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Introduction to RCM Theory Curt Renshaw 680 America’s Cup Cove, Alpharetta, Georgia 30005 USA ph: (770) 751-9481 fax: (770) 751-9829 email: crenshawteleinc.com web site: http://renshaw.teleinc.com ABSTRACT about length, time and additive velocities in order to support the observed invariance of the speed of light. The problem Maxwell's equations do not in themselves predict a specific with the theory of relativity is that it assumes that only one item value for the constant (or variable) c which appears in them. in our physics 'moves' as we would expect - light. All other This value is determined experimentally as the relative velocity items from muons and electrons to trains and planets 'move' in at which a photon must strike an observer in order to be a manner which makes it impossible to determine absolute absorbed. By modifying the second postulate to state: "The velocities, distances, lengths and times of events. These observed velocity of light is c from all frames of reference," the characteristics are all dependent on the frame of reference, and radiation continuum model (RCM) of electromagnetic radiation no 'absolute' frame of reference exists to use as a benchmark. is developed. This paper develops the model conceptually. This paper begins by abandoning the concept of a point of RCM is much simpler conceptually than special relativity, in light traveling at a constant velocity and goes on to show that, that it involves no length contraction or time dilation, and with this requirement relaxed, all the other objects in the restores layman concepts of simultaneity. On the basis of this universe behave as we would expect. That is velocity, time, model, a Galilean invariant form of Maxwell's equations is length and distances can be agreed upon by all observers, obtained. Reference to other published papers on this model is independent of their motion relative to each other. Thus the provided wherein are derived the Galilean invariant form of universe returns to its Galilean invariant form as the Maxwell’s equations, all transverse and radial Doppler uncomfortable Lorentz transformations will no longer be formulas, clock retardation due to motion and gravity, the necessary. The first step is to develop a model for light, which perihelion advance of Mercury, the deflection and time delay is unique in at least one characteristic from all other things in of solar grazing photons, and other results attributed to special the universe in that its velocity seems to be invariant from all and general relativity. frames of reference, and yet results in a more elegant model of the description and behavior of all other objects in the INTRODUCTION universe. Also, the observed "invariance" of light velocity will be demonstrated, contrasting this Galilean invariance with The 1890's gave rise to experimental evidence that the Lorentz invariance. speed of light appeared to be constant for all frames of reference. Since light was considered to be a point like object A MODEL OF LIGHT traveling forward at a constant velocity, the theory of relativity was born to describe how its velocity could seem to be In short, quantum mechanics, special relativity, and realism invariant from all frames of reference. This required cannot all be true. developing a coordinate transformation algorithm which would Arthur Robinson, Science map any moving or stationary reference frame of space and time into any other reference frame. The only constant in all At the turn of the twentieth century, a revolution occurred. reference frames would be that the speed of light = c. The Thousands of years of slow and steady progress in transformation developed initially by Lorentz (and hence understanding the nature of physical laws had led many known as the Lorentz Transformation) was formalized and physicists to conclude that their work in the theoretical realm expanded upon by Einstein in his special theory of relativity, was nearly finished. Yet almost simultaneously new which, in turn, was expanded into the general theory of discoveries were made concerning the nature of atomic relativity. structure, electricity, magnetism, and the energy and velocity of An interesting result of this transformation is that no two light. Attempts to correlate these discoveries led to the special observers in different reference frames will agree on the and general theories of relativity and laid the foundation for velocity of a third object. For example, two objects traveling quantum theory. in opposite directions toward each other, each at a constant Despite the almost universal acceptance of the special and velocity of .6c from an outside reference point will each see the general theories of relativity, there are problems. Beginning in other approaching at a velocity equal to .88c. An additional the 1920's, the field of Quantum Mechanics began to dominate outcome of these transformations is the realization that no physicist's attempts to understand the basic workings and object can travel faster than the speed of light. The term object nature of the physical world of which we are a part. Einstein can even be extended to mean any information, mass or energy was very uncomfortable with the precepts of this new theory, as well. stating at one point that "God does not play dice," referring to This is an affront to our Newtonian/Galilean way of with the probabilistic nature of the rules governing the physics of the end result that we must abandon all our comfortable notions the quantum. He collaborated with Podolsky and Rosen on a thought experiment which demonstrated the foolishness (or 1 incompleteness) of the theory. Einstein's conclusion from this table. The cup will appear to you to be stationary whether you hypothetical situation was that the theory of quantum are seated at the table, or running past the table in any mechanics, though not necessarily completely wrong, is at best direction. The reason is that you are using the room you are in incomplete. as a point of reference for you and for the cup and table. When Recent advances in experimental tools have allowed