Lectures on Physics, by Joseph M. Brown, 143 pages.  ©1999

ISBN 0-9626768-2-9 $19.95

Space

Space is what remains of the universe when everything is removed. Remove the buildings, the earth, the planets, the stars, yourself and everyone else, all the light, the elusive neutrinos physicists talk about, and the ether which pervades all of space and which transmits light. Everything in the universe is removed, then space is left.

Space has three independent directions. We can move in one direction while not moving in two other directions. In order to have three independent directions, each one must be perpendicular to the other two directions. For example, in the only space we know it is possible to move up and down while not moving forward and backward, as well as not moving left and right.

It is very difficult to imagine a universe which is not three-dimensional. Engineers frequently study two-dimensional bodies. Two-dimensional physical items actually extend in three independent directions, of course. However, when nothing varies in one direction--such as having a slab of constant thickness--we often consider this item as being two-dimensional. Similarly, a rope or string is often considered as having only one dimension.

Try to imagine an organism with only two dimensions. Consider an amoeba, which is an organism that can be obtained by scraping the inside of your mouth. If these scrapings are placed on a moist glass slide as used for viewing with a microscope, then the amoeba approximates a two-dimensional organism. The primary motion of an amoeba is in two directions. A funny thought just occurred--the primary motion of humans also is two-dimensional. Their principal motion is very close to the surface of the earth. Returning to an amoeba, it would never describe another amoeba as a tall amoeba, just wide or long (if they could distinguish front, back, and sides). I can hear the girl amoeba say it now, "That girl is just too long!"

Try to think of four dimensions--up and down, back and forth, side to side, fourth dimension and fourth dimension. The fourth dimension is incomprehensible to our senses of the actual universe. Mathematicians have geometries of one, two, three, four, on to n dimensions. As each dimension is added, they retain all the axioms, theorems, and other structures of the geometry with one less dimension. However, there is no physical interpretation of space beyond three dimensions.

Some people think of four dimensional space-time. One of the simplest of these concepts is to have three space dimensions represented by length coordinates and a separate time coordinate which can refer to the contents in space at one time, then after a time interval passes while the spatial coordinates change (i.e., while motion occurs); then the new spatial coordinates of things in the universe can be given. However, time in this system is not a distance measure, and is independent of the space coordinates.

Try though we may, there does not seem to be any way to physically interpret a fourth independent direction in space. Space simply is three-dimensional. I try to think of a fourth independent direction which somehow is metaphysical. Again, I cannot obtain any meaningful concepts.

We can ask why the universe is three-dimensional. Why was it not constructed six-dimensional? I can ask, but I feel there is no answer.

When developing a theory of physics, we just "assume" or, better, "postulate" that a three-dimensional space exists. We do this by using "space" as a postulated word which can not be defined in simpler terms.

How far does space extend? Certainly a great distance--as far as one can see. We assume it extends indefinitely in all directions. For lack of a better answer, we assume a space of infinite extent.

Where did space come from? What was in the universe before space was here? For lack of a better answer, we just say space was always here and always will be here--and it has always been three-dimensional.

Geometry

Let us begin trying to develop physics with what must be the simplest concept for mass. Let us start with a spherical ball of mass. Further, let us assume everything in the universe consists only of these spherical balls. We assume the particles are all exactly alike, and that there is a lot of space between them, in most cases.

First we had space. Now we have something in space. We have an infinite space with an unlimited number of basic particles.

We will start with these identical, spherical balls and develop geometry. Take a single basic particle and "fix" its center. Take a second particle and constrain it only by requiring that it remain in contact with the first. This second particle can move in two independent directions relative to the first particle. It can move so that the contact point moves tangentially in one direction, and then can move tangentially perpendicular to this first motion. We say that the second particle has two degrees of freedom.

Take a third basic particle and require it to remain in contact with the other two particles. Relative to the first two particles, this third particle can move so that the two contact points trace out circles, and the velocities are always parallel to each other (see Figure 1). We thus note that if the first two particles are fixed, the third particle can move only in one direction relative to the first two. Incidentally, we exclude motion of rotation about the centers since we want to assume the balls are perfectly "slick" so that we can not sense rotation about their own centers.

Now, let us fix the three basic particles, and add a fourth one which remains in contact with the original three particles. There are exactly two places the fourth particle can be placed--either

Figure 1. Three Basic Particles

Figure 2. Four Contacting Particles

in front or in behind the three particles shown in Figure 2. The fourth particle is shown by the dotted lines. This fourth particle contacts the first three particles in three places, and cannot move relative to the other three--it has zero degrees of freedom. This fourth particle can not move (with respect to the other particles) as long as the contacts are maintained and as long as we neglect the three rotational degrees of freedom each particle has.

In order to better understand the configuration resulting when the particles are placed together to form a rigid structure and are placed for closest packing, consider several three-ball assemblages stacked as shown in Figure 3. The three dashed lines pass through the centers of all the balls. Assume that we add an unlimited quantity of three-ball assemblages on each end of the structure shown in Figure 3. Now, let the diameter of each ball be halved while still retaining all the contacts. Continually reduce the diameters by one-half--all at the same rate. In the limit for any increment of length there will be an unlimited number of center points on the lines and, in the limit, the three lines will become one line. In the limit the assemblage of center points comprise a line and, in this case, the line is straight. The objective of this discussion is to emphasize that lines consist of an ordered set of points. Every segment of the line, no matter how short, has an infinite set of points. The points are ordered; each one has a predecessor and a successor. Further, and extremely significant, the development of the line shows what is meant by the line being straight.

Let us develop the concept of a plane. Take n assemblages, like those in Figure 3, of unlimited extent in both directions and place them as shown in Figure 4. The assemblages are packed so that there are no degrees of freedom for any ball. We place these assemblages on the

Figure 3. Packing Geometry for a Line of 3-Ball Assemblages

Figure 4. Packaging Geometry for a Plane of "Line Assemblages"

right and left side, extending indefinitely in both directions. Next we half the diameter of each ball, still retaining the same point of contact. We repeat this process indefinitely. In the limit of this process the center of the balls form a plane. The plane is "flat" as a result of the formation process. Further, for any region of the plane there is an unlimited quantity of points. Furthermore, for any line segment consisting of points of the plane and extending from one boundary to another boundary of any region of area, there is an unlimited quantity of points.

If we take these line assemblages and begin adding them to an initial segment so that the cross section, as seen looking along the dashed lines of Figure 4, grows uniformly in all directions, we can then fill all of space with the balls. Now, still retaining contacts so that no ball has a degree of freedom, let us reduce each ball's diameter by a factor of 2. We continue this process indefinitely; then the ball centers will form a solid. However, the volume still is unlimited in extent in all directions. Any volume of space, no matter how small, will contain an unlimited quantity of points. Also, any line consisting of points from any volume and extending from one boundary to the other will contain an unlimited quantity of points.

Geometry can be constructed from any two of the primitive concepts of point, line, plane, and solid. We argue here that these are basic physical concepts, and the remaining development of geometry is logic and mathematics.

Mathematicians often consider points and lines, for example, simply as undefined concepts, and then develop geometry. However, they certainly are aware of their physical interpretation. In these lectures, the physical interpretation and use of these concepts is of tantamount importance. With this background on the foundation of geometry, we proceed to the development of physics.

Reference Frames

Consider one basic particle which is isolated from all other particles. Take the center of this particles as the origin of a three-dimensional x, y, z right-angle coordinate system, i.e., fix the origin to the center of the particle, see Figure 5. The coordinate system can rotate independently about each one of the three coordinate axes. Thus, the system has three degrees of freedom.

Assume we can find another basic particle which is not moving with respect to the first basic particle. Let the x-axis of this coordinate system pass through the center of this particle, see Figure 6. Before fixing the x-axis to this particle, the x-axis had two independent degrees of freedom--it could move, for example, up and down and clockwise and counterclockwise. Fixing the x-axis to this second particle thus eliminates two degrees of freedom for the coordinate axis system.

Assume we can find a third basic particle which is not moving with respect to the first two basic particles, and whose center lies in the y-z plane. Let us rotate the coordinate system about the x-axis until the y-axis passes through the center of this third particle, see Figure 7. This third fixed particle fixes the coordinate system in space. Such a coordinate system is called a reference frame. Further, this frame is an inertial frame. This frame is tied to three particles of mass and the particles are isolated (i.e., no forces are acting upon them); thus, the reference frame is neither rotating nor accelerating linearly in any direction, which means that it is an inertial frame.

