The explanations in the previous sections of this work regarding the hidden aether and accelerated time reference frames lead to a new possiblity for describing quantum phenomena. Conventional interpretations of special relativity assume that the only position determinations that can be physically verified are those made by the observer in the relevant motionless non-dilated frame. However, this presumes that the observer can perceive only observations which are unique to his own frame, ignoring the possibility that moving alternative non-dilated frames and accelerated time reference frames could in a manner influence the velocities and positions of entities as perceived by a motionless observer. In the previous section titled, "A hidden aether", I put forward the proposition that position determinations of entities in motion in the context of the whole Universe must include an expanded definition of a reference frame, one that includes the influence non-dilated versions of dilated frames. These non-dilated versions of dilated frames though can also be considered to be accelerated versions of dilated frames. I now propose that position deteminations on the sub-atomic scale must be made relative to reference frames that inludes the influence of non-dialted versions of dilated frames and also accelerated time reference frames. Accepting that this is the case, it then becomes possible to account for the quantum nature of motion using the concept of time acceleration. Essentially, the premise is that at microscopic distances velocity and position determinations are influenced by two extra reference frames, these being a time reference frame that is accelerated relative to the dilated frame, this creating an alternative non-dilated frame, and also, a "stretched out" space-time reference frame that is accelerated relative to both the motionless non-dilated frame and the moving alternative non-dilated frames. Consequently, the complete a picture of a moving mass particle must include it's dilated state, it's alternative non-dilated state, and it's accelerated state, all existing simultaneously, and all simultaneously determining the positions of sub-atomic particles.
Earlier I explained how a frame that is accelerated relative to a non-dilated frame can be understood to be spread out as compared to a non-dilated frame. In that explanation it was presumed that the accelerated frame simply had a linear motion relative to the non-dilated frame, but this is not necessarily the case. I propose that on the sub-atomic scale accelerated and non-accelerated reference frames should be considered to move in an oscillating motion relative to each other, these oscillations defined relative to the point within the non-dilated frame where there exists zero motion relative to the accelerated frame. This oscillatory relationship reflects the fact that the space of an accelerated frame is simultaneously "stretched" in size and "folded" in shape relative to the space of a non-dilated reference frame. I propose that this oscillating motion is in fact in a manner observed from the perspective of an observer in the motionless non-dilated frame, and the observable results are what we now consider to be the consequences of quantum phenomena. These observed variations in the positions of sub-atomic particles should actually be understood to be the result of the existence of both alternative non-dilated reference frames and accelerated time reference frames, and it is because of the nature and structure of space-time as determined by contraction that these accelerated frames exist and become relevant frames of reference for determining the positions of sub-atomic particles.
In regards to a particle's total mass-energy as measured when it is considered to be in an accelerated frame as compared to a non-dilated or dilated frame, it's rest mass in terms of an accelerated frame will be less than it's rest mass as measured in terms of a non-dilated and dilated frame. However, because the particle is moving faster relative to the accelerated frame as compared to the non-dilated frame, energy is added by this extra motion, and consequently it's total mass-energy as measured from the accelerated frame is the same as that measured from the non-dilated frame.
The fact that a particle which is defined as being in an accelerated state has a velocity relative to the zero-velocity of the relevant accelerated time reference frame explains why a time acceleration for the particle is not easily detected from the perspective of a non-accelerated, non-dilated frame. The velocity relative to the zero-point velocity of the relevant accelerated frame puts the particle in a dilated state relative to that frame. This time dilation counters the time acceleration, and the result is a time state that approximates the original dilated state of the particle. The difference between a particle in this combination accelerated-dilated state and a particle in a simple conventional dialted state is reflected in both measured energy and position variations, these normally attributed to quantum phenomena.
The concept of a particle state being defined as a combination of an accelerate and dilated state parallels the concept introduced in the previous section on special relativity which revealed that the distribution of matter within the Universe is determined by a multitude of non-dilated frames, and not just the non-dilated frame of a particular observer.
The variations in position due to the oscillating motion between an accelerated frame and a non-dilated frame as previously described can be made to be consistent with the variations predicted by the probability wave of quantum theory to a degree, but the explanation above still doesn't provide a complete solution though, because of the non-localized condition that is observed for particles under certain conditions. The solution to this problem lays in a proper understanding the structure of frames that are accelerated relative to a non-dilated frames, as determined by the contraction approach to understanding space-time, which shows that accelerated frames are actually expanded relative to non-dilated frames. This is not a straight forward expansion though, as there is a contraction associated with it. The best way to conceive of this is to view space in terms of individual units laid end to end, with these units contracting in size, but also separating from each other, as they enter into a time acceleration. In a particular way, space "breaks up" and separates when it is accelerated relative to the normal non-dilated time reference frame. This separation exists only from the perspective of someone in the normal non-accelerated frame though, since from the perspective of someone in the accelerated frame space remains continuous, since for this observer this frame is the normal reference frame.
With the above explanation there are now have two aspects of time acceleration, one aspect measured relative to a dilated time frame, this producing an alternative non-dilated frame and the local variations in the expected positions for microscopic particles, and the other aspect measured relative to the normal non-dilated frame, this producing a discontinuity in space as perceived from the perspective of the non-dilated frame, though space is still continuous from the perspective of an observer in the accelerated frame, and this produces the non-localized variations in the expected positions of microscopic particles. Ultimately this leads to the description of a particle in terms of two distinct parts, or aspects, one part being that which is substantially measured, and which partakes in the previously mentioned oscillating motion, and the other part being a type of ghost particle that can only be indirectly measured, but which indicates, like a pilot wave, where a particle will manifest itself in the future. A proper way to picture this is to see that while the measurable part of the particle goes through a cycle of oscillations at the local level at a particular position in space during the period of that cycle, the ghost particle moves to another point in space (or the same point under some conditions) as determined by it's accelerated state. At the end of the period of the cycle of local oscillations the measurable aspect of particle disintegrates at it's current position while beginning another cycle of oscillation at the new location as determined by the ghost particle. In regards to mass-energy, we can say that the ghost particle has an undetectable minuscule mass (possibly sub-planckian based), with it's measure based upon the accelerated time reference frame (that is, the frame accelerated relative to both the dilated and non-dilated frames, not just the dilated) associated with it, this ghost particle actually representing the non-dilated version of the particle in terms of this accelerated state. This means that though the ghost particle moves relative to an observer in the normal non-dilated frame, in terms of this accelerated frame it represents the frame's motionless position, and thus any particle that we observe is actually moving at a certain velocity relative to this accelerated frame's motionless position, and it is this motion that gives it the masss-energy that we observe. With these two time accelerations just described we can exactly account for all changes in positions for microscopic particles, including the seemingly discontinuous changes.
