13junposi

b. Position determination

According to quantum theory, the de Broglie wavelengths and waves that are associated with an entity in motion represent the probability over a period of time that the entity will be found at a particular position in space. The waves of contraction theory, which I'll refer to as ex-con waves, can be considered to be longitudinal waves that actually shift the position of the center of an entity relative to the position that it would have if it's position were solely determined by it's conventional velocity (the velocity associated with a particular time dilation). This shifting in position, at a rate that seems to be faster than possible and without the changes in energy and momentum that one would normally expect, is made possible by time acceleration.

According to quantum theory, localized particles are described by a summation of waves. This is the essential theoretical reason that in general they cannot be considered to have only one energy, as it takes many different energies, each defined by a particular wavelength, to describe the particle as a localized particle. In the contraction approach, all entities of matter can be described in terms of an alternating expansion from and a contraction towards a point in space. This expansion and contraction both defines the entity and affects it. However, the entity can always be considered to have a center, a point relative to which other aspects of the entity, and other entities and space, have motion. While the center of the entity and other aspects of the entity can be undergoing many different motions, the entity can always be defined in terms of a basic expansion and contraction. Mathematically, this motion can be described in terms of a rotating vector (using only the real part, when appropriate). The rotating vector representing a photon would have a length equal to (c)x(1), and it's origin would have a linear velocity of (c). It would have frequency equal to E/h, where E is the photon's energy, and wavelength equal to c(h)/E.

A particle of matter can also be described in terms of an alternating expansion and contraction from and towards a point in space, and thus, as a rotating vector. The best way to conceive of this is to consider the vectors that represent the photons that comprise a matter particle to have a common origin which is moving in a circular path, with a velocity of c. This can be described by a new rotating vector. If we assume that the frequency of this vector is equal to mc2/h, then the length of the vector representing a mass (m) equals (c)(h)/2pi(mc2), since the rotating velocity of the vector is a constant (c). The linear velocity of this new vector is undetermined.

With the ex-con wave representation of matter we can now explain the continual variations in the position of the center of an entity, this determining it's measured position, that occur because of time acceleration. Because of the simultaneous existence of the past and present, the wave representing the past existence of the particle interferes with the wave representing it's present existence, this causing variations in the particles rates of expansion and contraction. This causes the entity to be affected by accelerated time reference frames, since a particle's relevant time condition is determined by it's relative rates of expansion and contraction. These accelerated time reference frames are characterized by reductions in mass, this caused by the interference of the past aspects of the entity with the present aspect, but these reductions in mass are coupled with corresponding velocities which are oscillatory in nature. These velocities, which I'll refer to as ac motion, restore the measured mass of the particle. They also can be considered to be circular in nature and can also be described in terms of a rotating vector. The combination of mass reduction and ac motion means that the measurement of the mass-energy of the particle remains approximately the same as that determined by it's conventional velocity, though now the mass has a shifting in position as compared to the position as determined by the conventional velocity.

The mass waves (not meaning conventional usage of the term) representing the past and present aspects of an entity should actually be described in terms of two wave groups, one representing the past existence of the particle, the other the present existence, this due to the layered nature of the contraction and expansion that exists in reality. The summation of these two wave groups defines a third wave group with a varying amplitude. This amplitude then describes both the continually varying mass and an inversely corresponding velocity for the entity.

The variations in ac velocity can be further described in the following manner. In the contraction approach, the de Broglie waves and wavelengths which are associated with an entity reflect the fluctuations in amplitude of the ex-con waves associated with the entity. To account for all possible positions of a particle, however, there must be two types of ex-con waves (ac waves) associated with the motion of an entity, each associated with two different aspects of the particle. This concept of two different aspects was described for a photon in the previous section, and is basically the same for a mass particle. Each aspect of the particle is described by a wave group, each group being the summation of the past and present wave groups mentioned earlier. The first group of waves, which I'll refer to as ac-1 waves, shifts the position of the entity within a range of +- 1/2 the de Broglie wavelength. Thus, the maximum amplitude (Amax) of this wave group is +- 1/4 the de Broglie wavelength. The second set of waves, which I'll refer to as ac-2 waves, shifts the position of the entity in increments of +/- N/2 x (de Broglie wavelength), where N is equal to a whole number, and the distance traveled over a base time period (an eignstate of the de Broglie time period) falls within a range that is less or equal to the length (L) of the space surrounding the entity. (L) is always equal to a whole number times one half the de Broglie wavelength. Also, there is a maximum possible value (B) for the amplitude of the ac-2 wavepacket, and this is determined by the mass and energy of the entity, and a constant, (b), derived from (Tp), the age constant.

