Beyond A Uni-dimensional Perception of TIME
In his examination of the natural laws
or facts of the Universe, man is greatly handicapped by the fact, insofar as
time is concerned, he has never progressed beyond a uni-dimensional perception.
Those who are familiar with the
analogies used to explain some portions of the theory of relativity, will
recall that in attempting to achieve a concept of a four dimensional continuum,
the reader is asked first to imagine a man who is conscious of only one
dimension in space. His entire universe consists of a single line. If a dot
were placed on the line in front of him, and behind, he would be completely imprisoned,
since he would not be able to conceive of going over or around them. As his
intelligence and consciousness developed, he would eventually become aware of a
second dimension, and to imprison him then, it would be necessary to enclose
him in a circle. With further development, he would become
aware of a third dimension in which a
sphere would be a prison, and so on.
We are now conscious of three
dimensions of space, and have done considerable mathematical reasoning in
regard to a fourth. Unfortunately, insofar as time is concerned, our
consciousness has never progressed beyond the first dimension. We are confined
to a single line in time. We have no concept of lateral motion, nor can we even
turn around upon that line. We can only go forward. Many of the difficulties
which we encounter in our attempt to understand the operation of the natural
laws arise because of our severely restricted concept of the nature of time.
Time has often been referred to as the
"fourth dimension" by those who attempt to explain our present
concept of relativity. It is usually pointed out that, since all known bodies
of matter in the Universe are constantly in motion with respect to each other,
if we wish to describe the position of any body, it is necessary to give a
point in time as well as a spatial relationship to any other body or bodies.
There is, however, a more convincing method of demonstrating that time is a
dimension, although we believe it would be more precise to consider it as the
first dimension rather than the fourth since it is the one dimension in which
all motion must take place.
We are at the present, conscious of
three dimensions of space, and we know that motion can take place in any one of
the three, but whichever dimension of space is involved, the motion must also
take place in time. Our term for the rate of motion is the word velocity, which
is defined as being the degree of change in location per unit of time. If an
object has a velocity of 1000 feet per second, with respect to our point of
observation, we will see that in one thousandth of a second the object will have
moved one foot. In one millionth of a second it will have moved only one thousandth
of a foot, and so on. We can easily see that if the time becomes zero, the motion
must also become zero.
The science of photography has reached
a state of development which permits us to take photographs with very short
exposure times. By the stroboscopic method of photography, which has been superseded
by even faster methods, we were able to take several hundred thousand
consecutive pictures in one second. In these pictures even the fastest
projectile seems frozen into immobility. We have taken pictures of a rifle
bullet penetrating an ordinary electric light bulb, in which several complete
and consecutive pictures have been made between the time the bullet first
touched the bulb and the time that the first crack appeared in the glass. In
these pictures, the bullet appears to be completely motionless. Of course the
taking of the pictures actually did involve a very small elapse of time, and so
a very small amount of motion did occur during the taking, but it again
illustrates the fact that no motion
which we can perceive, can take place
except within that dimension of time of which we are conscious.
Having pointed out the limitations of
our consciousness concerning this factor which we call time, let us now go back
and examine it as best we can, with that degree of consciousness and
understanding which we have. We will again attempt to choose the simplest
possible definition. We defined space as that which separates bodies of matter,
so we will define time as that which separates events. (If there is no
discernible separation in this respect, the events are said to be
simultaneous.)
Of course we immediately hear the
objection that events may be separated by space as well as by time, or that
they may be separated by space without being separated by time. This statement,
while usually considered to be true, yet forms a stumbling block which has
precipitated many a philosopher into the
quagmire of misunderstanding and
paradox. The difficulty arises in our attempt to define the term simultaneous.
If two events are separated by space, how shall we determine whether or not
they are separated by time?
