a greater velocity than light itself can travel it would certainly
not be true that light, under such a condition, would register a
constant velocity. But such a rate of motion is manifestly impossible
of physical attainment, light being considered to possess the maximum
velocity greater than which no material body can travel. In other
words, 186,300 miles a second is the limiting velocity beyond which
physical phenomena does not reach, because all matter would evidently
suffer complete dissolution, being reduced to the state of free
electrons, by the time such a velocity would be attained. Light is
matter in the free electronic state, and the velocity of such a form of
matter is known to be 186,300 miles a second, as has been stated.
Light, being a form of matter, is acted upon by gravitation. This was
first demonstrated during the solar eclipse of May 29, 1919, when
photographs were taken of various stars whose light at that season had
to pass very near the sun in order to reach us. Three months later
photographs were taken of these same stars after they had moved from
their former positions. Their normal relative motion being known, it
was easy to determine from the two sets of photographs whether their
displacement was entirely due to that motion. It was found that their
displacement was considerably less than it would have been under normal
conditions, thereby indicating that the light from these stars had been
deflected as it passed near the sun’s rim, making it appear to the
observer that these stars then occupied positions which they did not
occupy. See Fig. 3.
[Illustration: FIG. 3.]
=Electronic Structure of Matter=
Light and electricity both travel at the same velocity, and in the
final analysis they are the same form of matter. All ponderable matter
is made up of molecules, and molecules consist of atoms of varying
elements, except where the substance is elementary throughout, in which
case the molecules are made up of a certain number of atoms of the same
element. An atom is an aggregation of negatively charged particles of
electricity, called electrons, which revolve and vibrate at enormous
rates around a central nucleus of “protons” carrying a positive charge.
If we conceive of a handful of sand as whirling around and around at
such an enormous velocity as to appear as a globe several feet in
diameter we have a visualization of the ultra microscopic atom and its
comparative dimension to that of the individual electrons and protons
which compose it.
Electrons and protons are manifestly identical in all form of matter,
but all atoms do not contain the same number of them. An atom of
hydrogen contains only one electron and one proton, while atoms of
heavier matter contain a vast number. It is the _number of electrons
and protons per atom_, together with their respective vibratory
rates, that constitute the difference between elements. Hence every
known form of matter, if reduced to the electronic state, would be
found to consist of the same original stuff. Light, therefore, may be
termed _free electrons_, i. e., electrons which are not bound into
atoms, and consequently glide off in every direction at the highest
possible velocity of which matter is capable, viz., 186,300 miles per
second.
Thus it may be seen that all other forms of matter, since they consist
of electrons in the atomic or “bound” state, could not possess a
velocity equal to that of _free_ electrons. But electrons do not
become “free” simply by reason of matter undergoing a change of form.
Water, for instance, may be changed into a solid (ice) or into gas
(steam), but the electrons continue to revolve around their nucleus
in true atomic order, and the atoms continue to hold together in the
molecular state, the only change being in their rate of vibration which
affects the degree of elasticity between the molecules and between the
atoms. Hence whether water be in the solid, liquid or gaseous state,
the molecules thereof will be found intact, each consisting of two
atoms of hydrogen and one atom of oxygen (H₂O).
When matter is being burned up, producing a flame or a glow of light,
this phenomenon indicates that some of the electrons have been freed
from their atomic condition and have started off on their journey in
the form of light rays, while another portion of them remain bound as
atoms but undergo a change of form, becoming either gas or ashes.
=Michelson-Morley Experiment=
Returning now to Einstein’s second postulate, that the velocity of
unobstructed light rays appears to be constant to all observers
irrespective of the relative velocity between the observer and the
source of light. The evidence on which this theory is based was first
produced by Michelson and Morley in 1887 who at that time undertook an
experiment to ascertain if possible the velocity of the earth relative
to the ether. The experiment revealed that light registers a constant
velocity, whether it travels in the direction of the earth’s rotation,
or against the rotation, or at right angles thereto. The experiment
was repeated many times with different apparatus and under various
conditions, but always with the same result.
It is interesting to note the details of this experiment. Light is
known to travel in waves, because rays coming against each other
from opposite directions can be made to “interfere” in precisely the
same manner as waves in water. If waves in the ocean come together
from different directions, one of two things will happen; they will
either unite and produce a larger wave, or else they will strike in
a manner to measurably kill off both waves. If the crests of the two
waves coincide they reinforce each other, but if they strike at right
angles, the destruction of the wave motion results. This is called
“interference.”
