Maxwell's equations do not in themselves predict a specific value for the constant (or variable) c which appears in them. This value is determined experimentally as the relative velocity at which a photon must strike an observer in order to be absorbed. By modifying the second postulate to state: "The observed velocity of light is c from all frames of reference," the radiation continuum model (RCM) of electromagnetic radiation is developed. This paper develops the model conceptually. RCM is much simpler conceptually than special relativity, in that it involves no length contraction or time dilation, and restores layman concepts of simultaneity. On the basis of this model, a Galilean invariant form of Maxwell's equations is obtained. Reference to other published papers on this model is provided wherein are derived the Galilean invariant form of Maxwell’s equations, all transverse and radial Doppler formulas, clock retardation due to motion and gravity, the perihelion advance of Mercury, the deflection and time delay of solar grazing photons, and other results attributed to special and general relativity.

The 1890's gave rise to experimental evidence that the speed of light appeared to be constant for all frames of reference. Since light was considered to be a point like object traveling forward at a constant velocity, the theory of relativity was born to describe how its velocity could seem to be invariant from all frames of reference. This required developing a coordinate transformation algorithm which would map any moving or stationary reference frame of space and time into any other reference frame. The only constant in all reference frames would be that the speed of light = c. The transformation developed initially by Lorentz (and hence known as the Lorentz Transformation) was formalized and expanded upon by Einstein in his special theory of relativity, which, in turn, was expanded into the general theory of relativity.

An interesting result of this transformation is that no two observers in different reference frames will agree on the velocity of a third object. For example, two objects traveling in opposite directions toward each other, each at a constant velocity of .6c from an outside reference point will each see the other approaching at a velocity equal to .88c. An additional outcome of these transformations is the realization that no object can travel faster than the speed of light. The term object can even be extended to mean any information, mass or energy as well.

This is an affront to our Newtonian/Galilean way of with the end result that we must abandon all our comfortable notions about length, time and additive velocities in order to support the observed invariance of the speed of light. The problem with the theory of relativity is that it assumes that only one item in our physics 'moves' as we would expect - light. All other items from muons and electrons to trains and planets 'move' in a manner which makes it impossible to determine absolute velocities, distances, lengths and times of events. These characteristics are all dependent on the frame of reference, and no 'absolute' frame of reference exists to use as a benchmark.

This paper begins by abandoning the concept of a point of light traveling at a constant velocity and goes on to show that, with this requirement relaxed, all the other objects in the universe behave as we would expect. That is velocity, time, length and distances can be agreed upon by all observers, independent of their motion relative to each other. Thus the universe returns to its Galilean invariant form as the uncomfortable Lorentz transformations will no longer be necessary. The first step is to develop a model for light, which is unique in at least one characteristic from all other things in the universe in that its velocity seems to be invariant from all frames of reference, and yet results in a more elegant model of the description and behavior of all other objects in the universe. Also, the observed "invariance" of light velocity will be demonstrated, contrasting this Galilean invariance with Lorentz invariance.

In short, quantum mechanics, special relativity, and realism cannot all be true.

Arthur Robinson, Science

At the turn of the twentieth century, a revolution occurred. Thousands of years of slow and steady progress in understanding the nature of physical laws had led many physicists to conclude that their work in the theoretical realm was nearly finished. Yet almost simultaneously new discoveries were made concerning the nature of atomic structure, electricity, magnetism, and the energy and velocity of light. Attempts to correlate these discoveries led to the special and general theories of relativity and laid the foundation for quantum theory.

Despite the almost universal acceptance of the special and general theories of relativity, there are problems. Beginning in the 1920's, the field of Quantum Mechanics began to dominate physicist's attempts to understand the basic workings and nature of the physical world of which we are a part. Einstein was very uncomfortable with the precepts of this new theory, stating at one point that "God does not play dice," referring to the probabilistic nature of the rules governing the physics of the quantum. He collaborated with Podolsky and Rosen on a thought experiment which demonstrated the foolishness (or incompleteness) of the theory. Einstein's conclusion from this hypothetical situation was that the theory of quantum mechanics, though not necessarily completely wrong, is at best incomplete.

