How can the MMx math be corrected?
in [Relativity]
|
Prev: What is the experimentally measurable difference between rest mass and the 'relativistic mass' of the photon ??!!
Next: Dark Matter hipotessis
From: Paul Stowe on 3 May 2010 12:18 On May 3, 7:35 am, PD <thedraperfam...(a)gmail.com> wrote: > On May 1, 11:27 am, Paul Stowe <theaether...(a)gmail.com> wrote: > > > > > > > > > > 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. > > > > > > 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? > > > Sigh, the quote provided WAS FROM Einstein's 1905 paper. > > Yes, I know. This is an exquisite demonstration that your eyes can > fixate on a line or two from a paper, having completely forgotten what > was said earlier or later in the paper. I haven't forgotten, but words don't trump mathematics. Introduce any non-zero velocity (a vector) AND! Einstein's second postulate, and the result is (or should be) obvious. It is physically impossible for the 'relative' speed of light to be isotropic in moving systems. Note, I did NOT! say measured speed. > > And > > Einstein's postulate that light speed is invariant and not affected by > > the speed of the emitter/receiver pretty much negates isotropy. > > Uh, no. If light speed is invariant with respect to the speed of the > receiver, then the receiver will ALWAYS measure light speed to be > isotropic. Perhaps there is a confusion in terms here. Forget measurements (and the limitations on same) for the moment. For given that we 'define' speed as distance traveled per unit time then, if both distance traveled and time it takes to do so (which it would for independent propagation) increases at the very same rate with increasing motion, then the computational result is invariant. However, this does NOT! address the issue of isotropy of propagation speed wrt a moving system. As far as I can tell, THE ONLY process that can result in 'actual' isotropic c in moving systems is the ballistic theory of light. However, by definition, then Einstein's second posulate would have to be false since light would be emitted at c + (v Cos t). Even then, it certainly isn't for any observer moving wrt to the emitting element(s). > > I > > don't argue with his other postulate either (nor did Lorentz or > > Poincare) one can indeed, set up their system of measure in such a way > > as to make it appear to be 'isotropic' for them. However, the very > > existence, and need for, the LT in transforming coordinates between > > moving systems along with the postulate about light speed invariance > > 'should be' indisputable proof that Poincare & Lorentz's take on this > > is the right one. > > Again, I go back to my earlier question about how, if you can derive > the very same LTs from two opposite claims about light speed isotropy, > you then are able to discern that one of them is right and the other > is wrong. I'm pointing logical inconsistencies in the basis. The fact is, even SRT must deal with the anisotropies introduced by motion... For example, we know the Earth, the solar system, our galaxy is not at rest by the 'measured' doppler in the CMBR. So, take the CMB dipole = 0 frame and, wrt to it, is 'relative' light speed 'isotropic' wrt to systems moving wrt to it? > > Otherwise, my original question remains, Paul Stowe
From: Paul Stowe on 3 May 2010 12:25 On May 3, 9:11 am, Tom Roberts <tjrob...(a)sbcglobal.net> wrote: > PaulStowewrote: > > [...] the magnitude of the physical field distortion > > (Contraction in the direction of motion) is solely a result of the > > instantaneous velocity affecting the field at any given moment. When > > the fields constituting the material arms of an interferometer are > > rotated they maintain their physical orientation wrt to the motion, > > thus the overall length changes as the angle to the motion does. [...] > > Yes, it is physically impossible to get a null result without this > > effect and I don't think Tom disputes this. > > OF COURSE I dispute that! Your claim that it is "physically impossible" for > there to be any other explanation is JUST PLAIN WRONG. In particular, SR > provides a quite different explanation. > > As you seem to forget it, I'll repeat: the SR explanation is > that the local structure of spacetime and the behavior of > electromagnetic fields combine to make the vacuum speed of > light be isotropically c in any locally inertial frame. Since > the interferometer is at rest in such a frame to sufficient > accuracy, as long as the arms remain unchanged while rotating > (i.e. DO NOT "contract") the MMX will yield a null result.. > > Tom Roberts WOW, OK, so according to you, there is no Lorentz contraction. I stand corrected, but it seems to fly in the face of the experiments that suggest that such a cotraction exists and is quite real... Paul Stowe
From: PD on 3 May 2010 12:37 On May 3, 11:18 am, Paul Stowe <theaether...(a)gmail.com> wrote: > On May 3, 7:35 am, PD <thedraperfam...(a)gmail.com> wrote: > > > > > On May 1, 11:27 am, Paul Stowe <theaether...(a)gmail.com> wrote: > > > > > > > > > > > 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. > > > > > > > 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? > > > > Sigh, the quote provided WAS FROM Einstein's 1905 paper. > > > Yes, I know. This is an exquisite demonstration that your eyes can > > fixate on a line or two from a paper, having completely forgotten what > > was said earlier or later in the paper. > > I haven't forgotten, but words don't trump mathematics. Introduce any > non-zero velocity (a vector) AND! Einstein's second postulate, and the > result is (or should be) obvious. It is physically impossible for the > 'relative' speed of light to be isotropic in moving systems. Note, I > did NOT! say measured speed. I don't know why you'd say this. You may have some buried assumptions that are leading you to conclude that speed of light cannot be isotropic. Here are some candidate guess as to what those assumptions are: 1. That if there is an object in frame A that is moving with velocity v, and there is another frame B moving at u relative to A (in the same line as the object's motion in A), then the object must be moving in frame B at (v-u) or (v+u). Those are the only physical possibilities. 