You must understand that any corrections necessary are appreciated. The geometrical process spoken too here must be understood in it’s historical development to undertand, how one can see differently.
Euclidean geometry, elementary geometry of two and three dimensions (plane and solid geometry), is based largely on the Elements of the Greek mathematician Euclid (fl. c.300 B.C.). In 1637, René Descartes showed how numbers can be used to describe points in a plane or in space and to express geometric relations in algebraic form, thus founding analytic geometry, of which algebraic geometry is a further development (see Cartesian coordinates). The problem of representing three-dimensional objects on a two-dimensional surface was solved by Gaspard Monge, who invented descriptive geometry for this purpose in the late 18th cent. differential geometry, in which the concepts of the calculus are applied to curves, surfaces, and other geometrical objects, was founded by Monge and C. F. Gauss in the late 18th and early 19th cent. The modern period in geometry begins with the formulations of projective geometry by J. V. Poncelet (1822) and of non-Euclidean geometry by N. I. Lobachevsky (1826) and János Bolyai (1832). Another type of non-Euclidean geometry was discovered by Bernhard Riemann (1854), who also showed how the various geometries could be generalized to any number of dimensions.
These tidbits, would have been evidence as projects predceding as “towers across valleys” amd “between mountain measures,” to become what they are today. Allows us to se in ways that we are not used too, had we not learnt of this progression and design that lead from one to another.
8.6 On Gauss’s Mountains
One of the most famous stories about Gauss depicts him measuring the angles of the great triangle formed by the mountain peaks of Hohenhagen, Inselberg, and Brocken for evidence that the geometry of space is non-Euclidean. It’s certainly true that Gauss acquired geodetic survey data during his ten-year involvement in mapping the Kingdom of Hanover during the years from 1818 to 1832, and this data included some large “test triangles”, notably the one connecting the those three mountain peaks, which could be used to check for accumulated errors in the smaller triangles. It’s also true that Gauss understood how the intrinsic curvature of the Earth’s surface would theoretically result in slight discrepancies when fitting the smaller triangles inside the larger triangles, although in practice this effect is negligible, because the Earth’s curvature is so slight relative to even the largest triangles that can be visually measured on the surface. Still, Gauss computed the magnitude of this effect for the large test triangles because, as he wrote to Olbers, “the honor of science demands that one understand the nature of this inequality clearly”. (The government officials who commissioned Gauss to perform the survey might have recalled Napoleon’s remark that Laplace as head of the Department of the Interior had “brought the theory of the infinitely small to administration”.) It is sometimes said that the “inequality” which Gauss had in mind was the possible curvature of space itself, but taken in context it seems he was referring to the curvature of the Earth’s surface.
One had to recognize the process that historically proceeded in our overviews “to non-euclidean perspectives,” “geometrically enhanced” through to our present day headings, expeirmentallly.
Michelson interferometer(27 Mar 2006 wikipedia)
Michelson interferometer is the classic setup for optical interferometry and was invented by Albert Abraham Michelson. Michelson, along with Edward Morley, used this interferometer for the famous Michelson-Morley experiment in which this interferometer was used to prove the non-existence of the luminiferous aether. See there for a detailed discussion of its principle.
But Michelson had already used it for other purposes of interferometry, and it still has many other applications, e.g. for the detection of gravitational waves, as a tunable narrow band filter, and as the core of Fourier transform spectroscopy. There are also some interesting applications as a “nulling” instrument that is used for detecting planets around nearby stars. But for most purposes, the geometry of the Mach-Zehnder interferometer is more useful.
A quick summation below leads one onto the idea of what experimental validation has done for us. Very simply, the graduation of interferometer design had been taken to astronomical proportions?
Today the Count expands on this for us by showing other information on expeirmental proposals. How fitting that this historical drama has been shown here, in a quick snapshot. As well the need for understanding the “principal inherent” in the project below.
VLBI is a geometric technique: it measures the time difference between the arrival at two Earth-based antennas of a radio wavefront emitted by a distant quasar. Using large numbers of time difference measurements from many quasars observed with a global network of antennas, VLBI determines the inertial reference frame defined by the quasars and simultaneously the precise positions of the antennas. Because the time difference measurements are precise to a few picoseconds, VLBI determines the relative positions of the antennas to a few millimeters and the quasar positions to fractions of a milliarcsecond. Since the antennas are fixed to the Earth, their locations track the instantaneous orientation of the Earth in the inertial reference frame. Relative changes in the antenna locations from a series of measurements indicate tectonic plate motion, regional deformation, and local uplift or subsidence.