The observer cannot be present at the
site of both events, and so must observe one or both of them through the separation
of space, and therefore through the curvature of natural law which the
separation represents. In referring to this problem in the
introduction to his first book on relativity, Dr. Einstein pointed out that
since our only contact with the world about us is through our senses, and since
all of the knowledge which we have concerning the universe has come to us
through them, if we are to formulate mathematical rules based upon our
observations, we must begin with the postulate that the things which our senses
tell us are true. If we should observe through a large telescope, the creation
of a nova in a remote galaxy, and at the same time observe the eruption of a
volcano upon our own earth, we must assume, for the purpose of our mathematics,
that the two events are simultaneous.
This a postulate which is difficult to
accept because the faculty which we call reason immediately interposes the
objection that a separation in space involves an elapse of time between the
event and our perception of it. However, Dr. Einstein points out that if we
allow our reason to modify our observations, we will be evolving a concept
whose value is based only upon the validity of our reason rather than upon the
accuracy of our observations. We must postulate that events which are observed
simultaneously, occur simultaneously insofar as that observer is concerned, and
that, therefore, the
simultaneity of events is a condition
which depends entirely upon the position of the observer with respect to those
events.
Almost any student of physics today,
be he a beginner or a graduate scientist will argue that no man can ever travel
from the earth to the star Alpha Centauri in a period of less than four years,
because the laws of relativity state that matter can never move with a velocity
greater than that of light.
This is one of the prime fallacies
which has been created by misinterpretation of the mathematics. The mathematics
do not say that man cannot travel between the earth and Alpha
Centauri in less than four years. They say only that no observer on earth can
ever see him do it. Let us see if we can create an example by which this
statement may be more readily understood.
First we will assume that there is a
planet in orbit about Alpha Centauri. (Because of Alpha’s proximity to its twin
star Proxima Centauri, the orbit would be a rather eccentric one, but perhaps
it will do as a reference point.) Next we will build a small space ship, in
which we propose to pay a visit to this planet. Since a small space ship is not
a very comfortable place to spend long periods of time, the idea of being
confined to the craft for the four years, which relativity seems to say is the
shortest possible time, is a distasteful one, so we cast about for means to
shorten the journey.
If we do our engineering according to
the rules which are known as classical mechanics or ordinary engineering
practice, it will become apparent at once that we cannot use any source of
energy which originates within the ship. These rules of mechanics tell us that,
to accelerate a body of matter to a velocity of 3x10(10) centimeters per second
(the velocity of light) will require energy equal to 9x10(20) ergs per gram of
mass. Yet the rules of relativity (E=MC2) tell us that 9x10(20) ergs is the
total energy contained in a gram of mass. This means that if we wish to accelerate
the space ship to the velocity of light by energy created within the ship, we would
have to convert all of the matter within the ship, including our
own bodies to energy. We would then achieve the velocity of light, but we would
arrive at our destination, not as matter but as electromagnetic radiation.
Since we would much prefer to arrive
as matter, we must seek an accelerating force which will act from some
unlimited source of energy outside the ship. It is at once apparent that a
force field originating on earth would not be successful because the rate
of propagation of a field is the same as that of light, and no field can
accelerate us to a velocity greater than its own rate of propagation.
For the purpose of this example we
will simply postulate that we have available, a supply of energy form an
outside source, which we can use in any desired quantity, and which can be used
to create an instantaneous velocity so high that we will reach our destination,
four light years distant, in a single hour.
We will take off from a launching pad
which is situated near an observatory operated by a friend of ours, who is an
astronomer, and who has a telescope of unlimited power, through which he will
observe our progress. Since he can only observe us through the light which we
emit during the trip, we must also cause
the ship to emit a very large quantity of light.