Recent advances in experimental tools have allowed tests of the EPR paradox to be performed, most notably by Alain Aspect at CERN in 1982. The results of the experiment are quite striking. Either the notion of what we call reality is false, and the ideas of physical objects, sequenced events, history, dogs and planets are meaningless, or special relativity is incorrect. Specifically, that portion of special relativity that deals with the velocity of light being an absolute limit to the speed of objects or information transfer must be false. In short, the model of light proposed by Maxwell, Lorentz and Einstein, though not necessarily completely wrong, is at best incomplete.

Einstein developed the special and general theories of relativity to reconcile the amazing mathematical derivations of Maxwell's electromagnetic theory with the experimentally observed properties of light and gravity. The Michelson and Morley interferometer experiments demonstrated that light has an apparent constant velocity independent of any particular frame of reference. Lorentz and Einstein took this one observable characteristic of light, and, treating it as an absolute characteristic, developed a theory by which clocks in motion slow down, lengths contract in the direction of motion, and velocities of objects do not add in a common sense way. Combining this new model with Newton's laws of conservation of energy and momentum then required also that mass increases with velocity. This set an upper limit on attainable velocities at c, the "speed of light," since reaching this speed would require infinite energy. Generalization of the special theory of relativity to the case of free-fall in a gravitational field resulted in the theory that gravity curves space and time. The end result is a universe that is not only counterintuitive, but is practically inconceivable to the lay-person.

The weakness in the foundation of Einstein's theories lies in the assumption that the observed or measured invariant velocity of light represents an actual behavior of the light itself. This observed characteristic forms the basis for Einstein's second postulate: "The velocity of light is constant from all inertial frames of reference." We begin by modifying the second postulate to more precisely state: "The observed velocity of light is constant from all inertial frames of reference." In order to understand the distinction, we must develop a model which obeys the modified second postulate (with the word observed), but violates the original. Our initial approach is to consider the case of an idealized rubber band.

If you place a cup on a table, the cup will remain there, at rest, until some outside force, say a cat, moves it. Even if the table moves, the cup may remain at rest in its place on the table. The cup will appear to you to be stationary whether you are seated at the table, or running past the table in any direction. The reason is that you are using the room you are in as a point of reference for you and for the cup and table. When you move, you are aware of your motion, and your mind takes this into account in determining that the cup is not moving. Such accommodating reference frames cannot always be found. We’ve all had the experience of pulling into a parking space and coming to a stop, only to slam on our brakes as the movement of the car next to us caused us to think we were rolling forward. In this case our mind used the adjacent car as a stationary reference frame and judged our motion relative to it. When the stationary reference moved, which it was not supposed to do, we panicked.

Imagine sitting in a train, looking out a window at another train adjacent to you on a parallel track. Suddenly your train begins pulling away. If the motion is smooth enough, it is impossible for you to tell whether it is the other train moving or your own. All you know is that in your reference frame, the other train is moving. The speed you assign to the other train depends on the relative velocity between you and that train. Another passenger on a third train on the other side of the one adjacent to you will assign a different velocity to that train if his own velocity does not match yours. With no external reference frame we can only judge motion relative to ourselves. If the velocity of the third train is not equal to yours, it is practically impossible, except in error, for that passenger to assign the same velocity to the middle train in his reference frame as the one which you assign in yours. This said, we will now propose an experiment in which this is possible, involving several passengers traveling at different speeds who will each assign a velocity of zero to a an object outside their windows.

Suppose we take a piece of clear elastic, very resilient and pliable, and one foot in length. We fasten one end of this elastic to a pole, and stretch the other end to a distance of one thousand miles. While it is stretched to this length, we place a faint white line every foot from the pole to the thousand mile point. The elastic then looks like that in figure 1. Once we have completed marking the elastic, we allow it to return to its original one foot length, still anchored at a point.

An important point about the way an elastic material stretches is that any two points on the elastic always maintain the same relative separation. For example, if we place marks dividing the elastic into thirds, then, as it is stretched these marks will continue to delineate three equal sections, as in figure 2. An implication of this is that each point on the elastic is moving at a different speed as the elastic is being stretched. Thus if we pull the end of the elastic at three feet per second, the other marked sections will be traveling at one foot per second and two feet per second, respectively. These ratios of velocity and spatial separation hold for any combination of points on the elastic. In addition, for whatever speed the end of the elastic is moving forward, a unique point can be found somewhere on the elastic that is traveling at any speed we choose between zero and the speed of that end. In the example of figure 2, if one end is anchored while the free end is moving at three feet per second, and we wish to find a point traveling at two feet per second, that point will always be located at two-thirds of the distance from the anchored end to the moving end.

