This passage is taken from a book titled The River of Time by Igor Novikov and Vitaly Kisin (© 2001 Igor Novikov, Vitaly Kisin).
- Everyone knows that the space of
- the Universe is three-dimensional.
- This means that space is
- characterized by length, width
- and height. The same is true for
- any body. Somewhat differently,
- the position of a point in space is
- characterized by three numbers
- known as coordinates.
- If we draw straight lines or planes
- or complicated curves through
- space, their properties are
- described by the laws of geometry.
- These laws have been known to
- man since ancient times and were
- compiled by Euclid in the
- 3rd century BC. Euclidean
- geometry is studied in schools as
- a harmonious system of axioms
- and theorems that describe all
- properties of lines, surfaces
- and solids.
- If we wish to study not only the
- spatial position but also processes
- occurring in three-dimensional
- space, we need to add time as well.
- An event taking place at some
- point is characterized by the
- position of this point, that is,
- by indicating three numbers,
- and by a fourth number, that is,
- the moment of time at which the
- event occurred. For the event the
- time is its fourth coordinate.
- In this sense we say that our
- world is four-dimensional.
- All this is well known, of course.
- Then why wasn’t this formulation
- of four-dimensionality treated as
- serious and fraught with new
- knowledge before the theory of
- relativity was born? The catch lay
- in the fact that the properties of
- space and time seemed to be too
- dissimilar.
- Space is three-dimensional but
- time is one-dimensional. In fact,
- time was compared to a straight
- line even by the ancient
- philosophers, but this always
- seemed to be no more than a
- useful visual image without any
- profound meaning. Things
- changed drastically after relativity
- theory was discovered. We have a
- static mental picture in which
- bodies or geometric figures are
- fixed at a given moment.
- In contrast to this, time flows
- incessantly (always from the
- past towards the future) and
- bodies change their positions.
- In 1908, the German
- mathematician Hermann
- Minkowski developing further the
- ideas of this theory, said:
- ‘From now on, space as such
- and time as such must turn
- into fictions and only some
- form of combining them
- together will retain
- independence.’ What did
- Minkowski mean in this
- forthright and categorical
- declaration?
- He wished to emphasize two
- aspects. Firstly, that time
- intervals and spatial lengths are
- relative, depending on the choice
- of the reference frame. Secondly –
- and this was the more important
- part of his words – that space and
- time are connected inseparably.
- In fact, they are two facets of a
- unified entity: four-dimensional
- spacetime. The pre-Einstein
- physics knew nothing of
- these close ties.
- It may not be too hard to
- comprehend the three-
- dimensional unification of space
- and time. Imagining the
- four-dimensional world is far
- more difficult. The difficulty is
- not surprising. When we draw
- geometric figures in a plane,
- we usually encounter no
- difficulties in projecting what
- we want; these figures are
- two-dimensional (only have
- a length and a width).
- Quite a few people have a hard
- time imagining three-dimensional
- forms in space — pyramids, cones,
- planes intersecting them etc.
- As for creating an image of
- four-dimensional forms, it is a
- very demanding task even for
- experts who work with relativity
- theory all the time.
- I will quote the very famous
- British physics theoretician
- Stephen Hawking, an expert of
- incomparable standing in
- relativity theory. He says in his
- famous book A Brief History
- of Time: ‘I personally find it
- hard enough to visualize
- three-dimensional space!’ Which
- shows that the reader defeated
- by imagining four-dimensional
- world need not be unhappy.