tests you move, you are aware of your motion, and your mind takes of the EPR paradox to be performed, most notably by Alain this into account in determining that the cup is not moving. Aspect at CERN in 1982. The results of the experiment are Such accommodating reference frames cannot always be found. quite striking. Either the notion of what we call reality is false, We’ve all had the experience of pulling into a parking space and the ideas of physical objects, sequenced events, history, and coming to a stop, only to slam on our brakes as the dogs and planets are meaningless, or special relativity is movement of the car next to us caused us to think we were incorrect. Specifically, that portion of special relativity that rolling forward. In this case our mind used the adjacent car as deals with the velocity of light being an absolute limit to the a stationary reference frame and judged our motion relative to speed of objects or information transfer must be false. In short, it. When the stationary reference moved, which it was not the model of light proposed by Maxwell, Lorentz and Einstein, supposed to do, we panicked. though not necessarily completely wrong, is at best incomplete. Imagine sitting in a train, looking out a window at another Einstein developed the special and general theories of train adjacent to you on a parallel track. Suddenly your train relativity to reconcile the amazing mathematical derivations of begins pulling away. If the motion is smooth enough, it is Maxwell's electromagnetic theory with the experimentally impossible for you to tell whether it is the other train moving or observed properties of light and gravity. The Michelson and your own. All you know is that in your reference frame, the Morley interferometer experiments demonstrated that light has other train is moving. The speed you assign to the other train an apparent constant velocity independent of any particular depends on the relative velocity between you and that train. frame of reference. Lorentz and Einstein took this one Another passenger on a third train on the other side of the one observable characteristic of light, and, treating it as an absolute adjacent to you will assign a different velocity to that train if characteristic, developed a theory by which clocks in motion his own velocity does not match yours. With no external slow down, lengths contract in the direction of motion, and reference frame we can only judge motion relative to ourselves. velocities of objects do not add in a common sense way. If the velocity of the third train is not equal to yours, it is Combining this new model with Newton's laws of conservation practically impossible, except in error, for that passenger to of energy and momentum then required also that mass assign the same velocity to the middle train in his reference increases with velocity. This set an upper limit on attainable frame as the one which you assign in yours. This said, we will velocities at c, the "speed of light," since reaching this speed now propose an experiment in which this is possible, involving would require infinite energy. Generalization of the special several passengers traveling at different speeds who will each theory of relativity to the case of free-fall in a gravitational assign a velocity of zero to a an object outside their windows. field resulted in the theory that gravity curves space and time. Suppose we take a piece of clear elastic, very resilient and The end result is a universe that is not only counterintuitive, pliable, and one foot in length. We fasten one end of this but is practically inconceivable to the lay-person. elastic to a pole, and stretch the other end to a distance of one The weakness in the foundation of Einstein's theories lies thousand miles. While it is stretched to this length, we place a in the assumption that the observed or measured invariant faint white line every foot from the pole to the thousand mile velocity of light represents an actual behavior of the light itself. point. The elastic then looks like that in Figure 1. Once we This observed characteristic forms the basis for Einstein's have completed marking the elastic, we allow it to return to its second postulate: "The velocity of light is constant from all original one foot length, still anchored at a point. inertial frames of reference." We begin by modifying the second postulate to more 1 Foot precisely state: "The observed velocity of light is constant from all inertial frames of 1000 MPH reference." In order to understand the O 20 MPH 50 MPH P distinction, we must develop a model which obeys the modified second postulate (with the word observed), but violates the original. Our initial approach Figure 1 is to consider the case of an idealized rubber band. An important point about the way an elastic material AT REST IN ALL FRAMES OF REFERENCE stretches is that any two points on the elastic always maintain the same relative separation. For example, if we place marks If you place a cup on a table, the cup will remain there, at dividing the elastic into thirds, then, as it is stretched these rest, until some outside force, say a cat, moves it. Even if the marks will continue to delineate three equal sections, as in table moves, the cup may remain at rest in its place on the Figure 2. 2 the camera in the car, and will therefore appear as a distinct white line on the photographic plate. 