A NEW GENERAL THEORY

 

OF PHYSICS

 

Part II

 

  

James A. Putnam

 

Ó 1995-2007

 

 

 

PART I   PART II   PART III   PART IV

THEORY INTRODUCTION PAGE

FRONT PAGE OF WEBSITE

TABLE OF CONTENTS

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10.  Particle to Photon Energy Transfer 

 

The transition from general relativity type effects to special relativity type effects can be made using the equations and concepts already derived. It will also introduce a new perspective on the nature of force. Force can be expressed as the measure of change in energy with respect to distance. It is known that photons carry energy. This energy is given to the photon by an accelerating charged particle.

 

It is an incremental change in the kinetic energy of the particle that is given to the photon. The particle's kinetic energy is given by:

 

 

When the particle accelerates its kinetic energy changes. The differential expression of this change is:

 

 

This value of change in kinetic energy is emitted away in photons. For reasons to be made clear later, I assume photon length is very small and on the order of subatomic dimension.

 

I have not yet defined a new theory of electromagnetic effects at this point of the analysis. So, I will analyze photon energy in a more general manner. The analysis will include two components for the acceleration of the particle. For the first part of the analysis, the acceleration of the emitting particle is parallel to the direction in which the photon is being emitted. The counterpart situation, the acceleration of the particle being perpendicular to the direction of emission, will follow separately. Both components are necessary to speak about force in a general sense.

 

The incremental change in kinetic energy is stored onto a photon that is being emitted. This increment of kinetic energy is stored in the photon's very short length. Because of the very small values of length and time involved in photon calculations, I will often represent these increments, as well as the energy increment, in differential form. I will make it clear when I am doing this by using identifying subscripts on the appropriate variables.

 

The theoretical representation is that an incremental change in the particle's kinetic energy is communicated to a photon of incremental length. I will follow the process of emission of the photon, its travel through a changing environment and its reception by a second charged particle. I will derive the mathematics to describe this transfer of kinetic energy.

 

The increment of energy is transferred during an increment of time. This increment of time has a physical origin. It is the time dt_c required for the photon to be fully released. This is, of course, the fundamental constant increment of time of a photon passing a given point. During this increment of time, the emitting particle is accelerating. Therefore, I expect the leading end of the photon to be released at a different speed than is the trailing end.

 

The increment of particle acceleration is assumed to be much less in magnitude than the local speed of light. Therefore, the incremental distance dx_p moved by the particle during the release of the photon is much less than the length of the photon. The increment of kinetic energy given up over the distance dx_p is stored in a photon of length dx_c. The distances are not the same, but the time period for either to occur is the same. For this reason I use formulas which include acceleration as opposed to exceleration.

 

In the introduction of the acceleration due to gravity, I treated the accelerations of matter and of light as being equal with opposite signs. I will not do that in the analysis for this problem, the reason being that the physical circumstances are not identical. A negative sign would represent undue speculation about the nature of what are new and different physical circumstances.

 

The physical circumstances here do not make clear that there is a specific direction attached to the change in the speed of light. The empirical evidence of the aberration of light supports the approach that there is no favored direction. The relationship between the relative speed of matter and a change in the local speed of light is appearing here in a more general form than it did for gravity. In order to begin the analysis in this general manner, I use:

 

 

When this formula was first introduced in connection with an analysis of the acceleration due to gravity, it was interpreted to mean: It is the change in the speed of light that causes an equal change in the speed of a falling object. I move beyond the scope of this interpretation with:

 

 

I used this equation to suggest the possibility of the local speed of light being a function of the speed of an object with respect to the background light field. I now assume this effect to be real.  I am assuming the equation can be read in either direction and retain valid physical meaning. In other words, the equation is being read to say the change of magnitude of velocity of an object of matter will cause a change of the local speed of light.