Now, referring back to figure 1, suppose we take the loose end of the marked elastic and begin pulling it forward at a velocity of one-thousand miles per hour. At the same instant, two automobiles, driven by Alice and Bob, pass the starting pole, traveling in the same direction as the stretching elastic. Alice, in the first auto, is traveling at twenty miles per hour, while Bob, in the second, is traveling at fifty miles per hour. Further, each automobile is carrying a camera which it is pointing directly at the elastic stretching alongside. We assume a very low light level, such that a long time exposure is required to obtain any detail in a photograph taken by either camera. Any object not exposing the same surface of the photographic plate for at least twenty minutes will not appear in the photograph. Thus any object which is in motion at even a very slow speed with respect to the camera will not appear on the photographic plate at all. Each automobile begins a time lapsed photo thirty minutes after passing the starting pole, and allows the exposure to continue for thirty minutes.

After the experiment is complete and the photos are developed, Alice and Bob each have a photo containing one distinct white line and nothing else. The reason for this is as follows: Given an elastic with one end stationary and one end moving forward at one-thousand miles per hour, a unique point can be found on the elastic whose velocity corresponds to any given value between zero and one-thousand miles per hour. Further, an automobile traveling at twenty miles per hour and passing the pole at the same instant the elastic commences being stretched will remain adjacent to the very point on the elastic which is also traveling at twenty miles per hour for the duration of the trip. Since there is a white line on the elastic at this point, this line will appear to be stationary with respect to the camera in the car, and will therefore appear as a distinct white line on the photographic plate.

Since each of the marks on the elastic are separated by one foot when the elastic has attained its one thousand mile length, their separation will be much less than one foot at the start of the test. Each auto turns on its camera exactly half way through the test and therefore when the elastic is stretched to five hundred miles. At this time, the separation of each of the marks is six inches. Over the time of the rest of the test, this separation of the marks will increase to one foot. The mark initially six inches in front of the line traveling at twenty miles per hour will be traveling slightly faster than the automobile. Over the duration of the test, this line will continually increase its separation until it is one foot in front of the twenty miles per hour mark, and will therefore not expose any one point on the photographic plate long enough to produce an image. Likewise, the line initially six inches behind the twenty miles per hour mark will be traveling slightly slower than the automobile, and will also fail to expose any one point on the plate long enough to make an image. The same reasoning holds also for Bob's automobile traveling at fifty miles per hour.

When the experiment is over, Alice will conclude that the event she photographed was the release of an object with a faint white line at rest from her frame of reference (traveling at twenty miles per hour). Bob will conclude the event was the release of an object with a faint white line at rest from his frame of reference (traveling at a velocity of fifty miles per hour). If the experiment is repeated with many automobiles, all traveling at different velocities, the drivers will, after a time, conclude that the event was the release of an object with a faint white line exhibiting the unique property of appearing to be at rest from all frames of reference. In reality, the event was the release of, for all intents, an infinite stream of faint white lines, traveling at all velocities from zero to one-thousand miles per hour. The problem is that, due to the nature of the observer, only that aspect of the event remaining at rest with respect to the observer can be detected.

The important point to remember in the above experiment is that the obvious conclusions to be drawn from a set of measurements are not necessarily an accurate description of the system itself. We may develop a model of a system based on a set of observations, and this model may work quite well at predicting future observations made of a similar system under similar circumstances. However, the model is not the system itself, and when future observations produce results inconsistent with the model we have developed, it is the model that must be modified or abandoned in favor of reality, not the other way around.

