How can the MMx math be corrected?
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From: Paul Stowe on 1 May 2010 10:59 On May 1, 7:45 am, PD <thedraperfam...(a)gmail.com> wrote: > On Apr 30, 9:31 pm, PaulStowe<theaether...(a)gmail.com> wrote: > > > > > > > On Apr 29, 11:51 am, Tom Roberts <tjroberts...(a)sbcglobal.net> wrote: > > > > Da Do Ron Ron wrote: > > > > > [T. Roberts wrote:] > > > >> SR predicts a null result, with identical legs. > > > > > That is physically impossible. > > > > Nonsense! This is OBSERVED -- Michelson interferometers with identical legs give > > > null results (i.e. a fringe shift of zero within resolutions). > > > > > It is also theoretically impossible. > > > > More nonsense. It is essentially trivial for SR to predict a null result for the > > > MMX. Look in any SR textbook. > > > > Summary: in SR the speed of light in any inertial frame is > > > isotropically c, so for a Michelson interferometer with its > > > center of rotation at rest in any inertial frame, the position > > > of the fringes is independent of orientation, hence zero fringe > > > shift as the instrument is rotated. It's easy to show that the > > > non-inertial effects due to a laboratory on earth are vastly > > > smaller than the resolution of the best such measurement to date. > > > > Tom Roberts > > > If light is always isotropic then what is the basis for the roots (1 - > > v/c) & (1 + (v/c) in (1 - [v/c]^2)? > > > In Lorentz's version it's logically explained, and how it works but > > light isn't isotropic c. BUT!... you can pretend it is by using > > Einstein's clock synchronization definition and the inherent symmetry > > of the contraction. > > > However, if you 'assume' this the form of the Lorentz transform is > > just PFA a fudge that just happens to have an asymmetry for its > > roots. > > Oh good heavens, Paul, are you serious? > If you see a term in an expression that can be written (1-v/c) or (1+v/ > c), this means to you that anisotropy of the speed of light must be > implied by the theory? Even if the derivation DIRECTLY STEMS from an > assumption of the isotropy of the speed of light? You don't see a > problem with that kind of analysis??? So, there's a conflict between the 'assumption' and mathematical form. I'll take the math over 'assumption' every time. Especially given that in Poincare/Lorentz version of the derivation it has logical, derivable, basis. As, you should be aware, that basis isn't isotropy of light speed. Paul Stowe
From: PD on 1 May 2010 11:09 On May 1, 9:59 am, Paul Stowe <theaether...(a)gmail.com> wrote: > On May 1, 7:45 am, PD <thedraperfam...(a)gmail.com> wrote: > > > > > On Apr 30, 9:31 pm, PaulStowe<theaether...(a)gmail.com> wrote: > > > > On Apr 29, 11:51 am, Tom Roberts <tjroberts...(a)sbcglobal.net> wrote: > > > > > Da Do Ron Ron wrote: > > > > > > [T. Roberts wrote:] > > > > >> SR predicts a null result, with identical legs. > > > > > > That is physically impossible. > > > > > Nonsense! This is OBSERVED -- Michelson interferometers with identical legs give > > > > null results (i.e. a fringe shift of zero within resolutions). > > > > > > It is also theoretically impossible. > > > > > More nonsense. It is essentially trivial for SR to predict a null result for the > > > > MMX. Look in any SR textbook. > > > > > Summary: in SR the speed of light in any inertial frame is > > > > isotropically c, so for a Michelson interferometer with its > > > > center of rotation at rest in any inertial frame, the position > > > > of the fringes is independent of orientation, hence zero fringe > > > > shift as the instrument is rotated. It's easy to show that the > > > > non-inertial effects due to a laboratory on earth are vastly > > > > smaller than the resolution of the best such measurement to date. > > > > > Tom Roberts > > > > If light is always isotropic then what is the basis for the roots (1 - > > > v/c) & (1 + (v/c) in (1 - [v/c]^2)? > > > > In Lorentz's version it's logically explained, and how it works but > > > light isn't isotropic c. BUT!... you can pretend it is by using > > > Einstein's clock synchronization definition and the inherent symmetry > > > of the contraction. > > > > However, if you 'assume' this the form of the Lorentz transform is > > > just PFA a fudge that just happens to have an asymmetry for its > > > roots. > > > Oh good heavens, Paul, are you serious? > > If you see a term in an expression that can be written (1-v/c) or (1+v/ > > c), this means to you that anisotropy of the speed of light must be > > implied by the theory? Even if the derivation DIRECTLY STEMS from an > > assumption of the isotropy of the speed of light? You don't see a > > problem with that kind of analysis??? > > So, there's a conflict between the 'assumption' and mathematical > form. I'll take the math over 'assumption' every time. Especially > given that in Poincare/Lorentz version of the derivation it has > logical, derivable, basis. As, you should be aware, that basis isn't > isotropy of light speed. > > Paul Stowe So let's recap: Given two derivations of a common mathematical form, you feel free to interpret a term in the mathematical form to point to the premise of one derivation over the other, even though they both generate the same form from strict derivational deduction. Furthermore, you feel free to choose the premise of one of those derivations as being favored, because you like it better. Concretely, given a derivation that assumes isotropy of the speed of light and a derivation that assumes the anisotropy of the speed of light, and given that both derivations produce the IDENTICAL mathematical form, it seems obvious to you that the one that assumes the anisotropy of the speed of light is the correct one, by inspection of the mathematical form. Hmmm....
