Wednesday, February 19, 2014

Quantum-Geometry Dynamics in a Nutshell (update)

It is not the existence of preons that we question here, but rather the consequences that follow the assumption that they do and whether or not these consequences are in agreement with the experimental and observational data.

As the title suggests, the purpose of this post is to provide a summary of the basic notions of quantum-geometry dynamics. This post will be regularly refined and updated.

Particles: There are only two fundamental particles ; the preon(+) and the preon(-).

Forces: There are only two fundamental forces: p-gravity which acts between preons(+) and n-gravity which acts between preons(-)

Matter: All particles and structures are made of preons(+) bound through p-gravity.

Space: Space is discrete or quantum-geometrical, hence it has structure. The discrete components of space are preons(-). Spatial dimensions emerges from the n-gravity interaction between its component preons(-)

Distance: The distance between any two preons(-) is equal to the number of leaps a free preons(+) must make to move from one to the other.

Preons(+): Preons(+) are singularly kinetic and they move by leap from preon(-) to preon(-)

Mass: the mass of any particle or structure corresponds to the number of preons(+) it contains.

Momentum vector: The momentum vector is a vector which describes the direction and momentum of a particle or structure.

Momentum vector of a preon(+): The momentum vector of a preon(+) is fundamental and written as \vec{c}. The magnitude of the momentum vector of a preon(+) is a large integer expressed in units of n-gravity, which as we saw above, is the force that acts between preons(-), which force a preon(+) must overcome to move from preon(-) to preon(-). The momentum of a preon(+) is given by \left\| {\vec{c}} \right\|=c.

Momentum Vector of a particle or structure: the momentum of a particle or structure is the resultant of the vector sum of all the momentum vectors of all its component preons(+). It is given by {{\vec{P}}_{a}}=\sum\limits_{i=1}^{{{m}_{a}}}{{{{\vec{c}}}_{i}}} where {{m}_{a}} is the mass of the particle or structure, the number of preons(+) it contains, and {{\vec{c}}_{i}} is the momentum vector of its {{i}^{th}} component preon(+).

Momentum of a particle or structure: The momentum of a particle or structure is the magnitude of its momentum vector and given by \left\| {{{\vec{P}}}_{a}} \right\|=\left\| \sum\limits_{i=1}^{{{m}_{a}}}{{{{\vec{c}}}_{i}}} \right\|

Speed: According to QGD, speed is an intrinsic property of particles or structures and is the ratio of the momentum over its mass. Thus the speed {{v}_{a}} of a particle or structure a is given by {{v}_{a}}=\frac{\left\| \sum\limits_{i=1}^{{{m}_{a}}}{{{{\vec{c}}}_{i}}} \right\|}{{{m}_{a}}} .

From this definition of speed (one which does not require the use of the time concept) we can see that the maximum possible speed is achieved when all momentum vector of a particle or structure move in the same direction. In such case \left\| \sum\limits_{i=1}^{{{m}_{a}}}{{{{\vec{c}}}_{i}}} \right\|=\sum\limits_{i=1}^{{{m}_{a}}}{\left\| {{{\vec{c}}}_{i}} \right\|}={{m}_{a}}c, thus \displaystyle {{v}_{a}}=\frac{{{m}_{a}}c}{{{m}_{a}}}=c . So the maximum speed for any particle or structure is c , which is numerically equal to the momentum of a preon(+). We write “numerically equal” because speed and momentum are two different physical properties which are equal in magnitude in special cases only.

Energy: The energy of a particle or structure is equal to the sum of the momentums (not the momentum vectors) of all its component preons(+). It is given by {{E}_{a}}=\sum\limits_{i=1}^{{{m}_{a}}}{\left\| {{{\vec{c}}}_{i}} \right\|}={{m}_{a}}c.

Note that though the equation {{E}_{a}}={{m}_{a}}cis similar to the E=m{{c}^{2}} , the QGD equation expresses a proportionality relation between mass and energy and not, as the relativistic equation, an equivalence. QGD also provides a fundamental explanation of energy which is based on a fundamental explanation of mass and momentum.


Effects: Since according to QGD there are only two fundamental forces, it follows that all other forces are effects of n-gravity and p-gravity.

Gravity effect: Gravity is an interaction between two particles or structures and results from the combined effect of n-gravity and p-gravity. It is given by G\left( a;b \right)={{m}_{a}}{{m}_{b}}\left( k-\frac{{{d}^{2}}+d}{2} \right) . Gravity is shown to emerge naturally from QGD’s axioms.

Electromagnetic effect: The electromagnetic effect results from absorption of preons(+), which impart their momentums to the interacting particles.

Weak nuclear interaction: The so-called weak nuclear interactions, which results in nuclear decay, results from the effect of gravity (which because d is very small, is very strong at the nuclear scales) and the electromagnetic effect.

Strong nuclear interaction: The strong nuclear interaction also results from the effect of gravity and the electromagnetic effect.


For detailed explanations of any of the notions summarized here, it is suggested to search for and read previous articles using the search window at top left of read the relevant chapters of Introduction to Quantum-Geometry Dynamics or for a shorter (33 pages) yet good overview, you may also read An Axiomatic Approach to Physics.

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