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  • [SR] Demonstration of simplification

    From Richard Hachel@21:1/5 to All on Sun Mar 31 22:45:54 2024
    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.

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