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tech / sci.physics.relativity / Re: [SR] Demonstration of simplification

[SR] Demonstration of simplification

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From: r.hac...@tiscali.fr (Richard Hachel)

by: Richard Hachel - Sun, 31 Mar 2024 22:45 UTC

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.

Re: [SR] Demonstration of simplification

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From: ao...@uoilonuiai.jp (Bladimir Funakoshi)
Newsgroups: sci.physics.relativity,sci.physics,sci.math
Subject: Re: [SR] Demonstration of simplification
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Date: Mon, 1 Apr 2024 09:39:26 -0000 (UTC)
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by: Bladimir Funakoshi - Mon, 1 Apr 2024 09:39 UTC

Richard Hachel wrote:

> 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)

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Subject	Author
[SR] Demonstration of simplification	Richard Hachel
Re: [SR] Demonstration of simplification	Bladimir Funakoshi