2. The Need for an Extension of the Postulate of Relativity
In classical mechanics, and no less in the special theory
of relativity, there is an inherent epistemological defect which
was, perhaps for the first time, clearly pointed out by Ernst
Mach. We will elucidate it by the following example :-Two
fluid bodies of the same size and nature hover freely in space
at so great a distance from each other and from all other
masses that only those gravitational forces need be taken into
account which arise from the interaction of different parts of
the same body. Let the distance between the two bodies be
invariable, and in neither of the bodies let there be any
relative movements of the parts with respect to one another.
But let either mass, as judged by an observer at rest
relatively to the other mass, rotate with constant angular
velocity about the line joining the masses. This is a verifiable
relative motion of the two bodies. N ow let us imagine
that each of the bodies has been surveyed by means of
measuring instruments at rest relatively to itself, and let the
surface of 81 prove to be a sphere, and that of 82 an ellipsoid
of revolution. Thereupon we put the question-What is the
reason for this difference in the two bodies? No answer can
be admitted as epistemologically satisfactory,* unless the
reason given is an observable fact of experience. The law of
causality has not the significance of a statement as to the
world of experience, except when observable facts ultimately
appear as causes and effects.
Newtonian mechanics does not give a satisfactory answer
to this question. It pronounces as follows :-The laws of
mechanics apply to the space R1, in respect to which the body
81 is at rest, but not to the space R2, in respect to which the
body 82 is at rest. But the privileged space Rl of Galileo,
thus introduced, is a merely factitious cause, and not a thing
that can be observed. It is therefore clear that Newton's
mechanics does not really satisfy the requirement of causality
in the case under consideration, but only apparently does so,
since it makes the factitious cause R1 responsible for the observable
difference in the bodies 81 and 82,
The only satisfactory answer must be that the physical
system consisting of 81 and 82 reveals within itself no imaginable
cause to which the differing behaviour of 81 and 82 can
be referred.
The cause must therefore lie outside this system.
We have to take it that the general laws of motion, which in
particular determine the shapes of 81 and 82, must be such
that the mechanical behaviour of 81 and 82 is partly conditioned,
in quite essential respects, by distant masses which
we have not included in the system under consideration.
These distant masses and their motions relative to 81 and
82 must then be regarded as the seat of the causes (which
must be susceptible to observation) of the different behaviour
of our two bodies 81 and 82, They take over the role of the
factitious cause R1• Of all imaginable spaces R1, R2, etc., in
any kind of motion relatively to one another, there is none
which we may look upon as privileged a priori without reviving
the above-mentioned epistemological objection. The
laws of physics must be of suck a nature that they apply to
systems of reference in any kind of motion. Along this road
we arrive at an extension aUhe postulate of relativity.
Originally Posted by JMessenger
from 
. Instead of ad-hoc throwing the cosmological constant 
into the equation to account for dark energy, it should come naturally from the fundamental theorem of calculus so that (I am removing the other terms that are with the cc in order to make it more illustrative on what the paper is stating) 
.
, that would signal the spontaneously breaking of a gauge symmetry [21].
would seem to fit this definition.