 

This assumption will be kept as consistent as physical circumstances will permit with what has already been given concerning the potential energy of gravity. For example, a freely falling object approaching the earth is described as gaining kinetic energy. This kinetic energy is defined as having been potential energy stored in the force of gravity. The decrease in potential energy of the object is converted into an increase in kinetic energy.

 

The kinetic energy was defined by the use of v_p. An increment of kinetic energy involves the use of dv_p. The potential energy was defined with the use of v_c. An increment of potential energy involves the use of dv_c. In the example problem that follows, I remain consistent with this concept. The differential variables used in this problem will retain the same subscripts as used in the gravity example.

 

I wish to manipulate the acceleration equation into the form I need for the purpose of defining an increment of kinetic energy carried by a single photon.  I begin with:

 

 

This increment of time is not an arbitrary value. It is the time period required for a photon to pass a given point so I identify it as dt_c.

 

When I use the equation showing the equivalence of accelerations, I am interested in tracking the incremental changes occurring to both the particle speed and to the local speed of light during the time increment dt_c. I am also interested in comparing the incremental distances the particle and the photon travel during this time increment.

 

I use descriptive subscripts to depict each of these increments of change that occur during the event of a photon being released. The constant time increment fixes the distance increments:

 

 

I will substitute these two expressions, equaling the same increment of time, into the acceleration equation:

 

 

Performing the substitutions:

 

 

And, rearranging terms:

 

 

I want to arrive at expressions of increments of energy per increments of length, so I multiply both sides by the mass of the emitting particle:

 

 

Rearranging the terms so as to have just numerator and denominator on both sides:

 

 

The numerator on the left is the incremental change of kinetic energy of the charged particle during the time dt_c. This increment of energy is divided by the distance the particle traveled during the time dt_c. The complete term on the left side is the mathematical expression defining the increment of force applied to the particle in order to cause the particle to accelerate during the time dt_c.

 

Since the left side of the equation represents an increment of force then the right side must do the same. In other words, not only acceleration is conserved but force is also conserved. The known relativity type effect of relative speed on force has not yet become apparent.

 

Although the right side must be an equivalent expression of force, it is not given in the familiar form of the normal definition of force. That is, the increment of energy is divided by an increment of distance different from the increment of distance the particle moved. For that matter, the right side numerator, which is an expression of an increment of energy, is not the same magnitude as the numerator on the left side.

 

The left side of the equation is the definition of force from the perspective of the particle. The right side is a different kind of definition of force from the perspective of a photon. The right side is not less correct than the left side. The increment of force that accelerated the particle has been transferred to the photon and is recorded or stored on it.

 

When it reaches another particle, it communicates or delivers the increment of force to that particle. This increment of force is transported over any distance at the speed of light until it interacts with the new particle. The photon is the known carrier of information and the delivery system for force throughout the universe. It has its own mathematical expression for showing this.

 

The acceleration equation shows force is conserved. However, because of the different way in which this is expressed from the photon point of view, it is helpful to refer to the photon as carrying potential force. In principle, a photon has no original energy of its own. In practice, every photon must have at least some very small amount of energy due to there always being relative motion even in the background light-field.

 

What needs to be shown next is what happens to the increment of force carried by the photon as the photon moves from an area of one speed of light to an area with a different speed of light. I will develop a model to represent this phenomenon. The potential force stored in the photon is:

 

 

The m represents the mass of the emitting particle. The value of mass of the emitting particle is stored in the photon. We know from the conditions of origin of the stored increment of energy that all this information must be there even if it is combined into a single magnitude. I do know how this storage of the value of mass is accomplished; however, the explanation needs to be given later when the nature of mass is defined in this new theory.

 

The speed of light v_c1 is the speed of light within the area in which the photon is first located and from which it is moving. The speed of light is a variable. The incremental change of light speed dv_c caused by the acceleration of the particle is stored in the photon. The stored values of mass and incremental change of light speed are treated as constants. The reasons for this will become more apparent when I introduce electromagnetism and then later the nature of mass.

