[AntonioLao]

general relativity as a modern field theory undoubtedly is based on the concept of continuous matter field. This is analogous to classical fluid mechanics using Eulerian formulation with its dependent variables of velocity. For general relativity, this velocity is a scalar constant popularly known as the speed of light in vacuum. This speed gives an upper limit to all matter flow velocity components. Note that the expansion of physical space is not limited by this speed of light. This speed is an exclusive upper limit for the motion of matter and energy but not for the motion of space.

These velocity components are understood to be motion of matter in or out of a given control volume and believing that this volume is the integration over a closed control surface. But what happens if this volume is not closed with a minimum size hole of a mathematical point? The spatial dimension will be limited to 2 but if the motion is limited to one dimension analogous to earth's rotation along a latitude line then 2 distinct topologies of motion can be formed. Each topology is used to describe a unique local structure of spacetime's continuum. The odd number grouping of these topologies formed matter (fermions) and the even groupings formed energy or force particles (bosons). The odd-even groupings formed a quantized spacetime fabric.

[d p fitzpatrick]

Scalar field vs Quantum - They are both really the same.

Here's a letter I recently sent tp Mathematical physicist Dr. Milo Wolff explaining this.



Milo,

I know you don't like moving into Murray Gell-Mann's realm of the quark but here's where the String theorists WILL.
They will say a vibration is a vibration is a vibration.

What can be seen as a Doppler shift in one spacetime realm will be seen as a mere wave in another realm because motion doesn't transfer from realm to realm; only waves do.

The String theorists will see that from another realm the electron - a standing wave entity - can be seen as being built from momentary vector resonances at the de Broglie wavelength.

But these are vector resonances, not scalar resonances.

A quantum of energy is also a momentary vector resonance between a spin up-spin down pair of electrons which at that instant of energy exchange, together become a spin-balanced bosonic pair.

But many of these pair make up many quanta that build into this spherical, scalar light entity we see.

[Light also can - and WILL shortly be seen - as Tony Bermanseder has stated, ". . . as a standing wave characterized by invariance of c relative to any observer in SR, GR or QR (modified M-Theory)."]

String Theorists - now have the math for and - will soon mathematically prove that this vector quantum, many of which are producing scalar quanta light is the same as the de Broglie vector waves, many of which are producing the scalar standing wave of the electron.

They will also then see, as Tony Bermanseder and I have, that TIME and particles are produced by these spherical, standing wave, scalar resonances which you, Milo, have been the first to produce the formula for.

You need to do some serious thinking about all this, Milo and where it will eventually lead to. You really do.

It is terribly important.



Cheers

Daniel P. Fitzpatrick Jr.
The fundamental theory behind String Theory

[AntonioLao]

d p fitzpatrick,

in some respects, i agree with you in regard to the results of the scalar product. But it's the noncommutativity of position and momentum that remains a mystery to me.

antonio lao