Einstein's Theories of Relativity and Gravitation: A selection of material from the essays submitted in the competition for the Eugene Higgins prize of $5,000Bird, J. Malcolm (James Malcolm)
Philosophy
Einstein's Theories of Relativity and Gravitation: A selection of material from the essays submitted in the competition for the Eugene Higgins prize of $5,000
Bird, J. Malcolm (James Malcolm)
Relativity (Physics)
To describe the phenomena and derive laws from them, we locate them
in space and time. To do this we use geometry. Here it is that the
part contributed by the observer comes in. There are an infinite
number of geometries, and a priori there seems to be no reason to
choose one rather than the other. Taking geometry of two dimensions
as an example, we can draw figures on a piece of paper, and discuss
their properties, and we can also do so on the shell of an egg. But
we cannot draw the same figures on the egg as on the paper. The
ones will be distorted as compared with the others: the two surfaces
have a different geometry. Similarly it is not possible to draw an
accurate map of the earth on a sheet of paper, because the earth is
spherical and its representation on the flat paper is always more or
less distorted. The earth requires spherical geometry, which differs
from the flat, or Euclidean, geometry of the paper.
Up to a few years ago Euclidean (i.e. flat) geometry of three
dimensions had been exclusively used in physical theories. Why? Because
it is the true one, is the one answer generally given. Now a statement
about facts can be true or false, but a mathematical discipline is
neither true nor false; it can only be correct--i.e. consistent in
itself--or incorrect, and of course it always is correct. The assertion
that a certain geometry is the "true" one can thus only mean, that
it is the geometry of "true" space, and this again, if it is to have
any meaning at all, can only mean that it corresponds to the physical
"reality." Leaving aside the question whether this reality has any
geometry at all, we are confronted with the more immediately practical
consideration how we shall verify the asserted correspondence. There is
no other way than by comparing the conclusions derived from the laws
based upon our geometry, with observations. It thus appears that the
only justification for the use of the Euclidean geometry is its success
in enabling us to "draw an accurate map" of the world. As soon as any
other geometry is found to be more successful, that other must be used
in physical theories, and we may, if we like, call it the "true" one.
Public-domain text, read in full here on John Shaqi.
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