Introduction to Curvity
The text below was copied from Daniel Fry's Books and reformatted for the wiki, including new headings for important sections.
- 1 Description of the Craft's Propulsion
- 2 The Non Linearity of Physical Law
- 3 Gravity
- 4 Matter and Mass
- 5 Space
- 6 Quantity C
- 7 Time
- 8 New Galaxies
Description of the Craft's Propulsion
"You are seeing the parts of the ship and its mechanism which your mind is capable of grasping. The large drum like structure just above the central bulkhead is the differential accumulator. We can recharge it from the energy banks of our own ship but this is seldom necessary. In your stratosphere, for example, there are several layers of ionized gas which, although they are highly rarefied are also highly charged. By placing the ship in a planetary orbit at this level it is able to collect during each orbit several times the energy required to place it in orbit. It would also, of course, collect a significant number of high energy electrons from the sun."
"By the term 'charging the differential accumulator' I merely mean that a potential difference is created between two poles of the accumulator. The accumulator material has available free electrons in quantities beyond anything of which you could conceive. The control mechanism allows these electrons to flow through various segments of the force rings, which you see at the top and bottom of the craft. The tremendous surge of electrons through the force rings creates a very strong magnetic field. Since the direction and amplitude of the flow can be controlled through either ring and in several paths through a single ring, we can create a field, which oscillates in a pattern of very precisely controlled modes. In this way, we can create magnetic resonance between the two rings or between several segments of a single ring. As you know any magnetic field, which is changing in intensity will create an electric field, which at any given instant is equal in amplitude, opposite in sign and perpendicular to the magnetic field."
Artificial Gravitational Force Vector
If the two fields become mutually resonant, a vector force will be generated. Unless the amplitude and the frequency of the resonance is quite high, the vector field will be very small and may pass unnoticed. However, the amplitude of the vector field increases at a greater rate than the two fields which generate it and, at high resonance levels, becomes very strong. The vector field, whose direction is perpendicular to each of the other two, creates an effect similar to and in fact identical with a gravitational field.
Center of Force Field Propulsion
If the center of the field coincides with the craft's center of mass, the only effect will be to increase the inertia or mass of the craft. If the center of mass does not coincide with the center of force the craft will tend to accelerate toward that center. Since the system which creates the field is a part of the ship it will, of course, move with the ship and will continue constantly to generate a field whose center of attraction is just ahead of the ship's center of mass so that the ship will continue to accelerate as long as the field is generated."
The Non Linearity of Physical Law
For several thousands of years, the more advanced thinkers among the races of earth, have dreamed of the day when earthmen would succeed in breaking the bonds of his terrestrial prison, to soar freely out into space, and to explore at will, the utmost depths of a boundless universe. To most men, however, the dream had seemed to be one that was impossible of fulfillment.
Now we are suddenly awaking to the fact that the dream is becoming a reality, that this generation is going out into space.
The author has stated, in a number of recent lectures, his opinion that some of the young men who are now in their first or second year of high school, will stand upon the surface of Mars or Venus before they reach their thirtieth birthday. While this prediction may appear to be over optimistic to most readers, it is nevertheless a fact, that the development of the physical science progresses at a rate which constantly amazes, even those who are foremost in its pursuit.
Man's attempt to escape from the rather irksome confines of his tiny planet, has always been hampered by his lack of understanding of four of the primary factors of the universe: Gravity, Space, Time and Energy. It has always seemed that there was too much of gravity and space, and not enough of energy or time. About the year nineteen hundred and five, however, it was brought to man's attention that these factors were not the absolute and independent entities that he had always considered them to be, but that they were variable factors, each having a value which depended upon the value of others. Thus the first faint light of understanding began to filter through the dense screen of absolute determinism which had been erected about the physical science.
Unfortunately, our men of science, instead of pursuing this bright gleam of truth, attempted, from force of habit, to mould it into the common pattern of knowledge, by reducing it to a mathematical formula, which could be used without the necessity of understanding it.
The series of mathematical formulae which Albert Einstein gave to the world in 1905, he called "A Theory of Special Relativity." We have attempted to make of it a 'universal law of absolutes'.
We have ignored the foreword with which he prefaced the mathematics, and so have created the very thought blocks which he had hoped to prevent.
Apparently Different Laws in the Microcosm and Macrocosm
We will refer to this problem later on, but it might be wise first, to devote a little time to the consideration of what we will call 'the non linearity of physical law.' Until a few decades ago the physical laws which govern the universe were considered to be linear. That is: we had, by trial and error, by observation and test, developed a set of laws which apparently held true for all of the small segment of nature which we were able to observe at the time. We assumed therefore that these laws would hold true in any segment of nature, no matter how far removed from our point of observation. When, however, the study of physics moved into the microcosm, that is, when we began to examine the interior of the atom, we found that we were dealing with laws which did not agree with those to which we had been accustomed. These laws too appeared to be linear but followed a different ratio of response. The same disturbing situation was discovered in our examination of the macrocosm. When our astronomers developed the giant telescope capable of peering many millions of light years into space, they found that here too, the physical laws appeared to undergo a definite change.
For a time we attempted to accustom ourselves to the existence of three sets of physical laws, each set linear within its own range of observation, but having different fundamental characteristics. Then with the development of the principles of relativity, we began to understand; or at least, we should have understood, that these different sets of linear laws, were not actually linear, nor were they different sets of laws. They were simply three widely separated segments of the one great curve of natural law.
As long as we were dealing with quantities which could be observed with the unaided eye, or with simple instruments we were unable to detect the curvature, because the segment which we were observing constituted such a tiny portion of the curve that its deviation from linearity was too slight to be detected.
For most practical purposes connected with the ordinary mechanics of our daily lives, these laws are still considered to be linear. Calculations are simpler when they are so considered, and the resulting error is negligible. For the same reason, a surveyor who is surveying a small residence lot, does not find it necessary to take into consideration the curvature of the earth, because the error resulting from this neglect has no significant effect upon the placing of his stakes. If, however, the surveyor is to make accurate measurements of large areas such as a state or continent, it does become imperative to consider the curvature of the earth's surface, and to do this, of course, it is necessary to have a reasonably accurate knowledge of the radius of that curvature.
Radius of Curvature of Natural Law
The necessity of an accurate determination of the radius of curvature of natural law was first realized perhaps, by Dr. Albert Einstein, who devoted a large part of his life and his work to this problem. The results which he obtained have filled a number of textbooks, and have proved to be of inestimable value in the progress of the physical science. They pointed the way to the utilization of nuclear energy, and have many other implications which are sensed, but are not yet completely understood.
The difficulty with our present mathematical approach to the problems of relativity lies not in any error of the mathematics themselves, but in the fact that the methods and terms used in the attempt to explain them often lead to incorrect thinking and assumptions.
In the theories of relativity given to the world by Dr. Einstein, the natural laws, in general, are assumed to be linear, but the space in which they operate is considered to be 'curved.' This concept offers the simplest mathematical presentation, since all of the deviations from linearity can thus be explained by a single postulate. Unfortunately, like most of our mathematical presentations, the concept offers but little for the mind to grasp. A curved space cannot be pictured mentally, nor can it be drawn upon paper. The question always arises, if space is inside the curve, what is outside?
