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Re: Contradiction or my math/physics error?

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Trevor Lange wrote:

> Again, use units with c=1, and let v be the speed of S1 in terms of S0,
> and let V denote the initial speeds of the objects in the negative x
> direction when they respectively begin accelerating, and put the origin at
> the initial acceleration event of the object at lower x, so its equation
> of motion is x = -Vt + (1/2)at^2.

This is NOT a correct equation of motion in special-relativistic mechanics 
because given a constant force, the acceleration cannot remain constant.  
(if it would, the relative speed could exceed c):

  F = dp/dt = d/dt (γ m v) = m (dγ/dt v + γ dv/dt) = m (γ³ v²/c² + γ) a

⇔ a = F/[m (γ³ v²/c² + γ)] ≠ const. if F = const. as v is increasing. ∎

Forget about accelerations until you are able to handle them¹, and simply 
assume perpetual uniform motion at v⃗ that is just considered from t = 0.
After all, motion at constant (relative) velocity/speed is what “*inertial* 
reference frame” means.


PointedEars
___________
¹ <https://en.wikipedia.org/wiki/Acceleration_(special_relativity)>
-- 
Q: What did the female magnet say to the male magnet?  
A: From the back, I found you repulsive, but from the front
   I find myself very attracted to you.
(from: WolframAlpha)

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Contradiction or my math/physics error? "sepp623@yahoo.com" <sepp623@yahoo.com> - 2023-03-14 15:15 -0700
  Re: Contradiction or my math/physics error? Trevor Lange <trevorlange97@gmail.com> - 2023-03-14 18:08 -0700
    Re: Contradiction or my math/physics error? "sepp623@yahoo.com" <sepp623@yahoo.com> - 2023-03-16 08:05 -0700
      Re: Contradiction or my math/physics error? "mitchr...@gmail.com" <mitchrae3323@gmail.com> - 2023-03-16 12:03 -0700
        Re: Contradiction or my math/physics error? Laurence Clark Crossen <l.c.crossen@hotmail.com> - 2023-03-16 13:03 -0700
          Re: Contradiction or my math/physics error? Sylvia Else <sylvia@email.invalid> - 2023-03-28 20:04 +1100
            Re: Contradiction or my math/physics error? "gehan.am...@gmail.com" <gehan.ameresekere@gmail.com> - 2023-04-13 03:46 -0700
              Re: Contradiction or my math/physics error? Python <python@invalid.org> - 2023-04-13 12:50 +0200
                Re: Contradiction or my math/physics error? JanPB <filmart@gmail.com> - 2023-04-13 10:15 -0700
              Re: Contradiction or my math/physics error? Python <python@invalid.org> - 2023-04-13 12:50 +0200
                Re: Contradiction or my math/physics error? "gehan.am...@gmail.com" <gehan.ameresekere@gmail.com> - 2023-04-13 04:11 -0700
                Re: Contradiction or my math/physics error? Laurence Clark Crossen <l.c.crossen@hotmail.com> - 2023-04-13 06:20 -0700
                Re: Contradiction or my math/physics error? JanPB <filmart@gmail.com> - 2023-04-13 10:20 -0700
                Re: Contradiction or my math/physics error? Laurence Clark Crossen <l.c.crossen@hotmail.com> - 2023-04-13 11:37 -0700
                Re: Contradiction or my math/physics error? Tom Roberts <tjoberts137@sbcglobal.net> - 2023-04-15 14:52 -0500
                Re: Contradiction or my math/physics error? Laurence Clark Crossen <l.c.crossen@hotmail.com> - 2023-04-13 06:28 -0700
                Re: Contradiction or my math/physics error? Tom Roberts <tjoberts137@sbcglobal.net> - 2023-04-15 14:35 -0500
              Re: Contradiction or my math/physics error? Jane <Jane@home.com> - 2023-05-03 08:46 +0000
                Re: Contradiction or my math/physics error? Maciej Wozniak <maluwozniak@gmail.com> - 2023-05-03 02:16 -0700
                Re: Contradiction or my math/physics error? whodat <whodaat@void.nowgre.com> - 2023-05-03 09:25 -0500
          Re: Contradiction or my math/physics error? JanPB <filmart@gmail.com> - 2023-03-28 10:34 -0700
            Re: Contradiction or my math/physics error? Maciej Wozniak <maluwozniak@gmail.com> - 2023-03-28 10:36 -0700
        Re: Contradiction or my math/physics error? Sylvia Else <sylvia@email.invalid> - 2023-03-28 20:02 +1100
          Re: Contradiction or my math/physics error? "mitchr...@gmail.com" <mitchrae3323@gmail.com> - 2023-04-13 10:31 -0700
        Re: Contradiction or my math/physics error? JanPB <filmart@gmail.com> - 2023-03-28 10:32 -0700
    Re: Contradiction or my math/physics error? Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2023-03-28 01:57 +0200
      Re: Contradiction or my math/physics error? Trevor Lange <trevorlange97@gmail.com> - 2023-03-27 17:23 -0700
        Re: Contradiction or my math/physics error? Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2023-04-12 21:29 +0200
          Re: Contradiction or my math/physics error? Trevor Lange <trevorlange97@gmail.com> - 2023-04-12 22:28 -0700
  Re: Contradiction or my math/physics error? Sylvia Else <sylvia@email.invalid> - 2023-03-28 12:00 +1100
  Re: Contradiction or my math/physics error? JanPB <filmart@gmail.com> - 2023-03-27 20:22 -0700

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