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.