Light rays conduct themselves in the same manner, thereby revealing
their wave-like nature. This is not contradictory to the idea that
light rays really consist of individual electrons, freed from atomic
attraction. Possibly each separate electron which goes to make up a
ray of light vibrates in a wave-like manner, possessing a wave motion
within itself. Waves of light are exceedingly minute and we do not
ordinarily witness any reinforcement or interference of light rays
about us, because there is no occasion for them to “pile up.” However,
in laboratory experiments, interference of light waves has been
produced, and to whatever extent the interference kills off the wave
motion, to that extent darkness ensues irrespective of the brightness
of the light at its source.
Michelson and Morley worked on the theory that if they sent rays of
light from west to east (the direction of the earth’s rotation) and
then reflected them back over their course it should take longer
to make the eastward trip than the westward, because in the first
instance the earth is carrying the objective point away from the light
while in the latter instance it would be rushing to meet the oncoming
reflected rays. Under this condition there should be a noticeable
_interference_ of the light waves due to the difference in
distance and time involved in making the two halves of the round
trip. But to the amazement of all there was no interference whatever,
notwithstanding the fact that the apparatus was ten times larger than
it needed to be to reveal such interference of the waves had it really
occurred.
The conclusion reached by Einstein as a result of this experiment is
that since light rays consist of matter in its basic or electronic
state, freed from atomic attraction, they therefore possess the
limiting velocity of which matter is capable. Hence they could not
travel more rapidly than 186,300 miles a second even if given a quick
send-off, nor would our traveling toward the light affect its apparent
velocity to us--unless it were possible for us to be traveling forward
more rapidly than light itself can travel. This would undoubtedly be
impossible, inasmuch as any physical body would necessarily consist
of electrons in the atomic or “bound” state and therefore could not
possess the mobility that free electrons would enjoy. The universe,
then, being a four-dimensional continuum, is so constructed that the
velocity of light always appears constant to all observers within it.
This is what Einstein means when he postulates that light _in
vacuuo_ (i. e., unobstructed) possesses a constant velocity
irrespective of the relative velocity of observer and source of light.
That is, it is constant so far as the observer is concerned. Thus if
a flash should occur on any heavenly body and we were moving toward
the flash at say 40,000 miles a second and another observer were
moving away from it at say 60,000 miles a second, the experiment of
each observer would indicate that the light has reached him at exactly
186,300 miles a second, although according to Euclid’s conception of
space the light has been obliged to travel 100,000 miles a second
faster to reach the one observer than the other. But Euclid’s
conception is faulty, as will be seen shortly.
How, then, would it be possible for the light rays to possess the same
apparent velocity per second for the two observers? It would not be
possible if “time” and “distance” are absolute quantities having the
same meaning for all observers. But if “seconds” and “miles” mean one
thing to observer “A” and a totally different thing to observer “B,”
then the apparent contradiction of facts becomes harmonious. This
is the essence of the doctrine of relativity. Observer “A” himself
does not use the terms “seconds” and “miles” consistently, i. e., as
unvarying quantities, nor does anyone. They mean one thing today and
something else tomorrow, depending upon what we are measuring and the
relative velocity between the observer and the object. The observer
is not aware of this inconsistency. To him there is no inconsistency
whatever. Nevertheless, only by acknowledging the varying quantities of
time and of space, and admitting the geometry which combines the two
into one unit, can the Michelson-Morley experiment and other similar
observations be understood and explained.
=Simultaneity a Meaningless Term=
We have been taught that the true length of a moving body is “the
distance between _simultaneous_ positions of its end points”--a
very good definition, but impossible of application for the reason
that we cannot determine the _simultaneous_ positions of any two
points in the universe. Simultaneity is a meaningless term so long as
the absolute velocity of the observer and the absolute velocity of the
object being measured are unknown. We may know the _relative_
velocity between them, but that is not sufficient. The two may be
relatively at rest--but for all we know the entire universe may be
speeding through space at thousands of miles a second in either one
direction or another.
We may _see_ two events occur at the same instant, but that does
not prove that they actually _occurred_ simultaneously. Before we
could compute the exact time of the occurrence of either of the events
we must know the direction in which, and the velocity at which the
universe as a whole is moving, together with any and all velocities of
the observer at the moment. This knowledge we do not possess. Until the
_absolute_ velocity of bodies can be determined the question of
simultaneity must remain unsolved.
=The General Principle of Relativity=
When in 1905 Einstein published the foregoing postulates which are
limited to uniform, rectilinear motion he may have considered that
it would be expecting too much to look for a general principle of
relativity such as would hold good for all kinds of rotating and
irregular motions and by which observers of different and variable
velocities might agree as to the reality of things under their
observation. Concluding, however, that the universe must surely be
constructed in a consistent manner he finally set out to find some rule
or principle by means of which an observer in one region would be seen
to possess no advantage over an observer in any other region of the
great expanse in arriving at accurate conclusions.
