Yet Another Very Simple Argument Against Special Relativity

by

Ardeshir Mehta

Tuesday, October 9, 2001

Here is yet another very simple argument which proves that Special Relativity must be mathematically flawed, for the Lorentz transformation equations -- which are absolutely essential for the Special Theory of Relativity -- can give results which contradict the Special Theory of Relativity itself.

  1. Let's say that somewhere out in deep space, the United Federation of Planets has a fairly large mother-ship of rest-length D, and clamped to its hull there is a fairly small run-about of rest-length d -- both ships facing in the same direction.

  2.  
  3. Let's say that when the run-about is stationary relative to the mother-ship, the mother-ship is exactly ten times as long as the run-about.

  4.  
  5. Thus when the run-about is stationary relative to the mother-ship the ratio d/D is exactly 1/10 -- or expressed decimally, 0.1.

  6.  
  7. Now let's say the clamps on the run-about are released, and the run-about fires its engines, moving away from the mother-ship in a straight line, and eventually reaching a constant rectilinear velocity v relative to the mother-ship. 

  8.  
  9. According to the Lorentz transformation equations, the length of the run-about must now be contracted compared to what it was in 1. above, namely d

  10.  
  11. The contracted length, d', must be calculable by the Lorentz transformation formula d' = d/{1/[1-(v2/c2)]0.5}.

  12.  
  13. Of course d' cannot be greater than or equal to d, but must be less, because (v2/c2) must be a positive number, and so [1-(v2/c2)] must be less than 1, so the square root of [1-(v2/c2)] must also be less than 1, which means that {1/[1-(v2/c2)]0.5} must be greater than 1.

  14.  
  15. Under these conditions, however, the length D of the mother-ship cannot have changed from what it was when the mother-ship and run-about were clamped to each other, as was the case in 1. above.

  16.  
  17. So in 5. and 6. above, the ratio d'/D cannot be 1/10 or 0.1, but must be less, because d/D = 1/10, and d' < d.

  18.  
  19. Let the run-about now turn around, return to the mother-ship and be clamped back onto its hull. The ratio between the lengths of the two is once again 1/10.

  20.  
  21. Now let the clamps be released a second time, but instead of the run-about firing its engines, let's say the mother-ship fires its engines and it moves away in a straight line from the run-about, eventually reaching a constant rectilinear velocity of v relative to the run-about.

  22.  
  23. Under these condition, the length of the mother ship will now have contracted to D', and according to the Lorentz transformation formula, D' = D/{1/[1-(v2/c2)]0.5}.

  24.  
  25. And D' cannot be greater than or equal to D, but must be less, because (v2/c2) must be a positive number, and so [1-(v2/c2)] must be less than 1, so the square root of [1-(v2/c2)] must also be less than 1, which means that {1/[1-(v2/c2)]0.5} must be greater than 1.

  26.  
  27. Under these conditions, however, the length d of the run-about cannot have changed from what it was when the mother-ship and run-about were clamped to each other, as in 9. above (and in 1. above also.)

  28.  
  29. So now in 11. and 12. above, the ratio d'/D cannot be 1/10 or 0.1, but must be more, because d/D = 1/10, and D' < D.

  30.  
  31. But, and this is a B I G "but", according to the Theory of Relativity, there should be no difference whatsoever between 5. and 6. above on the one hand, and 11. and 12. above on the other: because the relative velocity between mother-ship and run-about is exactly v in all these cases!

  32.  
  33. This is contradicted by the fact that the results of the relative lengths of the mother-ship and run-about in 8. and 14. above are different from one another.

  34.  
  35. And this in turn proves that results obtained by using the Lorentz transformation equations -- which are absolutely essential for the Special Theory of Relativity -- contradict the Special Theory of Relativity itself … proving that the Special Theory of Relativity must be mathematically self-contradictory.

  36.  
P.S.: It should be noted that it is impossible for the length of the mother-ship to have contracted in 7. compared to what it was in 1., nor is it possible for the length of the run-about to have contracted in 13. compared to what it was in 9. That's because in both 1, and 7. above, absolutely nothing happens to the mother-ship; nor does anything happen to the run-about in 9. and 13. above. The only thing that happens in 7. above is that the run-about changes its own relative velocity compared to the mother-ship from what it was in 1. -- namely zero -- to v; and the only thing that happens in 13. above is that the mother-ship changes its own relative velocity compared to the run-about from what it was in 1. -- namely zero -- to v.
 
 

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