At a prearranged instant we will
takeoff and at once achieve a velocity that will take us to our destination in
an hour. After fifteen minutes we will have covered one quarter of the
distance, but the light which we emit at that point will require one year to
return to earth, and will reach the eyes of the astronomer one year and fifteen
minutes after takeoff. He will note in his logbook that we required a year and
fifteen minutes to reach the quarter point. After we have traveled for thirty
minutes we will have covered half the distance, but the light which we emit at
that point will require two years t return to earth, and so will reach the
astronomers eyes two years and thirty minutes after takeoff. After an hour has
passed we will have reached our destination, but the light emitted by the craft
will not reach the astronomer until four years and one hour after our departure
from earth. All of the light which we emit at intermediate points will, of
course, arrive at intermediate times so that the astronomer could observe our
progress constantly from the instant of takeoff to the moment of our arrival
upon the distant planet, four years and one hour later.
According to the primary postulate of
relativity that we must accept the evidence of our senses as being valid, the
astronomer must maintain that from his reference point we did not
quite achieve the velocity of light.
The fact that we may have returned
long before this, that we may be seated at his side, and may perhaps, be
assisting him in his work, does not in any way affect the validity of his
observations or the mathematics of relativity which he applies thereto. Let us
remember, however, the statement that, when our mathematics are complete, then
we may allow reason to deal with that which we have created. If we do this, we
will not fall into the common error of confusing relativity with a concept of
absolute determinism.
Let us reiterate Dr. Einstein=s
preface again: AIf we allow our reason to modify our observations before
our mathematics are complete, we will be evolving a concept whose value is
based entirely upon the validity of our reason rather than upon the accuracy of
our observations. After our mathematics are complete, then we can allow reason
to deal with the formula, but until the formula is complete, we must postulate
that events which are observed simultaneously occur simultaneously insofar as
that observer is concerned, and that therefore the simultaneity of events is a
condition which depends entirely upon the position of the observer with respect
to those events.
If we examine this concept carefully,
we find that time follows the same curve of natural law which is apparent in
the operation of all the basic factors of nature, and again the radius of that
curvature is measured by the quantity C.
We will now create another simple
analogy, in far greater detail, which may serve to make this statement more
readily understood. It will put us in a unique position from which we can, from
a single point in time, observe ourselves occupying three rather widely
separated positions in space.
Once again, we will start today to
build a space ship. We will postulate that the ship will require one year of
our time to build, and that when completed, it will be capable of infinite
acceleration. We will assume that a continuous supply of energy is available
from an outside source, and that the craft will continue to accelerate so long
as this energy acts upon it.
During the year which we spend in
building the craft, light is being reflected from us into space, so that an
observer with a telescope stationed at some other point in space could follow
the course of its construction. When we have completed the construction of our
craft we will enter it and take off for a destination which we will assume to
be a planet orbiting about Alpha or Proxima Centauri, our next nearest suns,
about four light years distant. We have a telescope of unlimited power in the rear
of the craft pointed toward the earth which we are leaving, and another
telescope at the front, focused upon the planet which is our destination. We
will set the field strength for a constant acceleration, and seat ourselves at
our telescopes to observe the result.
After we have risen a few miles from
the surface, we will, for the purpose of furnishing an additional reference
point, eject from the craft and its field, a cannon ball or other sphere of metal which has been
specially painted so that it can readily be observed from any distance with the
aid of our unlimited telescopes. Since we had not yet reached escape velocity
when the ball was ejected, we will observe that it soon begins to fall back to
earth.
As we continue to accelerate, we will
observe that the kinetic energy differential which we are producing between
ourselves and our points of observation is producing exactly the effect upon
time which is predicted by our postulate of the curvature of natural law. Since
the distance or degree of separation between ourselves and the earth is
increasing with time, the energy differential is negative,
which means that the natural laws at
the observed point will displaced towards the base or zero line of the sine
curve, insofar as our observations are concerned.
If we reach a velocity equal to one
half that of light, and then observe a clock on earth through our telescope, we
will see that in ten hours of our time, only five hours have been recorded by
the earth clock. If we observe the test sphere which we ejected during our take
off, (assuming that it has not yet reached the ground) we will see that it is
not falling at the rate predicted by our laws of gravitation, but at a rate only
half as great. We will also observe that the sphere is not accelerating at the
rate predicted by our laws, nor even at half that rate. Since we ourselves are
still accelerating, the observed acceleration of the sphere is diminished by a
factor which is proportionate to ours.
