THINGS ARE NOT ALWAYS ABOUT YOU, PIONEER
When I wrote about the Pioneer Anomaly as a clear indication that the Universe has actually FOUR NONCOMPACT DIMENSIONS I was in quite a hurry and should had written the paper, posting it in longhand or in a fool proof manner…J People never do their homework and simple reasoning have sometime to be explained by another reasoning that yields exactly the same result. A good theory should be like that. There should be many ways to reach the same conclusion if the logical framework is consistent.
When I calculated the acceleration or deceleration in this case, i realized that if you only consider the 3D spatial coordinates and miss the curvature of the 3D hypersurface within the 4D spatial manifold, one missed the centripetal acceleration, that is, at any given time; light while seeming traveling in straight lines, is actually making a curve to reach Pioneer. This incorrect perception easily explains a delay.
Let’s first review the amazing things that come out of the Pioneer Anomaly problem. First let’s review what the Pioneer Anomaly is:
The solution can be derived directly from the topology. It is our current understanding that only matter curves spacetime, this means that locally the curvature is quite well defined by the inexistence of localized matter and equal to zero..:) That is, without the obvious occurrence of matter we believe that we live in a locally flat space…
Let’s see what happens when one measures the speed of light. The measurement is shown below. First let’s think within our standard paradigm. Instead of getting lost on details like interferometric measurements etc, let’s consider just shooting a laser pulse to a mirror place at a known distance and measure the time delay for the echo (mirror reflection).
The measure time delay between shooting the laser pulse and measuring the reflection is equal to twice the distance divided by the speed of light. Simple problem, isn’t it…J
Under this paradigm, the time it takes for light to bounce back from a mirror is given by 2L/c. This considers that light and the mirror are traveling or existing in the same dimension (3D) which is not the Hypergeometrical Universe Paradigm. There, light (a spatially modulation of the source of a dilaton field) travels within the 5D spacetime (4D spatial manifold). Anything else just flows within the 3D Hyperspherical Universe, which itself travels through the 4D spatial manifold.
The answer to the second question is that one can only discover what is going on in a 5D spacetime while living in a extremely flat 4D spacetime if one uses the EYE OF THE MIND. One has to concoct an alternative paradigm that explains everything… Something that explains something is not enough… As you know, there are plenty of people who will make a living out of putting down new ideas… Only a complete paradigm would survive scrutiny. That is what I created in the Hypergeometrical Universe Theory. I had to provide a new model for matter that would provide the basis for Quantum Mechanics, a topology that would explain Universe Expansion, Giant Black Holes in the Early Stages of the Universe, Double Jet Black Holes, Cooper Pairs, Hund’s Law, Grand Unification as well as experimental applications like the Coherent Nuclear Fusion Experiment.
The situation is different if we consider that the Whole Universe as we Know it is traveling at the real speed of light perpendicularly to this experiment (no matter where we point the laser..:)).
The Hypergeometrical Universe paradigm draws a totally different picture for the same process:
If you consider our topology, it is clear that there is a curvature and that is equal to 1/R0.
Now let’s get down to the Pioneer Anomaly and how do we measure how long the Universe is alive from the Pioneer Spacecraft deceleration…J
The actual experimental setup is a complex interferometric process but it mimics the standard pulse experiment. Pioneer emits a microwave pulse at precisely measured intervals (dt). The measure interval on Earth depends upon Pioneers speed. 
The first thing to consider is what would be the perceived deceleration resulting from the geometry. To do this, we need to consider how much light has to travel back as a function of the farthest distance traveled by the spacecraft.
This figure shows what would be the path traversed by each pulse emitted by the Pioneer spacecraft. The angle of the light ray is always 45 degrees. The leftmost radial line represents Earth position. This means that when Pioneer is far from Earth by 45 degrees or PI/4*R0, light will never come back (the light ray will be parallel to the Earth radial line. Two parallel lines never meet…J
Let’s say that at time zero Pioneer is at R0 from the 4D Center of the Universe and L from Earth and let’s derive the deceleration from the simple geometry.
Let R(t) be the Radius of the Universe at the time t:
Where time is being measured after a light pulse is emitted from the Pioneer while it is at distance from the 4D Center of the Universe equal to R0.
The Cosmological Angle associated with Pioneer at time t given by:
The angle alpha is called Cosmological Angle and it is measured from the actual Center of the Universe.
The equation for the photon trajectory leaving the Spacecraft and reaching Earth later is given by: 
Equating this equation to zero and solving for t’, one obtains the time it takes from light to come from Pioneer to Earth at any given time or Pioneer position. Notice that this has nothing to do with Pioneer. This argument only refers to how the path traversed by light depends upon the spacecraft distance and Cosmological Angle.
The perceived distance traversed is given by c.t’:
Taking the second derivative, expand in Taylor Series and simplify to obtain the acceleration as:
The calculated acceleration is twice the observed acceleration since we calculate
The observed acceleration is 8.75e-10 m/s2, the speed of light = 299792458 m / s. This yields a value for R0= 2.05E+26 meters.
Since the 4D observed velocity is 
m this means that the Universe is 
years old or 1.5364E+10 years or
One salient point is that the Hypergeometrical Lightspeed Expanding Shockwave Universe expands at the observed speed of light, this means that the material world travels slower than the dilaton field, by a factor of cos(45) or 
.
This conclusion is very important because it breaks the symmetry between dilators and dilatons.
Up to now, I considered that dilators and dilatons always traveled at the only allowed speed (c).
Of course, I notice that dilators have inertia with respect to lateral motion but I thought that the radial motion was the natural motion of a metric deformation, thus requiring no initial push to be achieved.
If I accept that the dilaton speed or light speed is actually larger than the observed speed of light then the picture associated with the initial Big Bang changes from a simple decaying process into a tangential explosion which set the 3D Hypersphere to travel at the observed speed of light.
It is clear that a dilaton field cannot accelerate dilators to its speed (sqr(2)*c) because interaction has to occur through RETARDED POTENTIALS. Retarded Potentials always propagate at c (Lightspeed) due to the geometry.
The interaction of dilators with the retarded dilaton field from other dilators produces a distribution of tangentially dilators traveling at c which is also a distribution of radially traveling dilators at that same speed. In other words, a lightspeed traveling Hyperspherical Universe and an sqr(2)*c dilaton-dilator interaction are a consistent solution to the Big Bang problem.
This salient point can be summarized as:
The speed of light is SQR(2) times C or light is faster than the speed of light..
This is due to motion be part of a coherence that was placed in motion at the beginning of times through the interaction of near field dilatons. The interference pattern of near field radially propagating homogeneous dilatons travels along 45 degrees. This is a very salient point.
Cheers,
MP
PS- I only have a few minutes to think about this problem every other month…Please feel free to disagree and provide a counter argument. At this time in the morning and without my coffee, this seems to be the only possible conclusion…J
Cheers,