Suppose now we repeat the above experiment with the following changes. The light requires only one second to expose the plate, each automobile is a train, fifty feet in length, and the camera is propelled from the back of the train towards the front at a velocity of ten miles per hour (Alice and Bob's trains are still assumed to be traveling at velocities of twenty and fifty miles per hour, respectively). The plate is exposed for the first second of the camera's trip down the length of the train. Since everything the camera sees that is not stationary with respect to itself will be a blur on the photographic plate, and the camera is moving at ten miles per hour with respect to the train, we have created a 'device' which will record only objects that are moving at ten miles per hour with respect to the train. Thus, for a train moving at fifty miles per hour, to be recorded an object must travel at fifty miles per hour plus ten miles per hour or sixty miles per hour in the same direction as the train. In this manner, each train rider knows that the apparatus will record only objects that are traveling at ten miles per hour with respect to the velocity of his train. Clearly, from the above arguments, Alice will conclude the event produced a glowing object traveling at ten miles per hour from her frame of reference (traveling at twenty miles per hour), as will Bob (traveling at fifty miles per hour). If the experiment is repeated with many trains, the likely conclusion will be that the event was the release of an object exhibiting the unique property of an invariant velocity of ten miles per hour for all frames of reference.

Next imagine that we replace the camera in the above examples with a device that can only detect motion at the speed of light, c, relative to itself. The fast moving end of the elastic will need to move forward at a speed not less than c plus the velocity of any potential observer. For the time being, let us agree with Einstein and state that no observer will be traveling faster than c. This being the case, the elastic must be pulled forward with a velocity of at least two times c in order for all possible experimenters to record the white line phenomena. When the experiment is performed by many people, all traveling at different speeds, they will undoubtedly come to a common conclusion--the event appears to be the release of an object that travels at the speed of light, c, from all frames of reference.

If the experiencing and photographing of elastic bands as described in the first two experiments were a common occurrence, and if the true nature of the elastic and markings were not known, physicists would be pressed to devise a theory for an object that is at rest or slowly moving for all inertial frames of reference. This problem would be a little harder than the one Lorentz faced when developing his transformations, since, for any observer at a given velocity, other observers can be found traveling both faster and slower than the object being observed. In Einstein's theory, nobody and no object was found to be traveling faster than c, and so the possibility of these objects could be, and was, omitted. Our last example produced an event--the recording of a single white line on a photographic plate--that appears to travel at the speed of light from all reference frames. We have the advance knowledge of knowing exactly the true nature of the stretching elastic band, so we are not fooled into thinking that the "obvious" conclusion from the evidence on our photographs is the correct one. However, if we had not known in advance the nature of our experimental setup, what appears to us now as a far-fetched conclusion would seem very plausible indeed.

It is important to consider the context of Lorentz's work. Faced with the results of the Michelson-Morley experiment and with the incredible success of Maxwell's equations, Lorentz had to find a way to reconcile the two. The Lorentz transformations allowed the preservation of the form of Maxwell's equations in any inertial frame of reference while still supporting the results of the Michelson-Morley experiment, which showed that the "medium" of light propagation (the aether) was not dragged along by the earth. The Lorentz transformations, developed as a means to reconcile the unexpected results of the Michelson-Morley tests, predict that lengths should contract and clocks should slow down for a reference frame in motion. These transformations imply an invariant c for all inertial frames of reference, and are in fact developed under the assumption of an invariant value for c, but they do not force c to be invariant. In other words, the actual motion of light is not controlled by the equations Lorentz chose to model it, any more than a red light physically stops a car from crossing an intersection. Einstein used the Lorentz transformations to formulate his second postulate--that c is independent of the motion of the source. This postulate was given a strong boost because the required Lorentz length contraction could be interpreted to apply for all electromagnetic phenomenon. Since matter is electromagnetic in nature (composed of electrons, etc.), the supposed Lorentz contraction should apply to all matter. However, the Lorentz length contraction is merely a result of the particular transformations chosen to preserve the form of Maxwell's equations, but is not a necessity for all allowable transformations of the same, nor does it represent an actual physical effect of motion.

Leonhard Euler

In ancient or pre-scientific societies, light was considered predominantly as spiritual in nature. In the ninth century, the Islamic philosopher al-Kindi proposed that "everything in this world produces rays in its own manner...Everything that has actual existence in the world of the elements emits rays in every direction, which fill the whole world." From early time to the current day, the nature of light--spiritual, particle or ray--has been debated, with one idea prevailing for a time, only to fall to another. In 1864, after unifying electric and magnetic theory and developing the equations governing the waves of electromagnetic radiation, Maxwell concluded that "light is an electromagnetic disturbance propagating through the field according to electromagnetic laws. Current theory holds that light exhibits both wave-like and particle-like behavior, depending to some extent on the methods chosen to observe it.