Of course Einstein hardly expects to go to the Pleiades or to
Betelguese and from there take measurements and make calculations; he
is doubtless content to make all his observations from this earth.
But how may he be sure that observations made from a reference frame
located in this particular region of the universe will be true to the
reality since it is manifest that observers located elsewhere and using
different reference frames must necessarily reach conclusions different
from ours if they employed our accustomed laws? Maybe they would be
much nearer the reality than we! What right have _we_ to assume a
monopoly on truth! None whatever until we can formulate nature’s laws
in a manner that will hold good for every part of the universe alike.
Until we are able to do this our science must be like the vain efforts
of the unskilled fisherman who harpoons for fish. Ignorant of the
trick that water plays on the line of sight he strikes directly at
the spot where he “sees” the fish and always misses his prey. The
skilled harpooner, on the contrary, understands the law of refraction
of light rays in water, and knows how to allow for this refraction;
hence he strikes a little this side of where the fish appears to be
and is rewarded with success. He is guided by a proven law and thereby
ascertains the true location of the fish, whereas the other man follows
“blind” observation which is quite frequently deceptive.
Einstein’s “General Principle of Relativity” is not, in fact, a mere
generalization of the Special Theory in the sense that it simply
enlarges upon the two postulates which we have already considered.
On the contrary it handles the subject of Relativity from quite a
new standpoint, and therefore might be said to belong to an entirely
different school of thought. It does not lend itself to visualization
as readily as does the Special Theory, and is consequently more
difficult of explanation and comprehension. However, what we have
already learned concerning Relativity will materially aid us in
understanding what follows, for the two theories are, after all,
dealing with the same general subject matter. We shall therefore
endeavor to link the two phases of the subject in a logical and
consistent manner.
We know, as a matter of fact, that “uniform, straight-ahead motion”
which Einstein in his original theory assumed to exist, is an ideality
that does not appear in nature, because all motion with which we are
familiar is to some extent irregular, nor does any material object
move in a perfectly straight line. But realizing the necessity for a
standard from which to proceed, Einstein properly enough assumed a
standard of absolute perfection and absolute simplicity of motion,
even though it does not actually exist anywhere around us. In exactly
the same manner Euclidean geometry assumes and deals with theoretical
points, lines and planes which have no material existence in fact.
As set forth in Einstein’s first postulate of the Special Theory, an
observer on a uniformly moving system could not possibly detect the
motion of his system without making reference to some outside object.
In the case of bodies or systems moving irregularly (i. e., with
acceleration) however, an observer thereon would detect “forces” acting
upon himself and upon all other objects on his system, due, of course,
to the acceleration. Recalling the illustration of the moving train:
so long as it is moving with perfect uniformity an observer thereon
would not know he is in motion at all until he made a comparison
with some outside object. But if the train suddenly slows down he is
thrown forward in his seat; if it speeds up he is thrown backward.
This force is called _inertia_. Now if we had never experienced
it before and were put aboard a noiseless and uniformly moving car
from which we could not see out we would be unable to interpret these
strange “forces” that we would feel as the motion of the car became
accelerated. We would probably attempt to explain them as some sort
of magnetic attraction, exactly as we are accustomed to explain the
“force” of gravity.
=Gravitation and Inertia=
In the General Principle of Relativity Einstein deals with these forces
(inertial and gravitational) and attributes them to a common cause,
viz., acceleration of motion, and has put the matter upon a consistent
mathematical basis which at once accounts for certain discrepancies
long observed in Euclidean geometry and in Newton’s laws. It is obvious
enough that where there is no acceleration of motion there could be no
centrifugal or inertial force exhibited: but we have been accustomed
to looking upon gravitation as something entirely different--as a
mysterious drawing power or attractive force that is somehow inherent
in matter. But gravitation is non-existent if we fall with the proper
acceleration. To use Einstein’s own illustration: if we were in a
closed room poised somewhere in gravitational space, and began to
fall with the acceleration common to that field, there would be no
gravitational effects to be observed. Objects released by our hand
would not fall but would remain where they are, and we could raise
ourselves from the floor and stand midway between the floor and the
ceiling as easily as upon the floor itself.
Again assume we are in a closed room poised in space, in a region
remote from any gravitational field whatsoever. Then suppose we began
to rise with a constant acceleration. Forthwith we would feel our feet
pressing against the floor. Objects released from our hand would strike
the floor by reason of the floor rising up to meet them, and in all
respects the effects would be identical with that of gravitation. In
other words we would have created an artificial gravitational field,
and it would be due to our accelerated motion.
The characteristics of gravitation and inertia are identical. No
amount of insulation or screening will diminish the “pull” of gravity
on anything. Furthermore, gravity acts on every kind and quantity of
matter alike, so that if a feather weighing less than an ounce and
a pig of lead weighing a ton were held side by side at the top of a
great vacuum tube and allowed to drop at the same instant, the feather
would reach bottom within the same time as the lead, each falling at an
acceleration of approximately 32 feet per second. It is the resistance
of the air that retards the fall of light materials, such as a feather,
but in a vacuum there is no resistance and gravity is found to act on
all matter to the same degree under such conditions. The same is true
of inertia _in vacuuo_.
When this relationship between the two forces is recognized we are
prepared to believe Einstein when he states that inertial force and
gravitational force are due to a common cause, viz., acceleration. This
does not mean that our earth, for instance, is being accelerated in all
directions at once, expanding out to meet “falling” objects such as in
the case of the artificial gravitational field mentioned in the above
paragraph. It does mean, however, that the falling objects themselves
are accelerated, but as will be presently seen this acceleration is not
due to any attractive force exerted by a “center of gravity” but rather
to a warped condition of space which surrounds all bodies of matter.
Neither Newton nor Einstein have attempted to analyze the structure
of matter and on this basis explain the phenomenon of gravitation.
Newton evidently believed, however, that every particle of matter
exerts a drawing force upon every other particle of matter, hence he
formulated his law which specifies this attraction between bodies as
being directly proportional to the product of their mass and inversely
proportional to the square of the distance between them. But he did not
attempt to make clear what that “drawing force” is, or _why_ it is
inherent in all matter, nor did he explain how or through what medium
or mechanism it operates.
Newton contented himself with merely dealing with the phenomenon
of gravitation in the abstract. So does Einstein, but with this
difference: the latter denies the existence of any mechanism whatever
in connection with gravitational force so far as any attractive power
from within is concerned, and accounts for it on purely geometrical
grounds. This is the most difficult phase of the Einstein theory
for the layman to grasp, for the reason that it involves the whole
structure of non-Euclidean geometry with which the public is generally
unfamiliar.
=Non-Euclidean Geometry=
Euclid, the famous Greek mathematician, in the third century B. C.
published the first systematic treatise on geometry (the science of
space and its measurement), and his axioms and theorems are generally
taught in our high schools and colleges today. Euclid proceeded upon
the simple theory that all space consists of points, lines and planes.
He defined a _point_ as that which has position but not size; a
_line_ (continuity of points) as possessing length but no breadth
or thickness; and a _plane_ (continuity of lines) as having length
and breadth, but no thickness. They are simply abstract terms having
no physical existence in nature, except as they exist in our minds.
Nevertheless they have proved themselves convenient in measurement and
calculation.
But when mathematicians, after centuries of earnest effort, were unable
to prove Euclid’s postulate concerning parallel lines, it occurred
to some of them that possibly the whole Euclidean system rests upon
a faulty foundation. Then it was that Saccheri in Italy, Legendre
in France, Gauss in Germany, Bolyai in Hungary and Lobatschewsky in
Russia, all masters of Euclidean geometry, conceived of other methods
of decomposing space than that proposed in Euclid’s _Elements_.
Thus it was that early in the nineteenth century, almost simultaneously
in many countries, did many non-Euclidean geometric works come to be
published. These were of the same general character or form, commonly
called Hyperbolic geometry. Each of them is as consistent in itself
as is the geometry of Euclid. But to Riemann belongs the credit of
formulating a geometry which in the light of Einstein is seen to
approach much nearer to the reality of nature than does the Euclidean
or any other system.
Riemann produced his general work along this line in 1854 which was
far ahead of his time. He actually prophesied the connection of
geometry with matter, and had he possessed a little more vision he
would doubtless have worked out the details as well as the principles
underlying gravitation in much the same manner as Einstein has done.
Riemann’s efforts in the field of non-Euclidean geometry has materially
aided Einstein in the development of the present theory. Minkowski’s
work was utilized by Einstein to much profit in the outworking of the
Special Theory, particularly his clarification of _time_ as a
fourth dimension.
=Time as a Fourth Dimension=
[Illustration: FIG. 4.]
It is natural for us to think of all matter as possessing but three
dimensions--length, breadth and thickness--and we have been accustomed
to making our measurements of matter and of space on that basis. Using
the formula of Pythagoras we have ascertained the distance between any
two points in a _plane_ (a two-dimensional area) by extracting the
square root of the sum of the squares of the co-ordinate axes, i. e.,
the base and the altitude as in the accompanying diagram. See Figure 4.
If point A is 8 miles south and 6 miles west of point B then A and B
are 10 miles apart, thus:
The square of 8 is 64
The square of 6 is 36
---
The square root of 100 is 10
Likewise, the distance between any two points in a three-dimensional
region (as from an upper to the remotest lower corner of a room) is
generally considered to be “the square root of the sum of the squares
of the three sides” (Fig. 5).