 

The value of the speed of light will change as a function of the changing environment encountered by the photon traveling on its way. For this example, the photon moves out of its original light speed environment into a new environment with a different local speed of light. This change is represented by:

 

 

The subscript 2 used on the right side depicts the changed values of the two variables. These changes in magnitude are caused by the variation of the speed of light.

 

The length of the photon changes along with the change in light speed just as in the analogous example of gravity. The relationship between the two lengths is also the same:

 

 

Substituting this relationship into the transfer expression above:

 

 

Simplifying:

 

 

Or, as is obvious from this result:

 

 

I can then write:

 

 

The transfer expression has revealed itself to be equality. This means that force, active or stored, is conserved as the photon moves through a changing speed of light. The conservation of force, as depicted by the transfer of energy from a particle to a photon, applies not only at the point of the transfer but also applies as the photon travels through space.

 

11.  Speed and Special Relativity Type Effects 

 

I will now analyze the complete transfer process of a single photon between two particles of matter. Each particle has its own independent speed with respect to the background light field. Each particle is accelerating at different values. They are sufficiently separated to allow for the region between them to be considered as unaffected by their motion.

 

Particle one's motion decreases its local value for light speed. This value is identified as v_c3. The middle region has the light speed of the background light field v_c1. The motion of the second particle causes its own decrease in its local light speed v_c2.

 

The work above shows the entire transfer process can be set up as a series of equalities of force. The physical circumstances in order of occurrence are these:

 

 

a.  There is an infinite, homogeneous background light field represented

      by the light speed v_c1.

 

b.  A charged particle of mass m has an initial velocity relative to the background

      light field. The particle's relative speed lowers the local speed of light to a

      value represented by v_c3.

 

c.  This same charged particle is accelerated to a higher relative speed by

      an incremental amount during the time d_tc. This positive acceleration

      drops the local speed of light by an incremental amount as

      represented by d_vc.

 

d.  A photon is released during d_tc, the time unit of incremental acceleration.

     The photon begins to be released at the light speed of v_c3. At the

      time the end of the photon is released the local light speed has

      decreased by the incremental amount d_vc. The local light speed is

      assumed to be much larger than this incremental decrease in light speed.

      Therefore, the new speed of light can be approximated as equaling the

       initial local light speed of v_c3.

 

e.  The photon moves away from the particle entering an unaffected region

      having the background light speed of v_c1.

 

 f.   At some further distance away there is a second charged particle also of

      mass m. This particle has an initial relative velocity v_p with respect

      to the background light field. The particle's relative motion lowers the

      local speed of light to v_c2.

 

g.  The photon approaches very close to the second particle, and is now

      moving at very close to the speed v_c2.

 

h.  The photon then interacts with the second particle. The particle receives

      an increment of positive acceleration from the increment of force that

      was stored in the photon. In other words, the potential for force is

      converted into the act of applying force to the particle.

 

 

I observe that throughout this exchange both acceleration and force are conserved. I will next work through the full exchange using the individual expressions of the increment of force for each step. This complete transfer process can be represented in a simplified way by a series of equalities describing either active force or stored force.

 

The expressions representing what is occurring to the particles are expressions of applied force. The expressions representing the photon are expressions of stored force. These expressions of force form a series of equalities written as the products of mass times acceleration:

 

 

This redundant looking formula does say something important. It says Newton's force equation is valid on a local basis. However, it doesn't show the details of what changes are occurring all along the process. By converting from expressions using an increment of time to expressions using increments of length, I can rewrite the series. It will say the very same thing; however, it gives the details of the events involved. This converted equivalent expression is:

 

 

It is instructive to slightly modify the positions of some quantities in order to show each equation in the form of increments of energy per distance traveled. I do not say per unit of distance because the incremental measures of distances traveled are different for each expression. The modified series of equalities is:

 

  

a.  The first term represents the incremental change in kinetic energy

      of the first charged particle divided by the incremental distance

      it moved while acquiring the increment of increase of speed.