Sine Wave & Zero Point
We have discovered that the linear mathematics which we commonly apply to the 'laws' or rules of nature, do not hold true when carried to an extent which permits the error to be measured, because they do not follow a straight line reaching to infinity, but a curve of finite radii. In a timeless universe, this curve, in any given plane, would be represented by a circle, but since the laws operate through time as well as space, the curve may be more readily understood if represented by a 'sine curve' or 'wave.' The 'base' (which is the center line of the curve) represents zero, while the portions above and below the zero line represent the positive and negative aspects of the law.
Thus we see that there are positions and conditions in which the effect of a natural law will reach zero value with respect to a given reference point, and that beyond these positions and conditions, the law will become negative, reversing its effect with respect to the observer. (The constant repetition of the term 'reference point' or ‘observer' is necessary to emphasize the frequently forgotten fact that none of the basic factors of nature have any reality or significance except when considered from a specified position, or condition.)
If, therefore, we exchange the existing mathematical postulate of linear laws operating in a curved space, for a concept based upon the curvature of natural law, we will find that we have not invalidated or changed any of the presently accepted mathematics which we apply to these concepts. They can still be applied in the same way, and will give the same results. By the exchange, however, we will have achieved a position from which the operation of the natural laws can be pictured by the mind, and can be charted upon paper. Thus we will have taken a great step in the direction of understanding.
Perhaps the greatest obstacle to man's achievement of his dream of space travel has been a factor which has been given the name of Gravity. Its 'discovery' is usually credited, in elementary school text books, to a seventeenth century mathematician and physicist, Sir Isaac Newton. Actually, of course, every man 'discovers' gravity soon after birth; and the stone age man who first rolled a boulder down upon the head of the cave bear who was attempting to scramble up the cliff after him, was making a practical application of this force. It was, however, Sir Isaac Newton who first made a complete mathematical analysis of the subject. His conclusions were compatible with subsequent observation and test, and were virtually unchallenged until the dawn of the era of relativity.
In brief, his conclusions were that gravity is a quality which is inherent in all matter, and that it manifests itself as a mutual attraction between all bodies of matter. The value of this attraction between any two given bodies was said to be directly proportionate to the product of their mass and inversely proportionate to the square of the distance between them.
The attraction between the earth and an object near its surface is an example of this force, although it is usually described as being the 'weight’ of the object.
The difficulty with the statement that the force varies inversely as the square of the distance lies in the implication that if the distance becomes zero, the force should become infinite. Thus it would at first seem that a man standing or lying upon the surface of the earth would be one of two bodies between which the distance was zero, therefore, the weight of the man should be infinitely great. The reply to this assumption is that the force acts as though it originated at the center of the mass, called the 'center of gravity, and that the man on the surface of the earth is still some four thousand miles from its center of gravity. This explanation, however, creates a new problem in that, if we accept it literally, we must assume that if there were a well or shaft extending to the center of the earth, and if a man descended this shaft, his weight would increase as he approached the center of gravity, becoming infinite as he reached it. Actually, of course, his weight would decrease, becoming zero when his center of gravity coincided with that of the earth. So we are forced to the further explanation that gravity is inherent, not in 'bodies’, but in particles of matter, and since a man at the center of the earth would have an equal number of particles attracting him from every direction, the resultant of the forces would be zero.
Gravity in the Atom
If we assume the gravity to reside independently within each atom, our problem is solved as far as the man and the earth are concerned, but if we look within the atom itself in the attempt to find the point where the distance becomes zero, and the force infinite, we find that the same problem again confronts us. We have not solved it, we have only changed our scale of observation. There is conclusive evidence that the attraction, called the binding energy, which exists between the Newtonian particles, (the protons and the neutrons) is intense almost beyond our ability to describe. This force, however, does not increase uniformly with increasing mass, but at certain points not only reaches zero but actually becomes negative.
We can demonstrate this fact by adding a single unit of Newtonian mass, a neutron, to the nucleus of an atom of Uranium 235. When this is done, we find that the gravitational force within the nucleus, instead of increasing becomes negative, that is, the attraction between its parts becomes a repulsion, and the parts begin to separate with considerable brisance. During the expansion, however, several new centers of gravity are formed, which, because of the smaller amount of mass involved in each, are strongly positive. The result is that two or more simpler atoms are formed.
Atoms Not Split
In most text books, this phenomenon is described as the 'splitting' of the atom. There is an implication that it is the 'impact, or the kinetic energy of the neutron which causes the atom to split. If this were true, then obviously, a high speed neutron would split the atom more easily and surely than one with much lower speed. Actually, the opposite situation is true. The high speed neutron will not split the uranium atom at all. It must be slowed to thermal velocity so that it can settle into the nucleus before fission occurs.
Occasionally a neutron will be captured by a uranium atom, without falling directly into the nucleus. The neutron may orbit the nucleus for a very long time (as time is counted in nuclear physics), perhaps several seconds or even minutes. Eventually the neutron drops into the nucleus, and 'delayed fission' occurs, again demonstrating the fact that it is not the impact of the neutron, but its presence in the nucleus, which results in its expansion.
The expansion and subsequent condensation into several simpler atoms is a completely random process. Many simpler types of atom can, and do result from the condensation, in each case however, the smaller atoms cannot contain as many neutrons in proportion to the number of protons as the larger atom, so there are always several neutrons left over.
This phenomenon, if carefully examined and considered, will furnish several strong clues to the nature of gravity itself, but let us for the moment, content ourselves with the observation that it demonstrates that a gravitational field can, under certain conditions, become negative.
Gravity Can Go Negative
Because of the manner in which our gravitational laws have been expressed, it has commonly been assumed that a gravitational force can manifest itself only as an attraction between two bodies of matter. This is not, however, a necessity of thought, since there is no logical reason why it should necessarily be true. In fact if it were true, it would set gravitational fields apart as the only force fields with which we are familiar which could not produce a repulsion, as well as an attraction between bodies of matter. The reason for the assumption of a universal attraction is simply that all of our early and limited observations seemed to indicate that this was true. However, as we have already mentioned, any number of observations, if made on a sufficiently limited scale, will tend to indicate that the earth is flat, rather than spherical.
Origins of Levity Explained
For many years a school of thought existed which recognized that gravitational fields, like all other fields, must possess a dual polarity. They called these poles, gravity and levity. They assumed that some objects and materials normally possessed the quality of gravity, while others normally possessed the quality of levity. An object possessing levity would be repelled by all objects possessing gravity. The theory eventually became discredited, and was almost universally discarded, not because it was ever disproved, but because so many attempts had been made to assign this quality of levity to objects and materials which did not actually possess it. For instance it was, for a time, assumed that gases such as hydrogen and helium possessed levity because when they were contained in a light bag or envelope, they were observed to rise against the gravitational field. It was soon demonstrated, however, that their rise was not caused by any quality of levity, but simply because their specific gravity was less than that of the air they displaced. After a number of unsuccessful attempts to assign the quality of levity to specific materials and objects, the theory fell into disrepute to the extent that the very word levity has become synonymous with humorous nonsense. Nevertheless, the philosophers who developed the theory were perfectly correct in their primary postulate. They erred only in failing to realize that gravity and levity are not properties of specific materials but are conditions under which all matter may come.
We have now observed negative gravitation in the microcosm (the interior of the atom), we also observe it in the macrocosm (between the galaxies).
