Re: Length contraction in Special Relativity

[Brent Meeker]

On 9/13/2024 3:06 AM, Alan Grayson wrote:


On Thursday, September 12, 2024 at 11:07:49 PM UTC-6 Alan Grayson wrote:

    On Thursday, September 12, 2024 at 11:00:21 PM UTC-6 Brent Meeker
    wrote:




        On 9/12/2024 9:21 PM, Alan Grayson wrote:


        On Thursday, September 12, 2024 at 3:55:45 AM UTC-6 Quentin
        Anciaux wrote:



            Le jeu. 12 sept. 2024, 11:53, Alan Grayson
            <agrays...@gmail.com> a écrit :



                On Thursday, September 12, 2024 at 2:40:56 AM UTC-6
                Quentin Anciaux wrote:

                    I just gave you a full proof that as long as the
                    expansion is uniform and expansion rate > 0, then
                    it follows objects will sooner or later recess
                    from each other at speed > c.


                What was the justification for the geometric
                progression? I made no such assumption in my "proof".


            As explained multiple times and in the quote you made,
            expansion is uniform and happens at every point in space.


        What bothers me about your method is that you*assume* a
        geometric increase in the separation distance, when, IMO,
        that's the variable that must be calculated (which I did). So
        no matter how many times you affirm your proof as valid, I
        can't agree. AG

        You didn't calculate the expansion parameter, which is the
        Hubble constant.  It's an observed value.

        Brent


    Why must I do that, when I just want to show that eventually the
    recessional velocity exceeds c? Also, I don't see why theta is
    fixed, when the end of the arc defines the position of the
    receding galaxy. AG


Now I am not sure I proved the recessional velocity is greater than c, 
after some time has passed. If the sphere is expanding, then the 
distance between any two fixed points on the sphere will increase as 
time passes. But that was obvious due to the expansion. What's wrong, 
if anything? AG
Because you don't pay attention to the dimensionality of the values you 
confuse distance increasing with speed of recession increasing as though 
those were the same thing when in fact they are only related because of 
Hubbles constant.

Brent

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