A major characteristic difference between ac-1 motion and ac-2 motion is that while the position changes caused by ac-1 motion can be measured continuously, the position changes due to ac-2 motion can only be measured incrementally. The ac-2 wave itself is continuous, but it just indicates where the entity will be measured at the next interval of time, this interval an eignvalue of the de Broglie period. This partially explains the quantum nature of measurement. Basically the ac-2 wave determines where a particle will be along the ac-1 wave. It is a pilot wave which can be considered to be superimposed over the ac-1 wave, and which does not affect the ac-l wave.

The conceptual foundation of this structure is as follows. The ac-1 motion of an entity shows the path of it's center as the center changes position while the entity contracts with time. When it reaches the end of the path, this at the completion of the relevant time period, it will begin another path of contraction, either in the same area of space or another one, this determined by the ac-2 wave group, or in other words, the pilot wave. Consequently, during each pulse of contraction, ac-1 motion determines the location of the center of the entity and the path that it takes during a pulse, and ac-2 motion determines where that path will be positioned during the next pulse of contraction.

A third factor determining the position of a particle is the shape of the path of the ac-2 wave. This is determined by the "shape" of the space that it is in. In the contraction approach, space can be "folded" over onto itself in such a way that each "fold" of space does not interfere with other folds, while existing in what seems to be, from our vantage point, the same space. The net result is that while a particle might be moving in one particular direction along the ac-2 wave, since the space in which the ac-2 wave exists is folded, the particle will oscillate, following the folds of space. Thus, while the particle moves in only one direction in terms of it's motion along the wave, since the wave follows an oscillating path through space, so does the particle. This "folded" path can be represented mathematically as a circular path.

Each position determining factor, the ac-1 wave, the ac-2 wave, and the "shape"; of space, which I'll refer to as the ac-3 factor, can be considered to act within it's own level of physical reality. The first two factors, described by the ac-1 and ac-2 waves, can be considered to be internal to a particle, while the ac-3 factor can be considered to be external to the particle, though the particle itself affects it's value.

A wavepacket of ac-1 waves can be deduced in the following way. Since the interpretation of the de Broglie wave is that it indicates the probability that a particle will be found in a particular position, it also describes the variations in the ac-1 wavepacket's amplitude. Assuming that there is a de Broglie frequency, (fdeB), which equals mv2/2 h, and the de Broglie wavelength, equal to h/mc, each are base eignvalues of the ac-1 wavepacket, and realizing that the de Broglie wavelength divided by four indicates the maximum possible amplitude of the ac-1 wavepacket, then with the use of Fourier transforms it is possible to determine a summation of waves that describes the ac-1 wavepacket. The equation describing the ac-1 wave group would take the form of a time dependent Fourier wave equation, with the de Broglie frequency being an eignstate of the base angular frequency (wn).

An equation describing ac-2 motion can be deduced in a similar manner, with one major difference. There are two different groups of ac-1 waves, with the first group, which I'll call the expansion group, having wavelengths equal to less than one half the length (L), and the second group, which I'll refer to as the expansion group, having wavelengths greater than (L)/2. The amplitudes and numbers of the expansion group's waves are equal to the contraction group, but the two groups are 180 degrees out of phase. Thus, when there is sufficient space, greater in length to 2(L), surrounding a particle, the two wave groups cancel each other out, and the particle is localized. However, when the particle is in a space with a length of less than 2(L), it will begin to spread, because the contraction group of waves begins to diminish in number, eventually numbering zero at a length of 2(L). This results in the particle's center being relocated to different positions, as determined by the ac-2 expansion waves, within the boundaries. Otherwise, ac-2 waves can be described in a similar manner to ac-1 waves. The length (B) represents the maximum possible amplitude, (A2max), for the sum of the group of ac-2 waves. The frequency, (fa2), of these waves are eignvalues of both the de Broglie frequency (fdeB), and a base ac-2 frequency (fac-2), equal to (fdeB)/(a2). The wavelengths of these waves are eignvalues of both the de Broglie wavelength and the de Broglie wavelength multiplied by the ac-2 acceleration factor, (a2). The ac-2 acceleration factor can have a value greater, less, or equal to one. The equation describing the group of ac-2 waves also takes the form of a time dependent Fourier wave equation, again with the de Broglie frequency being an eignstate of the base angular frequency (wn).

