around on a sheet of paper. With your vermicular mind you doubtless
would take a superficial view of the universe and find it as impossible
to imagine a third dimension as man does a fourth. If in the course
of your crawling you came across a triangle you might--if you were a
measuring worm--pace it off and find that the distance from _A_ to
_B_ was 8 inches, from _B_ to _C_ was 6 inches and from this data,
if you knew the law of the hypothenuse, you might calculate that the
distance from _A_ to _C_ was 10 inches. On measuring it you would find
your prediction verified and so gain perfect confidence in your plane
geometry. But unbeknownst to you, poor worm with your eyes fixed on
the paper, some man may have picked up the sheet and crumpled it up
or rolled it over so that _A_ and _C_ are only one inch apart--in the
third dimension. The worm is right when he thinks the distance between
these points is 10 inches: so is the man right when he says it is one
inch. It depends on the point of view.
Now in Einstein’s view something of this sort happens to our
three-dimensional space when matter gets into it. We know for instance
that if you divide the circumference of any circle by the diameter
the ratio figures out as 3.1415+. It has been calculated to 707
decimal places but we can dispense with the rest of them and call the
whole thing Pi for short. Write it in Greek as π and it looks more
learned. Now if you place a heavy particle, say a lead bullet, in the
center of a circle the ratio of the diameter to the circumference,
according to Einstein, becomes a little less than Pi, for the circle
has been warped, so to speak, into the fourth dimension by the strain
of gravitation. The difference in such a case is too small to be
measurable by any known means, but it is supposed to be an actual, not
an imaginary, deviation from the geometrical law.
Now the sun being a big heavy body must extend its gravitational
strain for a considerable distance around and a ray of light passing
through this crumpled up space would not be able to pursue a straight
course. And, according to the eclipse observations, it does not.
Light like everything else follows “the easiest way” and this is not
always the straight and narrow path. A river takes the easiest, not the
shortest, way to the sea and this leads it through many meanderings.
Most of us, I suppose, have a mental image of Newton’s gravitation as
a sort of rope by which the sun pulls the earth into its orbit when
it is disposed to fly off on a tangent. But from Einstein’s viewpoint
we should rather think of the earth as picking its way as best it
can through a space-and-time combination that has been strained and
distorted by the power of the sun. I visualize Einstein’s solar system
as a spider web with the sun in the middle like the spider and the
planets like flies trying to get around through the tangled strands.
But it is more complicated than that for each planet has its own lesser
web of radiating influence to drag about with it wherever it goes.
Newton’s idea is simpler, but unfortunately light at least seems to
follow Einstein’s law, not Newton’s. That is why Einstein is such
a troublesome fellow. If he would confine himself to metaphysical
speculation nobody need bother about these strange notions of his. But
when he points how they can be proved and then British astronomers and
American physicists find things according to his deductions he cannot
be ignored. The man does not seem to have that decent respect for the
opinions of mankind that leads most of us to limit our logic to the
sphere of common sense. When he gets an idea in his head he follows it
wherever it leads him even though he bumps up against Euclid and Newton
and the rest of us. For instance, if you admit the second of his two
fundamental postulates, that the speed of light is constant, regardless
of the velocity of its source, you are irresistibly led--unless you
let go of his hand somewhere on the way--to the conclusion that time
is a local affair; that there is no way of telling by light signals
whether two clocks at a distance are keeping the same time, or whether
two events at different places occur simultaneously. You could not tell
this even if you could shoot a watch from one place to the other with
the speed of light, for no matter how many seconds--or years--the watch
might be on its way it would register the same time. If instead of a
watch a man could travel at that speed he would not grow old on the
way. According to Einstein no man, watch or any other material thing
can travel with the speed of light, for it would require an infinite
force to give the smallest particle such a velocity. But let us suppose
that a hollow projectile holding a man, such as Jules Verne and Wells
used on their voyages to the moon, should be sent off into space with
a velocity one twenty-thousandth less than light. If at the end of a
year the projectile should be caught like a comet by the gravitation of
some star and be swung around and sent back to the earth, the man on
stepping out of his shell would be two years older but he would find
the world two hundred years older. This would be, as Professor Langevin
suggests in _Scientia_, 1911, an interesting way to study history,
but it would be risky, not to say impossible. Still French scientists,
like Napoleon, have no place in their dictionaries for so stupid a word
as “impossible” and M. Esnault-Pelterie has figured out that a thousand
pounds of radium would be sufficient to carry a man to Venus in 35
hours if a hollow projectile could be fitted up like a rocket with the
radium in the rear sending out a rapid fire of electrons.
