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Article #5686Re: DIVINE ALBERT, POINCARE, NON-EUCLIDEAN GEOMETRY
From: xxein
Date: Thu, 31 Jan 2008 23:49
Date: Thu, 31 Jan 2008 23:49
60 lines
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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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X-Google-Thread: 10f545,2875c24c3759b3e4 X-Google-Thread: 10b271,2875c24c3759b3e4 X-Google-Thread: fa4c1,2875c24c3759b3e4 X-Google-Thread: f55d3,2875c24c3759b3e4 X-Google-Thread: 1139f8,2875c24c3759b3e4 X-Google-Attributes: gid10f545,gid10b271,gidfa4c1,gidf55d3,gid1139f8,public,usenet X-Google-Language: ENGLISH,ASCII Path: arc1-ca.pugleaf.net!g2news1.google.com!news2.google.com!postnews.google.com!s19g2000prg.googlegroups.com!not-for-mail 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) Organization: http://groups.google.com Lines: 60 Message-ID: <e3083d83-0e92-4f51-8f2d-61d81a11957c@s19g2000prg.googlegroups.com> References: <1a2ecc3d-c1c4-407f-acbf-7693d1543c85@p69g2000hsa.googlegroups.com> <50c4d3b3-f2c5-4cdd-8095-1760a4851e85@i72g2000hsd.googlegroups.com> <xT9oj.42589$Kt4.4960@fe3.news.blueyonder.co.uk> NNTP-Posting-Host: 76.110.125.239 Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable X-Trace: posting.google.com 1201823380 10921 127.0.0.1 (31 Jan 2008 23:49:40 GMT) X-Complaints-To: groups-abuse@google.com NNTP-Posting-Date: Thu, 31 Jan 2008 23:49:40 +0000 (UTC) Complaints-To: groups-abuse@google.com Injection-Info: s19g2000prg.googlegroups.com; posting-host=76.110.125.239; posting-account=A1RDBQoAAACgoKLKH2mnXq_HaAxmyWw6 User-Agent: G2/1.0 X-HTTP-UserAgent: Mozilla/4.0 (compatible; MSIE 7.0; Windows NT 6.0; SLCC1; .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506),gzip(gfe),gzip(gfe)