We must remember that we can only
observe events through the light which is emitted or reflected by the objects
concerned with those events, and if we ourselves have a motion equal one half
that velocity in the direction in which the light is moving, then a column or
sequence of light impulses which were emitted from the earth during a five hour
period, would require ten hours to pass our point of
observation.
When the velocity of our craft reaches
that of light with respect to the earth, there will be a negative energy
differential, equal to the quantity C, existing between us and our point of
observation. We will observe that all natural laws upon the earth have reached
zero value with respect to us.
All motion and all changes have ceased.
If we observe our test sphere we will
see that gravity is no longer acting upon it, since it has ceased to fall. All
laws of motion are in abeyance and the factor which we call time has ceased to
have any significance.
To make these observations, of course,
we would require one of the new telescopes which operate on the retention of
vision principle, where the last image to arrive remains upon the viewing
screen until a new light image arrives to change it. When we reach the velocity
C, no new light will arrive, hence the picture will not change until we change
our velocity. Since we postulated at the beginning of this analogy that our
craft was capable of unlimited acceleration, and since the postulated force
continues to act, our velocity will continue to increase and we will have
between ourselves and the earth, a rate of
increase in the degree of separation
which is greater than that specified by the
quantity C. We can do this from our
point of reference although, as will be explained later, we cannot do it from
the point of view of an observer upon the earth.
When we have passed through the
velocity C, a startling change occurs in our observations. We no longer observe
the earth from the telescope at the rear of the craft. The earth now appears in
the telescope at the front, and we are no longer leaving the earth, we are now
approaching it. We will see a craft which is identical to ours, and which is
indeed our own craft, detach itself from us and move back
toward the earth ahead of us at a rate
which is proportionate to our excess over the velocity C.
If we observe the earth, we discover
that all natural laws are operating in reverse.
If we observe the test sphere we will
see that it is now falling away from the earth rather than
towards it. Gravity between the earth and the sphere has become negative with
respect to our point of reference as have all the natural laws. We
observe this through the forward telescope rather than that at the rear,
because we are now overtaking the light which had passed us before we had
reached the velocity C, and since we are now overtaking it, we encounter first
the light which had passed us last.
All events occur in reverse, just as
would the scenes in a motion picture film which is being run backwards.
If we complete our journey to the
planet which is our destination, at an average velocity equal to 4 times C, we
will arrive with an elapsed time of one year as measured by the clocks on our
own craft. During the journey, however, we will observe the elapse of five
years of time upon the planet which we are approaching, and the elapse of three
years of negative time upon the earth which we are leaving.
In other words we will arrive at our
destination three years before we left the earth.
If immediately upon our arrival we
seat ourselves at a telescope of sufficient power to observe the earth at close
range, we will see ourselves going about the daily tasks which we performed two
years before we began to build the space craft in which we made the journey. If
we then focus the telescope upon the proper point in space we will see
ourselves in our space craft, flying backwards toward the earth.
We are now in a position from which we
can observe the sine curve nature of all natural law, and to measure precisely
the radius of the curvature. If we observe the earth, we see that time there is
positive. That is: it is moving in the direction which we consider normal.
Since there is no significant energy differential, the time rate is essentially
the same, but because of the degree of spatial separation there will be a displacement
along the time curve, between the observer and the point which he is
observing.
According to our theory of the
curvature of natural law, this displacement should be equal to D divided by C,
where D is the distance and C is our basic factor. In the case of our present
observation the distance is equal to 4.C.years, which if divided by C will
equal 4 years, which is precisely the degree of displacement which we observe.
If we now turn our attention to the space
craft, we find that we are observing it through an energy differential which
exceeds the quantity C and therefore the craft is within the negative portion
of the curve, and all natural laws will be operating in reverse at that point.