From: Paul Stowe on 1 May 2010 11:54 On May 1, 8:09 am, PD <thedraperfam...(a)gmail.com> wrote: > On May 1, 9:59 am, PaulStowe<theaether...(a)gmail.com> wrote: > > > > > > > On May 1, 7:45 am, PD <thedraperfam...(a)gmail.com> wrote: > > > > On Apr 30, 9:31 pm, PaulStowe<theaether...(a)gmail.com> wrote: > > > > > On Apr 29, 11:51 am, Tom Roberts <tjroberts...(a)sbcglobal.net> wrote: > > > > > > Da Do Ron Ron wrote: > > > > > > > [T. Roberts wrote:] > > > > > >> SR predicts a null result, with identical legs. > > > > > > > That is physically impossible. > > > > > > Nonsense! This is OBSERVED -- Michelson interferometers with identical legs give > > > > > null results (i.e. a fringe shift of zero within resolutions). > > > > > > > It is also theoretically impossible. > > > > > > More nonsense. It is essentially trivial for SR to predict a null result for the > > > > > MMX. Look in any SR textbook. > > > > > > Summary: in SR the speed of light in any inertial frame is > > > > > isotropically c, so for a Michelson interferometer with its > > > > > center of rotation at rest in any inertial frame, the position > > > > > of the fringes is independent of orientation, hence zero fringe > > > > > shift as the instrument is rotated. It's easy to show that the > > > > > non-inertial effects due to a laboratory on earth are vastly > > > > > smaller than the resolution of the best such measurement to date. > > > > > > Tom Roberts > > > > > If light is always isotropic then what is the basis for the roots (1 - > > > > v/c) & (1 + (v/c) in (1 - [v/c]^2)? > > > > > In Lorentz's version it's logically explained, and how it works but > > > > light isn't isotropic c. BUT!... you can pretend it is by using > > > > Einstein's clock synchronization definition and the inherent symmetry > > > > of the contraction. > > > > > However, if you 'assume' this the form of the Lorentz transform is > > > > just PFA a fudge that just happens to have an asymmetry for its > > > > roots. > > > > Oh good heavens, Paul, are you serious? > > > If you see a term in an expression that can be written (1-v/c) or (1+v/ > > > c), this means to you that anisotropy of the speed of light must be > > > implied by the theory? Even if the derivation DIRECTLY STEMS from an > > > assumption of the isotropy of the speed of light? You don't see a > > > problem with that kind of analysis??? > > > So, there's a conflict between the 'assumption' and mathematical > > form. I'll take the math over 'assumption' every time. Especially > > given that in Poincare/Lorentz version of the derivation it has > > logical, derivable, basis. As, you should be aware, that basis isn't > > isotropy of light speed. > > > PaulStowe > > So let's recap: > Given two derivations of a common mathematical form, you feel free to > interpret a term in the mathematical form to point to the premise of > one derivation over the other, even though they both generate the same > form from strict derivational deduction. Furthermore, you feel free to > choose the premise of one of those derivations as being favored, > because you like it better. > Concretely, given a derivation that assumes isotropy of the speed of > light and a derivation that assumes the anisotropy of the speed of > light, and given that both derivations produce the IDENTICAL > mathematical form, it seems obvious to you that the one that assumes > the anisotropy of the speed of light is the correct one, by inspection > of the mathematical form. > Hmmm.... I guess I missed it, where does Einstein derive the gamma factor from assumed isotropy? What I see is, "...it being borne in mind that light is always propagated along these axes, when viewed from the stationary system, with the velocity Sqrt(c^2 - v^2)..." For any v > 0 that equation gives us a light velocity not equal to c in the stationary system. YES! c 'appears' to measure as invariant but, if we take that quote of Einstein verbatim it certainly IS NOT ISOTROPIC. It looks to me that he derived gamma from assumed anisotropy when moving. Yes, both versions, Einstein's and Lorentz/Poincare's predict the same measurables but perhaps you can show how the LT gets derived from assumed isotropy. Paul Stowe
