The evolution of scientific thought from Newton to EinsteinD'Abro, A. (Aram)
Science
The evolution of scientific thought from Newton to Einstein
D'Abro, A. (Aram)
Relativity (Physics); Science -- Methodology
If a Galilean frame moves away from us with a speed and if,
with respect to this frame and in the direction of its motion, a
bullet speeds with a velocity , the resultant speed of the bullet
might be only provided our methods of measuring a velocity,
and those of the observer in the Galilean frame, were identical; that
is, provided our measurements of space and time were identical. This
was always tacitly assumed to be the case by classical science; but
we know that in Einstein’s theory the identity of our standards of
measurement no longer holds, since such a state of affairs would be
incompatible with the invariance of the velocity of light.
We may therefore assimilate the conditions surrounding the various
space and time measurements in Einstein’s theory to those which would
endure in classical science if by reason of some law of nature it
were impossible for the observer in the train to fire a bullet in the
precise direction of the train’s motion. In other words, in Einstein’s
theory, velocities lying in the same direction add up like algebraical
numbers, provided the velocities we propose to add and subtract are
computed under exactly the same conditions, that is, by the same
Galilean observer. It is when one observer computes one velocity
and a second observer, in relative motion, computes the second velocity
that the classical law of addition is at fault.
Very similar to this problem of the addition of velocities is that
of simultaneity. Thus, Einstein’s theory implies that if two events
and occur simultaneously for one observer, John, and if
in the opinion of another observer, Peter, in motion with respect to
John, the event and another event occur simultaneously,
it is not correct to assume that and will be simultaneous
in the opinion of either of the two observers. Here the critic
assumes, without further ado, that the symbolic expression of these
relationships would be as follows: ; ; .
Therefrom he infers that the theory of relativity is contrary
to logic and is a manifest absurdity. And yet, if we examine these
statements carefully, we shall have no difficulty in seeing that the
error in logical reasoning lies not with Einstein but with the critic
himself.
In order to dispel any doubt on this score, let us ask the critic what
he intends to convey by the symbol =. Suppose, for example, that we
are considering two objects, and , of the same size. Are we
entitled to write ? The answer should be: Yes, if the symbol =
stands for “is of the same size as”; or No, if it stands for most other
types of identity. In order to avoid confusion let us then represent
the symbol by ( standing for size) and let us
write .
Public-domain text, read in full here on John Shaqi.
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