TURNING TIME BACKWARD
To loosen up our conventional ideas of the fixity of time and space we
may accept the aid of the scientific romancers. Camille Flammarion, the
famous French astronomer, wrote a fantastic little book called “Lumen”
which tells of a man who died in 1864. His soul flew straight to its
heaven which was one of the planets of Capella, the largest star in
the constellation Auriga. Here he found the benevolent inhabitants of
that sphere, who were endowed with superhuman powers of sight, watching
with great distress the bloody scenes of the French revolution of 1793,
and wondering how it would come out. To the visitor from the earth
this was an old story, to the people of Alpha Aurigae it was a present
spectacle, for the distance of the star was such that it took light 72
years to travel from the earth, so they were 72 years belated in their
observation of current events on our planet.
The spirit of the defunct Parisian, having the power of flying through
empty space at any speed he chose, found that he had thereby also
acquired control of time and could hasten, retard, stop or reverse the
course of events at will by simply varying his speed. If he remained
stationary, scenes on the earth would unfold at their normal rate and
in regular order. If he traveled away from the earth with the speed
of light everything seemed to stand still. If he traveled faster than
light he overtook the rays that had left the earth farther and farther
back in the past so he saw through them events in the reverse order.
For instance when he looked down on Waterloo he saw the battlefield
strewn with corpses and Napoleon walking toward Waterloo backward
pushing his horse by the bridle. This is how the battle looked to the
interspatial observer:
When my sight was sufficiently habituated to the scene, I perceived
some soldiers coming to life out of the eternal night, and by a single
effort standing up. The dead horses revived like the dead cavaliers,
and the latter remounted them. As soon as two or three thousand men
had returned to life, I saw them form unconsciously in line of battle.
The two armies took their places fronting one another, and began to
fight desperately with a fury that one might have taken for despair.
As the combat deepened on both sides, the soldiers came to life more
rapidly....
At each gap made by the cannon in the serried ranks a group
of resuscitated dead filled up the gaps immediately. When the
belligerents had spent the whole day in tearing one another to pieces
with grape-shot, with cannons and bullets, with bayonets, sabers and
swords--when the great battle was over, there was not a single person
killed, no one was even wounded; even uniforms that before it were
torn and in disorder were in good condition, the men were safe and
sound, and the ranks in correct form. The two armies slowly withdrew
from one another, as if the heat of the battle and all its fury had
no other object than the restoration to life, amid the smoke of the
combat, of the two hundred thousand corpses which had lain on the
field a few hours before. What an exemplary and desirable battle it
was!
Another literary curiosity on the same theme is “Ignis” by Comte Didier
de Chousy. This tells of certain engineers who attempted to utilize
the internal heat of the earth by running the waters of a lake into a
deep boring. The result was an explosion that blew off a piece of the
planet. But the passengers on this artificial asteroid on looking down
through their well at the earth they had left could see the lake and
city undisturbed and watch themselves at work as they were before the
place blew up. The explanation was that this fragment of the earth was
projected into space more rapidly than the speed of light and so was
catching up with the rays that had gone out before the explosion; these
rays, of course, carried the picture of earlier scenes. But Einstein
would say that this story--as we might ourselves have suspected--must
be fiction for according to his theory the speed of light is the
absolute limit of motion, the infinity of velocity, which no material
body may excel or attain. He does not, however, say anything about the
possible speed of a disembodied spirit such as Flammarion employed in
his imaginary exploration of space.