From: PD on 1 May 2010 12:09 On May 1, 10:54 am, Paul Stowe <theaether...(a)gmail.com> wrote: > On May 1, 8:09 am, PD <thedraperfam...(a)gmail.com> wrote: > > > > > On May 1, 9:59 am, PaulStowe<theaether...(a)gmail.com> wrote: > > > > On May 1, 7:45 am, PD <thedraperfam...(a)gmail.com> wrote: > > > > > On Apr 30, 9:31 pm, PaulStowe<theaether...(a)gmail.com> wrote: > > > > > > On Apr 29, 11:51 am, Tom Roberts <tjroberts...(a)sbcglobal.net> wrote: > > > > > > > Da Do Ron Ron wrote: > > > > > > > > [T. Roberts wrote:] > > > > > > >> SR predicts a null result, with identical legs. > > > > > > > > That is physically impossible. > > > > > > > Nonsense! This is OBSERVED -- Michelson interferometers with identical legs give > > > > > > null results (i.e. a fringe shift of zero within resolutions). > > > > > > > > It is also theoretically impossible. > > > > > > > More nonsense. It is essentially trivial for SR to predict a null result for the > > > > > > MMX. Look in any SR textbook. > > > > > > > Summary: in SR the speed of light in any inertial frame is > > > > > > isotropically c, so for a Michelson interferometer with its > > > > > > center of rotation at rest in any inertial frame, the position > > > > > > of the fringes is independent of orientation, hence zero fringe > > > > > > shift as the instrument is rotated. It's easy to show that the > > > > > > non-inertial effects due to a laboratory on earth are vastly > > > > > > smaller than the resolution of the best such measurement to date. > > > > > > > Tom Roberts > > > > > > If light is always isotropic then what is the basis for the roots (1 - > > > > > v/c) & (1 + (v/c) in (1 - [v/c]^2)? > > > > > > In Lorentz's version it's logically explained, and how it works but > > > > > light isn't isotropic c. BUT!... you can pretend it is by using > > > > > Einstein's clock synchronization definition and the inherent symmetry > > > > > of the contraction. > > > > > > However, if you 'assume' this the form of the Lorentz transform is > > > > > just PFA a fudge that just happens to have an asymmetry for its > > > > > roots. > > > > > Oh good heavens, Paul, are you serious? > > > > If you see a term in an expression that can be written (1-v/c) or (1+v/ > > > > c), this means to you that anisotropy of the speed of light must be > > > > implied by the theory? Even if the derivation DIRECTLY STEMS from an > > > > assumption of the isotropy of the speed of light? You don't see a > > > > problem with that kind of analysis??? > > > > So, there's a conflict between the 'assumption' and mathematical > > > form. I'll take the math over 'assumption' every time. Especially > > > given that in Poincare/Lorentz version of the derivation it has > > > logical, derivable, basis. As, you should be aware, that basis isn't > > > isotropy of light speed. > > > > PaulStowe > > > So let's recap: > > Given two derivations of a common mathematical form, you feel free to > > interpret a term in the mathematical form to point to the premise of > > one derivation over the other, even though they both generate the same > > form from strict derivational deduction. Furthermore, you feel free to > > choose the premise of one of those derivations as being favored, > > because you like it better. > > Concretely, given a derivation that assumes isotropy of the speed of > > light and a derivation that assumes the anisotropy of the speed of > > light, and given that both derivations produce the IDENTICAL > > mathematical form, it seems obvious to you that the one that assumes > > the anisotropy of the speed of light is the correct one, by inspection > > of the mathematical form. > > Hmmm.... > > I guess I missed it, where does Einstein derive the gamma factor from > assumed isotropy? What I see is, > > "...it being borne in mind that light is always propagated along > these axes, when viewed from the stationary system, with the > velocity Sqrt(c^2 - v^2)..." > > For any v > 0 that equation gives us a light velocity not equal to c > in the stationary system. YES! c 'appears' to measure as invariant > but, if we take that quote of Einstein verbatim it certainly IS NOT > ISOTROPIC. It looks to me that he derived gamma from assumed > anisotropy when moving. Uh, no. So