Many technical articles have been written in recent years concerning "Our Expanding Universe," yet where, in any of them, can we find any logical explanation or reason why it should expand at all? Under the theory of universal attraction, all of the matter in the universe should be rapidly coalescing into one gigantic lump. Instead, we find that every one of the large groups of stars which we call 'galaxies' or 'galactic clusters' are retreating from every other group, at velocities which increase with their distance from the observer. Velocities of recession approaching that of light have been calculated for those which are most distant from us.
A number of interesting but hardly convincing theories have been advanced in the attempt to reconcile the observed state of the universe with the existing concept of universal attraction. Some of our cosmic theorists have proposed that at one time all of the matter in the universe was contained in a single tremendous star, or 'atom'. For some reason, which is not given, this atom exploded, hurling outward the matter which has become the star clusters, and imparting to them the motion which we now observe, several billions of years later. This theory, first propounded by Abbe Lemaitre, has become known in colloquial parlance, as "The big bang theory." It was popular for a time, but as knowledge of the size and nature of the universe increased, it became obvious that such a theory would not stand up if examined under the existing concept of linear natural laws.
Why Black Holes Don't Exist
In the first place, such an inconceivably huge mass of matter, even at the very great temperature which was assumed for it, would, under Newtonian laws, produce a gravitational field so intense that no velocity less than that of light itself would be an 'escape' velocity. In fact it has been calculated that even the light emitted by this huge sun would not escape completely, but would circle in a comparatively small orbit around it. Through the concept of the curvature of physical law, however, we see that the addition of mass to an existing body does not, necessarily, increase the force of attraction between its parts, but may, under certain conditions, cause the field to become negative, and the attraction to become a repulsion. We can explain the observed actions of the present universe by postulating that an attraction exists between the individual bodies within a galaxy, because their total mass and distance is such that they are within the positive portion of the gravitational curve with respect to each other. In the vast spaces between the galaxies however, the curve dips below the zero line, with the result that a repulsion exists between
Parry Moon Paper
In July 1958. Parry Moon, of the Massachusetts Institute of Technology, and Domina Eberle Spencer of the University of Connecticut, published an excellent paper in the Journal of the Franklin Institute, titled "The Cosmological Principle and the Cosmological Constant." This paper demonstrates, logically and mathematically, that the assumption of a positive gravitational force within galaxies or galactic clusters, and a negative gravitational force between the clusters, offers the only practical means of explaining the observed actions of these bodies.
In the January 1959 issue of the magazine "Astronautics', Fritz Zwicky of the California Institute of Technology, published an article headed, “Is Newton's Law of Gravitation Really Universal?" In this article Zwicky pointed out that present observations indicate rather conclusively that the gravitational fields of the galactic clusters reach zero value between the galaxies themselves. This also explains why matter, although rather evenly distributed throughout the known universe, is not distributed uniformly, but is found in quite similar concentrations at comparatively regular distances.
How Not to Control Gravity
At this point we hear someone say, "These explanations may be very interesting to the astronomer or to the theoretical physicist, but how can they help us in achieving space travel?" The answer is, of course, that we must have some understanding of the physical laws before we can make the proper use of them in attaining our own personal ambitions.
In his dream of space travel, man has generally considered only three possibilities of escaping from the earth. First, gravity must be destroyed. That is, the operation of the gravitational field must cease between the space craft and the earth, so that it will not hinder the departure of the craft. While a number of highly imaginative stories have been written along this line of thought, no theory has ever been evolved, or test conducted which could give us any hope that such a condition can be achieved.
Despairing of the first possibility, we pass on to the second. Gravity must be shielded. Some type of screening material must be interposed between the craft and the earth to cut off or absorb the gravitational field so that while it still exists, it will no longer act upon the craft.
Here again we have found imagination raising our hopes, and reality disappointing, for no material has been discovered which shows any promise of fulfilling such a function. With our hopes considerably subdued, we pass on to the third possibility. Gravity must be overcome. We must apply a greater force, so that we can rise against the pull of gravity, even though we must pay an exorbitant tribute of energy for each foot of progress. In this last plan, we have achieved a certain degree of success. Instrument packages have been placed in orbit about the earth, one has been dispatched to the moon, and several have been placed in independent orbits about the sun.
It does not appear however, that the proper solution has yet been achieved.
When man attempts to attain his ends by pitting one natural law against another, he usually finds that it is a wasteful and laborious process. While it is true that it is perfectly possible to propel a rowboat by throwing rocks from the stern, it is not a method which an intelligent man would choose if he were aware of other possibilities. In the first place, the thrown rock must accelerate, not only the boat, bur all the rocks which remain to be thrown. If a long journey were planned, the greatest problem would be to find enough room in the boat to store the required number of rocks. Since the thrust produced is equal to the mass of the rock multiplied by the velocity of its ejection, it is obvious that there are three limiting factors.
First, there is the total mass of the available rocks, which is limited by the size of the boat which contains them. Second, there is the total amount of energy available. (This is a factor only because we have so little understanding of the true nature of energy.) The third, and at the present time the most serious factor, is the limited mechanical strength of the throwing arm.
In a rocket motor, the 'rocks' are represented by a gas produced by combining or 'burning' the fuels within the combustion chamber, the gas, at a high temperature and pressure, is expelled through an opening or 'venturi' in the stern. Since the amount of fuel is limited by the size of the rocket, the only means of increasing the total thrust is to increase the velocity of ejection, but this can only be accomplished by increasing the temperature and pressure of the gas within the combustion chamber. Regardless of the amount of energy which is available, the amount of thrust which can be produced is limited by the ability of the chamber to withstand the temperatures and pressures involved. Since these limits are reached (and often exceeded) by ordinary chemical energies, it is clear that the vastly greater energies available in nuclear reactions, are, at the present time at least, of academic interest only to the rocker engineer. In the case of craft which remained in our atmosphere, of course, more 'rocks' could be taken aboard while in flight, by scooping up the atmosphere through which the ship was traveling, and allowing the surplus energy to act upon it. In space flight, however, this is not practical.
Attempts are being made to overcome this problem through the concepts of the "Ionic" or the 'Photonic' drive, in which ions or photons are used as the 'rocks' to be thrown overboard. Ions and photons have a basic advantage over atoms or molecules in that they achieve much higher velocities without the necessity of high temperatures or pressure.
There are, however, great obstacles to the embodiment of these concepts in practical devices, and it appears unlikely that either will lead to economical space travel in the near future.
It is time to re-examine our position to see if there is not something we have overlooked. Have we forgotten the old saying, "If you can't lick 'em join 'em?"
We have tried for centuries to 'lick' the force of gravity. We have tried to destroy it, and failed. We have searched for some method of shielding ourselves from its effect. We have not discovered it. We have attempted to overcome it by opposing it with superior force, and found it a wasteful and cumbersome process. Isn't it about time we gave up the idea of fighting the force of gravity, and began to consider the possibilities of making use of it?
We have learned that gravity, like all natural factors, has a negative, as well as a positive value. If after building our space craft, we could arrange conditions so that the ship was in the negative portion of the gravitational curve, it would fall away from the earth as easily and as naturally as a stone dropped from a tower falls toward the earth.