We are now in a unique position, in that we now can, from a single point in
time or at least from a single point in the only dimension of time of which we
are conscious, observe ourselves occupying three rather widely separated positions
in space.
First: our
position at the telescope as the observer. At this point time is positive.
Second: our
position on the surface of the earth. Here time is also positive but has a negative
displacement upon the time curve which is equal to four years.
Third: our position
in the space craft: here time is negative, as demonstrated by the fact that we
observe it flying backwards toward the
earth, and all actions taking place within it occur in reverse order. This is,
of course, due to the fact that the craft had a velocity greater then that of C
and so was constantly leaving behind the light which was emitted or reflected
from it. As we observe the craft from our new reference point, the last light
which it emitted arrives first.
If we continue to observe for several
years, we will eventually see ourselves build the craft and take off into
space. At the same time we can see ourselves in the same craft hurtling
backward through space toward the inevitable meeting point where the past and
the future join to become the present.
Since we are observing ourselves simultaneously
occupying three different positions in space, we can readily see that we are
forced to a concept of time which includes more than one dimension. If we
continue to observe the two craft, we
will see that the one which is moving away from us is constantly slowing down,
while the one coming toward us from the earth is accelerating. At the instant
in which the velocity of the receding craft reaches zero, the approaching craft
will reach it, coincide with it, and both craft will disappear completely from
view. Our lateral excursion into time
has completed its
curve
and we have returned to the starting point of our unidimensional concept.
There is only one thing left to do. We
immediately leap into our space craft and begin our return journey to earth. As
before, we achieve an average or mean velocity equal to 4 C. We land our craft
near the observatory of an astronomer who is a friend of ours, and rush in to
tell him of our return. We find him seated at his telescope observing our
landing upon the planet which we had set out to visit. When we inform him that
we achieved an average velocity of 4 C, his reply is that this is impossible
since the laws of relativity clearly state that no object can achieve a velocity
in excess of C (with respect to a given reference point.).
He will also point out that he has
been observing us constantly since our take off from the earth and that only
now, today, five years later, were we observed to have reached our destination.
Since the journey required five years of earth time, our average velocity was
only four fifths that of light.
Again, we must restate with emphasis:
according to the primary postulate of relativity, that for mathematical
purposes we must accept the results of our observations as valid, the
astronomer is perfectly correct in his statement that we did not, and could not
have exceeded the velocity C. The mere fact that we have returned, be seated at
his side, and may perhaps be assisting him in his work, does not in any way
affect the validity of his observations nor the mathematics of relativity which
he applies thereto. He can only state that our arrival upon the distant
planet, and the moment of our return to earth were in fact simultaneous.
We can see that, even if our energy
level had been so close to infinite that the outward trip had required only one
second, if during the one second trip we had emitted enough light to make
observation possible, the astronomer upon the earth would note that the trip
required four years and one second, and so would have undeniable proof of the
mathematics which postulate that only with infinite energy
may the velocity C be achieved.
While the astronomer’s statement is
perfectly correct with respect to his reference point upon the earth, if we leave the surface of the earth, our
reference point will go along with us, and the limitations of relativity will
always precede us at a distance equal to the quantity C. We need not fear
that we will ever overtake or be hampered in any way by those limitations. We
can now clearly see a number of those aspects of the principles of relativity which
have created what we have described as thought blocks in the minds of many students,
scientists and engineers. We have shown that these thought blocks are not actually
inherent in the mathematics of relativity, but are obstacles created by the arbitrary
interpretations which we have placed upon those mathematics. The obstacles are
illusionary only. We must realize that the rules of limitation found in our
mathematical approach to nature, are limitations only of our own perception and
consciousness; and have no absolute significance insofar as nature itself is concerned.
For those that wish to read ahead: 1. General Definitions – critical 2. The Nonlinearity of Physical Law 3. Gravity 4. Matter and Mass 5. Space 6. The Quantity C 7. Time
The far more fundamental and simpler definitions of space time mass matter energy gravity become mandatory:
