In his book, A Brief History of Time, Stephen Hawking's comment that, "Every mathematical equation used results in the loss of one-half the number of readers," is essentially true. His acceptance of the basic principles of general relativity and unified field theory is unfortunate, but in no way reflects upon the integrity of the man.

The concept of time as used in the referenced work depends upon the General Theory of Relativity as developed by Albert Einstein. The basic postulate of that theory was given by Galileo in the statement: The laws of physics take the same form with respect to all inertial reference frames. To this postulate Einstein added: The velocity of light is an absolute constant with respect to all observers under all conditions of motion.

There will be no mathematics used in this present work. Mathematics serves only as a tool to reveal the ultimate consequences of the basic postulates. It follows that no theory is any more valid than the postulates on which it is based.

The first question to be raised is that of the meaning of an inertial reference frame. Galileo was instrumental in the development of the laws of momentum and inertia. These may be stated: An object in motion under the action of no external force moves in a straight line at constant velocity. Also: An object at rest remains at rest in the absence of external forces.

Implied but not discussed is the assumption that the condition of rest and the condition of motion can be defined. Further, it is assumed that mass objects can move without affecting other mass objects or being affected by them. In this case, the magnitude of the mass in motion is immaterial and can be replaced by an abstract reference frame. Then we can visualize any number of disembodied reference frames moving in straight lines with various constant velocities and phasing through each other without the slightest effect of mutual disturbance.

The conclusion is that in the universe of reality, there exists no such thing as an inertial reference frame. It follows that at least one of the postulates of General Relativity is in error.

To this point there has appeared no discussion of rotational motion. The universe as we know it contains a virtual infinity of planetary systems. Since the hydrogen atom is simple enough to lend itself to mathematical analysis, we refer to this unit. The nucleus of the hydrogen atom is a single proton. There exists one electron in a planetary orbit.

It is not possible to imagine anyone taking the view that the proton orbits the electron. Since the proton is much heavier in mass than the electron, we assume the electron to be in orbit around the proton. Applying quantum theory to the possible orbital states, we can predict the spectral series to be expected. We find a consistent error which can be removed only by introducing a correction in which the proton and the electron rotate about a common center of mass.

If we can assume that the universe acts in a self-consistent manner, we now are in a position to correct Galileo's statement of the relativity principle. We find: The laws of physics take the same form with respect to all mass-centered systems.

The fundamental units of mechanics are mass, length, and time. Of the three, the nature of time is the most obscure. We can approach it only in its historical aspects. We observe that the earth rotates on its axis, and the days pass. The earth continues its orbit around the sun, and the years pass. Since these may notbe convenient intervals, we can divide the day into hours, the hour into minutes and seconds. Whatever we do, we find that our concept of time involves motion.

Now we invent a stopwatch which may be accurate to hundredths of a second. We apply this device to time a runner covering a given distance. We define his speed in terms of distance covered per unit time. In this case we have committed the unpardonable blunder of circularity. We have defined time on the basis of motion and then defined motion on the basis of time.

The final conclusion is that time can be given no other meaning than that of a comparison of events. We can say that the runner covered the given distance while the earth went through a fraction of a degree rotation. We can say that the distance was covered in the interval of a certain number of ticks of the stop watch. In any case we can only compare two events.

The difficulty is that a comparison implies a ratio. This ratio necessarily takes the form of a fraction having a numerator and a denominator. In any given system in the universe, any contraction in the denominator requires the same contraction to apply to the numerator. The only conclusion to be reached is that in any system in the universe, time is an invariant form. It follows that the time transformation of General Relativity does not exist.

There is a difficulty which appears. The time transformation has been shown to exist by an endless variety of applications of the atomic clock. Then we must examine the basis of measurement. We find that the action of the atomic clock depends on the internal frequency of the atom. When the clock is put into motion, the internal frequency is reduced. The period of the frequency is thereby increased. Since this is the basis of the time measurement, it is said that the passage of time is delayed.

Now we refer to that pesky quantum theory. Planck's Constant multiplied by frequency is a measure of energy. Then we find that the reduction in frequency in the case of the atomic clock is an indication of a reduced internal energy. In this case we are describing an energy conservation law. We state: The acceleration of an object under the action of a contact force is conservative. As long as no impact damage results, the increase in the energy of motion results in a decrease in internal energy in such a manner as to conserve the total original energy.

We have found a fundamental flaw in the structure of physics as presently interpreted. The assumption that the total energy of an object is increased by the application of an accelerating force is without foundation. The conclusion is confirmed by the application of Newton's third law. Since the forces of action and reaction are equal and opposite, integration through any finite distance requires that the work done on the accelerated object must be equal to that done by the object on the source.