Of course, we hear at once the objection that, while negative gravitational fields have been shown to exist, they have been found only within the atom and at inter-galactic distances. How can we place a space ship within the negative portion of the curve, with respect to the earth? The answer to this question lies in the fact that, as we have already learned, the natural laws are not absolute, but relative. That is, the size and shape of the curve of one law is dependent upon the value and position of the others. We have seen that the nucleus of the atom of uranium 235 dips below the zero line with the addition of only one mass unit, making a total of 236, yet the nucleus of the atom of uranium 238, although close to the zero line is still on the positive side of the curve because of the fact that the shape of the gravitational curve is modified not only by the mass present but also by the number and position of the electrical charges.
When we acquire a better understanding of the laws, we will be able to produce any shape of curve we desire, with the earth as one reference point and the spacecraft as the other.
Suppose you were to hand a bar magnet and a similar bar of soft iron to a man who was intelligent, but uneducated, with the request that he examine and test the two objects in order to determine their properties. One of the properties which the researcher would be certain to list would be the 'inherent' property of mutual attraction between the two objects. He would observe that when either end of one bar approached either end of the other bar, a condition of attraction was observed. He would probably conclude that the attraction was an inherent quality of these objects, and that it would continue to persist regard-less of anything which could be done.
We know, of course, that if a length of insulated wire were wound around the soft iron bar, and a flow of electrons were induced in the winding, the two bars could be made to exhibit a repulsion as readily as an attraction. Note that in this case we have not destroyed the field of permanent magnet, we have not shielded the field, nor have we overcome it. We have simply produced a field which is in opposition to it, and the two objects now tend to separate rather than to come together.
The same possibility exists with respect to gravitational fields. While the results will probably not be achieved in the same way, it should not be too difficult to work out means of polarizing a gravitational field, once we discard the old assumption that it is impossible.
Matter and Mass
Much of the confusion which exists in our scientific concepts today is brought about by our failure to distinguish carefully between matter and mass. Until a comparatively few years ago, it was assumed that mass was a property which was exhibited only by matter. Upon closer examination, however, it appeared that energy also possessed mass, since when energy was added to a body of matter, the mass of the body was increased.
We have defined mass as being resistance to change in the existing state of motion. It is measured by the amount of the energy which is required to produce a given change in velocity. All matter has the property of mass, but not all mass has the properties of matter. For the purposes of this discussion, we will postulate that there are two types of mass, inertial mass, which is simply the property of resistance to change in a state of motion, and the mass inherent in matter, which we will call Newtonian mass, because it includes all mass which obeys the original laws laid down by Sir Isaac Newton. Since the reader may be under the impression that all mass obeys the Newtonian laws, let us pause here long enough to examine the facts and to point out the differences in the properties of inertial and Newtonian mass.
All physicists of today are agreed that the electron has mass. Yet if it were possible for us to hold an electron between two of our fingers and then suddenly release it, we would find that there was not the slightest tendency for the electron to fall to the earth (unless the surface happened to be positively charged at the moment). The electron is nor in the least affected by the gravitational field of the earth, so long as it is at rest with respect to that field (if the electron is moving through the field, however, the direction of the motion will be affected).
The electron has mass only because it has an electric charge. As we know, when an electric charge is accelerated in space, a magnetic field is produced, and energy is required to produce this field. The energy 'spent in producing this field, is said to be the 'mass' of the electron, since it is the entire cause of its resistance to acceleration. The greater the degree of acceleration, of course, the more intense the field, and the greater the amount of energy required to produce it. So we say that the electron gains 'mass' with every increase in its velocity. If an electron could be accelerated to the velocity C (commonly called the velocity of light), it would have acquired the maximum velocity with which energy can be propagated.
It is obvious, therefore, that no amount of energy could further accelerate this electron (with respect to its original reference point), so it would be considered to have acquired 'infinite' mass.
Let us take time to examine this statement carefully, since it is a point upon which there is much confusion. The electron would have acquired infinite mass only in reference to its original energy level. If observed from a reference point which had itself received the same degree of acceleration, the mass of the electron would not have changed a particle. This increase of inertial mass with increasing velocity, is simply the measure of the kinetic energy differential between the observer and the point which he is observing.
Infinite Energy Example - Gun & Cork
We will attempt a simple analogy, in the hope of making this more readily understood. An observer is stationed in 'free space' far from any gravitational or other fields which might affect the results of the experiment which he proposes to make. He has, in one hand, a sphere of cork or other light material which has a mass of 10 grams. In the other hand he has a pistol which fires bullets also having a mass of 10 grams and a velocity of 1000 feet per second. The man holds the ball out at arms length, and fires a bullet from the gun into it. We will postulate that the bullet is not absorbed by the cork, but shares its kinetic energy with it, so that after the impact, the bullet and the cork ball each have a velocity of 500 feet per second. The observer now fires a second bullet at the cork. This bullet also has a velocity of 1000 feet per second with respect to the observer, but now the target has a velocity of 500 feet per second in the same direction, so that there is a differential of only 500 feet per second which the bullet can share with its target. After this impact, the bullet and the ball each have a velocity of 750 feet per second. When the observer fires the third bullet, he finds that now there is a differential of only 250 feet per second between it and the target, so that the velocity of the target is raised by only 125 feet per second, and so on.
The observer notes that each succeeding bullet, although it has the same energy with respect to him, produces a smaller and smaller acceleration in the target. He would observe that the 'mass of the target' (its resistance to acceleration) appears to increase with its velocity. If he made mathematical calculations based upon his observations, they would show that the greatest velocity which he could ever induce in the target would be 1000 feet per second (the velocity of the bullets), and that to produce this velocity it would be necessary to fire an infinite number of bullets. His experiment demonstrates conclusively that as the velocity of the target approaches 1000 feet per second, his ability to further accelerate it approaches zero. Persons with lesser intelligence or insight than our observer might be convinced that this figure of 1000 feet per second was an absolute and inescapable limit.
The observer, however, as we said, has greater understanding. After he has accelerated his target to the 'limiting' velocity of 1000 feet per second (by firing an infinite number of bullets), he steps aboard a small space ship (with which he has thoughtfully provided himself), and takes off in the direction of the target. He accelerates his ship to a velocity of 1000 feet per second, with respect to his starting point, and now finds that he is back upon exactly the same energy level as his target. If there were no other bodies of matter in the universe, there would be no way in which he could determine that either he or the target were in motion, since there would be no relative motion between them, and no other reference points from which motion might be determined. In fact, he finds that the situation is exactly the same as it was before he fired the first shot, and he can now begin his shooting all over again. He does so and observes that his first bullet accelerates the target to a velocity of 500 feet per second with respect to his new reference point, and he notes that the 'infinite mass' of the target returns to its original 10 grams, as soon as he reaches the same energy level. He realizes then that the 'increasing mass' of the target is only the measure of the kinetic energy differential which exists between them. The mass approaches infinity only as the energy level approaches that of the accelerating force. (In this case it is 1000 feet per second.) In the case of the quantity C, usually called the velocity of light, the differential is equal to 3 x 1010 centimeters per second, or if we convert this velocity to its equivalent energy we would have 9 x 1020 ergs per gram of mass.