At about the same time that Maxwell was deriving his equations, the observable speed of light was experimentally measured to be approximately 300,000 km/sec. Since this velocity was shown to be the same from all inertial frames of reference, Lorentz and Einstein proposed that the dimensions of space and time are dependent upon the relative motion between the observer and the thing being observed or measured. With Einstein’s theory we instantly run into the problem of developing a model and confusing it with the reality of the thing being modeled. Lorentz and Einstein had concluded from the available observations that the speed of light itself was exactly c in all frames of reference, without considering the role of the observer in making the measurements.

In quantum theory, the observer is all important. Any book one reads on the subject raises the issue as to whether anything exists on its own accord without the presence of a conscious observer to give it substance. This hardly seems like a question for physicists. However, in trying to understand some of the perplexing implications of the theory, one is often left to ask questions such as this. This is not a shortcoming of Quantum theory, but is instead a result of continually trying to reconcile quantum mechanics with the theory of relativity. And at that, it is mainly relativity's second postulate--the absolute constancy of the speed of light--that produces all the dilemmas.

The speed of light in a vacuum was determined by making physical measurements (observations) on light itself, and on the electric and magnetic properties of materials in the case of radio energy. The speed of light was not predicted from any application of first principles, nor has any analysis of the observed data yielded any explanation as to why the velocity should be strictly c instead of any other value. The role of the observer appears to be of utmost importance in the determination of any physical quantity in the realm of quantum theory. Clearly the only means by which the velocity of light has been specified is through the analysis of physical measurements, yet the velocity of light is stated as an absolute, independent of any observer or any preferred frame of reference.

Based on the examples in the previous sections, let us propose what we will call the radiation continuum model (RCM) of light. In this model, light does not radiate from its source at a constant velocity of c, but rather emanates in the same manner as a piece of elastic, anchored at the source, with one end pulled forward at a constant velocity C, with the upper case C denoting a velocity which is potentially much greater than c. This being the case, there will be a component of the light that is traveling at any speed we pick in the range from zero to C. Another characteristic of light, and of living and electro-mechanical observers, is that only that component of light that is striking the observer at a relative velocity of c in his frame of reference will be detected. Because of this, as in the case of the "device" described earlier which detects only motion at ten miles per hour in its frame of reference, we are left with the conclusion that the observed velocity of light is invariant for all inertial frames of reference. That is to say that regardless of our velocity, any light we perceive will appear to be striking us at approximately 300,000 kilometers per second (km/sec).

As an example, choose an event such as an instantaneous burst of light from a satellite at a fixed location in space (The satellite is chosen so that we may speak of distances and motion relative to the satellite and distances and motion relative to the "event" as synonymous. When one tries to discuss motion relative to an instantaneous event, the concepts of "motion", "location", and "event" become blurred in a strict interpretation of the terms). If we choose one observer, not in motion relative to the satellite, he will observe that component of the burst of light that is traveling at the velocity c. Another observer, moving away from the satellite at a velocity of 0.2c, will observe that component of the burst of light that is traveling past him in his frame of reference at a velocity of c. From the satellite's frame of reference, this component of the light burst must leave at a velocity of 1.2c. (If you wish to pass a car at twenty miles per hour, and that car is traveling at thirty miles per hour, your speed must be fifty miles per hour, the sum of the two velocities).

One of the more significant implications of the radiation continuum model of light is that it allows a more intuitive "Galilean" structure of space and time. By Galilean, we mean that the laws of electromagnetic radiation would conform to Galilean transformations, just as Newton's laws of motion do. Under such a transformation the concepts of space and time are absolute. This does not require that there is some preferred rest-frame against which all motion is measured. It simply means that agreements can be reached as to the simultaneous occurrence of distant events, and that transformations from one observer's point of view to that of an observer with a different velocity are straightforward and consistent with our everyday experience. For example, consider two rockets traveling toward each other, each at a velocity of 0.4c. Following the tenets of special relativity and the Lorentz transformations, the two rockets would be approaching each other at a combined speed of only 0.7c. Under a Galilean transformation the rockets will approach each other at 0.8c, just as two cars speeding towards each other at fifty miles per hour each will collide at one-hundred miles per hour. The effect is the same as if one car was parked and the other hit it head on at one-hundred miles per hour. This is the transformation we use in our day to day experience. The frame of reference of the observer is irrelevant to the outcome of the experiment and to the damage inflicted on each car.