Any reference frame which is translating (i.e., not rotating) at a constant velocity relative to another inertial frame itself is an inertial reference frame.

Figure 5. Coordinate System Fixed to One Basic Particle

Figure 6. Coordinate System Fixed to Two Basic Particles.

Figure 7. Coordinate System Fixed to Three Basic Particles

How do we detect an inertial reference frame? First of all, assume we observe a hunk of mass. Somehow we are able to determine what forces are acting upon the mass. Let us say we deduce that the net force on the body of mass is zero. Now we select a frame such that we observe that the mass is moving at a constant velocity. This frame could be an inertial frame. If the x-axis of the reference system passes through the center of the mass, and if we note that the body is not rotating with respect to this reference system, then we know the frame is an inertial frame--unless the frame and body are rotating about the x-axis. If we locate another body of mass which has no forces acting upon it and whose center of mass is not on the x-axis, and if this body is not accelerating, then we know our frame is an inertial frame. This foregoing discussion should indicate the practical difficulties in determining an inertial reference frame.

There is something mysterious about an inertial frame. Say there was nothing in space at all, then we placed an orthogonal x-y-z axes system in space. If it had no mass, it could be linearly accelerating and, even if it had mass, it could be rotating. Now, if we were fixed to the frame and saw a free particle of mass, we could suddenly discover that our frame is rotating. We might say that the particle has peculiar behavior or that our reference frame is peculiar. However, viewing things from our complex universe, we are so familiar with the law of inertia that it does not seem strange. Non-inertial reference systems are used, but infrequently.

Locations and Displacements

The location of a basic particle can be described only relative to another basic particle. For example, we can say that two basic particles are touching each other. Also, we can say that two basic particles are separated by a distance (along a straight line) of n basic particle diameters.

What we do, in practice, is to select a coordinate system, select a "metric" (i.e., a unit of

length), and then locate the center of a basic particle by listing its x, y, and z coordinates (see Figure 8). The center of the basic particle, point P, is located at the intersection of the three planes parallel to xy, yz, and xz planes. For example, the y coordinate of P is given by the perpendicular distance from the xz plane to the plane through point P which is parallel to the xz plane. Thus, values of x, y, and z locate the point P. The distances x, y, and z can be given as so many basic particle diameters or as a constant factor times the number of particle diameters.

The reference frame x y z is taken to be an inertial reference frame. Let the particle move from position P₁ to position P₂ (see Figure 9). The initial location of the particle is specified by the coordinates , and the final location by the coordinates We show the coordinates also by the notations and which means that the locations are functions of the coordinates. For a general location of the basic particle, we use the notation

(see Figure 9).

The amount of displacement of the particle as it moves from P₁ to P₂ is measured by the component of displacement parallel to x, i.e.,.x; the component parallel to y, i.e.. y; and the component parallel to z, i.e., z. The total displacement from P₁ to P₂ is

Figure 9. Locations and Displacements

Figure 10. Displacement of P

The value of displacement given by the square root of the sum of the squares of the components equals the actual path length from P₁ to P₂ only if a straight line path were followed. Any other path would be longer.

Relative Displacements, Time, and Velocity

When a displacement occurs, time passes. A displacement is the very essence of time. If no displacements ever occurred in the universe, then the concept of time would be meaningless.

When we speak of velocity, we are only comparing displacements which occur simultaneously--or during the same passage of time. We think of distance as an absolute quantity, but when we state an amount of distance, it is always a comparison of one distance to another. For example, we can say a distance is a certain number of basic particle diameters--or, as is quite often done, we say a distance is a certain number of meters long.

Let us give some concrete examples of relative displacements--or of displacement of something while something else displaced a certain amount. Consider the two basic particles shown in Figure 10. Basic particle A moved a distance of eight particle diameters. Simultaneously, basic particle B moved four particle diameters. When we speak of a velocity, we must always have a reference displacement. If we use as the reference the displacement of B and name that displacement a "yearsec" and, noting that particle A moved eight basic particle diameters, we say that the velocity of Particle A is eight basic particle diameters per "yearsec." What we really mean is that particle A moved eight diameters while the reference particle moved four diameters. Incidentally, if eight basic particles had a length of eight meters, then we would say the velocity of A is eight meters/yearsec.

Let us say particle A moved 80 basic particle diameters while⁽¹⁾ particle B moved back and forth from the initial position to the final position ten times (i.e., five round trips). We then

Figure 11. Displacements of Two Particles

compute the velocity of A as 80 basic particle diameters divided by ten reference displacements or 80/10 = 8 basic particle diameters per yearsec.

The displacements usually used for reference almost always are cyclical processes. The time unit (or reference displacement) of a year is the displacement of the earth making one complete revolution about the sun. The time unit of a second is derived from the earth rotating about its axis one complete revolution. Thus the second is one part in 24 hours x 60 minutes per hour x 60 seconds per minute--or one part in 24 x 60 x 60 = 86,400 of the earth's revolution.

If a displacement occurs, we know that time passed. Displacement and time are inseparably connected. A velocity of something is simply the displacement it undergoes while a reference displacement occurs. Time is a displacement. For example, a second is the rotational displacement of the earth by 1/86,400th of a revolution about its axis.

Mass and Collisions

All of the basic particles are exactly alike. This means that the particles have exactly the same "mass." What do we mean by "mass?" Consider two particles viewed from an inertial reference frame. Assume they have paths which are colinear, as shown in Figure 11. Since the particles' paths are colinear and the velocities are directed as shown, the particles will experience a head-on collision.

Let the velocities be equal and opposite, i.e., The collision mechanism is such that:

1. The interaction time is zero

2. The velocities are exactly reversed during the collision

The first assumption means that the particles are perfectly hard. The second assumption means that the particles are perfectly elastic, and that their "mass" is exactly the same. If the velocities after the collision were equal but smaller than the pre-impact velocities, then the particles would be inelastic--or partially plastic. If the particles were perfectly elastic and particle A rebounded at a velocity less than particle B, then we would know that particle A was more massive than particle B.

For a head-on collision with equal pre-impact velocities, if the post impact velocities are equal to each other, then the particle masses are the same.

The concept of mass is very elusive in a universe made only of particles exactly alike. If we compared the observations made at one time, and then suddenly made every one of the particles exactly a hundred times more massive, we would not be able to detect the difference. We really never detect (or measure) forces--we detect displacements, velocities, and differences in velocities (i.e., accelerations). This seems incredible!! It would appear that the amount of mass a basic particle has is of no significance-- as long as they interact with each other through the collision mechanism we discussed above (and as long as all particles have the same mass). Mass itself is simply the number of particles times a scaling factor!

We assume that basic particles are never created, nor ever destroyed. This assumption is the law of the conservation of mass.

The law of the conservation of mass most often, in physical science, is used in the following manner. We take a volume of space and count the number of basic particles in the space at a given time. If the center is inside the volume, we count the particle; if outside, we omit it.. Incidentally, our actual procedures for counting particles clearly is not in the detail just stated. However, this is the way we count in principle. We wait an increment of time. During the waiting time we count the particles going in and count the particles going out. We "predict" the number of particles at the end of the time interval by stating the number is the beginning number plus the number which entered less the number which exited. We count those inside at the end of the time period, and it will agree with the predicted number (unless we miscounted), and that is the result of the law of the conservation of mass.

We need to generalize the collision process from the equal-opposite velocity head-on collision. When viewing a head-on collision from an inertial frame, if the velocities are unequal we can view the collision from a frame which is translating with respect to the initial frame, and for which the velocities are equal and opposite. This is called the center of mass frame. We know the collision mechanism for the equal-opposite head-on impact. We then transform back to the original frame.

Consider the head-on collision shown in Figure 11 in which As a result of the collision, the particles simply exchange velocities. It is almost as if the "mass" or "insides" of the one particle went through to the other particle. However, when we consider oblique impacts, it will be clear that the mass does not transfer.

Figure 12 shows the general impact and we have previously derived what happens to the normal component. Thus, the y and z components and are exchanged, and the normal components and just exchange particles.

What we have learned is that the amount of mass is simply the number of basic particles usually times a scaling factor. When collisions occur, the tangential components are unchanged, and the normal components are interchanged.