The method described above is only one possible way to determine the waves comprising the ac-1 and ac-2 wavepackets which describe the variations in velocity and mass caused by time acceleration. Another method is to simply take hypothetical positions with time which satisfy quantum predictions, then determine the Fourier transforms. The frequencies and wavelengths obtained in this manner should in some way correspond to frequencies that are obtained in the above manner. However there is also another approach, one based upon the summation of waves and frequencies that naturally occur in reality because of the structure of space-time as determined by contraction. In this approach, a minimum energy (equal to h/Tp) for electromagnetic energy, determined by using the radius of the Universe as the maximum possible de Broglie wavelength, can be used to determine a minimum velocity for any particular mass. This can be used to define a minimum frequency for the ex-con waves of any mass quantity. Using the constant Tp (and roots, explained later), wavegroups for any mass in motion can be constructed. I am presently developing this approach.

c. Energy and momentum fluctuations

As presently understood in the quantum approach, the measure of the energy and momentum of a free particle cannot be exactly determined. This means that if a particle is considered to have a particular velocity as it moves through free space, natural variations in the measure of energy and momentum will exist. According to quantum theory, these variations in measurement reflect the nature of the structure of the wavepacket representing the particle. Since the particle is considered to be a wavepacket, each wave of the wavepacket, all with different energies and momentum, must be considered to be an integral part of the whole. Thus, the energy and momentum cannot be determined exactly, but only predicted within limits. This problem does not exist in the contraction approach because in this approach a particle is not a composition of different waves, it's position and energy are simply determined by waves which result from the ex-con motions that define the entity. In contraction theory, the variations in the measure of energy and momentum that occur for a localized particle in motion as described in quantum theory reflect variations in the inverse proportionality of the mass fluctuations and the ac-1 velocity that affects an entity because of it's time acceleration state. Consider that a free particle of particular mass and fixed velocity can have a variety of possible measures for it's de Broglie wavelength. According to quantum theory this is because the particle is considered to be a summation of waves of different wavelengths, while according to contraction theory, this is actually the result of the variety of possible sets of ac-1 velocities that a particle of a particular mass and velocity might have. This variety of sets of ac-1 motion correspond with the variety of possible measurements for energy and momentum for that particle.

According to contraction theory, mass, velocity, and the amount of space surrounding a particle are what determine the degree to which the h-based measures of it's momentum and energy vary. The mass measurement fluctuations and the ac-1 motion associated with the time accelerated state of a particle must inversely correspond to each other in order for the measure of the energy and momentum of the particle to remain constant. If these variations don't correspond, there will be a measured change in the particle' s energy and momentum.

As explained early, there are two types of ac-2 waves associated with a particle, one type I call expansion ac-2 waves, the other contraction ac-2 waves. When the contraction waves are cut off by boundary conditions, the expansion ac-2 waves give the particle and expanded realm of positions. When the contraction ac-2 waves are not cut off though, the particle will be localized and the combination of ac-2 expansion and contraction come to affect the ac-1 mass and velocities variations of the particle, this resulting in a change in it's measured energy and momentum.