Our present view of the universe is a combination of magic and insanity. The magic of the ancients was replaced by the insanity of relativity. We consider the nature of the black hole. As the hydrogen gas of space collects under the action of gravitational forces, the increase in mass results in an increase in the gravitational forces acting. The increase in internal pressure results in a fusion of hydrogen into helium as well as deuterium and tritium. The resulting partial collapse of the surface of the star increases the internal attractive forces to the point that further fusion and further collapse occurs. In the limit, it is possible to conjecture that the collapsing surface attains the velocity of light. Since time does not pass at this velocity, the collapsing surface can continue to fall forever without getting anyplace. Then we are forced to conclude that the faster a thing moves, the slower it is until it reaches the velocity of light. When this occurs, there is no motion at all. Whether this constitutes magic or insanity is a moot point.

For the best available description of the universe, Hawking invokes two (partial) theories. These are the general theory of relativity and quantum theory. It is certain that GTR is much in need of modification, but it is interesting to note that there exists a single four dimensional equation which incorporates all of the valid results to be derived from both theories. This material is covered in the book, "The Energy of Physical Creation," copyright 1985 in the name of the present author and published by the Carroll Research Institute, P.O. Box 3425, Columbia, SC, 29230.

In reference to the four dimensions of relativity, it is shown that the fourth dimension describes an internal circulation velocity associated with spin. The elementary particle is a toroid with a sink-source flow at right angles to the motion of spin. This is the only configuration which will insure stability. If there exists a steady state universe, it must have a toroidal configuration.

The fact of the existing red shift in the radiation from distant stars does not prove that the universe is expanding. In the calculation of the gravitational deflection of photons, the original assumption was that of a straight line path through a curved space. Such a concept fails to account for an energy loss which must accompany any such deflection. Random deflections tend to preserve a general straight line path, but every gravitational interaction results in an energy loss which is cumulative with distance. The mathematical treatment is to be found in the October 1992 issue of Apeiron published by C. Roy Keys, 4405 St. Dominique, Montreal, Quebec Canada H2W2B2. The title of the article is "Physical Reality and Cosmology" by the present author. The analysis also indicates a variable velocity of light in a gravitational field.

The concept that creation occurred in space is an error of the first magnitude. This requires a pre-existing space. In terms of mass, length, and time and the assumption of the prior existence of the space-time continuum, two-thirds of creation existed prior to creation. As opposed to magic or insanity, such a concept is pure idiocy.

If we examine the work of the Greek geometers such as Euclid, we observe that their geometric figures occupied a certain volume of space but had no association with it in any other way. The concept of a linear and infinite space was a convenience and a necessity in the sense that it made possible the development of a universal geometry. It was so convenient that when the natural philosophers got around to describing the motion of objects, these objects moved with respect to a homogeneous infinite space which stayed put as the objects moved through it. The concept of a Euclidean space permeates the entire history of physics.

In the work of Lorentz, the Euclidean space became the Luminiferous Ether which was uniform and infinite and acted as the carrier of light waves. Einstein didn't like the concept so he renamed it the space-time continuum. This formed an all-pervasive background so intense that even the presence of the stars could have only very minor effects. It seems a shame to destroy all of the confusion that has existed so long in the field of physics, but we are forced to replace the outmoded and erroneous relativity principle with a much simpler concept presently being termed the mass-space principle. The article describing the principle has been accepted for publication by the editor of Galilean Electrodynamics published in Boulder, Colorado. The concept requires that space exists only by virtue of the mass which determines it. The energy in the space of an object is tensional in nature and is equal to the internal energy of the object itself. It follows that there exists no background of space separate from the matter which establishes it.

Analogy often serves as a valid teaching aid. In the present instance there exists a certain analogy with the material atmosphere. The limitation of the Mach number in the atmosphere is well-known. At one time the experts were giving solemn assurances to the effect that no aircraft would ever exceed the velocity of sound in the atmosphere because the drag rise was so extreme as the velocity of sound was approached that the plane would be destroyed. Somehow that sounds very similar to the present concept that no material object will ever exceed the velocity of light in space.

The supposed limitation is nothing short of ridiculous. In the case of the atmosphere, the Mach number imposes no limitation at an elevation of a hundred miles because the energy density in the atmosphere is so insignificant that no Mach number can be defined. Since the energy content of the space of an object must be finite and equal to that of the object itself, calculation shows that the energy density of any given space falls off as the inverse fourth power of the radius vector in the case of a spherical mass object such as the earth. The concept of the existence of a homogeneous and infinite space is completely absurd and must be abandoned if any real knowledge of the universe is desired.