if you don't understand how relativity was derived from an assumption of isotropy, just say so. It's actually pretty clear from the original paper in 1905. > > Yes, both versions, Einstein's and Lorentz/Poincare's predict the same > measurables but perhaps you can show how the LT gets derived from > assumed isotropy. You really need it trotted out here? Would you like a reference? It's done in the 1905 paper by Einstein. It's done a slightly different way but from the same premises by Taylor & Wheeler in Spacetime Physics, pgs 95-102. It's done in yet a slightly different way but from the same premises by Griffiths in his Intro to Electrodynamics, chapter 12. Need more? > > Paul Stowe
From: harald on 1 May 2010 12:26
On May 1, 4:59 pm, Paul Stowe <theaether...(a)gmail.com> wrote: > On May 1, 7:45 am, PD <thedraperfam...(a)gmail.com> wrote: > > > > > On Apr 30, 9:31 pm, PaulStowe<theaether...(a)gmail.com> wrote: > > > > On Apr 29, 11:51 am, Tom Roberts <tjroberts...(a)sbcglobal.net> wrote: > > > > > Da Do Ron Ron wrote: > > > > > > [T. Roberts wrote:] > > > > >> SR predicts a null result, with identical legs. > > > > > > That is physically impossible. > > > > > Nonsense! This is OBSERVED -- Michelson interferometers with identical legs give > > > > null results (i.e. a fringe shift of zero within resolutions). > > > > > > It is also theoretically impossible. > > > > > More nonsense. It is essentially trivial for SR to predict a null result for the > > > > MMX. Look in any SR textbook. > > > > > Summary: in SR the speed of light in any inertial frame is > > > > isotropically c, so for a Michelson interferometer with its > > > > center of rotation at rest in any inertial frame, the position > > > > of the fringes is independent of orientation, hence zero fringe > > > > shift as the instrument is rotated. It's easy to show that the > > > > non-inertial effects due to a laboratory on earth are vastly > > > > smaller than the resolution of the best such measurement to date. > > > > > Tom Roberts > > > > If light is always isotropic then what is the basis for the roots (1 - > > > v/c) & (1 + (v/c) in (1 - [v/c]^2)? > > > > In Lorentz's version it's logically explained, and how it works but > > > light isn't isotropic c. BUT!... you can pretend it is by using > > > Einstein's clock synchronization definition and the inherent symmetry > > > of the contraction. > > > > However, if you 'assume' this the form of the Lorentz transform is > > > just PFA a fudge that just happens to have an asymmetry for its > > > roots. > > > Oh good heavens, Paul, are you serious? > > If you see a term in an expression that can be written (1-v/c) or (1+v/ > > c), this means to you that anisotropy of the speed of light must be > > implied by the theory? Even if the derivation DIRECTLY STEMS from an > > assumption of the isotropy of the speed of light? You don't see a > > problem with that kind of analysis??? > > So, there's a conflict between the 'assumption' and mathematical > form. I'll take the math over 'assumption' every time. Especially > given that in Poincare/Lorentz version of the derivation it has > logical, derivable, basis. As, you should be aware, that basis isn't > isotropy of light speed. > > Paul Stowe Paul, this started apparently with a misunderstanding by Tom Roberts of what DDRR meant; and he insisted in keeping that misunderstanding (as MMX is repeated at different times of the year, at least at some times the interferometer has a speed v relative to the chosen frame and the arms are then *not* identical in the sense that one is shorter than the other). Next you added to the confusion by simply talking about "isotropy" of the speed light, while you probably (and as I now see, certainly) mean that the one-way closing speed of light is anisotropic. Usually people talk in this context about the operational two-way speed of light, which is supposed to remain isotropic. And that is again different from what is meant in a general discussion: Lorentz and Einstein based their derivations on the assumption of an isotropic, constant speed of light in whatever "rest" system; that stemmed logically from Maxwell's theory and Einstein turned it into a postulate. Harald |