Figure 13. General Head-On Collision

Figure 14. General Case of Impact

Linear Momentum

Consider a system of one of more particles. If the particles do not collide, the algebraic sum of the components of the velocities do not change. If any two particles do collide, the algebraic sum of the components of the velocities also do not change since part of the components simply change particles. Thus, the sums of the components never change. Furthermore, the sum of the components times the same scalar multipler times each component will remain unchanged. A scalar factor times a component of velocity is the mass (in some unit) times the velocity. We call the mass times the velocity the linear momentum.

Our first great conservation law is that mass is conserved. We now come to our second great conservation law: Each of the three components of linear momentum for any given system of isolated basic particles never changes. Since, in general, there are three components of linear momentum, this conservation law gives us three independent scalar equations which must always be satisfied.

If we let n be the number of particles in a system and m be the mass of each (i.e., the mass scaling factor), then the total mass of the system is The component of momentum in the x-direction is

where v_mx is the average of the velocity components in the x-direction. Thus we have the result that the total particle mass times the average component of velocity in the x-direction is conserved. The same is true for the y- and z-directions. The mass times the average component of velocity is the component of momentum in that direction. Now, for an isolated system of particles we see that the total momentum component in each direction is constant. Using vector notation which define the total linear momentum for a system of particles. Also, is the mean velocity vector. Each component and the total vectors remain constant with time if the particles are isolated.

Energy

The energy of a basic particle is simply the mass of the particle times the square of its velocity. The energy of particles which do not collide is invariant since their velocities do not change. Consider the collision of two particles such as shown in Figure 10. The energy of the two particles before collision is The energy after collision is It can be seen that the above two sums are equal since the second sum differs from the first sum only by the order of listing of the x-component terms. Thus the energy of a system of isolated particles is invariant with time. This is our third great conservation law: The energy of an isolated system of basic particles does not vary with time.

We note that and (momentum and energy) are conserved during a collision, and we find these conservation laws useful in predicting the future behavior of particles. The collision mechanism also shows that , where i is a coordinate direction and where n > 2 also is conserved during a collision. Why, for example, does not the conservation of lead to a useful conservation law? Finally, we note that is a measure of transport and is a measure of pressure. We will discuss these questions later.

Acceleration and Force

Consider a single basic particle being impacted repeatedly head-on by other particles (see Figure 13). Let particle "P" be the particle which is repeatedly impacted, and let "O" represent all the outside particles which are going to impact "P." Let the outside particle velocities always be v larger than the impacted particle velocity. After each impact will be v larger. Further, let the rate of impact be constant, i.e., let the number of impacts per second be constant. The velocity of "P" will now vary as shown in Figure 14. We note that the velocity of P increases in steps, and the average slope is If we were to decrease the increment of velocity by the same factor and continue this indefinitely, we would have a straight line whose slope is

  In the limiting case this quantity is the acceleration "a" of the particle P. thus If we multiply the time rate of change of velocity by the mass being accelerated, then we say that is the force being applied to the mass. Thus .  We also can write as the change in momentum of the accelerated particle, then is the average time rate of change of momentum. In the limit

Figure 15. Particle Impacted by Chasing Particle

Figure 16. Velocity of "P" versus Time Acceleration and Force

In this case we can have mass changes as well as velocity changes as long as the product of mass and velocity is used. Thus, we can say that the force experienced by a particle is the mass times the acceleration on the time-ratio of change of momentum it experiences.

An interesting and useful fact of the above force-acceleration analysis is that the system of impacting particles, as a whole, experiences the same force, but is directed in the opposite sense, and its time rate of change of momentum is the same, but directed in the opposite sense.

For the particle P we say that the outside environment applied a force, and the particle responded by accelerating in the direction of the force--or, its time rate of change of momentum was equal to the force applied. We also can say that the time rate of change of momentum of the system of particles is equal to the force applied to the system by the particle "P." The acceleration of the center of mass of the system of the particles times the total mass considered to compute the center of mass also is equal to the force applied by particle "P."

Environment for a System of Particles

Consider a system of n basic particles where n can be anything from one particle to any finite number. What we will do in this section is develop a description of the types of forces and moments which particles external to the system can develop. Then we will describe the response of the system of particles to these external factors.

First, let us review a system consisting of one particle. The most common way of dealing with a single particle is to consider that the external universe (or environment) applies a force to the particle, and it accelerates. The force is equal to the particle's mass times its acceleration. The particle itself also can be considered the environment, and the particles involved in applying the force in the former case can be considered as the system of particles being acted upon by the single particle. The center of mass, then, of the system of particles will be accelerated in the opposite direction of the single particle, and the force acting upon the system would be exactly equal and opposite that for the opposite case, and the system mass times acceleration would be exactly equal and opposite to that of the single particle.

The complementary nature of the giver and receiver can better be illustrated by using time rate of change of momentum. Recall that a force is developed by considering repeated applications of momentum and, quite simply, force is defined as the time rate of momentum imparted. Further, mass times acceleration can be written as --which itself is the time rate of change of momentum. Thus, all that "force is mass times acceleration" states is that "time rate of change of momentum applied is the time rate of change of momentum response."

Let us take a moment to review "center of mass." If two basic particles are a distance one meter apart, their mass is equal to the mass of two particles and the center of mass is half way between them--or one-half meter distant from either particle. If n equal real matter particles were attached by some weightless structure and were hung from a string above the earth's surface, then the structure would swing so that the string would pass through the center of mass.

The line of action of a force is similar to the center of mass concept. Assume that we have a system of many basic particles, and many other basic particles are colliding repeatedly with our system of particles. At any one time these external collisions make up a composite force with a single line of action. This is the force acting upon the system of particles.

If the composite force passes through the center of mass of our system of particles, then its center of mass will respond as given by i.e., the applied force equals the mass of our system of particles times the acceleration of its center of mass.

If the force does not pass through the mass center, then the center of mass will still have its acceleration given by just as before. However, our system of particles, as a whole, will begin to accelerate angularly about the center of mass. The amount of angular acceleration depends upon the magnitude of the force times the perpendicular distance from the force to the center of mass. The angular acceleration also depends upon the number of particles and their individual locations.

Following we will illustrate angular acceleration with the simple case where all the forces and motions are parallel to a plane, i.e., for planar motion.

We define the "moment of momentum," which is also called the "angular momentum" for an axis perpendicular to the plane as the product of the momentum of a particle times the perpendicular distance from the particle path to the axis (see Figure 15). For this case the angular momentum is .

Angular momentum is always conserved, just as in linear momentum. We prove angular momentum is conserved for the simple case shown in Figure 16. The angular momentum of the pair of particles before collision is and, after collision, is , where we write the terms for the particles from left to right. Clearly these two sums are the same, and angular momentum is conserved for this simple case. It is easy to generalize for any type of situation. Thus, we have a fourth great conservation law: The angular momentum of a system of isolated basic particles is always the same.

Let us now illustrate the effect of the environment on a simple system of particles which is accelerated linearly and angularly. Figure 17 shows two basic particles which are (2a) apart, shows the center of mass (cm), the particle velocities, the geometry, and the forces acting. The total force acting on the two particles is The acceleration of the center of mass is or Of course, the acceleration of particle A

will be four times the rate of particle B , but the average acceleration of both will be

A force is the time rate of change of momentum applied to a mass. A torque is the time rate of change of angular momentum applied. In the example of Figure 17, the torque about "0" is the product of the force times the perpendicular distance to point "0." Thus

Figure 17. Angular Momentum

Figure 18. Angular Momentum Conservation

Figure 19. Angular Acceleration

The moment of momentum (or angular momentum) about "0" is and the time rate of change of momentum is .  Using gives . Thus, we see that which shows that the time rate of change of angular momentum is the torque applied.

The torque applied to a system of particles can be represented by a vector perpendicular to the plane defined by the force and the line mutually perpendicular to the force and the axis, and with a sense defined by the direction using the "right hand rule." With the right hand rule, if you wrap your fingers around the axis and the force twists in the direction of your fingers, then the torque vector will point in the direction of your thumb. Thus, in general, a torque will have three components, and the angular momentum will have three components, Thus, three scalar conservation equations result from the law of conservation of angular momentum.

Let us summarize what we have presented. The law of conservation of linear momentum for a system of particles leads quite simply to Newton's law of motion where the underline denotes a vector so that and are vectors. Thus, this gives three scalar equations which must be satisfied in an analysis to predict the behavior of particles. Next, the law of the conservation of angular momentum gives a vector equation relating torque and the time rate of change of angular momentum which, in general, will give three scalar equations of the form for the three different axes.

Finally, the conservation of mass and the conservation of energy leads to two more equations. Thus, there are eight equations in all which must be satisfied in the analysis to predict the behavior of a system of basic particles.

In the analysis of a system of particles, we do not necessarily define the individual forces and trace all of the individual particles. For example, there are many different configurations of particles which will satisfy all the conservation laws and have the same total mass, total energy, total linear momentum, and total angular momentum. Thus we need at least one more relation. One procedure is to use a simple equation of state. We will discuss this later.

Before leaving this section, let us give a simple example of the energy balance when applying a force to a system of particles. For simplicity, apply a force through the center of mass. Work is defined as force times distance. Thus, the differential work is Fds, but we have 1. "While" means "during the time."

Thus or the work is the work done as the mass center moves from position 1 to position 2.

The quantity is the kinetic energy which is half the (translational) energy of the system of particles. The particles also could have "internal energy," which is the energy of motion relative to the center of mass.

Systems with Varying Quantities of Particles

Consider the case now where particles are added to a system of particles. Let s be the system of particles with mass m at time t. Let its velocity be v so that its momentum is mv (see Figure 20). Let be the mass and let be the initial velocity of the added particles. The velocity of the system with the added particles is . Let F be the force required to push the particles in. The momentum balance equation is Solving for the impulse gives

or, omitting , we obtain

Thus, going to the limit where u is the relative velocity. If the mass added is moving at the same velocity as the system of particles, then the force required is zero; neither velocity changes, but the energy changes. The energy change is of course.

Figure 20. Addition of Particles to a System

The Particle Continuum

We have already used the concept of a continuum of force brought about by a large number of repeated collisions (see Figure 16). We also want to use such continuum concepts throughout the remainder of these lectures. We cannot analyze, or even measure or observe, individual particle effects since there are so many particles. We can measure forces, pressures, densities, and motions of large numbers of the basic particles.

Consider first mass density. We select a volume and let n be the number of particles in the volume. Now, if we select a volume which has very few particles, then this same amount of volume at different locations, or at different times, may have great variations in density, i.e., particle number density or mass density . However, for our purposes we are always measuring the effect of extremely large quantities of particles. We assume our detection schemes require billions of particles. Thus we can take density to be a continuum-type parameter--just as water is considered as a continuous fluid.

The concept of pressure is obtained from the repeated impacts giving a total time rate of change of momentum applied to a unit area. Temperature is a constant times the average kinetic energy of the basic particles.

When basic particles are in the equilibrium state, they have an average velocity which depends upon the temperature. We denote this average velocity by The particle velocities are distributed around this mean value to very few at very low velocities; many have velocities in the region of , and very few at very high velocities.

The mean velocity of n particles is simply the absolute value of the velocity of each particle added, then divided by n. The flow rate, or transport, of particles depends upon the mean speed. There also is an important velocity average obtained by squaring the velocity of each particle, adding the squares, taking the square root of the sum, then dividing that result by the number of particles. This "average" is called the root-mean-square, or rms, average. We denote this average by Forces and pressures depend upon the rms velocity. In the homogeneous equilibrium state of basic particles, the rms speed is related to the mean speed by

Consider a given location in space. Letting be the fraction of particles per unit value of velocity between  v  and  we can then show how the number of particles vary with velocity. Now will be the fraction of particles between v and v + dv. Further, which means that all particles are included. The function is given in terms of velocity and temperature T by  where k is the Boltzmann constant. Further we have Substituting into the equation for gives where .   Figure 21 shows a plot of versus for This is the Maxwell-Boltzmann distribution of speeds.

Figure 21. Velocity Distribution Function

The Search for an Inhomogeneous State

Atoms, molecules, and even macroscopic-sized particles which are moving at high velocities relative to each other and which do not have forces of attraction, will disperse and tend to fill their containers. This phenomenon is so common that if it does not occur we always look for some hidden forces which are holding the particles together.

If particles are elastic, have no attractive potentials, have high relative velocities, are spherical,⁽¹⁾ and are confined in an elastic enclosure, their configuration will change as required to approximate the "homogeneous" configuration. A homogeneous gas is one in which the mass density and pressure are uniform throughout the container. Further, the velocity distribution is Maxwell-Boltzmann.

For over a century scientists have searched for an inhomogeneous state, and also have searched to prove the homogeneous state is the only possible "force-less" steady state--all to no avail.

From the big picture of the universe as a whole, we see innumerable examples of organized entities moving toward uniformity. We also see small things, such as molecules, getting organized to form biological entities which are due to electromagnetic attractive forces. We see large scale organizing processes, such as those involved in producing stars, and these phenomena are due to gravitational attractive forces. Finally, on the human-size scale, we see hurricanes, tornadoes, and vortex tubes which indicate there may be ways for particles without attractive forces to tend toward organization.

On the microscopic scale and on the cosmologic scale, the organizing processes almost universally are considered not to be thermodynamic processes. Almost no one would think that electric charge or gravitation could be produced by the motion of kinetic particles having no inherent attractive forces. We will present arguments which indicate that electromagnetism and gravitation are produced by kinetic particles.

Person-sized phenomena such as hurricanes and tornadoes have not been modeled theoretically so that for given conditions the effect can be predicted. We believe there may be some self-organizing phenomena taking place in these weather storms which have not been identified.

A vortex tube is a hollow cylinder which can be closed on one end and, at that end, gas is pushed in tangentially as shown in Figure 22. As the gas enters and rotates in the tube, and advances along the longitudinal axis, the gas molecules separate by energy so that higher speed (hotter) particles move to the outer radius of the tube and lower speed (cooler) particles move toward the center. Large temperate gradients can be developed -- 100C in a 5 cm diameter tube 20 cm long. Scientists have not been able to develop a predictive analytical model for this type flow.

Everyone knows that forces of attraction occur in the universe. Scientists almost universally do not know what produces attractive forces. We believe there is a good chance that the known forces are produced by kinetic particles which interact only by repulsion (when they collide).

Figure 22. Vortex Tube

The fundamental requirement and starting point for the development of these attractive forces requires the existence of a stable, inhomogeneous assembly of the basic particles which we have been considering. This inhomogeneous assembly consists of a torroidal (sink-source) flow coupled with rotation, and which translates with respect to the background ether. We will explain what we know about such a flow pattern in the following sections.

Flow Down a Straight Channel

The inhomogeneous state we are trying to evaluate completely condenses the gas of ether particles. In order to achieve complete condensation, the particles must flow into a small region and turn so that they can come back into this region. The first step in the process is to flow in a straight converging stream tube.

We can visualize this flow into a converging straight tube as shown by Figure 24. Let us assume that the large tank which supplies the gas is maintained at a constant pressure . In the left region let the pressure initially also be . Now, as the pressure in the left region begins reducing, i.e., as becomes less than , then gas will flow. The rate of flow will continue decreasing until the pressure reaches a value , which is approzimately . . If the pressure is reduced below , the flow rate will not increase--even if becomes zero.

The maximum flow velocity reaches a value approximately equal to 0.8 times the rms speed of the gas in the supply tank, i.e., the speed of sound.

If a diverging tube is placed at the exit of the converging channel and the pressure at its exit is maintained at zero, then the flow velocity will increase along the diverging channel but the mass flow rate will not increase.

The analysis for the converging as well as the converging-diverging channel flow is straightforward, and the results are well known.

Now, if we take two concentric spheres--one inside the other--and place conical (straight) stream tubes with their centers passing through the centers of the two spheres, we can fill the volume between the spheres with these sections (see Figure 25).

Figure 24. Converging Tube Flow

Figure 25. Concentric Spheres Filled with Conical Streamtubes

Let us say these spheres are in the atmosphere. Let be the radius of the center sphere and

be the radius of the inner sphere. Now, without specifying how we will do this, assume we have a method of removing air from the inner sphere at the maximum rate it can come down the channels. This will require keeping the pressure in the inner sphere below , or approximately 0.6 the atmospheric pressure. A steady flow into the outer sphere will result.

One method of removing particles from the center of the sphere and still approximate the spherical inflow is to insert a pipe into the center of the sphere. Let this pipe extend a great distance from this sphere, then maintain a low pressure at the exit end (see Figure 26).

