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Originally Posted by Hilton Ratcliffe
CC, with the greatest respect, your last post consists of precisely the arena of purely mathematical argument that I wish at all costs to avoid for the rest of my life.
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Hello Hilton, Hello all,
I was referring to observations (specifically regarding the deviation from linearity observed in the spectra of Type Ia SNe), not mathematics.
How does one determine the geometry of spacetime (whether it be Euclidean, Riemannian or Lobachevskian) other than by measuring the distance of celestial objects, standard candles, at great distances (assuming, indeed, SNe Type Ia can be used as standard candles)?
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Originally Posted by Hilton Ratcliffe
This has nothing to do with how intricately I can twist space in my imagination. The example of 1a SNe is a very good example of how mathematical sophistry together with model-dependent bias can lead us up the garden path.
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I agree that the standard garden variety interpretation to which you refer is model-dependent and rests solely on ad hoc parameters (DE and DM) to fix it.
The garden variety couple; non-baryonic dark particles and the dark energy, have yet to observed or tested empirically. The story, quintessentially melodramatic, over-the-top backstage family squabbling, bitching, moaning and groaning in a luxurious Cambridge physics department, has just one running gag—anything this couple does in private is likely to be far more sensational than what they do on the Universal stage.
But let's take observations independently of a particular model: How do you determine distance without considering redshift or light curves?
How do you know Euclidean geometry is operational in the real world, in light of the fact that a deviation from linearity with respect to SNe Ia has been observed?
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Originally Posted by Hilton Ratcliffe
To me, the first step would be to return to Euclidean geometry, because it is real-world.
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Again, how do you know Euclidean geometry represents the real-world?
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Originally Posted by Hilton Ratcliffe
Euclid's 5th, like Beethoven's, is beautiful. Nothing wrong with it. ... If lines intersect anywhere at all, then they are obviously not parallel!
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Yes, beautiful they are indeed. But it has been shown that parallel lines can diverge or converge (from the perspective of any observer relative too his-her-its rest frame) and yet remain parallel in the real world (geodesics), both mathematically and (arguably) observationally.
How do you determine which geometry to use?
If your answer is: "by observation of the real world," then please tell me what you are observing (if it is not SNe Ia)?
Thanks in advance...
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“The very name geometry indicates that the concept of space is physiologically connected with the Earth as an ever present body of reference…The purely logical (axiomatic) representation of Euclidean geometry has, it is true, the advantage of greater simplicity and clarity…The fatal error that logical necessity, preceding all experience, was the basis of Euclidean geometry and the concept of space belonging to it, this fatal error arose from the fact that the empirical basis, on which the axiomatic construction of Euclidean geometry rests, had fallen into oblivion. [Furthermore]…we have not yet arrived at a new foundation of physics concerning which we may be certain that the manifold of all investigated phenomenon, and of successful partial theoretical systems, could be deduced logically from it.” (Einstein 1936, see 1954, p. 297, 298, 301)
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CC