In our discussion of non-linearity of physical law, it was pointed out that the energy inherent in a gram, or any other quantity of matter is precisely the quantity of energy necessary to accelerate its mass to a velocity equal to the quantity C by energy conversion. This statement may be hotly disputed by some students who have not yet learned to distinguish between matter and mass. Their argument is to the effect that no mass can ever be accelerated to the velocity of light since the mass would then be `infinite' and consequently the energy required to produce the velocity would also be `infinite.' The incorrectness of this assumption can be demonstrated simply by pressing the button of a pocket flashlight. A beam of light will be produced which any physicist will agree has mass and which, by its very definition, is moving at the velocity of light. Yet all the energy required is released by a small amount of chemical change taking place within the cells of a battery.
Among all of the great basic factors of the Universe, perhaps the most difficult to define or explain is that which we call space. While many of our greatest philosophers and scientists have attempted definitions, few have succeeded in offering anything which the average mind could readily grasp. The German mathematician Leibnitz said, "Space is simply the order or relation of things among themselves." Several centuries afterwards, the late Dr. Einstein used almost identical terms. "Space has no objective reality except as an order or arrangement of the objects we perceive in it."
The average man's definition of space is: "That in which matter can be placed" or "that which matter occupies." This last definition is subject to dispute by those who maintain that matter does not occupy space, but is itself, only a warp or distortion in space. Another school of thought insists with equal vigor, that while matter does occupy space, it creates a warp or distortion in the space surrounding it. Since both of these concepts are subject to the same set of mathematical laws, the same laws can be offered in support of either. There is little, however, in either of these postulates which seems to furnish a good foundation for understanding and it is understanding rather than algebraic formulae that we are seeking in this discussion.
For our purpose, a simple definition will suffice. Space is that which separates bodies of matter, whether these bodies be atoms, galaxies or any component part of either. We can extend this definition by stating that the degree of separation which exists between any two bodies is determined by the degree of curvature of the natural laws which exist between them. In making observations, of course, we must remember that, since the natural laws are relative, the mass of the body itself influences the degree of curvature. In the theories of relativity given to the world by Dr. Einstein, the natural laws, in general, retain their linearity, but the space in which they operate is considered to be curved. This concept offers the simplest mathematical presentation, since all of the observed deviations from linearity can thus be explained by a single postulate. Unfortunately, like most of our mathematical presentations, the concept offers but little for the mind to grasp. A curved space cannot be pictured mentally, nor can it be drawn upon paper. There is always something remaining outside the curve. Furthermore, attempts to rationalize this concept lead to many paradoxical statements which become more and more evident, the greater the effort to explain.
One of the best efforts to bring to the average mind an understanding of the principles of relativity, was made by Lincoln Barnett in his well known book, "The Universe and Dr. Einstein." Because of its careful preparation and its explicit presentation of present theory however, it brings out very clearly the paradox which must exist between successive assumptions. For instance: reference was made, as has already been noted, to the theory of Abbe Lemaitre, which supposed that at one time all the matter in the universe was contained in one huge lump or star. Since the curvature of space is considered to be determined by the amount or density of the matter present in it, at that time the universe was very small. That is, it had a very high degree of curvature. Light and other forms of energy do not move outward from this curve, but follow the circumference, so that the light emitted by this body, after a comparatively short journey, returned to its starting point.
No attempt was made to speculate upon the length of time in which this body had existed, or the origin of the matter and energy of which it was composed. The theory merely supposed that, after perhaps an infinity of quiescence, this body suddenly exploded. Portions of the mass moved outward in all directions and thereby enlarged the radius of space. If the radius of space was increased, it is obvious that the matter did not follow the curvature of space, but actually moved perpendicularly to it, (or perhaps at a tangent). At any rate, we see that while the radiated energy followed the 'curvature' of space whose radius was determined by the mass and density of the matter, when the matter itself expanded, instead of following the curve, its motion increased the radius.
It is interesting to note that the statement is repeatedly made that this sudden expansion began about two billion years ago, yet in the preceding paragraphs it has been stated that the calculated radius of the universe is now about 35 billion light years. Simple calculation would indicate then that the universe, or at least that portion which we call space, must have moved outward at an average velocity equal to about seventeen times the velocity of light. Either this velocity of expansion is still maintained or at some period in the past it must have been even greater.*
These statements raise some perplexing questions. In our theories of relativity it is assumed that light follows the 'curve' of space. Yet it is difficult to picture a photon following a curve whose radius is expanding at a rate equal to seventeen times the velocity of the particle.
In the book "The Universe and Dr. Einstein" it is also stated that: while space is expanding rapidly, the matter of the universe, which is likened to "inelastic patches on the surface of an expanding balloon," is not expanding with the space, since if it were, we could not detect the expansion.
If it is space that is expanding, it is difficult to understand why we have never detected the increasing distance between the earth and the moon or the sun. No attempt was made to explain why the space which exists between the individual atoms, and between the component parts of those atoms, should not expand also.
None of these difficulties, of course, invalidate any of the mathematical laws from which the concepts have been derived, but they do emphasize the great need for explanations which are more compatible with reason and understanding. For instance, in the above case would it not be simpler to assume that the degree of separation which exists between the Galaxies, when considered as individual bodies, is apparently increasing because they occupy opposite portions of the sine curve of natural law?
If we exchange our postulate of linear laws and a 'curved space' for a concept which incorporates the curvature of natural law, we find that we have not thereby destroyed or invalidated any of our present mathematics, but we have achieved a position from which the operation of the natural laws can be pictured by the mind, and can be charted upon paper. Thus we have taken a great stride in the direction of understanding.
In summing up our discussion of space we should recall
1. Our definition- Space is that which separates bodies of matter. This separation is a vector function of the time, energy and mass differentials.
2. The degree of separation which exists between any two bodies, or reference points, determines the degree of curvature of the natural laws between them.
3. The natural laws are relative. That is, the value of one can be altered between any two reference points by altering the value or relationship of the other. This last fact should always be borne in mind when we hear some dogmatist solemnly declare that we are forever barred from reaching the stars by the hopelessly great degree of separation which exists between us.
We have seen that the factor known as the quantity C has a greater significance than is usually credited to it. It is not merely the velocity with which light and other forms of energy are propagated in a vacuum. The quantity C is a degree of energy differential. We can define it as the maximum differential which can exist between two reference points in the factor which we call matter. We can also define it as the minimum differential which can exist between a reference point in matter, and one in energy. This is only true, however, when the reference point in matter is at the same energy level as the observer.
One of the postulates of the theory of relativity is that as a body of matter accelerates and approaches the velocity of light, or a kinetic energy differential equal to the quantity C with respect to a given observer, the body loses dimension in the direction of motion. If the velocity reaches the velocity of light it will appear to have lost all of its dimension in this direction. To this observer it would no longer be matter, since matter, by definition, requires three dimensions. The matter would have become energy insofar as the original observer was concerned since it would now exhibit a kinetic energy differential equal to the total energy inherent in the original matter.
