functions of Green’s symmetry

[AntonioLao]

In the theory of differential equations, the influence function describes the effect of a force at a point s has on an arbitrary point at x, denoted by G(s, x). Further analyses discovered the fact emphasizing the important of Maxwell-Raleigh reciprocity law that these Green’s functions are symmetrical: G(s, x) = G(x, s), a force at the point x gives the same effect on a point at s. This symmetry always holds for two variables s and x or force and distance.

Einstein had realized this physical symmetry even before developing relativity. When he observed that the electromagnetic force generated by a moving electric field with a stationary magnetic field is the same as that generated by a moving magnetic field with a stationary electric field. What counts is just relative motion and not absolute motion which is not detectable. Furthermore, a point force of finite magnitude is, of course, a mathematical fiction not physical reality. A nonzero force concentrated at a single point would imply infinite pressure. On the other hand, the symmetry of Green’s functions in general applies to two physical variables of force and distance whose product is an energy function. If either the magnitude of force or distance or both is zero then the energy function is also zero. Since zero-point energy is finite even though very weak none of these variables can be identically zero. Nonetheless, mathematical normalization setting to unity is allowed for either variable by rational functions.

If the time is an implicit parameter of the functions then the symmetry is broken thus violating gauge invariance. However, at infinitesimal local region of spacetime, symmetry is conserved only for squares of the energy functions.

[mkirkpatrick]

Part of symmetry must also include the absolute pressure that bears down on all
existence,that subtle pressure that allows a mushroom to displace,and at times dislodge,
paving stones thousands of times heavier that itself.



regards michael/

[AntonioLao]

mushroom

Not the armageddon one as foretold by prophesy.

[mkirkpatrick]

Not the armageddon one as foretold by prophesy.

Thats right,and this is no toads-tale?


regards michael.

[AntonioLao]

this is no toads-tale?

Or dragon tales.

[mkirkpatrick]

Or dragon tales.

The scales of the dragon are worth a fortune in Chinese medicine!



regards michael.

[Dr. Waldrope]

M,

No price info for dragon scales but dragon bone (long gu) is $4.79 / lb. and dragon teeth (long chi)is $10.49 / lb.

Antonio,

Can you explain to me why your statement, " If either the magnitude of force or distance or both is zero then the energy function is also zero. Since zero-point energy is finite even though very weak none of these variables can be identically zero. Nonetheless, mathematical normalization setting to unity is allowed for either variable by rational functions", is true. If space is finite, I suppose this would make sense. If it's not, well...

remember,I'm the guy who thinks Pi are round.

yours,
dr.w

[AntonioLao]

If space is finite, I suppose this would make sense. If it's not, well...

Using a non-metrical topology there is no way to prove that space is finite or infinite. On the other hand, if a minimum length is defined such as Planck length then zero length is meaningless. So, if force and distance are both measured by this defined minimum length then taking the values of zero becomes meaningless. All laws of physics breakdown at the singularity of black hole.

[Dr. Waldrope]

Thanks Antonio. I will ponder this.
dr.w