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Lorentz Transformation

Lorentz Transformation
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2019-05-21 00:06
CalculusTransformationGeometric Construction
This example demonstrates the geometric meaning of the Lorentz transformation, a crucial transformation in special relativity used to describe coordinate transformations between different inertial reference frames. By using the commands in the construction summary, we can see how to implement this transformation in GeoGebra. This example is suitable for high school physics and mathematics courses, especially for students studying special relativity and transformation theory.

GeoGebra Commands & Parameters

  1. Point(eq1) → A'
  2. Intersect(g, h) → B
  3. Line(A', B) → r
  4. Line(A', h) → i
  5. Intersect(g, i) → D
  6. Line(A', g) → f
  7. Intersect(h, f) → C
  8. Line(C, D) → j
  9. Intersect(r, j) → E
  10. Line(A', j) → k
  11. Line(B, j) → l
  12. Line(D, r) → m
  13. Line(C, r) → n
  14. Intersect(l, n) → F
  15. Intersect(l, m) → G
  16. Intersect(k, m) → H
  17. Intersect(k, n) → I
  18. Mirror(r, m) → r'
  19. Mirror(r, n) → r'_1
  20. Mirror(n, r'_1) → n'
  21. Mirror(r'_1, n') → p
  22. Mirror(n', p) → n''
  23. Mirror(m, r') → m'
  24. Mirror(r', m') → r''
  25. Mirror(p, n'') → p'
  26. Mirror(j, l) → j'
  27. Mirror(l, j') → l'
  28. Mirror(j', l') → j''
  29. Mirror(j, k) → j'_1
  30. Mirror(k, j'_1) → k'
  31. Mirror(j'_1, k') → q
  32. Mirror(k', q) → k''
  33. Intersect(k, yAxis) → T
  34. Mirror(m', r'') → m''
  35. Mirror(r'', m'') → r'''
  36. Mirror(m'', r''') → m'''
  37. Mirror(r''', m''') → s
  38. Mirror(m''', s) → t
  39. Mirror(n'', p') → n'''
  40. Mirror(p', n''') → p''
  41. Mirror(n''', p'') → a
  42. Mirror(p'', a) → p'''
  43. Mirror(q, k'') → q'
  44. Mirror(k'', q') → k'''
  45. Mirror(q', k''') → q''
  46. Mirror(k''', q'') → b
  47. Mirror(q'', b) → q'''
  48. Mirror(a, p''') → a'
  49. Mirror(s, t) → s'
  50. Mirror(t, s') → t'
  51. Mirror(l', j'') → l''
  52. Mirror(j'', l'') → j'''
  53. Mirror(l'', j''') → l'''
  54. Mirror(j''', l''') → c
  55. Mirror(l''', c) → d
  56. Mirror(c, d) → c'
  57. Mirror(d, c') → d'
  58. Mirror(c', d') → c''
  59. Intersect(eq1, yAxis, 2) → A
  60. Intersect(r, j) → J
  61. Intersect(r, j'_1) → K
  62. Intersect(r, k') → L
  63. Intersect(r, q) → M
  64. Intersect(r, k'') → N
  65. Intersect(r, q') → O
  66. Intersect(r, k''') → P
  67. Intersect(r, q'') → Q
  68. Intersect(r, b) → R
  69. Intersect(r, q''') → S