THE METAPHYSICS OF THE MOVIES
But from such fantasies we can see that the order in which we view
events depends upon how fast and in what direction we are moving and
that past and future may be reversed to our vision. This is easily
made apparent by means of motion pictures. If the film is reeled off
in the wrong direction the action is reversed. So we see divers rising
gracefully out of the water and landing on the spring board. Newly
hatched chickens, dismayed at the sight of this unfriendly world,
calmly tuck themselves back into their broken shells which close in
upon them. When we have come to the close of a perfect Thanksgiving
Day the obliging operator may give us an encore of the dinner reversed
by running his machine backward. Then we see pieces of turkey politely
picked out of the mouths of the diners with their forks and replaced
upon the plates. When these are passed back to the carver he puts the
slices neatly in their places and the fowl is then sent back to the
oven to be unroasted. The cook then sticks on the feathers. The hired
man carries the turkey out to the chopping block where with one swift
stroke he restores the head and the fowl runs off backwards. This
is just as correct as the ordinary order. The sequence of events is
the same. Cause and effect are linked together as firmly as before,
only they have exchanged places. A scientist knowing nothing of our
world except from watching such reversed motion pictures might deduce
from them the same consistent and logical system of natural laws that
we now have although some of them, for instance, the second law of
thermo-dynamics, would be reversed in form.
The motion-picture man has also the power to alter the speed of the
passage of time as he will by turning the crank faster or slower.
Sometimes he is quite too careless in the way he employs this
prerogative. If he is behind time on his schedule he will rush through
a lazy siesta scene in a Mexican plaza with all the fury of a Mack
Sennett farce. But this telescoping of time can be used to advantage
as when he shows us the growth of a plant, the unfolding of its flower
and the ripening of its fruit, all in fifteen minutes. On the other
hand motion may be slowed up by taking twice as many pictures a minute
as usual and projecting them at the ordinary rate. For instance, if
it is a dog jumping up to grab a piece of meat from his master’s
hand, we see the dog rise slowly from the ground and, while poised in
mid-air, eye the meat carefully to select the best point of attack,
then deliberately take it between his jaws and gradually descend.
Now notice that this is just as true a picture of the dog’s jump as
any other. The movie man has simply expanded time measurements as he
expands space measurements when he shows us a close-up. A close-up with
a face covering a sixteen-foot screen is just as true as a smaller
picture. It is what we should always see if the lens of our eyes were
a bit more convex. We look through the small end of an opera-glass and
objects seem magnified. We look through the large end and objects seem
minified. This is not an illusion. The opera-glass _does_ actually
enlarge or reduce _what we see_.
So, too, time intervals can be lengthened or shortened. Take a dose
of hashish--no, don’t--I should say, if you did take a dose you would
find that your perception of duration was prolonged. If while under the
influence of the drug you drop a book it will seem an hour getting to
the ground. De Quincey describes such experiences in his “Confessions
of an Opium Eater.” But without entering into such abnormal states we
all know by everyday experience how time flies or lags according to
the number of our sensations. Bergson’s philosophy is built upon the
distinction between the idea of duration as experienced by all of us
and the idea of time as established by the physicists for comparative
measurements.
We live in deeds not years; in thoughts not breaths;
In feelings not in figures on a dial.
--_Festus._
For all we know an ephemeral insect that dies in a day may live a
longer life than a Galapagos turtle that exists for two centuries.
What Mark Twain said about classical music applies also to science; “It
is not so bad as it sounds.” The thing that the chemist calls “sodium
chloride” other folks call “salt”--and so does he when he is off duty.
