In reality, if we stop to think a minute, there is no valid
reason for the non-existence of a fourth dimension. If one, two
and three dimensions, why not four--and five and six, for that
matter? Theoretically at least there is no reason why the limit
should be set at three. However, our minds become sluggish when we
attempt to picture dimensions beyond three; just as an extraordinary
effort on our part is needed to follow Einstein when he "juggles"
with space and time.
Our difficulty in imagining four dimensions may be likened to the
difficulty two-dimensioned beings would experience in imagining
us, beings of the conventional three dimensions. Suppose these
two-dimensional beings were living on the surface of the earth;
what could they see? They could see nothing below and nothing above
the surface. They would see shifting surfaces as we walked about,
but being sensitive to length and breadth only, and not to height,
they could gain no notion whatsoever of what we really look like. It
is thus with us when we attempt to picture four-dimensional space.
Perhaps the analogy of the motion picture may help us somewhat. As
everybody knows, these motion pictures consist of a series of
photographs which are shown in rapid succession on the screen. Each
photograph by itself conveys a sensation of space, that is, of three
dimensions; but one photograph rapidly following another conveys
the sensation of space and time--four dimensions. Space and time
are interlinked.
The Time-space Idea Further Developed. We have already alluded to the
fact that objects in space moving with different velocities build up
different time intervals. Thus the velocity of the star Arcturus, if
compared with reference to the earth, moves at the rate of 200 miles a
second. Its motion through space is different from ours. Objects which,
according to Lorentz, contract in the direction of their motion to an
extent proportional to their velocity, will contract differently on
the surface of Arcturus than on the earth. Our space is not Arcturus'
space; neither is Arcturus' time our time. And what is true of the
discrepancies existing between the space and time conceptions of the
earth and Arcturus is true of any other two bodies in space moving
at different velocities.
Public-domain text, read in full here on John Shaqi.
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