your thoughtful comments, Paul. Kind regards, Sue... |
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"sue jahn" wrote in message ... "Harry" wrote in message ... "sue jahn" wrote in message ... Annotated Exerpt from: XII. The Behaviour of Measuring-Rods and Clocks in Motion Albert Einstein (1879-1955). Relativity: The Special and General Theory. 1920 http://www.bartleby.com/173/12.html ============================================ [Begin non-clock fluff] A priori it is quite clear that we must be able to learn something about the physical behaviour of measuring-rods and clocks from the equations of transformation, for the magnitudes x, y, z, t, are nothing more nor less than the results of measurements obtainable by means of measuring-rods and clocks. If we had based our considerations on the Galilei transformation we should not have obtained a contraction of the rod as a consequence of its motion. 4 Let us now consider a seconds-clock which is permanently situated at the origin (x' = 0) of K'. t' = 0 and t' = 1 are two successive ticks of this clock. The first and fourth equations of the Lorentz transformation give for these two ticks: t = 0 and (eqution for interval t) [End non-clock fluff] As judged from K, the clock is moving with the velocity v; as judged [ note that judgement over a non zero length path is the only mechanism stated to cause a variation in local and remote clocks] from this reference-body, the time which elapses between two strokes of the clock is not one second, but http://www.bartleby.com/173/M5.GIF (equation for interval) = gamma seconds, i.e. a somewhat larger time. [here we must make the assumtion that the clock is moving away from the observer. if it was moving toward the observer, he would say "a somewhat smaller time" ] Certainly not! As judged from K, the observer corrects for the (classical) Dopper effect, assuming that light speed = c , homogeneously wrt K. As a consequence of its motion [away from the observer] [Doppler effect] the clock goes more slowly than when at rest. Completely erroneous, as I explained above. Doppler effect and time dilation Your argument is circular. This clock IS the only basis for "time dilation" Sue... The Doppler effect is not even taken into account in the above discussion. Deconfuse "time dilation" from the much larger Doppler effect by using local detectors, and you will start to understand why your above misinterpretation is erroneous. are fully independent, and the Doppler effect is not taken into account in the above discussion. However, due to the fact that in observation the two effects are combined, the combined equation is often used and it's called "Relativistic Doppler". Perhaps that is the cause of your confusion. Here also the velocity c plays the part of an unattainable limiting velocity. [the result of Coulomb coupling to matter in the local FoR] Did you mean the unattainable infinite magnetic field energy? Well? ======================== Comments You already gave a completely erroneous comment as "entree"... I can't wait to see where you are heading! ;-) The clock described, in order to slow with motion, depends on the *inclusion* of an optical path delay, which increases with the motion. No it does not. You may use local detectors anywhere along K. The clock is not characterized for motion which would decrease the path length. ?? Well? Absent is any inversse form of equation http://www.bartleby.com/173/M5.GIF Why would you want that? I repeat, why would you want to do that? As someone pointed out (was it Lorentz?), the inversion is only apparently contradictory, as the equations don't point to identical measurements: In one case a certain clock's delta-t (let's say of clock A) is compared with two other clock times (let's say clocks C and D), while in the "inverse" case a certain clock-time of clock A is compared with a certain clock time of another clock (B), with which the delta-t of, let's say clock C, is compared. further absent is a rigorous demonstration that such inverse application will conserve all clock strokes emitted as images. Hmm, I once did that for myself (with a spreadsheet) and it was enlightening. I can recommend it, nothing better than to do such an exercise yourself! BTW, there have been papers with full descriptions, for example Builder's 1957 paper on the Twin paradox and I think you can also find such description on internet. Cheers, Harald BTW Harald, I forgot my manners. Thank you for your thoughtful response and the suggestions for other sources. Kind regards, Sue... You're welcome! I can send you the above-mentioned paper if you like (PDF). Harald |
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#9
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"Harry" wrote in message ... "sue jahn" wrote in message ... "Harry" wrote in message ... "sue jahn" wrote in message ... Annotated Exerpt from: XII. The Behaviour of Measuring-Rods and Clocks in Motion Albert Einstein (1879-1955). Relativity: The Special and General Theory. 1920 http://www.bartleby.com/173/12.html ============================================ [Begin non-clock fluff] A priori it is quite clear that we must be able to learn something about the physical behaviour of measuring-rods and clocks from the equations of transformation, for the magnitudes x, y, z, t, are nothing more nor less than the results of measurements obtainable by means of measuring-rods and clocks. If we had based our considerations on the Galilei transformation we should not have obtained a contraction of the rod as a consequence of its motion. 