Three Craft Example
This statement, however, seems to produce a misconception in the minds of many students of physics. We will therefore attempt to clarify the concept by the use of a simple analogy. We will assume that we have three space ships assembled at a given point upon the surface of the earth, (or at a given point in space.) For the purpose of this analogy we will assume that the ships are capable of any desired degree of acceleration. We will dispatch two of these ships into space, flying side by side in a given direction. We will launch the remaining craft in the opposite direction in space. We have an observer upon each of the three craft and a fourth observer who remains at the point from which they departed. We will designate the ships which departed together as A and B, the ship which is moving in the opposite direction as C, and the observer at the starting point as D. When we have accelerated all three of the ships to a velocity equal to one half that of light, (with respect to the starting point) we pause to determine what changes, if any, have taken place. To the observer at the starting point D, the three ships have become slightly shorter in the direction of their motion, and have gained a small amount of `mass,' but are otherwise unchanged. The observer upon the ship C, however, discovers that while he and his own ship appear to be unchanged, the ships A and B have lost all dimension in the line of motion, because they have reached the velocity C with respect to his reference point. They have ceased to exist as matter and have entered the plane of energy. The two observers upon the ships A and B also note that C has ceased to exist as a material object, but when they examine themselves and each other, they find that no change whatever has occurred to them or to their ships since they are all upon exactly the same energy level and no differential exists between them.
We will now accelerate all three ships to the velocity C with respect to their starting point D. At this velocity the three ships cease to exist materially insofar as the observer at D is concerned, since they have entered the plane of energy, and are also at the zero point of the curve of time with respect to him. The observer upon the ship C would note that the ships A and B were again in existence but that they were now in the negative portion of the curve. Since this concept may prove somewhat difficult to grasp at the first attempt, it will be explained further and a simple analogy given in the chapter on Time.
The foregoing analogy also demonstrates that the term velocity has no meaning or significance except as an observed kinetic energy differential between two specified points of reference.
The Only True Constant C
If we examine this analogy carefully, we will find that we have demonstrated the most important aspect of the factor which we have named the quantity C. C is a constant, the only true constant in the universe, because it is the pivotal point about which the natural laws become manifest. It is the factor for which many great physicists have spent years of search, even though they had it constantly in their possession. In short, the quantity C is the measure of the radius of curvature of natural law. It is the factor which will enable us to determine precisely the degree of change in the curvature of one law which will be brought about by a specified change in the application of the others. It is the factor which will eventually tell us how to place our spacecraft in either the positive or negative portion of the gravitational curve with respect to the earth or any other planet which we may choose to visit.
When we state that the quantity C is the radius of the curvature of natural law, we mean simply that if a differential of energy equal to this quantity exists between the observer and the point which he is observing, the natural laws will be suspended. If the energy differential is in excess of the quantity C, the laws will appear to operate in reverse at that point. As we stated earlier, this effect will be demonstrated by a simple analogy in our discussion of the factor called time.
Consider C as Frequency
While we have repeatedly referred to the quantity C as an energy differential, we have heretofore considered it only in terms of kinetic energy. Some may believe that it can be reached only when there is a rate of increase or decrease in the degree of spatial separation between the reference points, equal to 3x1010 centimeters per second, or in simpler terms, a velocity equal to that of light. It is necessary therefore to point out the fact that an energy differential does not necessarily manifest itself as a velocity. It can also exist as a frequency. Our present laws of physics state that the energy level upon which an electron, a photon, or other particle exists is proportionate to its frequency. The mathematical rule is E equals Fh where E is the energy, F is the frequency and h is a factor called Planck's constant.
We can now see that a frequency differential which by the above formula is equal to 9x1020 ergs per gram also represents the quantity C. When such a frequency differential exists between the observer and the point which he is observing, we again find that the natural laws at the observed point reach zero value with respect to the observer. If the frequency differential exceeds this value, the action of the laws will become negative. A material object such as a spacecraft upon or near the surface of the earth would cease to exist as matter and would enter the plane of energy insofar as the observer on earth was concerned, but as we have previously pointed out, an observer upon or within the object, whose frequency or energy level had been raised to the same degree as that of the craft, would be unable to detect any change.
We must clear our minds of the thought block produced by the assumption that the quantity C is a factor of absolute limit. We must realize that it is a limiting factor only with respect to two given reference points, and that it is perfectly possible to conceive of a series of consecutive reference points between each two of which a differential equal to the quantity C may exist.
In his examination of the natural laws or facts of the Universe, man is greatly handicapped by the fact that 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 one 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 is now being superceded by an even faster method, 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 three 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.
What Does Simultaneous Mean?
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 apace 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.
Flight to Proxima Centauri Example
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. A simple analogy may serve to make this statement more readily understood. Suppose we were to 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 be 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 to 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 operates 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 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.
Position to Observe the Sine Wave
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 4C 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 than 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 our view. Our lateral excursion into time has completed its curve and we have returned to the starting point of our uni-dimensional 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 4C. 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 4C, 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.
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 may 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 bad 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.
At this point in our progress of understanding, we shall embark upon a most ambitious journey. We are going out into space. Into the remotest depths of inter galactic space, so that we may observe, at close range, the birth processes of a new star cluster or 'Galaxy.' We will take along our consciousness, our ability to observe, and our understanding. We must, of course, leave our bodies behind, since they would not fare well in space, and also because their mass would create a gravitational field which would tend to alter the natural conditions at our point of observation. We will seek a spot which is at least a few million light years distant from any other galaxy or accumulation of matter; for it is only within these remote areas that we may observe the birth process of a new galaxy.
In the first part of this book, we discussed the almost inconceivably large number of particles which are found in each cubic inch of our atmosphere at sea level. As we move outward from the earth's surface we find that the number of particles diminishes rapidly, but still remains surprisingly large. When we have reached a height of one hundred miles we find that there are only about one millionth as many particles per cubic inch as we found at the surface, this is a density of matter so minute that we require very sensitive instruments, even to detect its existence. Yet, if we count the individual particles, we will find that there are still about 400 million, million particles in each cubic inch of space. At a few hundred miles elevation the density has diminished another million times, and we say that we have entered 'space', yet there are still many millions of particles per cubic inch.
We come to the startling realization that there simply is no such thing as 'empty space.' Astronomers have estimated that even in the remotest depths of intergalactic space, (which is our destination on this trip) there will still be found from twenty five to seventy five or more nuclear or atomic particles per cubic inch. Most of these particles are protons, or simple atoms which have attained escape velocity from the surfaces of some star, and which may have been wandering aimlessly about, perhaps for billions of years, coming into occasional collision with ocher particles, but usually with sufficient relative velocity so that mutual capture could not take place.
In the vicinity of existing galaxies, the gravitational fields created by the innumerable stars within those galaxies, tend to draw in the random particles, many of which eventually fall into one or another of the stars, and thereby assist somewhat in replenishing the mass which each star is constantly converting into energy.
We must, therefore, seek a spot which is remote from any of the existing galaxies, and approximately equidistant from the nearer ones. Even in this remote area of space we will find countless numbers of particles of matter, anti units of charge; electrons, protons or simple atoms, which have achieved escape velocity from some star, or which have been formed in space by random approach and capture. In short, we have all of the building blocks of nature, present in an exceedingly tenuous and diffuse state.
Since each of the particles of matter has mass, each has a force of attraction existing between it and ever other particle of matter in the area.
If we accept the concept of the non linearity of natural law as previously outlined in this text, we find that each of these particles is also being repelled slightly by the surrounding galaxies or galactic clusters. These forces are almost inconceivably small, yet the net result of their action is to create a tendency upon the part of each randomly moving particle to move ever closer to the center of the area of attraction, which is also approximately but not exactly the center or 'null balance' point of the repulsion of the surrounding galaxies.
