Field of Dreams

We are all familiar with wide open fields, the concept of area and volume. Since Newton discovered that his Law of Gravitation had an inverse distance squared dependence, we were inclined to conclude that Gravitation and later Electromagnetism were some kind of Force that spreads out (dilutes itself) onto an area.

The concept of field was introduced to associate an effect of the Force on any given point of space. A Force Field is like a strain on Space and it is an extensive property of the Force Generator, be it a charge or a mass. An Extensive Property is a property that scales up with the number of components, be they charge or mass.

Current Science still believes this and that poses barriers on the minds of scientists. First, they cannot come up with anything other than the concept of a Field, given that their most successful theory is called Quantum Field Theory, which has field in its name...:)

The concept of field and its geometric interpretation (basically a non-elastic strain) requires that the introduction of any dimension to be compact, like very, very, very small circles attached to each point of our 3D Space. If we disregard the silliness of having small circles all over the place, we can see the reason for the exclusion of non-compact dimensions.

1. The first one is if the dimension is non-compact, why can't I go there, that is, move from our current (x,y,z,R) to (x,y,z,R+1)?
2. Are there any other possible logical framework where "deformation of space" carried by the Field to be an extensive property? In fact, this question is never even asked.
3. If there is an extra non-compact dimension, would the field be diluted into a 'surface' that has a cubic distance dependence, so the Force would decay with the inverse distance cubic instead of the inverse distance squared?

ANSWERS:

1 - The first one is easily explained within the Hypergeometrical Universe Theory. HU considers the Universe to be a lightspeed expanding hypersurface moving inertially at the speed of light c as a result of a 4D Big Bang or Initial Dimensional Fluctuation Decaying Process. Interaction (both Gravitation, Electromagnetism and Light) is carried on the top of a dilaton field (elastic metric waves as opposed to inelastic metric strain). Light is seem as a spatial modulation of the dilaton field since the dilator is moved as an oscillating dipole during light emission. Why can't we move along R? The reason is due to momentum conservation along R. Interaction cannot change velocity along R. It can only change velocity tangentially (within the 3D hypersurface).

2- HU proposes a logical framework based on metric waves of very, very high frequency (10^(24) seconds) and less than a femtometer wavelength. Since interaction happens through waves, there is a need for some synchronicity mechanism, otherwise they would just average down to zero effect. This mechanism is the Quantum Lagrangian Principle, a fancy name for dilators always dilating in phase with the surrounding field. This resynching has the effect of creating a Cosmological Coherence, that is, the whole Universe is re-synched at each step of expansion. If metric wave generators are dilating space in phase, their amplitudes will add up extensively (that is, the wave of two dilators is twice as high, of three is three times as high as one, etc). Using this simple concept, HU was able to derive from first principles the Natural Laws. The QLP can be seen as a No-Work For Lazy Dilators or Space Deformation Quantization constraint. No-Work is the bread and butter of the Lagrangians...:)

3- Dimensionality Reduction. To understand how HU explains dimensionality dependence upon a Force, one has only to see the picture above (this plot is compressed on the vertical, so the angles are distorted - they should always be 45 degrees with respect to radial direction).

That is the cross-section of the proposed 4D Universe along xR, thus a 2D cross-section. The curved line is a line that intersects every circle at 45 degrees with respect to the radial line. Circles represent epochs of our Universe expansion. HU requires that light traveling on 4D, to have a speed sqrt(2)c. This means that light traveling at 45 degrees will always travel the same distance radially and tangentially. All all possible lines in surface connection the center of the 4D Universe to us, only one line (1D) satisfies the Time of Arrival Constraint. Any other path would arrive too early or too late (remember 4D speed of light is sqrt(2)c). Of course, dynamic forces like Electromagnetism and GyroGravitation still requires extra vectors pointing within the 4D space. Those vectors provide direction. The force intensity still only depends upon the curved line-of-sight distance.

The fact that light that reach us (at the top of the largest circle) can only travel through that curved Universe Timeline means that interaction disregard all the 2D paths to confine itself on a 1D because of Time of Arrival Constraint. This might seem like an argument for dimensionality reduction from a 4D to 3D interaction. In reality, it is an argument for dimensionality reduction from a 4D to 1D interaction. HU considers that interaction only depends upon a curved line-of-sight distance (and velocities/time for dynamic forces). This is the reason why HU derived Natural Laws from a simple calculation based on circles (as opposed to areas).

Since I cannot insert equations and pictures here, you might have to go to the rebuttal:

Natural Laws derivation is presented on the HU theory article (referenced within the Supernova article:

Hypergeometrical Universe Theory

My challenge to Cosmology is presented here:

Supernova High Z Predictions

Here is my rebuttal to Helyon:

Helyon may or may not reconsider my article publication in view of my rebuttal. I sent them a letter pointing to my arguments but didn't hear from them. Hopefully they will open their minds...:)

Elsevier has shown extreme courage in the past:

by publishing scientific articles of Jewish Scientists during the Nazi Era. It will take some courage and wisdom to revisit my rebuttal..:)

Cheers,

MP