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Article #5686

Re: DIVINE ALBERT, POINCARE, NON-EUCLIDEAN GEOMETRY

#5686
From: xxein
Date: Thu, 31 Jan 2008 23:49
60 lines
4873 bytes
On Jan 30, 8:54 pm, "Ockham" <m...@razor.shaves.close> wrote:
> "xxein" <xx...@comcast.net> wrote in message
>
> news:50c4d3b3-f2c5-4cdd-8095-1760a4851e85@i72g2000hsd.googlegroups.com...
> On Jan 30, 5:30 am, Pentcho Valev <pva...@yahoo.com> wrote:
>
>
>
>
>
> >http://hem.bredband.net/b153434/Works/Einstein.htm
> > Divine Albert: "In a space which is free of gravitational fields we
> > introduce a Galilean system of reference K (x, y, z, t), and also a
> > system of co-ordinates K' (x', y', z', t') in uniform rotation
> > relatively to K. Let the origins of both systems, as well as their
> > axes of Z, permanently coincide. We shall show that for a space-time
> > measurement in the system K' the above definition of the physical
> > meaning of lengths and times cannot be maintained. For reasons of
> > symmetry it is clear that a circle around the origin in the X, Y plane
> > of K may at the same time be regarded as a circle in the X', Y' plane
> > of K'. We suppose that the circumference and diameter of this circle
> > have been measured with a unit measure infinitely small compared with
> > the radius, and that we have the quotient of the two results. If this
> > experiment were performed with a measuring-rod at rest relatively to
> > the Galilean system K, the quotient would be [pi]. With a measuring-
> > rod at rest relatively to K', the quotient would be greater than [pi].
> > This is readily understood if we envisage the whole process of
> > measuring from the "stationary" system K, and take into consideration
> > that the measuring-rod applied to the periphery undergoes a Lorentzian
> > contraction, while the one applied along the radius does not. Hence
> > Euclidean geometry does not apply to K'."
>
> > Why does Divine Albert believe that, "with a measuring-rod at rest
> > relatively to K', the quotient would be greater than [pi]"? Obviously
> > because "the measuring-rod applied to the periphery undergoes a
> > Lorentzian contraction". Then why does the segment of the periphery,
> > to which the measuring-rod is applied and which moves together with
> > the measuring-rod, fail to undergo a Lorentzian contraction?
>
> > In 1902, in "La Science et l'hypothese", Henri Poincare, in order to
> > justify non-Euclidean geometries, presented a parabole. Bidimensional
> > creatures live on a disc. The disc is heated under its center so that
> > the temperature is high at the center and decreases towards the
> > periphery. The creatures use rigid measuring rods in order to
> > determine the geometry of their world. They know nothing about the
> > heater and accordingly discover that the ratio of the circumference
> > and the diameter is greater than [pi]. The creatures conclude that
> > Euclidean geometry cannot be true on their disc.
>
> > Pentcho Valev
> > pva...@yahoo.com
>
> xxein:  We are K' to any other observer (gravity or not).  For your
> question (sans gravity) who would not be K'?  How do WE get pi?
>
>  http://en.wikipedia.org/wiki/Computing_%CF%80- Hide quoted text -
>
> - Show quoted text -

xxein:  Geez, you stupid fart!  Can't you follow a discussion?
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From: xxein <xxein@comcast.net>
Newsgroups: sci.physics.relativity, sci.physics, fr.sci.physique, 
 fr.sci.philo, fr.sci.maths
Subject: Re: DIVINE ALBERT, POINCARE, NON-EUCLIDEAN GEOMETRY
Date: Thu, 31 Jan 2008 15:49:40 -0800 (PST)
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