Time-Stop Paradox

黒月樹人(KULOTSUKI Kinohito)[2]

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 Introduction

 This is a criticism page on Special Relativity of Einstein.
 On Special Relativity of Einstein, as the dormant system (the static system) time is t, and as the active system (the moving system) time is τ, there is an equation on t and τ.
     τ=[1/{1-(v/c)2}1/2]{t-(v/c2)x}        (1-1)
 Einstein substitutes (1-2) for (1-1) .
     x=vt                        (1-2)
 Thus he leads to an expression (1-3).
     τ=t {1-(v/c)2}1/2                (1-3)
 And he comments “The time τ of the moving system is smaller than the time t of the static system”. [1]
 Only such analysis results are spreading, and it has been considered that the time τ goes slowly with the ratio expressed by the formula (1-3) in all of the moving system
 However, considering the meaning of conditional expression (1-2) when Einstein leads (1-3), as can be seen by substituting (1-2) to (1-4),
     ξ=β(x-vt)                      (1-4)
     β=1/{1-(v/c)2}1/2                (1-5)
(1-3) is a relational expression limited to the position of
     ξ=0.                         (1-6)

 Time stops paradox

 Einstein substituted x = vt (1-2) into (1-1), but let's examine what it will look like when considering a different position.
 Now, (2-1) is substituted to (1-1). Here, α is an undetermined coefficient.
     x=αvt                        (2-1)
     τ=β{t-(v/c2)αvt }                 (2-2)
 Then, (2-2) will be (2-3).
     τ=β{1-α(v/c)2}t                  (2-3)
 Let’s find the condition of α at which τ is zero.
     α=(c/v)2                       (2-4)
 In order to understand the meaning of this expression (2-4), numerical calculation is performed. Let's assume the following (2-5). 
     v=0.8c                        (2-5)
 Then the value of α is (2-6) and x is (2-7).
     α=1.5625                       (2-6)
     x=1.5625×0.8ct
      =1.25ct.                       (2-7)
 When the value of α is 1.5625, since v = 0.8 c, x is 1.25 ct.
 Although it(x) exceeds the light speed c here, this is to calculate the distance of x from (x=)0, and something does not move beyond the light speed. If t is 1 second, x will exceed 300 thousand kilometers, but if you reduce this time, x gets smaller and smaller.
 Alternatively, as the coordinate ξ of the moving system, it can be rewritten as follows.
     ξ=β(x−vt)
      =(1/0.6)(1.25ct−0.8ct)                   (2-8)
      =0.75ct                         (2-9)
 As the coordinate ξ of the movement system, it is a distance of 0.75 ct.
 This position exists if the moving system spreads all the way.
 What will happen at this position?
 Since we decided α so that τ became zero in (2-3), the time τ of the moving system stops.
 It means that there is a position where the time τ of the moving system stops.
 I wonder what will happen there.

Fig.1  There is a position where the time of the moving system stops.

 (Written by KLOTUKI Kinohito, Aug 12, 2018)

 Reference(Appendix)

[1] Special Relativiti paper
[2] 黒(black)月(moon)樹(tree)人(man) as hundle name. The pronunciation of KULOTSUKI resembles 9621 in Japanese. So treeman9621 means Kinohito KULOTSUKI.
 Real name is 田中 毅 (TANAKA Takeshi). It is most commonplace name in Japan.

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