The above discussion is important to the future of space travel. Any velocity must be defined with respect to the space in which it occurs. If the space itself is too tenuous to be defined, it is a question whether or not the term velocity can be given meaning. Since each mass object carries its own space, it modifies the space through which it moves. The velocity of a small mass in the space of a dominant mass such as the earth can be defined, but, in the case of spaceship in the isolation of interstellar space, the ship itself is the dominant mass. Since the ship does not move with respect to itself, and the local space background has an energy density that approaches zero, the only limit on the velocity to be attained depends on the nature of the fuel to be used. Calculation shows that with respect to the external universe, velocities of the order of twenty million times the velocity of light are not impossible.

In terms of the postulates of general relativity, the first postulate was shown to be false on the basis of the necessity of referring the analysis to the mass-centered system. The second postulate has been shown to be false since the space-time continuum can have no existence in the real universe. In this case all relativity theory must be abandoned whether it was generated by Galileo, Einstein, or Joe Doakes from Podunk.

It is obvious that Einstein had not the slightest concept of the nature of the conservative field. His equation describing the energy of an object under the action of free fall in such a field is a case in point. In that equation, the assumption is that the total energy of the falling object is increased by the action of the field to increase the mass of the object in motion. In the case of an object under the action of contact, the work done by the applied force adds to the total energy of the moving object to increase its mass. Then we very glibly state: "The mass of an object increases with velocity" as if it had a very profound meaning. We have already found that the action of a contact force is conservative by Newton's third law. Further, the action of free fall must occur in such a manner that the potential energy of the object is reduced as the kinetic energy is increased to preserve the original total energy. There can be no mass increase with velocity in either case.

That there can be a mass increase in a particle accelerator is not a matter of dispute. In every such case it is found that a time-varying field is active. The implication is that the energy of the field is released to the particle to increase its mass. The mechanism is not that of free fall or contact. It is a tragedy that no one ever took the trouble to learn the basic principles of physics.

Newton used the concept of time as linear and unidirectional. This makes no sense since it implies a flow of some kind. The better view is that time and existence have the same meaning. Then we can only state that time is existence. It doesn't go anyplace or do anything. We may pass, but time abides. In this case it is not a physical entity and not subject to a velocity contraction or any other type of contraction. The concept of a beginning or an end has no meaning.

There is a distinction to be made between the nature of time and the measurement of the passage of time. The measurement is a matter of convenience and has no fundamental nature. In view of the definition of the day and the year, a cyclic nature is implied. Then we find all measurements of time depend upon a repetitive action of the nature of an oscillator. In terms of absolutes, one oscillator is no more fundamental than another.

As a case in point, the grandfather clock depends upon a pendulum motion under the action of gravity. If we change the length of the pendulum, the period of the oscillation is modified to correspond. In this case we make no assumption that the passage of time has been affected by the change. If we put the clock aboard a space shuttle orbiting the earth at a constant elevation, the zero net force occasioned by the balance of gravity and centrifugal force would stop the clock. It cannot be imagined that anyone would claim that time does not pass under these circumstances.

We have observed that a local velocity with respect to an external space cannot be defined in the case of an external space density of zero. If the conditions can be met, and the velocity of light with respect to a local space can be attained, in theory the internal frequency of an atomic clock would be zero. Also, the internal frequency of every atom in the human body would be zero. Under the circumstances, we should be glad that the condition is impossible. Since the space in the interior of the ship is determined by the mass of the ship, internal frequencies may be modified, but certainly not reduced to zero. Since the existence of the external universe is not affected, the slowing of the atomic clock, even if it occurs, has nothing to do with time.

Certain hazards associated with space travel begin to appear. Again we appeal to analogy. In the case of supersonic flight at sea level, shock wave formation in the atmosphere can be a hazard to the plane in flight. In the case of a space ship entering the dense space of a gravitational field in excess of the velocity of light, Cerenkov radiation may be sufficiently severe to destroy the ship. This effect is associated with the "warp factor" of Star Trek.

Another hazard of space travel is dependent on the rate of change of thrust. For a constant thrust level, a condition of equivalent to that of free fall must apply. In this case, passengers in the ship would experience no acceleration with respect to the ship itself. If the thrust level is changed too rapidly, inertia comes into play, and the ship accelerates with respect to the passengers. In the study of mechanics, the rate of change of acceleration is called jerk. Then we can give the warning, "Look out for that jerk in space." We wonder if there is a little humor involved.

In the case of the concept of time as presented here, the idea of a least time or the smallest time interval has no meaning. Neither does that of a least length or a least mass. All of the quantum numbers of physics can be developed from the general wave equation of space in conjunction with the matter wave equation, both of which are based on the concept of continuity of effects. The two equations in question can be developed from a more general potential equation in four dimensions.