We will assume that we have now reached the point from which we will observe the birth of our new galaxy.
This point is at the center of a sphere of space, perhaps thirty thousand light years in diameter, within which the final concentration of matter will take place.
We must be prepared to exercise a great deal of patience, because the forces involved, and the resulting accelerations are so minute that many millions of years will probably elapse before we can detect any significant increase in the number of particles per unit of volume. Nevertheless, all of the particles within several hundreds of thousands of light years are slowly but surely acquiring a velocity in our direction.
As the concentration of matter at the center of our system increases, the intensity of its field will also increase and will add, not only to the velocity, but also to the acceleration of the inward moving particles. We are observing the condensation of a tremendously large volume of exceedingly ratified gas into a relatively small volume.
Let us assume that one hundred million years have passed since we first occupied our point of observation at the center of the newly forming galaxy. All of the particles within some thousands of light years have now acquired a very respectable velocity in our direction, and the density of the gas surrounding us is increasing with comparative rapidity. We observe however, that the particles are not falling directly toward the central point of the condensation.
We can understand this if we realize that the center or null point of the force of repulsion is determined only by the distribution and the distance of the surrounding galaxies, while the center of the force of attraction is determined by the distribution of matter within the area of condensation. Since the center of 'push' is not at the same point as the center of 'pull', there is a tendency toward the creation of an angular velocity. That is: the particles, instead of falling directly toward the center, will tend to spiral inward. Eventually this rotational motion will become general throughout the mass.
The plane in which this spin begins is determined by the location of the existing galaxies and the relative density of particles in different parts of the condensing mass, but once begun, the motion tends constantly to increase as the condensation proceeds.
The particles which are upon either side of the central plane of spin tend to fall toward the plane as well as toward the center, while those particles which are nearly perpendicular to the center of the plane of spin rend to fall inward more rapidly because of their smaller rotational velocities.
Our gas cloud now begins to take on the shape of a disk with a somewhat oblate sphere at the center. The galaxy has begun to assume its final shape, though as yet, there are no stars within it nor does it emir any light. If we were to direct a large telescope on earth towards this gas cloud, we would not be able to see it at all. Since all of the light coming from the galaxies behind it is now being absorbed, we would see only that there was an unusually large dark area in space. We would probably refer to it as a 'dark nebula,' a tremendous body of gas, still somewhat rarefied according to our usual concept of gas; which emits no light, but which does absorb, and convert to lower frequencies, almost all of the light, and other forms of radiant energy which reach it from the countless radiating stars throughout the universe.
As the nebula continues to contract, areas of comparatively high density will develop in many parts of the mass. Each of these points will become a local center of gravity, and accelerated condensation will occur towards these points.
The gas cloud now becomes broken up into a multitude of individual spheres, each of which continues to condense upon its own center, just as a cloud condenses into myriads of tiny water droplets.
Let us now direct our attention to one of these 'droplets' which is eventually to become a star in our new galaxy. It is still several millions of miles in diameter, but shrinking rapidly.
As the gas cloud condenses, the energy which it contains, becomes concentrated. The particles which while they were drifting about in space, had almost infinitely long 'mean free paths’, now come into more and more frequent and more and more violent collisions.
The temperature of the mass constantly rises. The kinetic energy which the particles have been building up during the millions of years while they were accelerating toward the common center, is now being converted into thermal energy. Eventually the mass begins to emit photons having frequencies in the visible portion of the spectrum.
We can now say that the star has been 'born', although it may still have more resemblance to a nebula, than to a star. A great deal more contraction will take place before the internal pressure of the gas begins to balance the gravitational force.
The star which we have chosen for observation is one of the millions which are forming within the central portion of the nebula. Since the nebula was created by the gradual inward movement of particles from an immense volume of space, it is apparent that it is within the spherical area at the center that the gas will first achieve a density sufficient for the process of condensation into separate stars to begin.
By this time the entire nebula has acquired a fairly uniform rotation about its center of mass. The individual stars, during their condensation, will of course retain this rotation but will also develop a rotational motion about their own center of gravity.
As the gas at the core of the new star becomes denser, the gravitational field becomes more and more intense, and the surrounding matter falls, with ever increasing rapidity toward the center.
Most of the gas which, even during the dark nebula stage, occupied dozens of cubic light years, of space, now is compressed into a sphere only a few million miles in diameter.
Earlier in this text we observed that the temperature of a given gas will be inversely proportionate to the volume which that gas occupies, so long as the total thermal energy contained remains the same.
The gas which we are observing is now billions of times more densely packed than it was when the condensation began, and the temperature has risen from a fraction of a degree absolute, to several millions of degrees. This temperature continues to rise as the high kinetic energy which the incoming particles have acquired during their long fall, is converted into thermal energy as those particles impact the randomly moving particles at the surface of the star.
The condensation of the star, from the dark nebula to its present state of development has been comparatively rapid, only a few million years being required for the process. Most of the matter available to the star has now formed into a fairly compact spheroid, and comparatively little new matter is arriving at the surface.
As the mass continues to contract, the temperature within the body of the star continues to rise, but because of the tremendous amount of radiant energy which is now escaping from the surface, its temperature will remain far below that of the interior.
The star is now a member of the class which Walter Baade, then a member of the Mount Wilson Observatory staff, named Population I, a blue white star with a surface temperature of the order of 30,000 degrees absolute, and an internal temperature of several millions of degrees. It is emitting light and heat energy at a rate much greater than can be replaced by the comparatively small amount of material which is still falling into it from the nebular cloud.
If the life process of the star ended here, its period of luminescence would be very short. Within a few thousands of years, the surface temperature would begin to fall below the point of incandescence and the star would appear as a dull red body. The continuing contraction of its mass might maintain the star in this condition for a few thousands of years more, but eventually the surface would become almost entirely dark, and a liquid or solid crust would probably begin to form.
We know, however, even from our relatively short history of astronomical observations, that the active period of a star is much greater than this. Let us, therefore, return to our nuclear scale of observation to determine the source from which the star receives its continuing supply of energy.
We must remember that much of the matter which forms our new star, consists of atoms which, eons ago, escaped from the surface of some other star. Since the atom of normal hydrogen (1H1) is the lightest of the atom family, it will acquire, at a given energy level, a greater velocity than any other atom, and since velocity is the principal factor in the escape of atoms from the gravitational field of a star, we would assume that most of the particles to be found in open space would be hydrogen atoms.
The new, star, which is simply a condensation of these particles, would also be assumed to consist principally of hydrogen.
This fact, which we can predict from our simple study of the behavior of atomic particles, has been verified many times by spectrographic analysis of the newer stars in presently existing galaxies.
Let us examine the interior of the star, to see if we can discover the source of its great energy supply. (Since we left our bodies at home when we embarked upon this extra-galactic tour, we will not be unduly inconvenienced by the high temperatures and pressures which exist in the regions in which we must conduct our observations.)
