
For purposes of further clarification, let us now consider certain problems.
Let us first suppose two light signals flashed at a considerable distance
from each other at the same instant, from the point of view of a stationary
observer on the embankment of our frequently illustration, midway between the
flashes, and then let us suppose the train to be moving at the velocity of
161,000 mps, so that the train observer's position at the instant the flashes
are emitted, is at the midway point.  Will these two flashes reach him at the
same time?

Einstein's answer is that they will not.  He will see the flash toward which
he is traveling before the one from which he is traveling.  The first will
reach him before he is overtaken by the second.  But, as we have before
noted, the Professor intended this answer to apply only to classic standards.
According to the basic principle of the theory and of the Lorentz equations,
the flashes would still be simultaneous, as otherwise the train observer
would be able to detect his own motion through the ether.  At all events,
according to the theory each observer provided with the proper instruments,
will measure the velocity of both flashes at precisely the same amount of
186,000 mps.  The embankment observer will decide that they are simultaneous,
but that they cannot appear so to the train observer, who unaware of his own
motion, is rushing into one, from the former's standpoint, at the velocity of
347,000 mps and away from the other, which is overtaking him at the velocity
of only 25,000 mps.

(186,000 + 161,000 = 347,000) (186,000 - 161,000 = 25,000)

After this experiment, if the two observers should meet and the embankment
observer should inform the other that the reason he considered successive
what were in fact simultaneous flashes was because of his motion, or rather,
because he thought himself at rest and the rear flash to be traveling toward
him at 25,000 mps and the forward flash at 347,000 mps, the train observer
must reply that this cannot possibly be true, as he measured the velocity of
both flashes by unquestionable methods and obtained the same unquestionable
result in each case, a velocity of 186,000 mps.  THE DIFFICULTY IS THAT EACH
OBSERVER ASSUMES, WITHOUT RIGHT, THAT HIS OWN SYSTEM IS IN ABSOLUTE REST AND
THE OTHER IN ABSOLUTE MOTION.

These considerations lead to another problem the answer to which supplies us
with surprising results, which make clear the necessity of some kind of
scientific theory or picture to account for the mathematical reactions.  Let
us suppose that we have three observers whom we will designate as O, O', and
O".  O is stationary.  O' is on a system some distance away from O's system
and which is moving, relatively to it, to the right, at a velocity of 80,500
mps.  O's system is between that of O' and that of O", which is moving to the
left at a velocity of 80,500 mps.  The relative velocity of O' and O" will,
therefor, be 161,000 mps.  O' will see a yard stick on the O" system shrink
to 1/2 yard, while O" will see a yard stick on the O' system incur precisely
the same shrinkage.  But relatively to O, both O' and O" are traveling at the
velocity of 80,500 mps and O will see the yard stick on both the O' system
and O" system shrink only to 9/10 of a yard; and similarly both O' and O"
will see the yard stick on the O system shrink to 9/10 of a yard.

Now the attempt was made above to save the special theory, from ordinary
points of view, by reason of the same shrinkage occurring on each of two
relatively moving systems, by the suggestion that the motion energy expressed
itself in an actual space-time warp in some way covering both systems, and
therefore, actually shortening the dimensions of both systems, though not
appreciably to either observer with reference to his own, owing to the
corresponding shortening of his measuring rods.  This would not be a
satisfactory explanation, since it would not account for the fact that the
changes on one system would be perceptible from the other.  We might think
this should not be the case, since the measuring appliances on both systems
are similarly affected.  The relativist mathematicians, insist that from one
system the changes in the other must be discernible, as otherwise motion
relative to the ether could be detected; and we must accept this conclusion.

The difficulty is increased, by the solution of the last problem to the
effect that while, in the case of the two systems moving in opposite
directions and therefore at relatively double speed, the shortening is the
same quantity on each, to the relatively stationary observer between them,
the same supposed actual space-time warp produces a much smaller shortening.
This negatives the idea of an actual warp which includes all the systems,
since the effects are thus different.  Moreover, it could not plausibly be
imagined that if one moving system were a vast space-time distance from a
relatively stationary one, the supposed warp produced by the motion energy of
one system should, in all cases, extend through the intervening distance.

We can suppose that there may be 'actual' motion, which warps the space-time
of its own system only.  This being so, the observer on the actually moving
system perceives the phenomena of a stationary system through the warp of his
own space-time only.  The stationary observer perceives the system through
its warp.  The moving observer sees the phenomena of another system with an
actual and opposite motion through both warps, thus increasing the effect,
while if both systems be actually moving in the same direction and velocity
relatively to the stationary one, the two warps neutralize each other.  This
explanation, assumes actual motion, which Einstein denies, and contains the
same relativist proposition as before, that the changes on one system are
detectible from the other.

On reflection, it will be seen that in this discussion we have been guilty of
an extraordinary fallacy.  True, we have been using the term 'space-time',
but it will be clear from the context that we have been thinking of it
precisely the same way as we think of space.  We have been writing as though
we know something on a subject of which we know nothing.  We have been
applying the ideas of our 3-dimensional world to a 4-dimensional world,
which, entirely inconceivable, is only made manifest in the abstractions of
mathematicians.  We have forgotten that, as an eminent mathematician (Betrand
Russell) has said, "mathematics may be defined as the subject in which we
never know what we are talking about, nor whether what we are saying is
true." The mathematician is satisfied with consistent results from assumed
premises, and leaves it to others to attempt to conceive or picture them.

THE RELATIVIST WANTS US TO UNDERSTAND THAT THE REAL WORLD IS ONE OF FOUR
DIMENSIONS, OF WHICH TIME IS ONE AS TRULY AS ANY OF THE OTHERS.


That world he views as, in a sense, absolute, though it can only be known
relatively by observers having varying relations to it.  The forms in which
it and phenomena occurring in it appear to observers depend upon their
position and motion of their respective measuring appliances.  In other
words, the form of the appearance of the real world and its phenomena depends
upon the point of view.  This must be the real meaning of relativity.

