We know from school geometry that an ellipse is a plane curve surrounding two focal points, such for all points on the curve, the sum of the two distances to the focal points is a constant.
From the same source we know that a hyperbola is a set of points, such that for any point of the set, the absolute difference of the distances to two fixed focal points (the foci) is constant.
On the other hand, the creators of Special Relativity Theory (SRT) use the concepts of the ellipsoid of revolution and the hyperboloid of revolution (or Minkowski’s one-dimensional hyperbola) as basic geometric constructions describing, in their opinion, the physical relationships between spatial segments, into which a massive body moves in a fixed amount of time and spatial distances travelled in the same time by electromagnetic signals, exchanged between physical objects. At the same time, SRT advocates persistently avoid any mention of foci. (To be fair to you, William Moreau, "Wave front relativity", American Journal of Physics vol. 62, no. 5 (1 May 1994), pages 426-429 attempt to correct the situation by introducing an extended ellipse into consideration (instead of Einstein’s compressed one) but ignoring another important feature of electromagnetic radiation).
Is ignoring the notion of focal points of ellipsoids and hyperboloids of revolution in SRT an unfortunate accident, or does it reflects the fact that neither the ellipsoid of revolution nor the one-dimensional hyperbola have the slightest relationship to solving the problems that the relativism fathers set before themselves?
Sergey Sheludko , Some good questions. I've found a 'clean slate' works, if changing '05 'interpretation' of SR for Einstein's '52 reconception; as a hierarchy of bounded 'Spaces in motion within spaces'. Repolarisation on (QM) interactions gives ellipticities of polarity where, yes, a minor axis can reduce to near zero. 'Foundations of Physics' just accepted this paper focussing on the causal QM aspects. SR then only needs all re-emissions at local (re-emitter's) c. Preprint The Measurement Problem, an Ontological Solution
Dear Peter Jackson , thank you for your answer, but the letters «focus» I was able to detect only in the sentence: «Further word should focus on testing and refining the equations ». In other texts I find, for example, «Minkowski’s metric and Einstein’s 'infinitely many spaces' and 'spatially extended mass' were correct», but again, no hint of hyperboloid or ellipsoid foci.
Regards
Sergey Sheludko , No. Nowhere there. To simplify; 'Foci' is only plural of 'focus' An ellipse has TWO foci. The orbit of ALL planets for instance is an ellipse with the Sun at one of the two 'foci'. All light ALSO has some ellipticity of polarity (think of an ellipticised helix). That's physical reality. I can only say of 1 dimension that it's a simplified abstraction of reality (metaphysical maths) so, like Einstein, do NOT agree 'space-time' has any 'reality'.
Dear Peter Jackson ,
Thank you for the detailed explanation, but … I’ve always liked to use the rays with absolutely linear polarization, i.e. I’ve spent my efforts to rule out any elliptic polarity.
I do not, of course, claim that second-order curves do not exist; you can believe that I have almost every day successfully build some hyperbole. I only suggest that those for whom the second order of curves exceeds the level of intellectual development use only the lower order curves.
It seems to me that we (I, on the one hand, and you and Einstein, on the other hand) are slightly divided. And therefore, I have no choice but to retell Minkowski’s idea in my own words and to show that it is a funny idea. To my regret, it turns out that the whole story with 'space-time', 'ecumenical points and lines', our colleague named Pseudoeuclid and others is the greatest disgrace of science and linguistic play in the dualism of physical concepts is not an occupation worthy of men.
If I understand correctly, you insist on the idea that in 1905 Mr. M Besso explained very poorly to a young man, interested in Brownian movements, the essence of Mr Poincaré’s intellectual efforts, but in 50 years (in 1952), the young man wised up, making us happy with his statements: «... then the cavity of the box s is part of the hollow space of Box S; while the same «space» that contains both boxes belongs to each of them. ... Inertial spaces, together with their associated times, are privileged four-dimensional coordinate systems linked by linear Lorentz transformations»?
Curiously, you’d like to study the laws of physics sitting in the inertial space of the hold of a Galilean ship, knowing that because of some linear transformation, the space of your privileged hold - suddenly - would belong also to even more privileged guys (they can supplement their privileges with muskets) from the corsair watercraft?
Best regards
Sergey Sheludko , I entirely agree about 'space-time'. However you haven't (yet) perceived the beautiful and uniquely consistent logic of the DFM. It's about the 'walls' of those boxes, as Maxwell's Near/Far field transition zones (TZ's). We FIND them, at all shear planes, including as the ubiquitous 'two-fluid plasma' astrophysical shocks of space. It seems you've spent much time on C18th 'rays' and trying to deny elliptical polarity. It's ALL elliptical, as i.e. ALL planetary orbits!
My papers explain and as far as possible 'prove' the whole coherent solution. You need to read them. I can't re-write them here! 'Wire frame' co-ordinate systems don't exist! Light does c and the laws of physics are the same in the hold of that ship and all others doing different speeds, and on WHICHEVER PLANET!! The mental block is on realising the it CHANGES SPEED if it gets to move BETWEEN them (with birefringence during the Ewald-Oseen 'extinction' process; i.e. see J.D Jackson). Mine are here, and C.C. Su's will also help.
https://www.researchgate.net/profile/Peter_Jackson22/research
C. C. Su, “A local-ether model of propagation of electromagnetic wave”, European Physical Journal C, 21, pp. 701-715, Sept. 2001, DOI:10.1007/s100520100759, https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.509.6294&rep=rep1&type=pdf.
Dear Peter Jackson , I thank you for moving towards a more constructive discussion of the issue.
Yes, I must admit that I have not yet absorbed the beautiful and uniquely consistent logic of the DFM, but please excuse me. All I can justify is the lack of time: I have to either comprehend the mysteries of the DFM or concentrate on sticking all this relativistic madness into the mud, leaving no chance of propaganda of pseudo-science. I agree that there is no such thing as wire-shaped coordinate systems: only razor wire in the noggins of relativists, and Nature has no knowledge of Cartesian coordinate systems at all. Yes, light moves at a speed c= 1/ sqrt(εμ) relative to a specific Inertial System (IS), completely unresponsive to moving physical objects (IFRs) either outside or inside the IS.
Well, I must admit that I have never been able to observe even the slightest hint of the ellipticity of polarization, except in the case of optically active environments. I.e. there is no problem if we’re waxing the concept of the «polarizer» as a device which does not create new components of the electrical and magnetic components of the electromagnetic field, but only destroys excess, as the sculptor can only cut off some excess from the block of marble, but he can’t paste something new. Yes, I have seen Fig. 4 of your article «The Measurement Problem ...» which I completely understand, although I have always dealt only with incomparably more complex structures. Do I understand correctly that the polarizer A in the case of 4a can be discarded at all, since the polarizer B will not create any horizontal component, but will only destroy the vertical one? Similarly, the polarizer A in figure 4b does not create a beam polarized at an angle of 45°, but only reduces the amplitude of the vertical component (?). For me, this is an absolute truth, tested by many years of practical experience. But I’m ready to look at the results of a real experiment corresponding to Figure 4b. ... The simplest test is this. Set the reflector at Brewster’s angle and rotate around the axis of the beam falling on the mirror along with the detector. If you are right, the maximum and minimum intensity of the detector will be obtained by positioning the detector at angles of 45°, and if I am right, the maximum and minimum intensity will be in the vertical and horizontal position of the detector.
Regard
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