Don’t let the scientist bluff you by his polysyllabic propensity. Just
try to see what he means by such language. Now what these new-fashioned
non-Euclidean geometricians call “the four-dimensional space-time
continuum” is essentially the same system of reference as you have used
ever since you could toddle. Minkowski did not invent it. Everybody
thinks that way unless he is an idiot. Each one of us has had to build
up his own philosophy of the universe long before we went to school,
mostly before we could talk. We had to study geometry while we were
in our cradles--worse than that we had to work out a practical system
of geometry for ourselves without the help of Euclid or anyone else.
We had to excogitate a system of relationship between the sights and
sounds and touches that came to us before we could get along in the
world. Probably we all solve this riddle of the universe in about the
same way although since there is no way of directly comparing notes we
cannot be sure about that.
THE EGOCENTRIC THEORY OF THE UNIVERSE
But the framework that we construct to hold everything outside of
ourselves is essentially of the following form:
You are the center of your universe. Everything and every event that
you are considering is related to you here and now. Starting from
this, your point of place and time, you imagine eight straight lines
stretching out toward infinity in eight directions as divergent
as possible. These lines--call them destinations or directions or
dimensions or coördinates as you please--consist of four opposing
pairs, right and left, up and down, forward and back, future and past.
Somewhere along or between these four dimensional lines that cross
in your brain you can find a place for anything that you need; your
pencil, the discovery of America, the sun and next Friday. You can
connect up all these things by lines which may represent changes, that
is the tracks of movements in space and time. To connect the pencil
in your hand with the discovery of America you would have to count
back 428 years on the time line and measure off on the east-west and
north-south lines whatever distance you may be from San Salvador--not
to consider the motion of the earth.
Anything that exists, that is to say, persists, is moving along the
time dimension at what appears to be a uniform rate. Of course you
can, if you like, conceive of time itself as a stream flowing through
things. Since all motion is relative, that way of looking at it is
just as “true” as the other. But it is simpler and more sensible to
think of things moving through a stationary time just as we think of
them moving through a stationary space. A material point that is at
rest, such as the dot of an _i_ on this page, (we continue to
disregard the motion of the earth) is not moving about in space but
is moving forward in time. Its track then is a straight line along
the time dimension. That is, a material point is a line in the fourth
dimension. If you move the page to the right the forward movement
of the dot of the _i_ in the time dimension is combined with
the sideways motion in a single slanting line. If you move the page
simultaneously upward, rightward and backward the track of the point is
a line combining the movement in all four dimensions. Such a track of a
point moving through space and time is called its “world-line.” It is a
continuity of one dimension. Any event is the point of intersection of
one or more such world lines and we can never observe anything except
such intersections. That is to say, everything happens somewhere and
sometime.
A picture flashed on a cinema screen has three dimensions. It is, say,
10 feet long and 6 feet high and lasts ¹⁄₁₆ of a second, but it has no
thickness. A man necessarily has four dimensions. He may measure from
24 to 72 inches in one dimension, from 8 to 18 inches in the second,
from 4 to 9 inches in the third and 70 years in the fourth.
After all, the idea of the relativity of time ought to be easier to
accept than that of space for it is in accord with experience instead
of contrary to it. We drop off to sleep and wake the next instant if we
credit our personal perceptions. Why should we believe the sun and the
clock in preference to ourselves?
Bergson bases his whole philosophy upon the distinction between
_duration_ as it is felt by the individual while he is living
through it and _time_ as it is employed by the physicist in his
calculations. The latter conception, physical time, is, as Bergson
says, a mere invention of man and virtually a fourth dimension of
space, so he concludes:
To sum up; every demand for explanation in regard to freedom comes
back, without our suspecting it, to the following question: “Can time
be adequately represented by space?” To which we answer: Yes, if you
are dealing with time flown; No, if you speak of time flowing.[1]
Past and future are alike to the physicist, differing only in
direction, like east and west. But to the living person they are
altogether different things. For man rolls up his past, as a tourist
his rug, and carries it with him wherever he goes. That is why Wells’s
“Time Machine” and the reversed reels of the movies are so funny. There
is nothing absurd about running a wheel backward but there is about
running a man backward.[2] The physicist feels no reluctance about
turning the stream of time backward for all physical phenomena are
reversible under the proper conditions. If we interpret the universe
as merely matter in motion and imagine at a certain instant that every
individual particle reverses its motion and goes in just the opposite
direction at the same speed, then the whole history of the world would
be reënacted in the opposite order and the earth would return to its
primeval nebulæ.
