
It is not proper in relation to such a world to talk of measuring lengths and
time units.  It contains no such things.  They constitute the reaction of
particular observers to its real phenomena.  According to their motions, the
time unit lengthens and the measuring rod shortens actually in one sense, but
not in aaother.  The measuring rod will contain the same number of molecules,
whatever may be the point of view.  A time unit as such simply does not
exist.  The appearance to us of these measuring values is as we separate them
out in accordance with our own points of view.  Length and duration are not
inherent in the external world.  They constitute our reaction to external
realities.  Our own conditions, for example, as our state of mmotion, give
different mental meanings to them.  In a sense, we create our universe.  We
supply differing scales for the measurement of the same realities, which, for
the same observer, change precisely as the scales change.  Each observer,
according to his own condition, is interpreting in his own way the absolute
facts of the space-time world, and the appearance will vary according to the
condition, particularly according to the state of motion.  Compress the whole
universe to the size of an orange, everything in proportion, and no one would
be the wiser.  Perhaps, in fact, that would be no change at all.

In our own conditions, OUR MINDS HAVE CREATED SPACE AND TIME.  They are the
mental reactions of our pecular condition to phenomena occuring in the real
world.  In that world, a straight line ceases to be the shortest distance
between two points.  In fact, it is improper to speak of 'distance' at all,
unless we differentiate it by a special name such as 'space-time distance' or
'interval.' The longest 'world-line' or 'interval' between two events might
include the shortest space distance.  The space-time curvatures and twists
and the consequent shortenings and lenthenings exist, but are effected for
observers by their own different motions and conditions, these in turn not
being actual but relative.

Thus the only possible explanation of the results of the special theory is no
satisfying explanation at all, for we are called upon to posit, as containing
the phenomena of nature, an admittedly inconceivable, perhaps noumenal,
continuum, which certainly could have no scientific interest, were if not
that its propounder believes that, inconceivable as it is, it is yet able to
penetrate to our mentalities through empiric proofs.  This explanation is a
non- picturable world of four dimensions.

This notion of a kind of absolute four-dimensional world is, from every
aspect, the only outcome of the Einstein assumptions.  On the basis that
light's velocity is a constant STATED QUANTITY, irrespective of the motion of
the observer, the Lorentz transformations were produced.  The results of
those transformations seem remarkable unless that basis is constantly borne
in mind.  By their application it has been seen that a velocity of 186,000
mps for light in relation to a stationary system remains the same for a
system, in relation to which, according to classic standards, it should be
25,000 mps, or even 347,000 mps, according to the direction of the ray.  This
is due to the changing values of the time and space measuring units,
automatically yielding compensatory results by reason of the basic
assumptions.  But what reason can there be to assume that the never failing
outcome of a velocity of 186,000 miles in one second for light in all the
differing cases, is a constant, when it is measured in mile units and second
units differing in each of the supposed cases?  Is a velocity of 50,000 miles
of a certain kind in 50/186 of a second of a certain kind, although it
figures out 186,000 of such miles in one of such seconds, the same as a
velocity of 186,000 of a different kind of miles in a different kind of
second?  From this point of view, the Lorentz transformations alone do not
solve the problem, and there is no reason why our wizards of previous
sections should have emerged from their tubes at the same moment.

But on the assumption of the space-time world, this difficulty
disappears.  The measuring values and that which they measure do not really
change.  They are always the same.  The points of view of the measuring
observers, their mental scales change.  The inherent energies represented by
the same numerical velocities of the different scales are the same.  NUMBER
IS ABSOLUTE; SCALE IS RELATIVE.  True, there is not in the four-dimensional
world a real measuring length or time unit.  The facts of that world are of
an inconceivably different kind, but separated out by the mentalities of
observers of different viewpoints these standards APPEAR as real
things.  That for which the appearance stands is invariable, but to observers
of different relative motions the appearances differ.  THE MILE STICK AND THE
SECOND ARE ALWAYS REALLY THE SAME SO FAR AS THEY STAND FOR SOMETHING IN THE
REAL WORLD, BUT ACTUALLY CHANGE IN MAGNITUDE TOGETHER WITH WHAT THEY MEASURE,
ACCORDING TO THE STATE OF THE OBSERVER.  (This is why timepieces on a space
ship traveling near light speed would seem normal to those on board; but to
an Earth observer they would appear to be moving much slower.  Remember that
as you approach light speed, time approaches zero.)

The changes then are, after all, illusions, but not in the ordinary
sense.  The illusions have fixed and consistent mathematical relations.  They
are supposed to constitute our interpretation of deeper lying physical
realities, in the same way as the phiosopher supposes all phenomena to
constitute our interpretation of noumenal realities.  In the real world,
space and time measurement units thereof do not exist separately, as we
conceive them.