 

b.  The second term has an expression in the numerator for an increment

      of stored energy in the photon. The denominator is the photon length.

      The numerator and denominator are different from those contained

      in the particle's expression. However, they give the same measure

      of force.

 

c.  The third term represents the changes the photon has undergone as

      a result of moving a sufficient distance into the unaffected background

      light field. The photon's length has increased to dx_c1 consistent

      with the speed of light increasing to v_c1.

 

d.  The fourth term represents the changes the photon has undergone as

      it approaches very close to the second charged particle. Its length

      has decreased to the value dx_c2.

 

e.  The fifth term shows the second particle has been acted upon by the photon.

      The transfer of stored force has been completed, and the particle has

      changed its speed by an incremental amount.

 

 

It can be seen in this series that there are three attributes belonging to the first particle that are conserved all through the process. These attributes are the value of its mass, the increment of its acceleration and, these two things together making up the third, the force exerted upon the particle that caused its acceleration.

 

Three attributes of the photon are not conserved. The first is the speed of light that varies according to particle velocities and the dictates of the background light field. The other two are respectively the energy type expression in the numerator and the length of the photon in the denominator.

 

The conservation of force means Newton's law of force is invariant at every point. Even though this is true for a local observer, it is not true for the remote observer. It is this difference between local measurement and remote measurement that introduces relativity effects into the example problem.

 

For example, a remote observer standing stationary on the surface of the earth applies a constant force to a particle causing it to accelerate along a path in line with a stationary measuring rod. As the particle's speed increases the stationary observer will notice the applied force will result in less and less acceleration.

 

Even though the stationary observer sees a diminishing of the effect of force, this is not the case for an observer traveling with the particle. A local observer moving with the particle as it travels along the length of the stationary measuring rod sees the rod grow longer. His fundamental unit of measurement, the photon, is becoming smaller. The local observer is using dx_c2, and the stationary observer is using dx_c1 as their fundamental units of measurement. Locally all seems to be remaining normal, but the remote world appears to be expanding.

 

This causes the local observer to measure his distance traveled per increment of time at a greater value than does the stationary observer. Both observers are making their measurements between the same two points. The distance x_d between these two points does not change. Only the local measurement is varying. The local measurement of distance between the two points is larger than the remote measurement.

 

For the remote observer the measurement of the particle's velocity is:

 

 

The local observer measures the particle's velocity and finds:

 

 

In order to measure the velocity or change of velocity of the particle from the perspective of the local observer, it is necessary to use the ratio of the constant remote unit of measurement to the changing local unit of measurement. This ratio has been derived as:

 

 

The remote observer measures an increment of the distance x_d as dx_dR. The local observer measures this same increment of distance as dx_dL:

 

 

Therefore:

 

 

Substituting for v_c2 and simplifying:

 

 

The local observer can use his measurement of speed to calculate the force applied to his particle. Force is conserved locally, so he should calculate the true applied force:

 

 

If the source of force at the remote location is increased in a manner that causes the particle to maintain a constant acceleration as measured by the remote observer, then from a local perspective the acceleration increases in accordance with the change in the applied remote force. As the remote force is increasing the acceleration measured locally is correspondingly increasing.

 

The local observer does not measure a diminishing of the effectiveness of force with increasing speed. The arrival of force on the local level will produce the same measure of acceleration on the local level as would be expected from the perspective of the remote level if there were no relativity type effects. What the remote observer would predict as a result of non-relativistic calculations is what the local observer measures.

 

This formula for force can be used to calculate the expression for particle kinetic energy:

 

 

The solution of the kinetic energy equation, it will shortly be discussed further, is:

 

 

 

12.  Electromagnetism and Relativity Type Effects

 

The example problem used here is a single charged particle accelerated in a straight line by a force. As the particle is accelerated it releases a photon in a perpendicular direction. This event is the fundamental starting point for the theory of electromagnetic radiation.