In Wells’s story, “The New Accelerator,” a professor invents an
elixir that speeds up the rate of living a thousandfold. A person
taking a dose of it sees people as wax figures apparently motionless
in the midst of violent action. Falling objects seem to stand still
in the air. The music of a band is reduced to “a low-pitched, wheezy
rattle” or “the slow muffled ticking of some monstrous clock.” But in
compensation for this the accelerated drug-fiend could watch at leisure
the slow flapping of a bee’s wings.
But even Wells with his seven-league-boots imagination finds it
difficult to keep ahead of the march of science. What he then saw only
with his mind’s eye we can actually observe. By moving the accelerating
lever on your phonograph toward the S end of the scale you can slow up
the tune and lower its pitch until it becomes inaudible as music. The
new Pathé ultra-rapid camera can take pictures at the rate of 160 to
the second. When these are projected on the screen at the usual rate
of 16 to the second all movement takes place ten times slower than in
actual life. This gives opportunity for the study in detail of the
action of a ballplayer pitching a curve or of the wing motion of a
humming bird or of the splash of a marble falling into water or of the
flight of a bullet. We can magnify motion or minify it as much as we
will. The cinematograph owes its origin the desire of Senator Leland
Stanford to study the movement of a horse’s legs so as to find out why
one racer went faster than another.
Such playful flights of the scientific imagination as Wells and
Flammarion indulge in and such freaks of projection as the camera
man amuses us with are of use to those of us who find difficulty
in translating a mathematical formula into terms of everyday life.
There is no better place to study metaphysics than in the world of
the flickering screen, for there man has complete control of time and
space. He can enlarge and reduce any object. He can hasten, retard
or reverse any action. He can throw upon the screen at the same time
events happening months and miles apart. Therefore to those of us
who have had the advantage of an education in the movies, Einstein’s
ideas of the relativity of time and space do not seem startling or
inconceivable.
Kant not only conceived the possibility of more than three dimensions
but believed in the probability of it. His argument is based on greater
insight into the intentions of the Almighty than we of this day would
claim:
“If it is _possible_ that there be developments of other
dimensions in space, it is also very _probable_ that God has
somewhere produced them. For His works have all the grandeur and
variety that can possibly be conceived.”
In this temporal, spatial and material world of ours reality requires
that the four dimensions should hang together. But at an infinite
distance from all matter this fourfold combination would be dissolved
into a three-dimensional space and a one-dimensional time. In that
extra-mundane realm time ceases to flow, gravitation no longer drags
downward, matter is non-existent, light is immovable and change is
impossible.[3] Thus the new mathematics leads to a state curiously
like the conventional conception of heaven.
We talk as our forefathers did about “the ends of the earth” but
we know that one might start from his home and walk forever in any
direction without coming to an end of it. But though the earth’s
surface is infinite in the sense of endless, yet one never can get more
than 8,000 miles away from home where’er he may roam. If a man stood
on the top of the highest mountain on earth and aimed a level gun in
any direction, the bullet, if it could be given sufficient velocity to
counteract the influence of gravity, would go around the world and hit
him in the back of the head. Or if light were sufficiently deflected
by gravitation to follow a level line around the earth--another absurd
assumption--the man looking through a level telescope in any direction
could see how his hair was combed in the back. Such happenings, though
impossible, are not inconceivable but are logical consequences of our
knowledge that the world is round and that what we call straight or
level lines as measured on plain or sea are really great circles around
a center four thousand miles below.