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: PD on 3 May 2010 10:35 On May 1, 11:27 am, Paul Stowe <theaether...(a)gmail.com> wrote: > On May 1, 9:09 am, PD <thedraperfam...(a)gmail.com> wrote: > > > > > On May 1, 10:54 am, PaulStowe<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? > > 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. > 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. > 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. > Otherwise, my original question remains, > > Paul Stowe
From: harald on 3 May 2010 10:41 On May 2, 7:00 am, Tom Roberts <tjroberts...(a)sbcglobal.net> wrote: > harald wrote: > > On May 1, 8:56 pm, Tom Roberts <tjroberts...(a)sbcglobal.net> wrote: > >> all you need to do is LOOK at the MMX apparatus -- the two arms are indeed > >> identical in the sense that they have the same length. As I have stated before, > >> and is implicit in what we mean by "identical", the comparison is performed in > >> the rest frame of the arms. > > > As I stated before, the essence of the MMX was that the test must be > > done at different times of the year, in order to guarantee at least > > some of the time a significant velocity v, according to stationary > > ether theory. Looking back at it through SRT that translates to at > > least some of the time a significant velocity v relative to the frame > > of choice (usually the solar frame, but any inertial frame will do). > > In SR you can select ANY inertial frame. There is no need to select one frame > and use it throughout the year. Indeed it's not; and when you change inertial frame, you also declare your earlier measurement as having been done in a "moving" frame. > As I said, it is simplest to select the rest > frame of the instrument for any given measurement; that is necessarily a > different frame for each measurement. But still, the prediction of a null result > FOR EACH MEASUREMENT is clear and obvious. If each measurement is null, > that applies for measurements done at different times of the year. Sure - which is either misleading or completely besides the point of the OP (and this thread), just as it is either misleading or completely besides the point in a discussion on stellar aberration. > > Again, it's an essential aspect of MMX that it works in different > > seasons; if you were right then the Earth would be always considered > > to be "in rest" so that stellar aberration would be zero! > > That is not essential to the MMX at all, because if the motion of the instrument > relative to the ether cannot be measured at any time of the year, time of year > is irrelevant. Yes it is essential for stellar aberration -- it is the > non-inertial nature of earth's orbit that gives rise to stellar aberration > (or rather to its measurability). It's reassuring that you understand that the variation of velocity of the Earth is relevant for stellar aberration. But that makes it even more amazing that you cannot (or refuse to) understand that the variation in velocity is equally relevant for Lorentz contraction in SRT (which the OP called "SRT math"). No motion = nothing to discuss or consider; the OP (DDRR) obviously meant that it is "physically impossible" to get a null result with a *moving* interferometer without a modified length of at least one of the arms, assuming that the speed of light is completely unaffected by the speed of the Earth. But never mind, he/she seems to have abandoned this discussion by now! Harald
From: harald on 3 May 2010 11:12 On May 2, 2:20 am, Paul Stowe <theaether...(a)gmail.com> wrote: > On May 1, 3:21 pm, Tom Roberts <tjroberts...(a)sbcglobal.net> wrote: > > > PaulStowewrote: > > > On May 1, 11:56 am, Tom Roberts <tjroberts...(a)sbcglobal.net> wrote: > > >> Yes, but Einstein used the phrase "rest system" merely as a means of > > >> distinguishing this frame from others, and ANY inertial frame can be used as his > > >> "rest system". This differs from Maxwell and Lorentz, for whom "rest system" > > >> implicitly means the ether frame of their respective theories. The > > >> difference is essential, and profound. > > > > Essential yes, as it is to Einstein's work but, in what way practical > > > way is it profound to Lorentz's version? > > > Look right up there, my last sentence quoted: I said "The DIFFERENCE is > > essential, and profound [emphasis added]." You need to READ MORE CAREFULLY, > > because as I said, it is the DIFFERENCE that is profound -- thus it is not > > "profound to Lorentz's version", but rather what is profound is the COMPARISON > > between Einstein and Maxwell & Lorentz, and how they use similar phrases in VERY > > DIFFERENT WAYS. Not only did you miss my meaning completely, you also show that > > you failed to understand this difference in the original authors' words and > > approach. > [..] > > Tom Roberts > > No Tom, I did not misunderstand so, let me make myself more clear. > The only difference between Lorentz/Poincare's version and Einstein's > is that there IS a aether that regulates and causes the existence and > properties of both relativity and give light speed its > characteristics. What Einstein took for 'granted' they simply > understood was already quantified by the then existing aether model. That is correct, as was also admitted by Einstein. > Such as, finite velocity of light, source independence, Doppler > shifts, ... etc. There IS! nothing essential to Einstein's version or > profoundly difference. Lorentz in 1904 already showed that only the > delta change in velocity was necessary to computations and that, by > the way we define speed c would be