See:
Dialogos of Eide 
Plato,You have quoted nonsense about there being no spacetime fabric?;)Perhaps you forget FitzGerald showed that radiation pressure from the ‘ether’ caused the Michelson-Morley instriment to contract, cancelling out the absolute speed of light?As Eddington said, light speed is absolute but undetectable in the Michelson-Morley experiment owing to the fact the instrument contracts in the direction of motion, allowing the slower light beam to cross a smaller distance and thus catch up.Einstein’s admissions that the covariance of the general relativity theory violates the idea in special relativity that the velocity of light is constant:’This was … the basis of the law of the constancy of the velocity of light. But … the general theory of relativity cannot retain this law. On the contrary, we arrived at the result according to this latter theory, the velocity of light must always depend on the coordinates when a gravitational field is present.’ – Albert Einstein, Relativity, The Special and General Theory, Henry Holt and Co., 1920, p111.So general relativity conflicts with, and supersedes, special relativity. General relativity says goodbye to the law of the invariant velocity of light which was used in a fiddle, special relativity:’… the principle of the constancy of the velocity of light in vacuo must be modified, since we easily recognise that the path of a ray of light … must in general be curvilinear…’ – Albert Einstein, The Principle of Relativity, Dover, 1923, p114.Remember what Einstein said when he repudiated special relativity:‘The … action of magnetism on polarised light [discovered by Faraday not Maxwell] leads … to the conclusion that in a medium … is something belonging to the mathematical class as an angular velocity … This … cannot be that of any portion of the medium of sensible dimensions rotating as a whole. We must therefore conceive the rotation to be that of very small portions of the medium, each rotating on its own axis [spin] … The displacements of the medium, during the propagation of light, will produce a disturbance of the vortices … We shall therefore assume that the variation of vortices caused by the displacement of the medium is subject to the same conditions which Helmholtz, in his great memoir on Vortex-motion, has shewn to regulate the variation of the vortices [spin] of a perfect fluid.’ – Maxwell’s 1873 Treatise on Electricity and Magnetism, Articles 822-3Compare this to the spin foam vacuum, and the fluid GR model:‘… the source of the gravitational field can be taken to be a perfect fluid…. A fluid is a continuum that ‘flows’… A perfect fluid is defined as one in which all antislipping forces are zero, and the only force between neighboring fluid elements is pressure.’ – Professor Bernard Schutz, General Relativity, Cambridge University Press, 1986, pp. 89-90.Einstein admitted SR was tragic:‘The special theory of relativity … does not extend to non-uniform motion … The laws of physics must be of such a nature that they apply to systems of reference in any kind of motion. Along this road we arrive at an extension of the postulate of relativity… The general laws of nature are to be expressed by equations which hold good for all systems of co-ordinates, that is, are co-variant with respect to any substitutions whatever (generally co-variant). …’ – Albert Einstein, ‘The Foundation of the General Theory of Relativity’, Annalen der Physik, v49, 1916.‘Recapitulating, we may say that according to the general theory of relativity, space is endowed with physical qualities… According to the general theory of relativity space without ether is unthinkable.’ – Albert Einstein, Leyden University lecture on ‘Ether and Relativity’, 1920. (Einstein, A., Sidelights on Relativity, Dover, New York, 1952, pp. 15-23.)‘The Michelson-Morley experiment has thus failed to detect our motion through the aether, because the effect looked for – the delay of one of the light waves – is exactly compensated by an automatic contraction of the matter forming the apparatus…. The great stumbing-block for a philosophy which denies absolute space is the experimental detection of absolute rotation.’ – Professor A.S. Eddington (who confirmed Einstein’s general theory of relativity in 1919), Space Time and Gravitation: An Outline of the General Relativity Theory, Cambridge University Press, Cambridge, 1921, pp. 20, 152.The radiation (gauge bosons) and virtual particles in the vacuum exert pressure on moving objects, compressing them in the direction of motion. As FitzGerald deduced in 1889, it is not a mathematical effect, but a physical one. Mass increase occurs because of the snowplow effect of Higgs boson (mass ahead of you) when you move quickly, since the Higgs bosons you are moving into can’t instantly flow out of your path, so there is mass increase. If you were to approach c, the particles in the vacuum ahead of you would be unable to get out of your way, you’d be going so fast, so your mass would tend towards infinity. This is simply a physical effect, not a mathematical mystery. Time dilation occurs because time is measured by motion, and if as the Standard Model suggests, fundamental spinning particles are just trapped energy (mass being due to the external Higgs field), that energy is going at speed c, perhaps as a spinning loop or vibrating string. When you move that at near speed c, the internal vibration and/or spin speed will slow down, because c would be violated otherwise. Since electromagnetic radiation is a transverse wave, the internal motion at speed x is orthagonal to the direction of propagation at speed v, so x^2 + v^2 = c^2 by Pythagoras. Hence the dynamic measure of time (vibration or spin speed) for the particle is x/c = (1 – v^2/c^2)^1/2, which is the time-dilation formula.As Eddington said, light speed is absolute but undetectable in the Michelson-Morley experiment owing to the fact the instrument contracts in the direction of motion, allowing the slower light beam to cross a smaller distance and thus catch up.In fact, the fluid analogy shows that the ‘drag’ problem Feynman had is actually manifested in the causality of general relativity’s contraction term, and by the equivalence principle, the contraction of FitzGerald and Lorentz for moving objects. The ‘fluid’ of force-causing vacuum radiation is a perfect fluid, so it resists only accelerations. This is observed and called ‘inertia’ (for ‘stationary’ objects) and ‘momentum’ (for moving objects). The energy of the resisted acceleration goes into doing the work of physically contracting the object! Hence, contraction is an equilibrium state in which the vacuum radiation distorts the physical dimensions of matter according to its self-shielding (gravitation) and its motion.
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Whoops!I should mention that Dr Thomas Love of California State University sent me the Einstein quotations above!http://electrogravity.blogspot.com/2006/03/thomas-r.htmlAlso, I should add that Dr Edwin Budding, a Research Fellow of the Carter National Observatory in New Zealand, and currently at Canakkale Onsekin Mart University in Turkey, has sent me his paper on inertia and gravitational mechanism.It is 16 pages in length and the basic physical ideas for gravity and inertia are somewhat similar to http://feynman137.tripod.com/, although the mathematical treatment is interestingly different. It does not make the numerical connections and predictions, but it does formulate the mechanism of inertia and of the FitzGerald-Lorentz contraction physically, in the classical model of LeSage.http://electrogravity.blogspot.com/2006/03/edwin-budding-research-fellow-of.htmlBest wishes!
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