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Path: ...!3.eu.feeder.erje.net!feeder.erje.net!fdn.fr!usenet-fr.net!pasdenom.info!from-devjntp Message-ID: <lYswGe5sL5FTXNDCC00GhCLG580@jntp> JNTP-Route: news2.nemoweb.net JNTP-DataType: Article Subject: [SR] Demonstration of simplification Newsgroups: sci.physics.relativity JNTP-HashClient: XTydNDFQnSG8wCw6Vp4xZB556gU JNTP-ThreadID: p15djwwBrsq7B7GbUVvPR4bKGOU JNTP-Uri: http://news2.nemoweb.net/?DataID=lYswGe5sL5FTXNDCC00GhCLG580@jntp User-Agent: Nemo/0.999a JNTP-OriginServer: news2.nemoweb.net Date: Sun, 31 Mar 24 22:45:54 +0000 Organization: Nemoweb JNTP-Browser: Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/123.0.0.0 Safari/537.36 Injection-Info: news2.nemoweb.net; posting-host="e8cbf2474b472b9bb79db3dccb6a856bc1d05409"; logging-data="2024-03-31T22:45:54Z/8801048"; posting-account="4@news2.nemoweb.net"; mail-complaints-to="julien.arlandis@gmail.com" JNTP-ProtocolVersion: 0.21.1 JNTP-Server: PhpNemoServer/0.94.5 MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit X-JNTP-JsonNewsGateway: 0.96 From: Richard Hachel <r.hachel@tiscali.fr> Bytes: 2052 Lines: 27 Demonstration of the possible reduction from an accelerated frame of reference to a Galilean frame of reference over a very short duration or interval. We pose: ΔTo²=ΔTr²+ΔEt² ΔTo²=ΔTr²+Δx²/c² ΔTo²=ΔTr²+(1/4)(a²/c²)(Tr2²-Tr1²)² ΔTo²=ΔTr²+(1/4)(a²/c²)[(Tr2+Tr1)(Tr2-Tr1)]² ΔTo²=ΔTr²+(1/4)(a²/c²)(Tr2+Tr1)².ΔTr² ΔTo²=ΔTr²[1+(1/4)(a²/c²)(Tr2+Tr1)²] ΔTo²=ΔTr²[1+(1/4)(a²/c²)(2Trm)²] ΔTo²=ΔTr²[1+(a²/c²)(Trm)²] ΔTo²=ΔTr²(1+Vri²/c²) Let ΔTo=ΔTr.sqrt(1+Vr²/c²) and Voi=Vri/sqrt(1+Vri²/c²) As in the Galilean frames of reference. Note that the instantaneous speed given for frames accelerated by physicists is not correct, and that the correct formula is simply Voi/c=(1+c²/2ax)^(-1/2) It's a lot less than what they say. R.H.