quantized direction

[AntonioLao]

Let there be an enclosed volume of space-time, and inside there is an elementary particle fighting to get out against the infinity of points comprising the volume. In order for this volume to exist it must defines an equipotential surface. Using arguments from calculus of variations the maximum volume is that enclosed by a spherical surface. If the elementary particle is located exactly at the center of the sphere then it has infinite number of directions to choose or equivalently infinite degrees of freedom to reach any point on this surface of equal potential energy in equal time interval.

On the other hand if the particle is situated off-centered then the shortest path for it to reach the surface is to backsight the center and then to move forward along the same 180° foresight bearing. The longest path is along the backsight direction while the perpendicular path established a geometric mean such that the square of the mean is equal to the product of the longest and the shortest path. Furthermore, this shortest path can be used to determine a quantized direction of a least action. If the time derivative of the mean is set to light speed then the time derivative of the longest path becomes the superluminal speed and the time derivative of the shortest path becomes the subluminal speed. Although light always chooses to move along this quantized direction, only in empty space devoid of matter does it move at the maximum speed where the phase velocity is exactly equal to the group velocity and the square of this maximum velocity is the reciprocal product of electric permittivity and magnetic permeability.

Since potential forces can be defined as the space derivative of potential energy a quantized direction becomes the greatest infinitesimal vectors of providing motive forces for all elementary particles. These are the repulsive forces of electromagnetic radiations. But if the off-centered particle chooses to remain inside the volume then its quantized direction back to the center establishes a gravitational potential whose space derivative gives the forces of gravity.

[mkirkpatrick]

If I was a really determined particle,I would find a way out,prehaps tunneling?



regards michael.

[AntonioLao]

prehaps tunneling

The particle needs to know and how to apply quantum mechanics and appealing to its wave nature.

[mkirkpatrick]

The particle needs to know and how to apply quantum mechanics and appealing to its wave nature.

It knows,tunneling runs in the blood?



regards michael

[AntonioLao]

It knows,tunneling runs in the blood?

However, the probability amplitude of the tunneling wave is extremely small.

[mkirkpatrick]

However, the probability amplitude of the tunneling wave is extremely small.

Thats okay Antonio,we are talking sub-atomic here are we not!






regards michael.

[AntonioLao]

we are talking sub-atomic here are we not!

Yes. But I still wish that as a wave I could randomly walk through solid walls. And those who are heavily intoxicated even if the door is wide open would still miss it.

[mkirkpatrick]

Yes. But I still wish that as a wave I could randomly walk through solid walls. And those who are heavily intoxicated even if the door is wide open would still miss it.

Don't worry I will run a "dry" house for soused waves and pissed particles!



warm regards michael.