When there is not an exact correspondence between the mass and ac-1 velocity fluctuations, there will be a change in the measurement of it's energy and momentum. Fluctuations in the mass and ac-1 motion of a particle are described in terms of relativity in the following way. Normally, in relativity, an entity in a non-dilated frame has a faster rate for the passage of time, and has less energy and less momentum, these both being zero, than a particle in the slower dilated frame, which has energy and momentum described by (m-mr)c2 and c(m2-m2)1/2 respectively, where mr is mass as measured in the non-dilated frame. However, when the faster frame is considered to be an accelerated frame, that is , accelerated relative both a dilated frame and it's relative non-dilated frame, the velocity associated with the time acceleration gives the entity energy, restoring it to a level equal to that of the entity when it is in the dilated frame. This is perfectly consistent with special relativity, since the motion caused by the time acceleration simply causes the same changes as would motion for any entity, an increase in energy, restoring the energy to the entity that is lost due to the mass reduction which is associated with time acceleration. However, in the accelerated frame, in order for the h-based measurement of it's energy and momentum to remain constant, the ac-1 variations of mass must correspond with the variations in ac-1 motion. If they don't, there will be changes in the measured energy and momentum. When the degree of ac-1 mass reduction is less than it should be, or when the rate ac-1 velocity is faster than it should be, there will be an increase in the h-based measurement of it's energy and momentum, and when the degree of mass reduction is greater than it should be, or the ac-1 velocity is slower than it should be, there will be a reduction in the h-based measurement of it's energy and momentum.

In order to have the energy and momentum fluctuate to the same degree requires that there be an altered definition of the relationship between the energy of a particle and the velocity caused by time acceleration. The energy of a particle is normally define by the equation E=M(Csq.). For a particle in a time accelerated state, the equation describing it's energy should be changed to E= MC(Ca), where Ca represents the expanded velocity of light that results from time acceleration. Thus, even though in a time acceleration state mass is reduced by a factor of 1/a, where (a) equals the time acceleration factor, total energy remains constant.

The variation in the de Broglie wavelength and frequency which produces a change in the measurement of it's energy and momentum, in the contraction approach, corresponds with a variation in the amplitude of the ac-1 wave, and this amplitude is still measured relative to the position as determined by the velocity caused by the time dilation associated with the original energy. Thus, this must be evaluated in terms of the variation in the de Broglie frequency, and the de Broglie wavelength, and not a variation in the conventional velocity associated with a change in energy and momentum. Rates of ac-1 mass reduction and velocity are each determined by the structure of space-time, but are each influenced differently by changes in conditions, namely the amount of space that the entity is in. The amount of space that an entity is in also influences it's ac-2 velocity. Thus, variations in the measure of energy and momentum correspond with changes in the ac-2 wave group. The degree of energy and momentum measurement variation, which is obviously related to ac-1 motion since the de Broglie wavelength changes, is also related to the value of the ac-2 velocity of an entity. A completely non-localized entity can have an ac-2 velocity of up to +/-Nmax (v), where (v) is it's conventional velocity and (Nmax) represents the maximum ac-2 acceleration factor possible for the entity under the given conditions. For a completely localized entity, energy varies by the maximum degree possible, while the change in position due to the ac-2 velocity always equals zero. The variations in the maximum possible ac-2 velocity are due to the relative values of the oscillating periods of the sub-frames associated with the entity, and these are related to the rest mass and energy of the entity, and the amount of space surrounding it. The limit described above for the maximum ac-2 motion also defines the point where energy and momentum measurement variations begin to occur naturally, this causing a change in the cycle of time accelerations that the particle undergoes. Below this limit, the entity will maintain a constant energy unless energy is added from outside the system. When energy measurement variations occur naturally due to time acceleration, the time dilation associated with the entity doesn't change, whereas, when energy is added from outside of the system, the time dilation associated with the entity will change. I will present a more complete mathematical analysis and description in a forthcoming mathematical supplement.

d. Conclusion

On the previous pages I have attempted to show that the order of variation in both position and energy of an entity is determined by the expansion and contraction factors that describe an entity's position and energy, and that these can be described in terms of the sums of basic expansion and contraction factors. The orientation of these basic ex-con factors at any point in time determines the state of the entity, in terms of both position and energy. Groups of ex-con factors determine the dilated state and variations in the dilated state, while groups of con-ex factors determine the accelerated state and variations in the accelerated state of the entity. These factors are determined by the interaction of the basic ex-con factors affecting matter, energy and space. I've also presented a simple and direct formula for determining acceleration due to gravity, derived with the contraction approach, and I think this shows the unified nature of the contraction approach. On the following pages I will explore the concepts of contraction theory in more depth, describing the basic structure of space in terms of contraction and the basic ex-con motions involved in relativistic of motion.

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