Reading 4

This passage is taken from a book titled The River of Time by Igor Novikov and Vitaly Kisin (© 2001 Igor Novikov, Vitaly Kisin).

  1. Everyone knows that the space of
  2. the Universe is three-dimensional.
  3. This means that space is
  4. characterized by length, width
  5. and height. The same is true for
  6. any body. Somewhat differently,
  7. the position of a point in space is
  8. characterized by three numbers
  9. known as coordinates.
  10. If we draw straight lines or planes
  11. or complicated curves through
  12. space, their properties are
  13. described by the laws of geometry.
  14. These laws have been known to
  15. man since ancient times and were
  16. compiled by Euclid in the
  17. 3rd century BC. Euclidean
  18. geometry is studied in schools as
  19. a harmonious system of axioms
  20. and theorems that describe all
  21. properties of lines, surfaces
  22. and solids.
  23. If we wish to study not only the
  24. spatial position but also processes
  25. occurring in three-dimensional
  26. space, we need to add time as well.
  27. An event taking place at some
  28. point is characterized by the
  29. position of this point, that is,
  30. by indicating three numbers,
  31. and by a fourth number, that is,
  32. the moment of time at which the
  33. event occurred. For the event the
  34. time is its fourth coordinate.
  35. In this sense we say that our
  36. world is four-dimensional.
  37. All this is well known, of course.
  38. Then why wasn’t this formulation
  39. of four-dimensionality treated as
  40. serious and fraught with new
  41. knowledge before the theory of
  42. relativity was born? The catch lay
  43. in the fact that the properties of
  44. space and time seemed to be too
  45. dissimilar.
  46. Space is three-dimensional but
  47. time is one-dimensional. In fact,
  48. time was compared to a straight
  49. line even by the ancient
  50. philosophers, but this always
  51. seemed to be no more than a
  52. useful visual image without any
  53. profound meaning. Things
  54. changed drastically after relativity
  55. theory was discovered. We have a
  56. static mental picture in which
  57. bodies or geometric figures are
  58. fixed at a given moment.
  59. In contrast to this, time flows
  60. incessantly (always from the
  61. past towards the future) and
  62. bodies change their positions.
  63. In 1908, the German
  64. mathematician Hermann
  65. Minkowski developing further the
  66. ideas of this theory, said:
  67. ‘From now on, space as such
  68. and time as such must turn
  69. into fictions and only some
  70. form of combining them
  71. together will retain
  72. independence.’ What did
  73. Minkowski mean in this
  74. forthright and categorical
  75. declaration?
  76. He wished to emphasize two
  77. aspects. Firstly, that time
  78. intervals and spatial lengths are
  79. relative, depending on the choice
  80. of the reference frame. Secondly –
  81. and this was the more important
  82. part of his words – that space and
  83. time are connected inseparably.
  84. In fact, they are two facets of a
  85. unified entity: four-dimensional
  86. spacetime. The pre-Einstein
  87. physics knew nothing of
  88. these close ties.
  89. It may not be too hard to
  90. comprehend the three-
  91. dimensional unification of space
  92. and time. Imagining the
  93. four-dimensional world is far
  94. more difficult. The difficulty is
  95. not surprising. When we draw
  96. geometric figures in a plane,
  97. we usually encounter no
  98. difficulties in projecting what
  99. we want; these figures are
  100. two-dimensional (only have
  101. a length and a width).
  102. Quite a few people have a hard
  103. time imagining three-dimensional
  104. forms in space — pyramids, cones,
  105. planes intersecting them etc.
  106. As for creating an image of
  107. four-dimensional forms, it is a
  108. very demanding task even for
  109. experts who work with relativity
  110. theory all the time.
  111. I will quote the very famous
  112. British physics theoretician
  113. Stephen Hawking, an expert of
  114. incomparable standing in
  115. relativity theory. He says in his
  116. famous book A Brief History
  117. of Time: ‘I personally find it
  118. hard enough to visualize
  119. three-dimensional space!’ Which
  120. shows that the reader defeated
  121. by imagining four-dimensional
  122. world need not be unhappy.