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)
The purely relative aspect of the matter is further brought out if
we consider a single example both backwards and forwards. Systems $S$
and $S'$ are in relative motion. An object in $S$ which to an observer
in $S$ is $L$ units long, is shorter for an observer in $S'$--shorter
by an amount indicated through the "correction factor" $K$. Now if
we have, in the first instance, made the objectionable statement
that objects are shorter in system $S'$ than they are in $S$, it
will be quite natural for us to infer from this that objects in $S$
must be longer than those in $S'$; and from this to assert that when
the observer in $S$ measures objects lying in $S'$, he gets for them
greater lengths than does the home observer in $S'$. But if we have,
in the first instance, avoided the objectionable statement referred
to, we shall be much better able to realize that the whole business is
quite reciprocal; that the phenomena are symmetric with respect to the
two systems, to the extent that we can interchange the systems in any
of our statements without modifying the statements in any other way.
Objects in $S$ appear shorter and times in $S$ appear longer to the
external "moving" observer in $S'$ than they do to the domestic
observer in $S$. Exactly in the same way, objects in $S'$ appear
shorter to observers in the foreign system $S$ than to the home
observer in $S'$, who remains at rest with respect to them. I think
that when we get the right angle upon this situation, it loses the
alleged startling character which has been imposed upon it by many
writers. The "apparent size" of the astronomer is an analogy in
point. Objects on the moon, by virtue of their great distance, look
smaller to observers on the earth than to observers on the moon. Do
objects on the earth, on this account, look larger to a moon observer
than they do to us? They do not; any suggestion that they do we should
receive with appropriate scorn. The variation in size introduced by
distance is reciprocal, and this reciprocity does not in the least
puzzle us. Why, then, should that introduced by relative motion
puzzle us?
TIME AND SPACE IN A SINGLE PACKAGE
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