 

Before beginning to describe the transfer of energy to the emitted photon, it needs to be established that the acceleration of the particle will change the orientation of the released photon. In other words, the changing velocity of the particle will impart a tilt to the released photon. Before doing this I will first demonstrate when tilt does not occur. In the absence of a secondary or background light field, there can be no tilt.

 

The simplest example is to consider the event to occur in the absence of a background light field. If there is no background light field, then there is no way to define a change in speed. A change in speed has to be movement with respect to something. We cannot define motion of any kind with respect to space alone, because this implies detectable physical properties of space. The only thing established empirically about space is that it exists.

 

We know space is there because we measure distances in it. We cannot define a measurement of distance as occurring across nothing, so there must be something. This new theory makes no claim to predict physical properties for space other than to say it exists and gives us room to move about. In the absence of using space to serve as a source of control over either photons or matter, there is no basis upon which to determine any movement at all of an isolated particle.

 

Fortunately this situation does not represent the conditions of the universe. The introduction of a background light field approximates the real condition of the universe. So, I introduce into the example the existence of a background light field. The change in speed of the particle can now be measured against the reference frame of the background light field which, for this example, is considered to be stationary.

 

The problem is to analyze the emission process of the photon. The photon begins to leave the particle when the particle’s velocity is at the initial value. However, all through the very quick emission process the particle accelerates in a perpendicular direction. During this process the remaining part of the photon, not yet emitted, is dragged along with the particle as the particle’s velocity increases.

 

This is the case because of the relative strengths of the two light-fields. This conclusion results from the recognition there are two light fields at work here. There are both the background light field and the particle's light field. Each exercises the same fundamental method of control over photons. The background light field is composed of the combined effects of many light fields belonging to distant particles.

 

When the photon is very close to the particle, the particle's light field strength is high compared to the background light field. Therefore, it is the particle's light field that is the main reference of control for the photon. The propagation speed of the particle's light field is treated as being much larger than C and possibly infinite. As the photon moves away from the particle the particle's light field decreases rapidly in strength, and the photon becomes under the control of the background light field.

 

The speed of the photon is controlled by the combined effects of both light fields. At a point very close to the center of the emitting particle, the effect of the background light field can be approximated as not even existing. Therefore, at that point there is virtually no effect of relative speed. As the photon moves away, the effect of the background light field quickly becomes very significant. Under these conditions there is a very significant relative speed.

 

The result of this effect upon the photon, as it is released, is to cause the trailing end to be dragged along by the accelerating particle. As the photon is leaving the particle this dragging effect quickly diminishes and the leading end has a speed that is no longer referenced primarily to the particle. The leading end now has a speed strongly referenced to the background light field that is not moving. The resulting effect upon the photon is to be left with a constant tilt relative to the direction it is moving.

 

While I am offering this physical example as an aid to visualize what is occurring, I am not insisting this is the precise physical event that occurs. It is intended as an aid to show how I bring together what we have learned from empirical evidence and the mathematics of this new theory. The purpose of this visual description is to make it clear why I solve the problem by working with a common increment of distance. This method is different from the one used in the preceding analysis of the horizontal component of acceleration.

 

The analysis of the horizontal component used a common increment of time for the measurement process. In that case the distance traveled by the particle was not equal to the distance the photon traveled during the time of emission. In this new example, concerning a perpendicular component of motion for the photon, the two distances are the same. In other words, the increment of distance across which the particle accelerates during the time of emission can be approximated as being the same as the offset distance for the trailing end of the photon. Therefore, I must define a different cause for relativity type effects for this case.