It should be clear now that the plates making up the sides of the converging channels which define the stream tubes are superfluous. If these are removed, and since the two spheres are only mathematical entities, it is clear all that is necessary is to sustain the pressure inside which will maintain the prescribed mass flow rate through the mathematical sphere with radius . The flow we have described is the flow of gas into a sink, and is well documented, both theoretically and experimentally.

Figure 26. Pipe for Removing Gas from Sphere

Flow Down a Curved Channel

When the flow down the straight conical channel reaches the critical speed, approximately

, then, within the present state of the art, it would be anticipated that there would be no way to continue compressing the gas. On the other hand, we feel that it may be possible to obtain greater compression. The basic element of achieving greater compression is to let the gas take a rotary configuration which uses inertia to separate the particles according to their speeds.

The only substantial experiments which indicate that rotating a gas will separate the molecules by their velocities are the experiments with vortex tubes, which we have previously described. We assume that the average speed of a molecule in a rotating gas will vary linearly with distance from the center of curvature. The results of the vortex experiments show a non-zero mean speed at the center of curvature which, of course, depends only upon the temperature, and then a linear variation of mean speed with radius of curvature of the flow.

Figure 27 shows a simplification of the particle motion for rotary flow. The flow velocity varies from 0 to 4, and is linear with the radius. The gas is assumed to be represented by two particles at each value of the radius. The thermal velocity is the average of the two speeds which at the center is 4, at the outside is 12, and it varies linearly with radius. Also, the individual particle velocities vary linearly with radius.

Clearly, at any radius there will be a spectrum of velocities, but because the centrifugal forces varies linearly with radius, the average of the individual particle velocities will also vary linearly with radius. However, the density also can vary with radius, and it could vary linearly with radius, which could mitigate against the individual particle velocities varying linearly with

Figure 27. Particle Velocity Variation with Radius

radius. We thus do not have an ironclad argument to prove that the thermal velocity varies linearly with radius. We then return to our previously presented interpretation of the results from the vortex tube experiments to justify our assumption.

With the assumption that velocity varies linearly with radius and, thus, that temperature varies with the square of the radius, we can let the flow from the straight conical streamtube enter a curved streamtube. Due to the curvature, the higher speed particles move to the outer radius and lower speed ones move to the center. When the equations governing this flow are written and solved, they show that the area of the channel can be reduced and still maintain the mass flow rate down to where the straight converging channel previously had exited.

Let us return now to the big picture of what we are trying to do. We started with the straight cones, considered the flow into these, and generalized the flow to a complete sphere. We then argued that after the mass flow rate rached its maximum value independent of how low the exit pressure was reduced, the gas from a streamtube could be condensed further. This required a streamtube that provided the gas with a curved path. However, in order for the flow into a complete sphere to maintain the maximum flow rate it had achieved when the flow down to a particular radius was maximized by some imaginary or unidentified process of removing the particles, we need now to connect up some curved streamtubes which will keep the particles moving and keep condensing the gas. What we would like to do is completely condense the gas and send it out of the spherical surface in a single small, straight, cylindrical streamtube of particles completely packed together. Furthermore, for arguments which we will later provide, it is necessaary that all this flow take place inside a spherical region of the gas where the diameter of the sphere is on the order of one mean free path.

Before we go any further with this hypothesized flow, let us briefly review what we are fairly sure of and what we are conjecturing. Certainly we can pull air into a spherical sink simply by having a small, straight pipe begin in a large region of the atmosphere and connect the other end to a vacuum pump. We know that this will establish an essentially radial inflow into the pipe entrance. We are sure that the vortex tube experiments prove that by having a gas take a curved path, that since high speed particles obviously must migrate to the outside radius and low speed ones migrate to the inside radius to maintain the flow variation with radius, that the thermal fluctuation velocities must also be separated so as to be proportional to the radius. Theoretical experiments supporting this contention are not conclusive, but the experimental results clearly do.

Based on the observed law of thermal separation of velocity to give a linear variation with radius, we know that the gas dynamic equations can be solved rigorously to show that the maximum flow rate at the small end of a straight conical tube can be maintained further in a curved tube while the cross-sectional area is reduced further. We expect that this area reduction can continue until the gas is completely condensed.

Let us cite one more observation which supports the existence of such a flow pattern that we are trying to describe here. There are many reports of transient atmospheric disturbances which produce a long, fine thread of "angel-hair" which quickly evaporates when the disturbance is dissipated. Based upon our research into this stable inhomogeneous assemblage of basic particles, we conclude that if such an assemblage existed in the atmosphere, it would continually condense all the air flowing into a spherically shaped vacuum region whose diameter is one mean free path in the air, i.e., about   ( or in.).   If this condensation occurred, it would produce a thread of frozen air with a diameter of about cm. Clearly such a thread would evaporate quickly, but it probably could be observed during its fleeting moment of evaporation.

For many years we have tried to construct an assemblage of streamtubes which would continually curve until condensation occurred and which would fill the spherical volume inside the spherical shell ending where the straight tubes end. We do not know the flow configuration. We know the streamtubes must fill the volume. We know they continually curve so that we obtain thermal separation; we believe the side boundaries probably have matching flows so that there are no viscous forces to dissipate the flow; and the side boundaries are such that there is no thermal energy flow (even though there is the transverse temperature gradient which is produced by the inertial forces of the curved path).

Notwithstanding our lack of knowledge of how the gas gets condensed and turned so that all the inflow is directed along one axis, we think there is a reasonable chance that this flow actually would occur with the basic particles we have been considering.

If this flow occurs as we have envisioned, then we have coming out of this volume defined by two spherical shells a flow of particles whose velocities are essentially parallel. The flow velocity is the background mean speed--since we have neither accelerated nor decelerated the particles. We have only changed their directions to line them up to flow in the same direction. However, the particles do have a distribution of speeds. The rms speed of the particles where the velocities are measured relative to a frame fixed to the ether is the same as the ether background rms speed. However, the rms speed where the velocities are measured relative to a frame fixed to the flowing gas is over an order of magnitude less than that measured with respect to the background. Further, since the rms speed is less than 1/10th the background rms, it results that the temperature is less than 1/100th that of the background. Thus, the gas is very "cold" in this region of the flow.

One other point which should be emphasized is that nowhere in this flow are there any sharp gradients of density, flow velocity, or thermal velocity. In particular, the density continues to increase monotonically from the background density (close to the mean free path diameter from the central core) to the tightly packed density in the core.

In the next section we will describe the final condensation step which we believe is the source of all organization which takes place in the universe.

The Core

In our quest to find a stable state of kinetic particles which interact only by repulsion (when they collide), we have identified three regions of flow. The first region is defined by two concentric spheres, where the outer sphere has a diameter equal to the mean free path of the undisturbed background. The inner diameter is the place where the inflow reaches the speed of sound (approximately 0.8 , where is the rms speed of the undisturbed background).

Actually, there is inflow for the region outside this outer sphere which theoretically would have a mass inflow per unit area normal to the flow which decreases inversely with the square of the distance from the center of the spheres. Deviation from this inverse square inflow would result from the delay time between start-up of the sink flow into the sphere and upon how the particles get fed out of the sink back into the background.

The second region also is defined by two concentric spherical surfaces. This is the transition region which receives particles flowing at sonic speed in radial paths toward the center. In this region the particles are turned so that they are all essentially flowing parallel to each other, but the gas is still not completely condensed.

It is this third region, the sphere in which condensation is completed, that we will describe now. We realize that the arguments justifying the boundary conditions for this third region, the core, are tenuous. However, the core analysis, like the straight channel analysis, is straightforward.

The beginning flow into the core consists of particles with a flow speed of , where

is the background mean speed. The particle velocities are nearly parallel when viewed from a frame at rest with respect to the ether. Viewed from this rest frame, the rms speed is still the same as the background rms speed. However, viewed from a frame moving at the mean speed, the rms speed is greatly reduced; its value is the background rms speed less the background mean speed. Thus, the rms speed relative to the core

or less than 9% of the thermal velocity. The temperature, and thus the pressure, is reduced by the square of this amount; it is reduced by the factors 0.0072935 or 1/137.1087. We will later see the extreme significance of this numerical factor.

We now look at the final condensation process. We have a stream tube of particles which have almost parallel velocities whose mean speed is and whose rms speed is with respect to the background ether. The local environment produced by the inside of the transition sphere further compresses the gas so that the particles are packed solidly, and causes a single discrete value of translational velocity.