2. That if something is moving in a frame A with a velocity v, then in any other frame moving relative to A, the same something must be moving at a velocity different than v, regardless of the something or the value of v. Any conclusion that is at variance with one of those assumptions is therefore taken as impossible. Have I got that right? > > > > And > > > Einstein's postulate that light speed is invariant and not affected by > > > the speed of the emitter/receiver pretty much negates isotropy. > > > Uh, no. If light speed is invariant with respect to the speed of the > > receiver, then the receiver will ALWAYS measure light speed to be > > isotropic. Perhaps there is a confusion in terms here. > > Forget measurements (and the limitations on same) for the moment. For > given that we 'define' speed as distance traveled per unit time then, > if both distance traveled and time it takes to do so (which it would > for independent propagation) increases at the very same rate with > increasing motion, You mean, as in the (v+u) assumption? > then the computational result is invariant. > However, this does NOT! address the issue of isotropy of propagation > speed wrt a moving system. > > As far as I can tell, THE ONLY process that can result in 'actual' > isotropic c in moving systems is the ballistic theory of light. > However, by definition, then Einstein's second posulate would have to > be false since light would be emitted at c + (v Cos t). Even then, it > certainly isn't for any observer moving wrt to the emitting > element(s). > > > > I > > > don't argue with his other postulate either (nor did Lorentz or > > > Poincare) one can indeed, set up their system of measure in such a way > > > as to make it appear to be 'isotropic' for them. However, the very > > > existence, and need for, the LT in transforming coordinates between > > > moving systems along with the postulate about light speed invariance > > > 'should be' indisputable proof that Poincare & Lorentz's take on this > > > is the right one. > > > Again, I go back to my earlier question about how, if you can derive > > the very same LTs from two opposite claims about light speed isotropy, > > you then are able to discern that one of them is right and the other > > is wrong. > > I'm pointing logical inconsistencies in the basis. The fact is, even > SRT must deal with the anisotropies introduced by motion... For > example, we know the Earth, the solar system, our galaxy is not at > rest by the 'measured' doppler in the CMBR. It is not at rest with respect to the thermal horizon that EMITTED the CMBR. This is no different than saying that we are not at rest with respect to some galaxy. This does not at all imply that the light from this horizon or from the galaxy is received by us at anything other than c. And in fact, measurement indicates that it is indeed traveling at c. See some of the astronomical papers for the mass of the photon: http://pdg.lbl.gov/2009/listings/rpp2009-list-photon.pdf > So, take the CMB dipole = > 0 frame and, wrt to it, is 'relative' light speed 'isotropic' wrt to > systems moving wrt to it? > > > > Otherwise, my original question remains, > > Paul Stowe
From: PD on 3 May 2010 12:38 On May 3, 11:25 am, Paul Stowe <theaether...(a)gmail.com> wrote: > On May 3, 9:11 am, Tom Roberts <tjrob...(a)sbcglobal.net> wrote: > > > > > PaulStowewrote: > > > [...] the magnitude of the physical field distortion > > > (Contraction in the direction of motion) is solely a result of the > > > instantaneous velocity affecting the field at any given moment. When > > > the fields constituting the material arms of an interferometer are > > > rotated they maintain their physical orientation wrt to the motion, > > > thus the overall length changes as the angle to the motion does. [...] > > > Yes, it is physically impossible to get a null result without this > > > effect and I don't think Tom disputes this. > > > OF COURSE I dispute that! Your claim that it is "physically impossible" for > > there to be any other explanation is JUST PLAIN WRONG. In particular, SR > > provides a quite different explanation. > > > As you seem to forget it, I'll repeat: the SR explanation is > > that the local structure of spacetime and the behavior of > > electromagnetic fields combine to make the vacuum speed of > > light be isotropically c in any locally inertial frame. Since > > the interferometer is at rest in such a frame to sufficient > > accuracy, as long as the arms remain unchanged while rotating > > (i.e. DO NOT "contract") the MMX will yield a null result. > > > Tom Roberts > > WOW, OK, so according to you, there is no Lorentz contraction. I don't know why you would conclude that the isotropy of the speed of light and the principle of relativity is inconsistent with the Lorentz transformation, since one can derive the LT's from those principles, as I pointed out to you from a handful of readings. > I > stand corrected, but it seems to fly in the face of the experiments > that suggest that such a cotraction exists and is quite real... > > Paul Stowe
From: Tom Roberts on 3 May 2010 12:48
Paul Stowe wrote: > words don't trump mathematics. Sure. But CORRECT mathematics always "trumps" INCORRECT mathematics, and yours is the latter -- you make implicit assumptions that are not warranted, and thus erroneously exclude other valid possibilities. > Introduce any > non-zero velocity (a vector) AND! Einstein's second postulate, and the > result is (or should be) obvious. You implicitly assume Galilean relativity (i.e. the transforms between inertial frames belong to the Galilei group). What is "obvious" to you is really an unwarranted ASSUMPTION. Indeed, experiments show that the Poincar� group is a MUCH better description of the relationships between locally inertial frames in the world we inhabit. > It is physically impossible for the > 'relative' speed of light to be isotropic in moving systems. Not true. You need to learn some modern physics. Of course you also need to update your thought processes and terminology -- saying "moving systems" is woefully inadequate, and you must also specify what frame or system you consider to be "not moving". This error permeates everything you say around here. As I have said before, you need to learn how to read more accurately. And write more accurately. And most of all: THINK more accurately. You keep making grandiose claims about what is or is not "physically possible", without any significant understanding of basic modern physics. That's ridiculous -- we HAVE learned A LOT about the world we inhabit since the early 1900's. And most damningly to your claims, what you claim to be "physically impossible" is ROUTINELY OBSERVED in laboratories around the world (the different laboratories are "moving" relative to each other with speeds significantly larger than their measurement resolutions). Tom Roberts |