4 Let us now consider a seconds-clock which is permanently situated at the origin (x' = 0) of K'. t' = 0 and t' = 1 are two successive ticks of this clock. The first and fourth equations of the Lorentz transformation give for these two ticks: t = 0 and (eqution for interval t) [End non-clock fluff] As judged from K, the clock is moving with the velocity v; as judged [ note that judgement over a non zero length path is the only mechanism stated to cause a variation in local and remote clocks] from this reference-body, the time which elapses between two strokes of the clock is not one second, but http://www.bartleby.com/173/M5.GIF (equation for interval) = gamma seconds, i.e. a somewhat larger time. [here we must make the assumtion that the clock is moving away from the observer. if it was moving toward the observer, he would say "a somewhat smaller time" ] Certainly not! As judged from K, the observer corrects for the (classical) Dopper effect, assuming that light speed = c , homogeneously wrt K. As a consequence of its motion [away from the observer] [Doppler effect] the clock goes more slowly than when at rest. Completely erroneous, as I explained above. Doppler effect and time dilation Your argument is circular. This clock IS the only basis for "time dilation" Sue... The Doppler effect is not even taken into account in the above discussion. Call it what you like. Deconfuse "time dilation" from the much larger Doppler effect by using local detectors, and you will start to understand why your above misinterpretation is erroneous. Their is no basis for "time dilation" except as demonstrated by this particular clock. Leaps of faith are not a part of logical analysis. AFAIK this is the first mention of a clock affected by motion in the paper. The reader is owed more of a foundation than sleight of pen. The light path is offered as the mechanism. and we can certainly accept the but it is described for one direction only. BTW I am quite familiar with light clocks and their various characterizations but my purpose is to adhere as close as possible to the original formulation. It is not approprate use the device unless it is explained previously. Light clocks have their own metaphysical problems that will only muddy the water. are fully independent, and the Doppler effect is not taken into account in the above discussion. However, due to the fact that in observation the two effects are combined, the combined equation is often used and it's called "Relativistic Doppler". Perhaps that is the cause of your confusion. Here also the velocity c plays the part of an unattainable limiting velocity. [the result of Coulomb coupling to matter in the local FoR] Did you mean the unattainable infinite magnetic field energy? Well? ======================== Comments You already gave a completely erroneous comment as "entree"... I can't wait to see where you are heading! ;-) The clock described, in order to slow with motion, depends on the *inclusion* of an optical path delay, which increases with the motion. No it does not. You may use local detectors anywhere along K. The clock is not characterized for motion which would decrease the path length. ?? Well? Absent is any inversse form of equation http://www.bartleby.com/173/M5.GIF Why would you want that? I repeat, why would you want to do that? You need that so a returning twin will have consistant clock operation. As someone pointed out (was it Lorentz?), the inversion is only apparently contradictory, as the equations don't point to identical measurements: In one case a certain clock's delta-t (let's say of clock A) is compared with two other clock times (let's say clocks C and D), while in the "inverse" case a certain clock-time of clock A is compared with a certain clock time of another clock (B), with which the delta-t of, let's say clock C, is compared. The $2 Bell hop problem is apparently contradictory. Are we doomed to accept the mathematics that causes the conflict? further absent is a rigorous demonstration that such inverse application will conserve all clock strokes emitted as images. Hmm, I once did that for myself (with a spreadsheet) and it was enlightening. I can recommend it, nothing better than to do such an exercise yourself! BTW, there have been papers with full descriptions, for example Builder's 1957 paper on the Twin paradox and I think you can also find such description on internet. Cheers, Harald BTW Harald, I forgot my manners. Thank you for your thoughtful response and the suggestions for other sources. Kind regards, Sue... You're welcome! I can send you the above-mentioned paper if you like (PDF). Thanks for asking first because I am having some problems with large files and my ISP. If it is less than 200K I think it will work and I would be happy to receive a copy. Sue... Harald |
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#10