The discrete value of velocity is believed to be only or depending upon the conditions inside the transition sphere. Figure 28 shows the two cases. In Figure 28a the energy into the right end equals the energy out the left end and, since the flow velocity increases from

to , a force must be applied by the transition section to the side of the core. In Figure 28b the flow velocity remains the same and, thus, the energy in the right end is greater than the energy out the left end. Thus, thermal energy must be removed from the sides of the core and fed into the transition section.

Figure 23. Two Types of Core Flow

In the case of Figure 28a, the flow out the left end circulates back around the outer sphere (with the straight channels) to re-enter the sink. The back flow is at a velocity so that the net forward flow is at the velocity    It is not clear how, or even if, the second assemblage translates.

It is this backflow which limits the size of the complete inhomogeneous assemblage. If the assemblage is confined to a sphere with a diameter in the order of the mean free path, then the outflow from the region will produce a minimal disturbance to the inflow. If the assemblage extends for many mean free paths, then the outflow will produce an asymmetric flow inside the region and possibly destroy the flow configuration. It is for this reason that we believe this inhomogeneous assemblage is confined to a region of space in the order of the mean free path.

We have presented what we believe may be a configuration of kinetic particle gas flow which may be stable. We have presented the data and analytic arguments which support the hypothesized configuration. Significantly more experimental and theoretical work can and should be done before we could be assured that such a stable configuration exists.

Let us pause to reflect on the material which we have presented. We have presented a set of postulates of physics from which we have been able to rigorously derive some things about the universe which, prior to this century, were held to be undeniable truths. The postulates are: the three-dimensional space; the smooth, hard, spherical elastic particles; and their motions. We see that all of classical mechanics comes from these postulates. Newton's three equations of motion are derived rigorously. The conservation of mass, linear momentum, energy, and angular momentum result rigorously from the postulates.

However, there is not an inkling of evidence to indicate that such postulates would present even the faintest hope of producing all the observed concepts of modern physics. Observations such as exemplified by the quantum theory and the theory of relativity seem far removed from such a universe as we have postulated here. Well, there is one faint indication that the basic particles could represent something in quantum electrodynamics, and that is the numerical value of which is the value of the fine structure constant--at least to within one part in The importance of this accuracy should not be underestimated, however. This numerical value is not just some constants put together by numerologists, but depends upon a Maxwell-Boltzmann background gas which is characterized by one parameter relating to transport, or momentum, i.e., ; and another parameter relating to pressure or energy, i.e., . Later we will show how this parameter relates to modern physics.

Neutrinos

We believe that neutrinos are the assemblages of the basic particles which we have described in the past three sections.

The velocity of propagation of this assemblage is

We set this equal to the speed of light and, thus, .

As the basic particles flow into the core, if they were to flow radically starting at a sphere with a radius of half the mean free path, they would reach a diameter at which they would all touch each other. Using an area with this diameter to approximate the scattering cross-section of a neutrino, we obtain a relation between the background parameters and the measured cross- section of a neutrino. However, this relation is tenuous because of the flow model described above, and because of the errors in measuring neutrino cross-sections. In any case, this gives a second relation ( was the first ) between the background parameters and observed data. The relationship is

where is the scattering cross-section radius of a neutrino, is the radius of the basic ether particle, and is the mean free path of the background.

As the particles flow into the sink, they rotate about the axis of propagation and then get speeded up inside the core (from a flow speed of to flow speed ). The particles then flow out of the end and rotate in the opposite direction in order to balance angular momentum. However, as a result of the fact that the particle velocity increases by , there is a net angular momentum which can not be balanced, and this net angular momentum depends linearly upon . The magnitude, of course, is half the value of Planck's constant, i.e., . This mechanism gives a third relation to determine the basic constants of the ether. The relationship is

where is the background mass density.

Before leaving the neutrino there are several other characteristics worth mentioning. Neutrinos occur with a spectrum of energy (and here a "mass," of course). We believe the mass is all stored in the core which has negligible angular momentum, and the core mass depends only upon the mass deposited in the core when the neutrino was formed. The neutrino and anti-neutrino differ only in the direction of their spin. There are two kinds of neutrinos--e-neutrinos and µ-neutrinos. Possibly one is the momentum jump and the other is the energy jump type?

The first neutrino formed was formed by chance--and there are many chances in an infinite universe. Once the correct size neutrino was formed, by chance, which could produce matter. After matter was produced, then many neutrinos are formed often and routinely.

Another significant characteristic of a neutrino is its propulsive force. As the background flows into the sink and gets its velocity increased from to , the mass flow rates times this velocity jump is a force. It is a continuous force, and it propels the neutrino through the background at the speed of light. We can compute the magnitude of the neutrino propulsive force. This force has a value of lb--which is approximately equal the thrust of a Saturn space booster.

Protons

All types of neutrinos exist--right-handed, left-handed, variable masses. Each one has an angular momentum of /2. If one of these neutrinos gets hit properly, it can begin to take a circular path--where the large rocket force holds the mass in orbit (by balancing the centrifugal force). There is exactly one value of mass which can have the rocket force balance the centrifugal force and have an angular momentum of /2. That is the mass of the proton. The proton is shown in Figure 24. The radius of the proton is given by . Thus,



The proton thus is believed to consist of a single neutrino which takes an orbital path. There are many observations throughout basic particle research efforts to indicate that all matter has constituents moving at the speed of light--the primary observation being of electromagnetic nature. Thus, if we believe matter constituents at the subnuclear level are moving at the speed of light, then it is easy to understand that large centrifugal forces will be required. Of course, then, large forces will be required to balance these centrifugal forces and, of course, that is what we have with our model of the neutrino. Furthermore, these large forces require an extremely massive and hard ether, as the one whose characterstics we have evolved from the analysis of the ether.

The proton is very stable, possibly more stable than a neutrino because of the electron and the electromagnetic fields. However, if two protons were to collide at high speed, they could lose their orbital paths and return back to neutrinos. The energy of a proton clearly is its mass times the square of the velocity of the mass, i.e., .

The proton has an angular momentum of /2, and it is simply and

where is the proton mass and is its orbital radius. The proton centrifugal force is

Equating this force to the neutrino rocket force, we can then solve for the product of the ether mass density times the square of the mean free path. This gives .

Thus the proton gives the fourth and final relationship for determining all the constants of the kinetic particle theory.

The New Ether

The relationship from the proton analysis, added to the three relationships from the neutrino, give four relationships from which all four constants of the ether can be determined. The values are listed below:

rms speed of particles

mean free path

background density

basic particle radius

The first and last constants, and , are known with high accuracy. The second and third constants, and , are not known, even within several percent or tens of percent. However,

Figure 24. Proton

we use these latter two constants with the many figures in order to find more refined mathematical models of the phenomena being studied.

Using the man free path "" for the ether and the radius of the basic particle , we can compute the particle number density for the ether. The equation is

Thus, we see there is a tremendous number of basic particles in each cubic meter of space--the number is only 15 orders of magnitude less than a googol.

Consider now the particle mass density. The value is

This is an extremely large value. However, this density is miniscule compared to the mass density of the proton's neutrino--which is the density of tightly packed basic particles, and which is close to the density of a single basic particle. Using the particle number density and the mass density, we can compute the mass of the basic particle, which is

The density of a basic particle is .

Such a mass density value as this is almost incomprehensible.

The pressure of the background ether is given by




This is a large number!! The pressure produced by a hydrogen bomb is miniscule compared to this pressure.

This ether is not like any ether ever proposed in the literature. However, this type of ether is needed to develop the large forces required at the sub nuclear level. Also, something very unusual must be required to transmit a photon for a billion years with only a gradual degradation, at most.

This ether is so hard that the usual types of acoustic waves are just not transmitted. It would appear that energy transmitted in this ether is achieved by changing the direction of basic particles rather than changing the magnitudes of the velocities.⁽²⁾ Of course, we just saw that in the analysis of the neutrino's structure the ether particles were just aligned, but not otherwise changed, in the neutrino process. If there were some method of generating a sufficiently large disturbance, it could be transmitted acoustically by this ether. We do not know how to generate such a large disturbance other than, possibly, as a result of a supernova explosion.

The Electrostatic Field

The primary long-range disturbance produced by the proton is the oscillatory type of field produced in the background as the proton takes its orbital path. A long distance from the proton this disturbance appears as a wave produced by a breathing sphere with its center at the proton center. However, there is some twist (giving polarity) to the field as a result of the angular momentum of the neutrino comprising the proton. The anti-proton is made of a neutrino with opposite angular momentum and, thus, has polarity opposite the proton. These flow patterns produce force fields. These fields are the electrostatic fields of the proton and anti-proton.

In order to understand the electrostatic force, consider the well documented experiments and theoretical analyses of the interaction of two breathing spheres immersed in an elastic medium. Two equal diameter spheres breathing with the same frequency and immersed in water will attract each other if the breathing is in phase, and will repel if 180 out of phase.

These results were extended theoretically to cover rotating dumbbells, oscillating constant diameter spheres, and other cases --always with the same result. Further, if an acoustic medium is used where the time for a sound wave from one disturbance to the other is in the order of the period of oscillation, then the force will vary with separation distance from attraction to repulsion to attraction repeatedly.

Consider now the electrostatic interaction of two protons. Both protons act as two breathing spheres. However, due to the angular momentum of the proton neutrinos, the separation distance of the two protons can only be at discrete values, subject to the existing wave patterns of the two electrostatic fields. As a consequence, the two fields are out of phase and produce a force of repulsion.

The electrostatic field is produced by a neutrino which is orbiting at a translational velocity of "c" (which is ). The surrounding ether mass, of course, is not all moved at this velocity. What happens is that only part of the particles are moved, and their velocity is

. We can think of the surrounding regions as moving at c, but the amount of mass in motion decreases inversely with the square of the distance from the proton orbital radius. Again, the mass motion is achieved by changing the directions of the ether particles. Possibly this is accomplished by minimizing the number of particles disturbed, and this would result in maximizing the energy transferred per basic ether particle. If this were the case, then each affected basic particle would be lined up in the direction of energy transfer. Its effect, then, could be the same as a neutrino which transports energy at the speed . However, the detailed structure of the electrostatic field is not known with any certainty.

The Electron

The existence of an electron is observed primarily as a result of its electromagnetic field, but the mass also is observed in experiments. Some physicists speculate that only the field exists, and the mass observed is somehow the mass of the field. It is observed that the electron is tough--it almost seems indestructible. Also, it can be moved great distances from its proton and it still has all its intrinsic characteristics. Based on this background and our model of the proton, we think there is a good chance that the electron is a single orbiting neutrino.

When the proton is formed the localization of a neutrino results in the lowering of the mass below the background density as a result of the neutrino "pump." It pulls background particles in, accelerates from to and expulses them. As a result of this velocity jump, fewer particles are required in the proton region. This expulsed mass is believed to make up the mass of the electron.

When the proton is formed by the chance collision of two neutrinos (one with a mass very close to the mass of the proton), the electron mass is expulsed and formed into a neutrino. The neutrino is 1/1836th as massive as the proton, yet the neutrino force is the same as the proton's. Thus, the electron orbit radius is 1/1836 times that of the proton--or . The small mass and size may be the reason the electron core has not been detected.

At the same time the electron was formed, its electrostatic field was formed, as near as possible, to null out the opposite electrostatic field of the proton. However, due to the finite size of the basic ether particle comprising the two fields, it is possible only to balance the two fields within the constraint of the one basic ether particle.

Even though the electrostatic field is comprised of the motion of many individual particles, the electron was formed with it by the proton's doing the "molding"--and there is not an easy way to get rid of the field. It is thought that the electron circular path for balancing the centrifugal force would then trace out a spiral which would produce the electrostatic field. Thus, the field components would consist of a path with a "radius" of (see Figure 25).

Finally, the electron must have an angular momentum of /2 and, with its small mass, it requires a path with a large radius of . This path and the other two components are shown in Figure 25.

This model of the electron seems complicated. Based upon the proton and its utmost simplicity, the electron model would have been anticipated to be simple. However, this is the only model of which we have been able to conceive which satisfies all the known observables. The energy of the electron clearly is its mass times the square of its velocity, i.e.,

Figure 25. Electron Path

Hydrogen Atoms

When the proton is formed, the electron is formed simultaneously and, of course, the hydrogen atom results. The electrostatic fields interact by one field's "riding upon" another in opposite directions. If we think of one of the fields having a flow velocity of , then a disturbance to this moving field of a similar kind possibly would result in the disturbance moving as a pressure wave at a velocity equal to the square of times the velocity of light. The details of this obviously are obscure. However, using this velocity for the electron speed gives the value

We call the factor the electromagnetic coupling factor. We think of this quantity, which comes directly from the ether characteristics, as the fundamental electromagnetic factor.

The electron orbital velocity of along with the electron mass establishes the hydrogen atom orbital radius. The centrifugal force is

The electrostatic force of attraction is . Thus, the Bohr radius is .


The electrostatic field is characterized by waves--the waves produced by the neutrino as it goes through the cyclical orbit. The wave valleys occur in the radial direction, in the azimuthal direction, and in the elevation direction. Thus, each wave, as defined by the valleys, is a three-dimensional entity. We will call one of these entities a three-dimensional wave, or a 3d-wave.

The fields can only interact by their waves interfering or amplifying each other. Thus, there are only discrete orbital paths possible. The fields give the quantum characteristics of the hydrogen atom in a straightforward manner, using nothing but classical Newtonian mechanics.

Photons and Matter Waves

When an electron in an atom changes from an outer orbit to a smaller orbit, there is less energy stored in the electrostatic fields of the atom. This energy is emitted as a photon with energy , of course. The wave length depends upon the time of emission as the electron drops down to the lower energy orbit. The two electrostatic fields mesh differently, and expel the energy difference.

When the photon interacts with another matter particle, let us use the electron as an example. Then, in order to balance mass, momentum and energy, it is necessary that part of the photon be captured and part be scattered. Thus, the mass of the particle being accelerated will grow. Strictly using Newtonian classical mechanics, we find that the mass grows with velocity by the magnitude. This, of course, is the famous Einstein equation for mass growth, which is obtained in an entirely different way than here. The energy of the particle when at rest is , where is the mass at rest. When the particle captures the mass of the photon it occurs in the electrostatic field, not in the core.

When the photon is captured, the photon goes directly into the electrostatic field, which itself is moving at the velocity c, albeit in an orbital path. This increase in energy due to the captured part is simply the mass captured times the square of the speed of light.

The effect on matter of scattered photons repeatedly impacting matter is to consider them as producing a force. This force times the distance through which the force acts is work energy. The effect on the matter is to increase its kinetic energy, i.e., .

In the partial scattering, partial capture of the photon by matter, in order to conserve linear momentum when a very small amount of energy is captured, it must be captured at a large distance from the center of rotation of the matter neutrino. This results since the motion of matter relative to the ether is achieved only by adding mass to a field which, when the matter is at rest, is moving in a circular orbit about the mass center at the speed of light. The small mass will stick to matter at a large distance from the cener, and will take a long time to go around the mass center--and the mass center will move only a short distance during that time. Figure 26 illustrates the concept. The added mass takes a spiral path and the whole assemblage must have the same linear momentum as the captured mass and the momentum imparted by the scattered photon.

The electron at rest had a lot of wave characteristics--in particular, the electromagnetic field is just a large, three-dimensional wave. However, when we say an electron is a matter wave, we are talking about an electron in motion. The electron center of mass, as a whole, will move up and down, as shown in Figure 26, as a result of the eccentrically captured mass which translates the electron to the right at the low velocity v. This is the so-called deBroglie wave length of matter. The larger the mass captured, the closer the capture must be to the center of mass and, therefore, the shorter the wave length.

Quantum Mechanics

Quantum mechanics fundamentally comes into physical science because of observations occurring which always have discrete amounts of angular momentum. In our discussions of the neutrinos, we saw why all neutrinos have the same amount of angular momentum, i.e., /2, Later we saw why the change in atoms from one electron orbital configuration to another occurred in discrete amounts of angular momentum--the changes are always measured by n, where n is an integer.

The characteristics of this kinetic particle theory of physics which produces quantum mechanics are summarized now:

1. Everything observed in atom-sized experiments is the result of changes of angular momentum whose magnitude is a multiple of /2.

2. The electrostatic fields are all standing wave patterns.

3. The interactions of the atoms, and constituents of atoms, is through the electrostatic fields. These fields being standing waves causes the locations of the constituent parts to be quantized--only certain discrete geometries are stable.