1/3 2/3 3/3 Since each of the marks on the elastic are separated by one 1 fps 2 fps 3 fps foot when the elastic has attained its one thousand mile length, their separation will be much less than one foot at the start of 1/3 2/3 3/3 the test. Each auto turns on its camera exactly half way 1 fps 2 fps 3 fps through the test and therefore when the elastic is stretched to five hundred miles. At this time, the separation of each of the Figure 2 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 An implication of this is that each point on the elastic is initially six inches in front of the line traveling at twenty miles moving at a different speed as the elastic is being stretched. per hour will be traveling slightly faster than the automobile. Thus if we pull the end of the elastic at three feet per second, Over the duration of the test, this line will continually increase the other marked sections will be traveling at one foot per its separation until it is one foot in front of the twenty miles per second and two feet per second, respectively. These ratios of hour mark, and will therefore not expose any one point on the velocity and spatial separation hold for any combination of photographic plate long enough to produce an image. points on the elastic. In addition, for whatever speed the end of Likewise, the line initially six inches behind the twenty miles the elastic is moving forward, a unique point can be found per hour mark will be traveling slightly slower than the somewhere on the elastic that is traveling at any speed we automobile, and will also fail to expose any one point on the choose between zero and the speed of that end. In the plate long enough to make an image. The same reasoning example of figure 2, if one end is anchored while the free end holds also for Bob's automobile traveling at fifty miles per is moving at three feet per second, and we wish to find a point hour. traveling at two feet per second, that point will always be When the experiment is over, Alice will conclude that the located at two-thirds of the distance from the anchored end to event she photographed was the release of an object with a the moving end. faint white line at rest from her frame of reference (traveling at Now, referring back to Figure 1, suppose we take the loose twenty miles per hour). Bob will conclude the event was the end of the marked elastic and begin pulling it forward at a release of an object with a faint white line at rest from his velocity of one-thousand miles per hour. At the same instant, frame of reference (traveling at a velocity of fifty miles per two automobiles, driven by Alice and Bob, pass the starting hour). If the experiment is repeated with many automobiles, all pole, traveling in the same direction as the stretching elastic. traveling at different velocities, the drivers will, after a time, Alice, in the first auto, is traveling at twenty miles per hour, conclude that the event was the release of an object with a faint while Bob, in the second, is traveling at fifty miles per hour. white line exhibiting the unique property of appearing to be at Further, each automobile is carrying a camera which it is rest from all frames of reference. In reality, the event was the pointing directly at the elastic stretching alongside. We assume release of, for all intents, an infinite stream of faint white lines, a very low light level, such that a long time exposure is traveling at all velocities from zero to one-thousand miles per required to obtain any detail in a photograph taken by either hour. The problem is that, due to the nature of the observer, camera. Any object not exposing the same surface of the only that aspect of the event remaining at rest with respect to photographic plate for at least twenty minutes will not appear the observer can be detected. in the photograph. Thus any object which is in motion at even The important point to remember in the above experiment a very slow speed with respect to the camera will not appear on is that the obvious conclusions to be drawn from a set of the photographic plate at all. Each automobile begins a time measurements are not necessarily an accurate description of the lapsed photo thirty minutes after passing the starting pole, and system itself. We may develop a model of a system based on a allows the exposure to continue for thirty minutes. set of observations, and this model may work quite well at After the experiment is complete and the photos are predicting future observations made of a similar system under developed, Alice and Bob each have a photo containing one similar circumstances. However, the model is not the system distinct white line and nothing else. The reason for this is as itself, and when future observations produce results follows: Given an elastic with one end stationary and one end inconsistent with the model we have developed, it is the model moving forward at one-thousand miles per hour, a unique point that must be modified or abandoned in favor of reality, not the can be found on the elastic whose velocity corresponds to any other way around. given value between zero and one-thousand miles per hour. Further, an automobile traveling at twenty miles per hour and A CONSTANT VELOCITY FOR ALL FRAMES OF passing the pole at the same instant the elastic commences REFERENCE being stretched will remain adjacent to the very point on the Suppose now we repeat the above experiment with the elastic which is also traveling at twenty miles per hour for the following changes. The light requires only one second to duration of the trip. Since there is a white line on the elastic at expose the plate, each automobile is a train, fifty feet in length, this point, this line will appear to be stationary with respect to 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 3 trains are still assumed to be traveling at velocities of twenty It is important to consider the context of Lorentz's work. and fifty miles per hour, respectively). The plate is exposed for Faced with the results of the Michelson-Morley experiment and the first second of the camera's trip down the length of the with the incredible success of Maxwell's equations, Lorentz train. Since everything the camera sees that is not stationary had to find a way to reconcile the two. The Lorentz with respect to itself will be a blur on the photographic plate, transformations allowed the preservation of the form of and the camera is moving at ten miles per hour with respect to Maxwell's equations in any inertial frame of reference while the train, we have created a 'device' which will record only still supporting the results of the Michelson-Morley objects that are moving at ten miles per hour with respect to the experiment, which showed that the "medium" of light train. Thus, for a train moving at fifty miles per hour, to be propagation (the aether) was not dragged along by the earth. recorded an object must travel at fifty miles per hour plus ten The Lorentz transformations, developed as a means to miles per hour or sixty miles per hour in the same direction as reconcile the unexpected results of the Michelson-Morley tests, the train. In this manner, each train rider knows that the predict that lengths should contract and clocks should slow apparatus will record only objects that are traveling at ten miles down for a reference frame in motion. These transformations per hour with respect to the velocity of his train. Clearly, from imply an invariant c for all inertial frames of reference, and are the above arguments, Alice will conclude the event produced a in fact developed under the assumption of an invariant value glowing object traveling at ten miles per hour from her frame for c, but they do not force c to be invariant. In other words, of reference (traveling at twenty miles per hour), as will Bob the actual motion of light is not controlled by the equations (traveling at fifty miles per hour). If the experiment is repeated Lorentz chose to model it, any more than a red light physically with many trains, the likely conclusion will be that the event stops a car from crossing an intersection. Einstein used the was the release of an object exhibiting the unique property of Lorentz transformations to formulate his second postulate--that an invariant velocity of ten miles per hour for all frames of c is independent of the motion of the source. This postulate reference. was given a strong boost because the required Lorentz length Next imagine that we replace the camera in the above contraction could be interpreted to apply for all examples with a device that can only detect motion at the speed electromagnetic phenomenon. Since matter is electromagnetic of light, c, relative to itself. The fast moving end of the elastic in nature (composed of electrons, etc.), the supposed Lorentz will need to move forward at a speed not less than c plus the contraction should apply to all matter. However, the Lorentz velocity of any potential observer. For the time being, let us length contraction is merely a result of the particular agree with Einstein and state that no observer will be traveling transformations chosen to preserve the form of Maxwell's faster than c. This being the case, the elastic must be pulled equations, but is not a necessity for all allowable forward with a velocity of at least two times c in order for all transformations of the same, nor does it represent an actual possible experimenters to record the white line phenomena. physical effect of motion. When the experiment is performed by many people, all traveling at different speeds, they will undoubtedly come to a THE RADIATION CONTINUUM MODEL OF LIGHT common conclusion--the event appears to be the release of an Having spoken of the rays of the sun, which are the focus of all object that travels at the speed of light, c, from all frames of the heat and light that we enjoy, you will undoubtedly ask, reference. 'What are these rays?' This is, beyond question, one of the If the experiencing and photographing of elastic bands as most important inquiries in physics described in the first two experiments were a common Leonhard Euler occurrence, and if the true nature of the elastic and markings were not known, physicists would be pressed to devise a theory In ancient or pre-scientific societies, light was considered for an object that is at rest or slowly moving for all inertial predominantly as spiritual in nature. In the ninth century, the frames of reference. This problem would be a little harder than Islamic philosopher al-Kindi proposed that "everything in this the one Lorentz faced when developing his transformations, world produces rays in its own manner...Everything that has since, for any observer at a given velocity, other observers can actual existence in the world of the elements emits rays in be found traveling both faster and slower than the object being every direction, which fill the whole world." From early time observed. In Einstein's theory, nobody and no object was to the current day, the nature of light--spiritual, particle or ray-- found to be traveling faster than c, and so the possibility of has been debated, with one idea prevailing for a time, only to these objects could be, and was, omitted. Our last example fall to another. In 1864, after unifying electric and magnetic produced an event--the recording of a single white line on a theory and developing the equations governing the waves of photographic plate--that appears to travel at the speed of light electromagnetic radiation, Maxwell concluded that "light is an from all reference frames. We have the advance knowledge of electromagnetic disturbance propagating through the field knowing exactly the true nature of the stretching elastic band, according to electromagnetic laws. Current theory holds that so we are not fooled into thinking that the "obvious" light exhibits both wave-like and particle-like behavior, conclusion from the evidence on our photographs is the correct depending to some extent on the methods chosen to observe it. one. However, if we had not known in advance the nature of At about the same time that Maxwell was deriving his our experimental setup, what appears to us now as a far-fetched equations, the observable speed of light was experimentally conclusion would seem very plausible indeed. measured to be approximately 300,000 km/sec. Since this 4 velocity was shown to be the same from all inertial frames of satellite is chosen so that we may speak of distances and reference, Lorentz and Einstein proposed that the dimensions motion relative to the satellite and distances and motion of space and time are dependent upon the relative motion relative to the "event" as synonymous. When one tries to between the observer and the thing being observed or discuss motion relative to an instantaneous event, the concepts measured. With Einstein’s theory we instantly run into the of "motion", "location", and "event" become blurred in a strict problem of developing a model and confusing it with the reality interpretation of the terms). If we choose one observer, not in of the thing being modeled. Lorentz and Einstein had motion relative to the satellite, he will observe that component concluded from the available observations that the speed of of the burst of light that is traveling at the velocity c. Another light itself was exactly c in all frames of reference, without observer, moving away from the satellite at a velocity of 0.2c, considering the role of the observer in making the will observe that component of the burst of light that is measurements. traveling past him in his frame of reference at a velocity of c. In quantum theory, the observer is all important. Any From the satellite's frame of reference, this component of the book one reads on the subject raises the issue as to whether light burst must leave at a velocity of 1.2c. (If you wish to pass anything exists on its own accord without the presence of a a car at twenty miles per hour, and that car is traveling at thirty conscious observer to give it substance. This hardly seems like miles per hour, your speed must be fifty miles per hour, the a question for physicists. However, in trying to understand sum of the two velocities). some of the perplexing implications of the theory, one is often One of the more significant implications of the radiation left to ask questions such as this. This is not a shortcoming of continuum model of light is that it allows a more intuitive Quantum theory, but is instead a result of continually trying to "Galilean" structure of space and time. By Galilean, we mean reconcile quantum mechanics with the theory of relativity. And that the laws of electromagnetic radiation would conform to at that, it is mainly relativity's second postulate--the absolute Galilean transformations, just as Newton's laws of motion do. constancy of the speed of light--that produces all the dilemmas. Under such a transformation the concepts of space and time are The speed of light in a vacuum was determined by making absolute. This does not require that there is some preferred physical measurements (observations) on light itself, and on the rest-frame against which all motion is measured. It simply electric and magnetic properties of materials in the case of means that agreements can be reached as to the simultaneous radio energy. The speed of light was not predicted from any occurrence of distant events, and that transformations from one application of first principles, nor has any analysis of the observer's point of view to that of an observer with a different observed data yielded any explanation as to why the velocity velocity are straightforward and consistent with our everyday should be strictly c instead of any other value. The role of the experience. For example, consider two rockets traveling observer appears to be of utmost importance in the toward each other, each at a velocity of 0.4c. Following the determination of any physical quantity in the realm of quantum tenets of special relativity and the Lorentz transformations, the theory. Clearly the only means by which the velocity of light two rockets would be approaching each other at a combined has been specified is through the analysis of physical speed of only 0.7c. Under a Galilean transformation the measurements, yet the velocity of light is stated as an absolute, rockets will approach each other at 0.8c, just as two cars independent of any observer or any preferred frame of speeding towards each other at fifty miles per hour each will reference. collide at one-hundred miles per hour. The effect is the same Based on the examples in the previous sections, let us as if one car was parked and the other hit it head on at one- propose what we will call the radiation continuum model hundred miles per hour. This is the transformation we use in (RCM) of light. In this model, light does not radiate from its our day to day experience. The frame of reference of the source at a constant velocity of c, but rather emanates in the observer is irrelevant to the outcome of the experiment and to same manner as a piece of elastic, anchored at the source, with the damage inflicted on each car. one end pulled forward at a constant velocity C, with the upper Now, without specifying an upper limit on the speed of case C denoting a velocity which is potentially much greater light C, we have developed a model of light as an expanding than c. This being the case, there will be a component of the wave, anchored at its source and moving forward through light that is traveling at any speed we pick in the range from space at all speeds from zero to C. There is no obvious reason zero to C. Another characteristic of light, and of living and to set a bound on C at any value short of infinity, though for all electro-mechanical observers, is that only that component of our observable experience, the value of C could be capped at light that is striking the observer at a relative velocity of c in two times c. This is because no object has yet been observed his frame of reference will be detected. Because of this, as in that travels at speeds greater than c. In the case of an observer the case of the "device" described earlier which detects only moving at a velocity c relative to the source, the component of motion at ten miles per hour in its frame of reference, we are light traveling at 2c would appear to that observer to have a left with the conclusion that the observed velocity of light is velocity of c, though, as will be shown later, the frequency invariant for all inertial frames of reference. That is to say that would be shifted greatly. One might also argue that an upper regardless of our velocity, any light we perceive will appear to limit of infinity on C would imply infinite energy. While this is be striking us at approximately 300,000 kilometers per second strictly the case, it must be realized that this component could (km/sec). be observed only by an observer moving away from the source As an example, choose an event such as an instantaneous with infinite velocity--an unlikely scenario. Additionally, the burst of light from a satellite at a fixed