measured as the same value and that > this fact caused local observers to experience 'local time'. In fact Lorentz wasn't sure yet as he had not completely thought it through, and a little derivation error bugged him. > The > length contraction was already well understood so NO! in any practical > sense there is nothing essential or profound in Einstein's > metaphysical interpretation. Einstein's paper even reads as if he replaced at some places the word "ether" by "stationary system" after writing the draft version, and without perfectly covering it up... > The fact that there is nothing mathematically different and that both > Lorentz and Poincare had priority in publishing all the 'essential' > elements of Relativity prior to Einstein and that Lorentz's definition > of 'local frame' matches Einstein's definition of 'rest frame' suggest > that there is NO! practical difference either. No need to tell that to Tom - in a rather well written article that I found very helpful, he himself was one of the first to explain that there is no practical difference. > So, again, what is 'profoundly' different? That there is an aether > underpinning Lorentz's model? Well by 1920 Einstein had come to the > same conclusion on that too... Yes, although Einstein had tried so very hard to get rid of it, he later admitted that "the ether of the general theory of relativity is transmuted conceptually into the ether of Lorentz" if we reduce it to SRT ("if we substitute constants for the functions of space which describe the former, disregarding the causes which condition its state"). Cheers, Harald
From: Paul Stowe on 3 May 2010 11:19 On May 3, 7:41 am, harald <h...(a)swissonline.ch> wrote: > On May 2, 7:00 am, Tom Roberts <tjroberts...(a)sbcglobal.net> wrote: > > > > > > > harald wrote: > > > On May 1, 8:56 pm, Tom Roberts <tjroberts...(a)sbcglobal.net> wrote: > > >> all you need to do is LOOK at the MMX apparatus -- the two arms are indeed > > >> identical in the sense that they have the same length. As I have stated before, > > >> and is implicit in what we mean by "identical", the comparison is performed in > > >> the rest frame of the arms. > > > > As I stated before, the essence of the MMX was that the test must be > > > done at different times of the year, in order to guarantee at least > > > some of the time a significant velocity v, according to stationary > > > ether theory. Looking back at it through SRT that translates to at > > > least some of the time a significant velocity v relative to the frame > > > of choice (usually the solar frame, but any inertial frame will do). > > > In SR you can select ANY inertial frame. There is no need to select one frame > > and use it throughout the year. > > Indeed it's not; and when you change inertial frame, you also declare > your earlier measurement as having been done in a "moving" frame. > > > As I said, it is simplest to select the rest > > frame of the instrument for any given measurement; that is necessarily a > > different frame for each measurement. But still, the prediction of a null result > > FOR EACH MEASUREMENT is clear and obvious. If each measurement is null, > > that applies for measurements done at different times of the year. > > Sure - which is either misleading or completely besides the point of > the OP (and this thread), just as it is either misleading or > completely besides the point in a discussion on stellar aberration. > > > > Again, it's an essential aspect of MMX that it works in different > > > seasons; if you were right then the Earth would be always considered > > > to be "in rest" so that stellar aberration would be zero! > > > That is not essential to the MMX at all, because if the motion of the instrument > > relative to the ether cannot be measured at any time of the year, time of year > > is irrelevant. Yes it is essential for stellar aberration -- it is the > > non-inertial nature of earth's orbit that gives rise to stellar aberration > (or rather to its measurability). > > It's reassuring that you understand that the variation of velocity of > the Earth is relevant for stellar aberration. But that makes it even > more amazing that you cannot (or refuse to) understand that the > variation in velocity is equally relevant for Lorentz contraction in > SRT (which the OP called "SRT math"). No motion = nothing to discuss > or consider; the OP (DDRR) obviously meant that it is "physically > impossible" to get a null result with a *moving* interferometer > without a modified length of at least one of the arms, assuming that > the speed of light is completely unaffected by the speed of the Earth. > But never mind, he/she seems to have abandoned this discussion by > now! > > Harald Not one of its arms Harald, both of its arms, since the apparatus is rotated. Further, it makes no difference that Earth's speed varies with the seasons, 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. That is, specifically, what I was referring to with the equation Sqrt(1 - [v'/c]^2) and v' = v Cos t. Let angle t be zero in the direction of motion and you'll see that v' disappears at 90 & 270 degrees and becomes -v at 180. This is a necessary physical aspect of the system which maintains continuity of the field wrt to all of its elements given the actual invariance and source independence of c. Yes, it is physically impossible to get a null result without this effect and I don't think Tom disputes this. So, what, exactly, is your point? Regards, Paul Stowe
From: Tom Roberts on 3 May 2010 12:11
Paul Stowe wrote: > [...] 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 |