 

Since the distances traveled are the same, the change of velocities for both the particle and the speed of light can be treated in a manner analogous to an object falling freely between two points due to gravity. The previously derived equation, using exceleration, which I can use here is:

 

 

When I derived this equation, it described the effect of gravity. There was a clear singular direction for the gradient of the velocity of light. The direction of this gradient of v_c was unique so I included the appropriate sign.

 

In the example problem at hand, of a photon moving between two particles, the induced gradient of v_c may not have a singular direction. It may be the case that general relativity type effects are a special case of special relativity type effects. What I will try first is to apply opposite signs to the change in light speed and the change in particle speed. I also know that the change in kinetic energy of the particle has been of the opposite sign as that of the change in the energy of the light field.

 

Until the implications of this new approach are made clear, I will continue to use:

 

 

Next I wish to solve for momentum and, it can be calculated from:

 

 

So, I set up the increment of energy:

 

 

Substituting from three steps above:

 

 

The variable speed of light is given by:

 

 

Taking the differential:

 

 

I substitute this expression into the second increment of energy equation given above:

 

 

Simplifying:

 

 

Finally, dividing by the differential of particle velocity gives the momentum:

 

 

Newton's formula for force literally means the derivative of momentum with respect to time:

 

 

Then for this example:

 

 

At this point of this theory, the value of mass is treated as the constant rest mass, therefore:

 

 

The normal use of this formula in a standard derivation of energy will give the equation for particle kinetic energy previously derived in this new theory. That equation is:

 

 

This result is analogous to Einstein's energy equation. However, it will predict more. For example, there is a connection between this energy equation and our concepts of frequency and wavelength.

 

There is also an observation that can be made with respect to how a photon's energy will change as it descends through the earth's light field. The velocity of light is becoming less, therefore the length of the photon is becoming shorter. However, the perpendicular component of photon tilt, which is the origin of electromagnetism, has not been shown to also shrink.

 

This is a situation analogous to increasing the tilt of the photon. An increased tilt is representative of an increase in electromagnetic energy. This is a reason why a photon, which is slowing down as it approaches the earth, would actually increase its electromagnetic energy. I will more fully develop this new electromagnetic theory in later sections.

 

13.  Particle Energy and Frequency 

 

The concept of wavelength is accepted by quantum physics as a fundamental property of photons and matter. This new theory will present a different perspective on this concept. However, I will begin with the normal concept of wavelength for the purpose of using familiar theory to help introduce this analysis.

 

I earlier derived an equation defining the energy of a particle. I did not take the concepts of frequency or wavelength into consideration during its derivation, and yet it will inherently suggest a physical origin from which these proposed properties could be derived. In order to be able to conveniently relate this analysis to later work, I will not work directly with wavelength, but instead will first derive an interpretation of its counterpart, frequency.

 

The form of my energy equation is chosen to show its analogy to Einstein's energy equation; however, it has another useful form. I proceed through the following mathematical manipulative steps for the purpose of presenting my energy equation in a form where the origin of our concept of frequency can be seen.

 

I multiply the first term on the right side by an expression equaling unity:

 

 

Performing the multiplication:

 

 

Since:

 

 

I substitute this expression and have:

 

 

Now rearranging terms:

 

 

The form of the energy equation given above contains an expression within the parenthesis representing the physical origin of our concept of frequency. It says: Kinetic energy is equal to rest energy multiplied by this expression that I suggest is directly related to frequency. I will develop this relationship more fully.

 

The known empirical relationship between kinetic energy and frequency is given by:

 

 

Where w represents frequency, and h is Planck's constant. Setting the right sides of these two kinetic energy equations equal to each other produces:

 

 

Then solving for a value which I will call kinetic energy frequency:

 

 

The term inside the parenthesis is without units. The terms outside the parenthesis are all constants, and their combined units are inverse seconds; therefore, I will represent them by:

 

 

I will refer to this as the rest frequency of a particle. Substituting this into the kinetic frequency equation:

 

 

Now for kinetic energy I can write either:

 

 

Or: