Introduction to RCM Theory
                                                   Curt Renshaw
                               680 America’s Cup Cove, Alpharetta, Georgia 30005 USA
         ph: (770) 751-9481 fax: (770) 751-9829 email: web site:

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

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.

                                                                      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
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,
                                                                      '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
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
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
different velocity. Such is not the                  km                         300,000
case with light. If the truck driver                                            km
flashed his brake lights at you and
                                                                                                          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.
     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.
     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

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