Now, without specifying an upper limit on the speed of light C, we have developed a model of light as an expanding wave, anchored at its source and moving forward through space at all speeds from zero to C. There is no obvious reason to set a bound on C at any value short of infinity, though for all our observable experience, the value of C could be capped at two times c. This is because no object has yet been observed that travels at speeds greater than c. In the case of an observer moving at a velocity c relative to the source, the component of light traveling at 2c would appear to that observer to have a velocity of c, though, as will be shown later, the frequency would be shifted greatly. One might also argue that an upper limit of infinity on C would imply infinite energy. While this is strictly the case, it must be realized that this component could be observed only by an observer moving away from the source with infinite velocity--an unlikely scenario. Additionally, the frequency of the light at an infinite velocity would be shifted all the way to zero due to Doppler effects, and a zero-frequency signal contains zero, not infinite, energy. From here on, the meaning of c shall be taken to be a speed of 300,000 km/sec with respect to a particular reference frame, and should not be considered synonymous with the phrase "the speed of light", since light is henceforth considered to travel at all speeds from zero to some undetermined upper value C, such that C is at least as great as 2c and less than or equal to infinity.

The illustration utilized earlier of the elastic band all bunched up at one point waiting to be stretched out can not be carried too far. One shouldn't think of a photon as being coiled up inside an electron waiting to get out. Rather, the photon is created at a point in time, according to a well behaved set of rules. The creation of this photon wave is simply (and loosely) conversion of "mass" energy into "photon" energy. Typically a photon is created when an electron in an atom drops from a high energy state to a lower one. The entire photon wave is created in an instant, in the same respect that the entire photon wave collapses in an instant, when it is absorbed.

The invariance of the speed of light was detected by Michelson and Morley. What they discovered is that the speed of light appears to be the same whether the observer is moving toward the source, standing still, or moving away. Imagine trying to pass a truck that is moving twenty miles per hour faster than you. Each time you speed up, the truck is still moving twenty miles per hour faster than you. If you slow down, stop or go into reverse, the truck is still moving twenty miles per hour faster than you. This is fairly easy to explain, as the truck you are following can simply adjust its speed to match yours. But what if your friend is beside you in another car, and also sees the truck moving twenty miles per hour faster than him? Let us assume that you slow down while your friend speeds up. Now the truck will not be moving twenty miles per hour faster than both of you. He may be moving twenty miles per hour faster than you, but he will have a different speed with respect to your friend. The speed of the truck is not invariant. It is dependent on the speed of the observer, in this case you or your friend, and you each observe a different velocity. Such is not the case with light. If the truck driver flashed his brake lights at you and your friend, you would see the light arrive at a speed of c. Your friend would also see the light arrive at a speed of c. Any theory of light has to support this unusual feature, as it was tested and confirmed by Michelson and Morley in 1887. As the previous example with the satellite showed, this is not a problem for RCM theory, though it posed all manner of problems for Maxwell and Lorentz with the assumption of a constant velocity of light.

Despite the fact that the speed of light appears invariant under both RCM and relativity theory, there is a difference as to when and where observers in motion with respect to one another will actually see the light. In relativity, two observers in motion with respect to each other will each observe an oncoming pulse of light at the same place and at the same time. It is this conclusion that causes problems in the analysis of the simultaneity of remote events. This concept is a direct result of the second postulate--that the speed of light is a constant independent of the relative motion of source and observer. Figure 3 illustrates a ray of light exhibiting the RCM property one second after its release from an explosion in space. The purpose is to illustrate when and where each of several observers will perceive the light under different conditions. We have three witnesses to the event. Alice is stationary with respect to the explosion's source. Bob is moving toward the point of the explosion with a velocity of .5c, while Carol is moving away with a velocity of .5c. Consider first the case where all three observers see the flash at the same time. We wish to determine where they must each be located for this to occur. Alice, the stationary observer, is sensitive to that component of light leaving the source at a velocity of c. One second after the explosion this light will have traveled 300,000 km, and this then must be her distance from the explosion to see the flash at that time. Bob, moving towards the source at .5c, will see only that component of light traveling away from the event at .5c with respect to its source (reaching him at a relative velocity of c). This component will travel 150,000 km in one second. Bob must therefore be this far away from the source one second after the explosion in order to see the light at the same time it is seen by Alice. Carol, moving away from the source at .5c, will see only that component of light traveling at 1.5c with respect to the source (moving toward her at a relative velocity of c). After one second this light will be 450,000 km from the location of the blast, and this must also be Carol's location at the time of interest.