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"sue jahn" wrote in message ... "Harry" wrote in message ... "sue jahn" wrote in message ... "Harry" wrote in message ... "sue jahn" wrote in message ... Annotated Exerpt from: XII. The Behaviour of Measuring-Rods and Clocks in Motion Albert Einstein (1879-1955). Relativity: The Special and General Theory. 1920 http://www.bartleby.com/173/12.html ============================================ [Begin non-clock fluff] A priori it is quite clear that we must be able to learn something about the physical behaviour of measuring-rods and clocks from the equations of transformation, for the magnitudes x, y, z, t, are nothing more nor less than the results of measurements obtainable by means of measuring-rods and clocks. If we had based our considerations on the Galilei transformation we should not have obtained a contraction of the rod as a consequence of its motion. 4 Let us now consider a seconds-clock which is permanently situated at the origin (x' = 0) of K'. t' = 0 and t' = 1 are two successive ticks of this clock. The first and fourth equations of the Lorentz transformation give for these two ticks: t = 0 and (eqution for interval t) [End non-clock fluff] As judged from K, the clock is moving with the velocity v; as judged [ note that judgement over a non zero length path is the only mechanism stated to cause a variation in local and remote clocks] from this reference-body, the time which elapses between two strokes of the clock is not one second, but http://www.bartleby.com/173/M5.GIF (equation for interval) = gamma seconds, i.e. a somewhat larger time. [here we must make the assumtion that the clock is moving away from the observer. if it was moving toward the observer, he would say "a somewhat smaller time" ] Certainly not! As judged from K, the observer corrects for the (classical) Dopper effect, assuming that light speed = c , homogeneously wrt K. As a consequence of its motion [away from the observer] [Doppler effect] the clock goes more slowly than when at rest. Completely erroneous, as I explained above. Doppler effect and time dilation Your argument is circular. This clock IS the only basis for "time dilation" Sue... The Doppler effect is not even taken into account in the above discussion. Call it what you like. Deconfuse "time dilation" from the much larger Doppler effect by using local detectors, and you will start to understand why your above misinterpretation is erroneous. Their is no basis for "time dilation" except as demonstrated by this particular clock. Leaps of faith are not a part of logical analysis. You confuse faith with theory. Due to your bias against the theory, likely it will be impossible for you to understand it. Thus I won't try anymore, except if you open your mind. AFAIK this is the first mention of a clock affected by motion in the paper. The reader is owed more of a foundation than sleight of pen. The light path is offered as the mechanism. and we can certainly accept the but it is described for one direction only. The foundation is the experiments that led Lorentz and Poincare to that theory. The fact that Einstein tried to dispose of the ether by not explicitly using it in his derivation of the same theory doesn't discredit it. BTW, the same applies to classical mechanics: to me Newton's mechanics makes sense, not "Galilean" mechanics. But the equations are the same and they are considered to be the same "theory". BTW I am quite familiar with light clocks and their various characterizations but my purpose is to adhere as close as possible to the original formulation. It is not approprate use the device unless it is explained previously. Light clocks have their own metaphysical problems that will only muddy the water. - I didn't mention any light clock. - The metaphysics happens to be the problem in Einstein's discussion (and the cause of your resistance!), not the physics. SNIP Here also the velocity c plays the part of an unattainable limiting velocity. [the result of Coulomb coupling to matter in the local FoR] Did you mean the unattainable infinite magnetic field energy? Well? Well??? ======================== Comments SNIP The clock is not characterized for motion which would decrease the path length. ?? Well? Well?? Absent is any inversse form of equation http://www.bartleby.com/173/M5.GIF Why would you want that? I repeat, why would you want to do that? You need that so a returning twin will have consistant clock operation. Inexact, as I tried to explain below - and also Andersen, in his reply. As someone pointed out (was it Lorentz?), the inversion is only apparently contradictory, as the equations don't point to identical measurements: In one case a certain clock's delta-t (let's say of clock A) is compared with two other clock times (let's say clocks C and D), while in the "inverse" case a certain clock-time of clock A is compared with a certain clock time of another clock (B), with which the delta-t of, let's say clock C, is compared. The $2 Bell hop problem is apparently contradictory. Are we doomed to accept the mathematics that causes the conflict? I never heard about a $2 Bell hop problem... further absent is a rigorous demonstration that such inverse application will conserve all clock strokes emitted as images. Hmm, I once did that for myself (with a spreadsheet) and it was enlightening. I can recommend it, nothing better than to do such an exercise yourself! BTW, there have been papers with full descriptions, for example Builder's 1957 paper on the Twin paradox and I think you can also find such description on internet. Cheers, Harald BTW Harald, I forgot my manners. Thank you for your thoughtful response and the suggestions for other sources. Kind regards, Sue... You're welcome! I can send you the above-mentioned paper if you like (PDF). Thanks for asking first because I am having some problems with large files and my ISP. If it is less than 200K I think it will work and I would be happy to receive a copy. Sue... Too bad, it's a big, elaborate paper, explaining everything to the greatest detail. That results in a PDF of 1Mb... Harald |
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