4. The electron is observed almost completely by its electrostatic field. Thus, the electron acts as though it were spread out in space, and an energy density function can be used to represent its total mass times the square of its local velocity.

5. Finally, since matter consists of orbiting particles moving at the speed of light, when matter is accelerated "mass" is added eccentrically which gives the matter an undulatory motion.

With these characteristics, which are derived from classical kinetic particle theory, the theory of quantum mechanics can be derived. In particular, the Schroedinger wave equation results from this theory.

Relativity

Relativity is concerned with the shortening of matter, the lengthening of time required for processes, and the growth of mass as velocity is increased.

We have shown why mass must increase with velocity. All matter has neutrinos moving at the speed of light (in circular or elliptic paths) and has electrostatic fields which propagate at the speed of light (in circular of elliptic paths). To accelerate matter, mass is added and the amount of mass added is such that the moving mass has the value .

When matter moves it takes a spiral path, and the time to complete a circle is longer than when at rest. The cycle time when moving, , is related to the cycle time when at rest,

by the expression . Thus, if we are at rest and observe a moving process, it will take longer.

Matter shortens in the direction of motion because the longitudinal distance from the maximum forward point on the spiral path to the next maximum forward point shrinks by the factor . This is illustrated in Figure 26.

The known relativity observations are consistent with these results

Figure 26. Small Mass Added to Matter at Rest

Gravitation

The gravitational field of a hydrogen atom is the residual flow field resulting when the two opposite electrostatic fields are balanced as near as possible. The electrostatic field of the proton begins at the first possible wave outside the orbital diameter of the proton neutrino. The radial extent of this wave is so that the distance from the proton center to the center of the wave is . The proton wave is moving in one direction and the electron electrostatic field wave at this location is moving in the opposite direction. These two flow fields would exactly balance if the particles making up the flow fields were infinitesimal. The particles, however, are finite. The electron electrostatic field then is forced to move radially one basic particle diameter (double amplitude) as it rolls around the proton (at the velocity of light). This radial oscillation of the electron electrostatic field acts just like a sphere moving in and out. The field produced, however, is not polarized like the electrostatic field since it is produced by proton neutrinos with one direction of spin and electron neutrinos with the opposite direction of spin. However, the fields of two interacting hydrogen atoms must "mesh" to make the forces always remain in phase, independent of their (quantitized) separation distance.

With the above mechanism we have a sphere with a radius of oscillating back and forth at a half amplitude of (the basic particle radius) with a period equal to the time for one cycle of the proton neutrino . The attractive gravitational force between two hydrogen atoms, then, is where c is the speed of light and is the background density. The gravitational force times the square of the separation distance in terms of the Newtonian universal gravitational constant G and the hydrogen atom masses is

Solving these two equatios for G gives   

This value compares with the measured value of . Thus, the theoretical value is , or within 7 percent of the measured value.

The agreement of this theory with experiment is remarkable. Further, the mechanism is remarkably simple. The theory is based on a proton size dictated by the orbiting neutrino which gives the proton orbital radius as , the Planck length for the size of the basic particle radius, and then the background density which can be computed from the strong nuclear force in a very simple way. We feel reasonably certain that this is the mechanism of gravity.

One other topic which is closely related to the mechanism of gravity is the degradation of a photon as it translates. To approach this phenomenon, let us consider the kinematics of the balancing of the positive and negative charge fields in a hydrogen atom. Just at the outside of the proton the particle flow produced by the positive charge is in one direction and the particle flow produced by the negative charge is in the opposite direction. It is anticipated that these flows could be balanced only to within one basic particle, as is consistent with the mechanism of gravity. This same lack of balance is anticipated when the two electrostatic fields change their relative locations as they emit a photon. Thus, this may produce the effect of a photon's losing the energy of one basic particle for each wave length of travel. As visible light loses energy, the color shifts from blue toward the red. This phenomenon of losing energy--or more directly, of increasing wave length, is known as the "red shift."

Light received on the earth from the more distant galaxies is shifted toward the red. This phenomenon was first observed by Edwin Hubbell in 1924. Scientists almost universally attributed this shift to be the result of the universe expanding homogeneously. The farther away a galaxy, the higher its velocity; then, as a result of the Doppler effect, the longer the wave length. The relation of velocity with distance is given by the Hubbell constant H.

By interpreting the shift as being transmission loss (of the energy of one particle per cycle) instead of the emitter's moving away, we were able to obtain an estimate of the basic particle energy (and its mass, which is the energy divided by the square of the speed of light). This estimate was in error by over an order or magnitude. However, the result was encouraging to us in the development of the theory.

Neutrons

We have inferred the structure of the neutron almost solely upon the almost complete indictability of the electron (without its field) and a very promising concept for the weak nuclear interaction.

An electron has its electrostatic field and has a magnetic moment. All of its interactions which have been observed are as a result of these two characteristics and the electron mass. No scattering cross-section has been observed for the electron such as has been observed for a proton.

The mass of the proton is 1836 times the electron, which would mean that the core diameter, if spherical, would be         times  that of an  electron. Thus, if electrons were scattered with each other at high enough velocities so that the electromagnetic interaction did not mask the effect of a core-core impact, it would seem that the core cross-section could be discovered. However, as the energies get high, the electron mass (which is in the field) grows--which would tend to mask the effect of a core impact. Possibly new experiments can be performed to search for the core cross-section--or some old experiments can be examined to see if they will yield the cross-section.

The concept we have been considering for the weak interaction is as follows. Consider a proton and an electron orbiting each other at the Bohr radius . However, assume that the proton neutrino axis can point in any direction in space, relative to the electron, and be equally likely to point in any direction. If the proton neutrino output is assumed not to spread out in the travel from the proton out to the electron, then the mean number of cycles and then the mean time to impact is approximately 1000 sec, which is close to the half-life of the neutron.

In a hydrogen atom, the electrostatic fields are present so that the rocket tail of the proton neutrino may be constrained so it would not impact the electron. Further, the electrostatic fields possibly could restore the structure even if the electron core were impacted.

Now, in order to change the hydrogen atom into a neutron, we must completely null out the electrostatic fields inside the region from the electron to the proton as well as the electrostatic fields outside the electron orbital sphere. It may be possible to accomplish this by adding a significant amount of energy (in the form of photons, of course) at high pressure, such as in stars, to bring about this change. Thus, this concept of the neutron is a hydrogen atom with mass added in the form to null out the electrostatic fields--and make other more subtle changes.

We have searched endless models to represent the neutron, each of which turned up with one or more deficiencies. We have not found any deficiencies for the filled hydrogen atom model, but we may!

Another reason that the decay mechanism is of such great interest is that in the short-lived particles, particularly those with nuclear-sized cross-sections, the proposed decay model predicts decay times in the order of microseconds--which is in good agreement with particles which decay by the weak interactions.

The Atoms

When a neutron and a proton are bound (in a nucleus), the neutron does not decay. The only known ways for a proton to affect a neutron are through the angular momentum vector and the magnetic moment. Possibly if both of these were constrained in some manner, these neutron decay would be prevented. Of course, it is prevented, so we know there is a way to accomplish it.

Most neutrons almost certainly were made in stars as a result of the extremely large gravitational forces. Thus, the process of producing larger and larger atoms is straightforward. However, what limits the size of atoms?

Large nuclei possibly could decay by the same mechanisms as neutrons decay. It is observed that the limit on atom size is at a nucleus diameter of between 6 and 7 nucleons. By conceiving a viable mathematical structure of nucleons, it may be possible to evaluate the weak interaction mechanism for the decay of atoms.

The Cosmos

The basic particles are here in the beginning. On rare occasions neutrinos are formed by chance. The correct mass neutrino getting impacted the correct way (by another neutrino) produces a proton. In the process, the proton produces an electron to make the hydrogen atom. Hydrogen atoms have gravitational fields, so they assemble themselves into stars. Stars develop huge gravitational forces which change hydrogen atoms into neutrons. Larger atoms, then, are produced. As a star continue to grow, the gravitational forces grow, and they make all the atoms into assemblages of neutrons. As they grow further, the neutron structure collapses and neutrinos are released. The star then explodes, as evidenced by a super nova.

1. Spherical shape probably is not necessary, but it is convenient to consider spherical particles.

2. Acoustic waves are transmitted at a speed of about 0.8 the particle rms speed, while ether waves are transmitted at 0.08 of the rms speed. However, we have not investigated the microscopic mechanisms involved in acoustic wave propagation.