Next consider the case where all three spectators see the explosion at the same location. We would like to know when each would see the flash. Let's assume we wish all three to see the event at Alice's location, 300,000 km from the source. We have already determined that Alice will see the light after one second. The light that Bob sees is traveling at .5c. It will take two seconds for this light to reach Alice's location. Therefore Bob would need to make sure that he goes flying past Alice exactly two seconds after the explosion in order to observe the light flash at that point in space. The light that Carol sees is moving much faster at 1.5c. It will take only two-thirds of a second for this light to reach Alice, and Carol must plan to be passing Alice at that instant if she wishes to observe the flash where Alice is sitting. Thus each of the observers, Alice, Bob and Carol, can observe the same event, either at the same instant and at different locations, or at the same location but at distinctly different times. This marks the first major conceptual break with relativity theory. This is a testable difference, and it can be used to form the basis of an actual experiment to eliminate one of the two theories from consideration.

Figure 3

One question that comes to mind in the radiation continuum model of light is: Why is it that we perceive only that component of light that is arriving to us at a relative velocity of c? The "we" in the question applies to humans, cameras, radios and even objects which will reflect light (although objects which reflect light themselves act as light sources, reflecting the component that strikes them at a relative velocity of c at all speeds from zero to C).

In order for light to be seen, it must interact physically with the eye, which in turn converts this interaction into electrical activity. Similarly, a radio wave, to be detected, must interact physically with an antenna to produce an electric current in it, which is in turn interpreted by the radio electronics to produce an audible sound. A physical object that is reflecting light must physically interact with the incoming signal in such a manner that some of the "photons" are repelled from the object, in the same manner as if the object were itself a source of light.

Electromagnetic theory involves the mathematical description and interdependence of the following four quantities or fields: the magnetic and electric flux density, B and D respectively, and the magnetic and electric field intensity, H and E respectively. When one takes the units of B, D, E and H in the ratio HE/BD, the resulting units are equivalent to velocity squared. The H/B term is considered the magnetic charge, while E/D is called the electric charge. While the dimensional analysis of the above ratio yields a velocity relationship to these quantities, this analysis alone does not specify a value for that velocity. Maxwell's equations in and of themselves say nothing about the specific velocity of propagation of an electromagnetic wave, nor of the detectable velocity or range of velocities in any particular observer's frame of reference. Maxwell knew this when he derived the equations, but the coincidental timing of early measurements on radio waves and the determination of the velocity of light encouraged the conclusion that the velocity implied by the equations and the velocities as measured were one in the same. In the physical world of which we are a part, we can use physical devices and measuring apparatus to determine numerical values of the above four quantities in various physical settings. When the results of the values obtained from measurements of the physical interaction of electric charges with the experimental devices are combined in the above ratio, the result is always the same--the velocity implied by the measurements is 300,000 km/sec, or c. This conclusion that the speed of all electromagnetic propagation, including light, in free space, is c appeared acceptable to everyone at the turn of the nineteenth century, but one nagging question remained. In what frame of reference is the speed of light c? A train moving at eighty miles per hour in reference to the ground is only moving at sixty miles per hour in reference to another train coming from behind at twenty miles per hour. In this example, the Earth is considered stationary for all practical purposes, and is the preferred reference frame. What, though, could be the preferred reference frame for this velocity, c, of light?

Early theorists suggested a background "aether" in which sat and through which moved all objects in the universe. This undetectable aether was presumed to be the benchmark on which the speed of light was based. Thus, to a moving observer, the perceived velocity of light would be greater than or less than c, depending on the observer's velocity with respect to the aether, as with the slower moving train's velocity with respect to the Earth as described above. Since velocities of all things on Earth are slow compared to the speed of light, and given the limited capabilities of measurement at the time, this relative change due to motion could not be easily detected. However, the Michelson-Morley experiment, tested the possibility of Earth's motion through an aether background using interferometers. This test, performed over several seasons and equipment orientations, (along with several other experiments which eliminated the possibility of the Earth "dragging" a part of the aether with it as it moved) proved conclusively that there was no aether to use as a benchmark for light velocity measurements. The speed of light appeared to be c regardless of the relative velocity of the observer.