location in space (The frequency of the light at an infinite velocity would be shifted all 5 the way to zero due to Doppler effects, and a zero-frequency Despite the fact that the speed of light appears invariant signal contains zero, not infinite, energy. From here on, the under both RCM and relativity theory, there is a difference as meaning of c shall be taken to be a speed of 300,000 km/sec to when and where observers in motion with respect to one with respect to a particular reference frame, and should not be another will actually see the light. In relativity, two observers considered synonymous with the phrase "the speed of light", in motion with respect to each other will each observe an since light is henceforth considered to travel at all speeds from oncoming pulse of light at the same place and at the same time. zero to some undetermined upper value C, such that C is at It is this conclusion that causes problems in the analysis of the least as great as 2c and less than or equal to infinity. simultaneity of remote events. This concept is a direct result of The illustration utilized earlier of the elastic band all the second postulate--that the speed of light is a constant bunched up at one point waiting to be stretched out can not be independent of the relative motion of source and observer. carried too far. One shouldn't think of a photon as being coiled Figure 3 illustrates a ray of light exhibiting the RCM up inside an electron waiting to get out. Rather, the photon is property one second after its release from an explosion in created at a point in time, according to a well behaved set of space. The purpose is to illustrate when and where each of rules. The creation of this photon wave is simply (and loosely) several observers will perceive the light under different conversion of "mass" energy into "photon" energy. Typically a conditions. We have three witnesses to the event. Alice is photon is created when an electron in an atom drops from a stationary with respect to the explosion's source. Bob is high energy state to a lower one. The entire photon wave is moving toward the point of the explosion with a velocity of .5c, created in an instant, in the same respect that the entire photon while Carol is moving away with a velocity of .5c. Consider wave collapses in an instant, when it is absorbed. first the case where all three observers see the flash at the same time. We wish to determine where they must each be located THE INVARIANCE OF THE SPEED OF LIGHT for this to occur. Alice, the stationary observer, is sensitive to that component of light leaving the source at a velocity of c. The invariance of the speed of light was detected by One second after the explosion this light will have traveled Michelson and Morley. What they discovered is that the speed 300,000 km, and this then must be her distance from the of light appears to be the same whether the observer is moving explosion to see the flash at that time. Bob, moving towards toward the source, standing still, or moving away. Imagine the source at .5c, will see only that component of light traveling trying to pass a truck that is moving twenty miles per hour away from the event at .5c with respect to its source (reaching faster than you. Each time you speed up, the truck is still him at a relative velocity of c). This component will travel moving twenty miles per hour faster than you. If you slow 150,000 km in one second. Bob must therefore be this far down, stop or go into reverse, the truck is still moving twenty away from the source one second after the explosion in order to miles per hour faster than you. This is fairly easy to explain, as see the light at the same time it is seen by Alice. Carol, moving the truck you are following can simply adjust its speed to away from the source at .5c, will see only that component of match yours. But what if your friend is beside you in another light traveling at 1.5c with respect to the source (moving car, and also sees the truck moving twenty miles per hour faster toward her at a relative velocity of c). After one second this than him? Let us assume that you slow down while your friend light will be 450,000 km from the location of the blast, and this speeds up. Now the truck will not be moving twenty miles per must also be Carol's location at the time of interest. hour faster than both of you. He may be moving twenty miles Figure 3. per hour faster than you, but he will have a different speed with respect to c-v, (1-v/c) c, c+v, (1+v/c) your friend. The speed of the truck is not invariant. It is dependent on the speed of the observer, in this case you Bob Alice Carol or your friend, and you each observe a .5c .5c 150,000 different velocity. Such is not the km 300,000 case with light. If the truck driver km flashed his brake lights at you and 450,000 km A your friend, you would see the light c+v, (1+v/c) Carol 2/3 sec arrive at a speed of c. Your friend B would also see the light arrive at a speed of c. Any theory of light has to c, Alice 1 sec support this unusual feature, as it was tested and confirmed by Michelson and Morley in 1887. As the previous c-v, (1-v/c) Bob 2 sec example with the satellite showed, this is not a problem for RCM theory, though it posed all manner of V problems for Maxwell and Lorentz with the assumption of a constant velocity of light. 