As we approach the star, we first pass through a region which, in the case of our sun, we call the corona. It is the area about a star where the incoming particles first meet resistance in their long fall. The corona is a belt of exceedingly tenuous gas whose particles have random motions. This layer of gas is much like the upper layers of the earth's atmosphere except that its temperature is very much higher. We must remember that the tremendous gravitational field of the star is attracting particles from all parts of the space surrounding it, and that they acquire very high velocities. As they fall through the star's outer layer of gas, sooner or later, each falling particle comes into direct collision with a particle of the corona gas. The linear kinetic energy is converted to radiant energy of high intensity. We observe temperatures of one trillion degrees Fahrenheit and more. The gas is, however, so ratified that the total amount of heat created per unit volume of space is small compared to the much greater quantities of energy which are being radiated from lower levels.
After we have descended through the corona, we encounter another layer of gas, much denser than the gas of the corona. This layer we will call the photosphere, because it is within this layer that most of the visible light which the star radiates, is created.
Here the temperature, as measured by the activity of the particles, is much lower, only about 11,000 degrees F, yet the gas is so much denser that the energy contained per unit volume, is many times greater than that of the corona.
The photosphere is essentially the receiving and shipping department of the star, receiving great quantities of energy from deeper levels, and radiating that energy into space in a never ending stream.
As we descend deeper into the body of the star, we find that the temperature and the pressure constantly increase. This means, of course, that as the gas becomes denser, the mean free path of the particles is becoming shorter, and their velocity is ever increasing. The frequency and violence with which the particles impact each other becomes almost impossible to describe or imagine.
As we approach the central core of the star, we find temperatures upward of twenty millions of degrees, and pressures in the billions of pounds per square inch.
Although the material is still technically a gas, because all of the particles have velocities greater than their escape velocity from each other, its density is now about ten times that of solid steel.
If we remember that in our atmosphere at 32°F and only 14.7 lbs. per square inch, the average particle has a velocity of 1760 feet per second, and undergoes five billion collisions per second, it may give us some faint comprehension of the number and violence of the collisions which take place between the particles deep within the body of a star.
We see that the shell of force which the planetary electrons create about the nucleus, is not sufficient to withstand impacts of this order, and the nucleus is soon stripped of its planetary electrons. When the bare nuclei impact other bare nuclei at this energy level we see that fusion of the two may, and frequently does take place.
The fusion of two nuclei results in the formation of a single nucleus which has a mass slightly smaller than that of the two parts from which it was created. The mass which is lost, appears as a tremendous burst of radiant energy, most of which subsequently is converted to heat. We note that this fusion or joining together of nuclear particles may occur in a number of ways, but in every case where the resultant nucleus has a mass smaller than the mass of the atom of silver, large quantities of heat will be released as a result of the combination.
We also observe that when the mass of the resultant nucleus is greater than the mass of an atom of silver, a large quantity of energy is absorbed rather than radiated, but this event occurs so infrequently that only an insignificant amount of energy is thus subtracted from the total. It is this energy of fusion which constantly replaces that which is being radiated into space from the surface of the star.
The process of fusion also gradually builds up heavier elements from the hydrogen building blocks which were the principal material of the new star. Consequently we would assume that the life expectancy of a given star is determined largely by the amount of hydrogen which it has available for fusion.
If the principal subject of our study were astronomy rather than the larger field of cosmology, we might devote several chapters to the examination of the inherent stabilities and instabilities which affect the process of fusion within a star. If we had a few billion years to spare, we might watch the infant as it changed slowly from a medium sized blue white star, to a somewhat smaller and denser white, until the ever increasing instabilities of the nuclear reactions within it finally overcame the stabilizing factors, and the entire star suddenly erupted in the tremendous blast of inconceivable energy which we call a nova.
After a few months we would see all of the material which had not been blasted irretrievably into space, slowly settle back into a very small and exceedingly dense core which we would describe as a red dwarf.
Since we have already spent many millions of years in this observational expedition, perhaps it is time for us to consider returning to earth. After all, there are many interesting things going on there too!
Before we leave, however, there is one more pattern of development which we should observe because it is, to our own egos at least, the most important of all.
In the star which we have been observing, the condensation took place in a symmetrical manner, with the result that a single sphere was formed. If we had been able to observe all of the stellar condensations simultaneously, we would have observed that in approximately one our of four or five cases, the condensation did not proceed symmetrically. The reason for this is found in the position and size of neighboring condensations. As in the case of the galactic nebula, the stellar gas cloud also begins to rotate as it condenses, and again a plane of spin is created. The particles outside this plane of spin tend to fall toward the plane as well as toward the center. As the rate of spin increases, the gas at some distance from the center, approaches orbital velocity with respect to that center. In simpler words, the centrifugal force tends to balance the gravitational pull of the central mass, and secondary centers of condensation are formed which are in orbit about the principal mass. These secondary condensations are usually very, small in proportion to the main mass, just as the main mass is small in proportion to the galaxy.
(In extreme cases, the condensing cloud may divide into two or more roughly equal parts, each of which becomes a separate star, but which then arc in rotation about a common center of gravity.
It is in the smaller condensations however, that we are particularly interested at this point.)
These smaller bodies which, in the case of our solar system, we have named 'planets,' will always be found to contain a much larger proportion of the heavier atoms, than will be found in the body of the star.
The reasons for this fact become obvious from our previous examination of atomic behavior. In the first place, we have seen that the lighter atom has a higher velocity at a given temperature, and so will reach escape velocity from a given body at a lower temperature. The condensations which result in planetary bodies, being comparatively small, do not reach the very high temperatures found in the stars, but they do reach temperatures sufficiently high to cause most of the lighter particles to reach escape velocity from the relatively small gravitational field.
Because the body is small, and the temperature low, such nuclear reactions as may occur under these circumstances do not furnish sufficient energy to replace that which is radiated, and the planet soon begins to cool.
A solid crust forms upon the surface, and the elements begin to combine in countless molecular patterns. When the surface has reached a sufficiently low temperature, the stage is set for the creation of the amino-acids which are generally conceded to be the starting point in the development of the organic forms to which we refer collectively as 'life'. The process is a delicate one, and only a small percentage of the planets may develop conditions suitable for this type of synthesis. It is also possible that the process may take place upon only a small percentage of those planets which do have suitable conditions. Yet, among the tens of billions of planets in a single galaxy, it is a virtual certainty, from a statistical standpoint, that synthesis will occur upon at least a few hundred, or perhaps a few thousand planets. (If we assume that the creation of life is directed by Divine Will, then the number might be much larger.) If we wished to follow the development of these first life forms through all of the stages of evolution required to produce a sentient being, we might have to wait for a period of time as long as that required for the formation of the galaxy, but eventually such a genus would appear. A race of beings capable of originating complex thought patterns, followed by equally complex actions.
Sooner or later, such a race would tire of its confinement upon a single planet, and would seek means to broaden the scope of its investigations, and of its movements.
Having achieved space travel, the race would proceed to radiate in all directions from its point of origin, investigating many planets, and perhaps colonizing some of those which were suitable for life but upon which life had not yet developed.
We must recall at this point, that it is the central spheroid of the galaxy which is formed first. It is in the central portion, that planets would first reach conditions suitable for life, and it is upon these planets that life would first achieve a high degree of development. Intelligent life might therefore be said to radiate from the center of a galaxy outward toward the periphery. A process which might take place over a period of several millions of years after the first race had achieved space travel.
It is with this thought, and in a very humble frame of mind that we begin our return journey to our tiny planet earth; located almost on the extreme outer edge of our own galaxy.