[AntonioLao]

In 1937, John Archibald Wheeler introduced the S-matrix and this introduction was again repeated by Heisenberg in 1943. The elements of these matrices are the strengths of scattered wave and particle interactions.

Many years later, it is becoming a critical part of many modern quantum field theories. Some have always believed that it can be used to solve the problems of the strong interactions by ways of infinitesimal local descriptions of the color forces of gluons' interactions.

The fact that these gluons can never be detected indicates that the interactions can only be effective at short distances giving a theory that is purely a local gauge invariance. The gauge concept is used with the same meaning as Heisenberg's original proposal for a fundamental length in 1938.

[Guille]

By fundamental length do you meant he shortest space quanta? Like, for example, Planck's length?

[AntonioLao]

Maybe even shorter than Planck length or even zero length of null vectors. The great Eli Cartan, inventor of spinors mathematics, believed zero-vectors exist.

[Guille]

Originally Posted by AntonioLao

Maybe even shorter than Planck length or even zero length of null vectors. The great Eli Cartan, inventor of spinors mathematics, believed zero-vectors exist.

I don't think I'm smarter than him, but I am definatelly sure that zero things cannot "exist". At least in the normal meaning o fthis world.

[AntonioLao]

the zero of a vector field (of vector bosons having infinite directions to choose from) is the equivalence of a nonzero length scalar field ( of scalar bosons having no other choice but one direction only).

[Guille]

Originally Posted by AntonioLao

the zero of a vector field (of vector bosons having infinite directions to choose from) is the equivalence of a nonzero length scalar field ( of scalar bosons having no other choice but one direction only).

Oh. Is scalar opposite to vector and vice versa?

[AntonioLao]

scalar quantities only have magnitudes, e.g., temperature, energy, density, volume, mass. Vector quantities have both magnitudes and directions, e.g., force, pressure, velocity, gradient, acceleration, distance.

but infinitesimal orthogonal forces seem to act like scalars and this might be the reason why it is logical for them to participate in the Higgs mechanism creating masses for all the other elementary particles.

[Guille]

Originally Posted by AntonioLao

scalar quantities only have magnitudes, e.g., temperature, energy, density, volume, mass. Vector quantities have both magnitudes and directions, e.g., force, pressure, velocity, gradient, acceleration, distance.

Thus, vector quantities are scalar if their direction is indeterminate?

[AntonioLao]

Originally Posted by GUILLE

Thus, vector quantities are scalar if their direction is indeterminate?

directional indeterminatism is supposed to be answered by studying tensor analysis. My personal opinion is it more than add to the confusion than clarification.

[Guille]

Originally Posted by AntonioLao

directional indeterminatism is supposed to be answered by studying tensor analysis. My personal opinion is it more than add to the confusion than clarification.

Do you recomend me top study (or have a look) at tensor analysis? is it CRUCIAL to understand SR and GR?

By the way, is there a connection between LOE and local infinitesimal time? And, is there a local infinitesimal space? (could there be?)