6 Next consider the case where all three spectators see the encouraged the conclusion that the velocity implied by the explosion at the same location. We would like to know when equations and the velocities as measured were one in the same. each would see the flash. Let's assume we wish all three to see In the physical world of which we are a part, we can use the event at Alice's location, 300,000 km from the source. We physical devices and measuring apparatus to determine have already determined that Alice will see the light after one numerical values of the above four quantities in various second. The light that Bob sees is traveling at .5c. It will take physical settings. When the results of the values obtained from two seconds for this light to reach Alice's location. Therefore measurements of the physical interaction of electric charges Bob would need to make sure that he goes flying past Alice with the experimental devices are combined in the above ratio, exactly two seconds after the explosion in order to observe the the result is always the same--the velocity implied by the light flash at that point in space. The light that Carol sees is measurements is 300,000 km/sec, or c. This conclusion that moving much faster at 1.5c. It will take only two-thirds of a the speed of all electromagnetic propagation, including light, in second for this light to reach Alice, and Carol must plan to be free space, is c appeared acceptable to everyone at the turn of passing Alice at that instant if she wishes to observe the flash the nineteenth century, but one nagging question remained. In where Alice is sitting. Thus each of the observers, Alice, Bob what frame of reference is the speed of light c? A train moving and Carol, can observe the same event, either at the same at eighty miles per hour in reference to the ground is only instant and at different locations, or at the same location but at moving at sixty miles per hour in reference to another train distinctly different times. This marks the first major conceptual coming from behind at twenty miles per hour. In this example, break with relativity theory. This is a testable difference, and it the Earth is considered stationary for all practical purposes, and can be used to form the basis of an actual experiment to is the preferred reference frame. What, though, could be the eliminate one of the two theories from consideration. preferred reference frame for this velocity, c, of light? Early theorists suggested a background "aether" in which WHY IS THE OBSERVED SPEED OF LIGHT c? sat and through which moved all objects in the universe. This undetectable aether was presumed to be the benchmark on One question that comes to mind in the radiation which the speed of light was based. Thus, to a moving continuum model of light is: Why is it that we perceive only observer, the perceived velocity of light would be greater than that component of light that is arriving to us at a relative or less than c, depending on the observer's velocity with respect velocity of c? The "we" in the question applies to humans, to the aether, as with the slower moving train's velocity with cameras, radios and even objects which will reflect light respect to the Earth as described above. Since velocities of all (although objects which reflect light themselves act as light things on Earth are slow compared to the speed of light, and sources, reflecting the component that strikes them at a relative given the limited capabilities of measurement at the time, this velocity of c at all speeds from zero to C). relative change due to motion could not be easily detected. In order for light to be seen, it must interact physically However, the Michelson-Morley experiment, tested the with the eye, which in turn converts this interaction into possibility of Earth's motion through an aether background electrical activity. Similarly, a radio wave, to be detected, must using interferometers. This test, performed over several interact physically with an antenna to produce an electric seasons and equipment orientations, (along with several other current in it, which is in turn interpreted by the radio experiments which eliminated the possibility of the Earth electronics to produce an audible sound. A physical object that "dragging" a part of the aether with it as it moved) proved is reflecting light must physically interact with the incoming conclusively that there was no aether to use as a benchmark for signal in such a manner that some of the "photons" are repelled light velocity measurements. The speed of light appeared to be from the object, in the same manner as if the object were itself c regardless of the relative velocity of the observer. a source of light. In the face of this experimental evidence for the invariance Electromagnetic theory involves the mathematical of the speed of light, a model had to be developed that allowed description and interdependence of the following four this to be possible. Beginning with the Lorentz transformation quantities or fields: the magnetic and electric flux density, B and ending with the theory of relativity, an interesting and D respectively, and the magnetic and electric field mathematical model was developed that allowed light to intensity, H and E respectively. When one takes the units maintain this one, very confusing characteristic. Unfortunately, of B, D, E and H in the ratio HE/BD, the resulting units are the whole structure of the universe had to change to equivalent to velocity squared. The H/B term is considered the accommodate this. Clocks in motion slowed down, rulers in magnetic charge, while E/D is called the electric charge. While motion shortened, the mass of a moving object increased the dimensional analysis of the above ratio yields a velocity without limit as its speed increased, and as objects approached relationship to these quantities, this analysis alone does not each other at greater and greater speeds their combined specify a value for that velocity. Maxwell's equations in and of velocities increased more slowly until, at a great enough speed themselves say nothing about the specific velocity of (each at c), their combined velocities (measured with respect to propagation of an electromagnetic wave, nor of the detectable the system) would still be c. Consider, for example, the case of velocity or range of velocities in any particular observer's two objects approaching each other, each with a velocity as frame of reference. Maxwell knew this when he derived the viewed from a common rest frame of 0.9c. Their combined equations, but the coincidental timing of early measurements velocity under special relativity would be .99c, not 1.8c as our on radio waves and the determination of the velocity of light common experience would indicate. 