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)
Shall we carry over our idea (b) to answer the next question: "To
which material body shall we attach our framework?" To this question
Newton gave one answer and Einstein another. We shall first consider
Newton's position and then we may hope to see clearly where the new
theory diverges from the classical or Newtonian mechanics. Newton's
answer was that there is a particular material frame with reference
to which the laws of mechanics have a remarkably simple form commonly
known as "Newton's laws of motion" and so it is preferable to use
this framework which is called an absolute frame.
What is the essential peculiarity of an absolute frame? Newton was
essentially an empiricist of Bacon's school and he observed the
following facts. Let us suppose we have a framework of reference
attached to the earth. Then a small particle of matter under the
gravitational influence of surrounding bodies, including the earth,
takes on a certain acceleration $A_1$. Now suppose the surrounding
bodies removed (since we cannot remove the earth we shall have to
view the experiment as an abstraction), and another set introduced;
the particle, being again at its original position, will begin to
move with an acceleration $A_2$. If both sets of surrounding bodies
are present simultaneously the particle begins to move with an
acceleration which is approximately but not quite the sum of $A_1$
and $A_2$. Newton postulated there there is a certain absolute
reference frame in which the approximation would be an equality;
and so the acceleration, relative to the material frame, furnishes
a convenient measure of the effect of the surrounding bodies--which
effect we call their gravitational force. Notice that if the effect
of the surrounding bodies is small the acceleration is small and
so we obtain as a limiting case, Newton's law of inertia which says
that a body subject to no forces has no acceleration; a law which,
as Poincaré justly observed, can never be subjected to experimental
justification. The natural questions then arise: which is the
absolute and privileged reference-frame and how must the simple laws
be modified when we use a frame more convenient for us--one attached
to the earth let us say? The absolute frame is one attached to the
fixed stars; and to the absolute or real force defined as above,
we must add certain terms, usually called centrifugal forces. These
are referred to as fictitious forces because, as it is explained,
they are due to the motion of the reference-frame with respect to
the absolute frame and in no way depend on the distribution of the
surrounding bodies. Gravitational force and centrifugal forces have
in common the remarkable property that they depend in no way on the
material of the attracted body nor on its chemical state; they act
on all matter and are in this way different from other forces met
with in nature, such as magnetic or electric forces. Further Newton
found that he could predict the facts of observation accurately on the
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