In the face of this experimental evidence for the invariance of the speed of light, a model had to be developed that allowed this to be possible. Beginning with the Lorentz transformation and ending with the theory of relativity, an interesting mathematical model was developed that allowed light to maintain this one, very confusing characteristic. Unfortunately, the whole structure of the universe had to change to accommodate this. Clocks in motion slowed down, rulers in motion shortened, the mass of a moving object increased without limit as its speed increased, and as objects approached each other at greater and greater speeds their combined velocities increased more slowly until, at a great enough speed (each at c), their combined velocities (measured with respect to the system) would still be c. Consider, for example, the case of two objects approaching each other, each with a velocity as viewed from a common rest frame of 0.9c. Their combined velocity under special relativity would be .99c, not 1.8c as our common experience would indicate.

All of the analysis performed by Lorentz missed an important point, alluded to earlier. Maxwell's equations do not insist on a specific velocity of propagation. They also certainly do not insist on a velocity which is independent of the frame of reference of the observer. It is the experimental means by which we measure or observe the speed of light or the ratio of H, E, B and D that results in a frame invariant velocity of c. The distinction here is critically important. As in the case of the expanding elastic in the previous sections, the equations of motion of the elastic had little or nothing to do with the results achieved by processing the film of the moving observers. The observers came away with an experimentally verified test of an object that was at rest or moving slowly from all frames of reference. While their observations demonstrated this, the elastic itself did not actually exhibit the properties recorded. The experimenters developed a model that explained their results, but that did not reflect the reality of the situation.

The principle of equivalence tells us that if we are in a uniformly moving reference frame, then any experiment performed in that frame should produce the same results as if performed in a "stationary" frame. Clearly, therefore, the ratio of Maxwell's four quantities in the manner above will result in a measured "velocity" of c in any uniformly moving frame of reference. Thus each of several observers in reference frames moving at different uniform velocities will each measure or observe the velocity of light from a distant source to be traveling through their apparatus at a velocity of c. As far as the speed of light is concerned, this restriction on uniformly moving frames of reference will be lifted. In RCM the restriction is not required, as the observer simply becomes sensitive to higher and higher velocity components as he accelerates away from the source.

From the above reasoning, it makes sense to state that the observed velocity of all electromagnetic propagation, in free space, is c. Thus two observers in motion relative to each other at any velocity will each see a beam of light passing them at the velocity of c. Since it is the same beam of light, that beam of light must have components of velocity (with respect to the source) of c plus the first observer's velocity (with respect to the source), and of c plus the second observer's velocity (with respect to the source). Since the source has no idea who its observers are, nor of their velocities, it must produce light in a radiation continuum, at all velocities from zero to C. In this manner, there is a component of that light which will pass any observer, moving at any velocity, at a relative velocity of c. This is the speed at which electromagnetic radiation is capable of interacting with the physical world, as demonstrated by laboratory measurements of light and the four electromagnetic properties of Maxwell. Any component of light not at this velocity relative to the observer cannot produce any physical interaction, and is therefore undetectable by any physical observer. Stated more concisely:

Since light travels at all velocities from zero to C, no matter what our speed relative to the source, there is always a component of the radiation continuum which is passing us at a relative velocity of c, and which is thus able to cause the physical interactions necessary to be detected. The end result is the appearance of light having the invariant speed of c from all frames of reference. It is interesting and comforting to note that the experimentally determined values of the fields in Maxwell's equations predict that our observed speed of light is equal to the square root of the proportionality constant between mass and energy as derived by Einstein (denoted by c²). Of course this famous equation, E = mc², is not necessarily a consequence of relativity theory, but derives naturally from Max Planck's observations of light emissions from a heated object. However, given this important relation, we can gain additional insight as to why it is that we perceive light only at the velocity indicated by the c² quantity. Since the conversion of radiant energy to mass energy can occur only if the ratio of the two is given by c², it would seem obvious that c is somehow related to the velocity at which matter can absorb or release energy in its own frame of reference.

This concludes this conceptual, introductory paper. For a more rigorous treatment of RCM Theory and its implications and applications, please read the referenced articles. All of these may be accessed directly by visiting the following web site: http://renshaw.teleinc.com/