7 All of the analysis performed by Lorentz missed an of reference can produce any physical interaction and important point, alluded to earlier. Maxwell's equations do not hence be detected. All other velocity components of this insist on a specific velocity of propagation. They also certainly radiation are undetectable by that observer, or by any do not insist on a velocity which is independent of the frame of other electro-mechanical device which is stationary in that reference of the observer. It is the experimental means by frame of reference. Any observer in motion relative to the which we measure or observe the speed of light or the ratio of first observer will, in general, detect a different H, E, B and D that results in a frame invariant velocity of c. component of the radiation, that component being the one The distinction here is critically important. As in the case of which has a relative velocity of c in its frame of reference. the expanding elastic in the previous sections, the equations of motion of the elastic had little or nothing to do with the results Since light travels at all velocities from zero to C, no achieved by processing the film of the moving observers. The matter what our speed relative to the source, there is always a observers came away with an experimentally verified test of an component of the radiation continuum which is passing us at a object that was at rest or moving slowly from all frames of relative velocity of c, and which is thus able to cause the reference. While their observations demonstrated this, the physical interactions necessary to be detected. The end result elastic itself did not actually exhibit the properties recorded. is the appearance of light having the invariant speed of c from The experimenters developed a model that explained their all frames of reference. It is interesting and comforting to note results, but that did not reflect the reality of the situation. that the experimentally determined values of the fields in The principle of equivalence tells us that if we are in a Maxwell's equations predict that our observed speed of light is uniformly moving reference frame, then any experiment equal to the square root of the proportionality constant between performed in that frame should produce the same results as if mass and energy as derived by Einstein (denoted by c2). Of performed in a "stationary" frame. Clearly, therefore, the ratio course this famous equation, E = mc2, is not necessarily a of Maxwell's four quantities in the manner above will result in consequence of relativity theory, but derives naturally from a measured "velocity" of c in any uniformly moving frame of Max Planck's observations of light emissions from a heated reference. Thus each of several observers in reference frames object. However, given this important relation, we can gain moving at different uniform velocities will each measure or additional insight as to why it is that we perceive light only at observe the velocity of light from a distant source to be the velocity indicated by the c2 quantity. Since the conversion traveling through their apparatus at a velocity of c. As far as of radiant energy to mass energy can occur only if the ratio of the speed of light is concerned, this restriction on uniformly the two is given by c2, it would seem obvious that c is somehow moving frames of reference will be lifted. In RCM the related to the velocity at which matter can absorb or release restriction is not required, as the observer simply becomes energy in its own frame of reference. sensitive to higher and higher velocity components as he accelerates away from the source. References: From the above reasoning, it makes sense to state that the observed velocity of all electromagnetic propagation, in free Renshaw, Curt, IEEE: Aerospace and Electronic Systems, space, is c. Thus two observers in motion relative to each other "The Effects of Motion and Gravity on Clocks," Volume at any velocity will each see a beam of light passing them at the 10, Number 10, October 1995 velocity of c. Since it is the same beam of light, that beam of Renshaw, Curt, Galilean Electrodynamics, "The Radiation light must have components of velocity (with respect to the Continuum Model of Light and the Galilean Invariance source) of c plus the first observer's velocity (with respect to of Maxwell's Equations," Volume 7, Number 1, January, the source), and of c plus the second observer's velocity (with 1996 respect to the source). Since the source has no idea who its Renshaw, Curt, IEEE: Aerospace and Electronic Systems, observers are, nor of their velocities, it must produce light in a "Moving Clocks, Reference Frames and the Twin radiation continuum, at all velocities from zero to C. In this Paradox," Volume 11, Number 1, January 1996 manner, there is a component of that light which will pass any Renshaw, Curt, Galilean Electrodynamics, "Pulsar Timing observer, moving at any velocity, at a relative velocity of c. and the Special Theory of Relativity," Volume 7, Number This is the speed at which electromagnetic radiation is capable 2, March, 1996 of interacting with the physical world, as demonstrated by Renshaw, Curt, Aperion, "Apparent Super-luminal Jets as a laboratory measurements of light and the four electromagnetic Test of Special Relativity," Vol. 3, No. 2, 1996 properties of Maxwell. Any component of light not at this Renshaw, Curt, IEEE: Aerospace and Electronic Systems, velocity relative to the observer cannot produce any physical "The Time Delay of a Solar Grazing Photon," Volume 11, interaction, and is therefore undetectable by any physical Number 8, August, 1996 observer. Stated more concisely: Renshaw, Curt, Galilean Electrodynamics, "Fresnel, Fizeau, Hoek, Michelson-Morley, Michelson-Gale and Sagnac in Electromagnetic radiation propagates at all velocities from Aetherless Galilean Space," November, 1996 zero to some undetermined upper value C. As Renshaw, Curt, IEEE: Aerospace and Electronic Systems demonstrated by laboratory measurements, only that Magazine, "The Gravitational Potential for a Moving component of this radiation which passes a physical Observer, the Perihelion Shift of Mercury, and Photon observer at a relative velocity of c in the observer's frame Deflection," 1997, Volume 13 8 9