Natural Science Forum / Physics / Relativity / July 2005

Ken S. Tucker:

 No. It doesn't describe the photon. For one thing, the photon energy
isn't quantized. The energy levels of bound systems are quantized.
The photon is quantized by its spin, which is just 1 \hbar.

It would be most clear if I used a physical demo,
based on Coulombs Force , "q" and "Q" are charges.

F= qQ/x^2   and  qQ = Fx^2.

Among the most famous of torsions in spacetime
is the antisymmetric EM field tensor "F_uv",
however that tensor resists definition on a continuum,
i.e. at a point. Fortunately Mr. Francis permits a
tensor defined by a relation between two points
finitely separated, and we agree (I think) a torsion
needs two finitely separate points.

Allow me to set two separate CSs (Coordinate Systems),
with an origin on charge "q" and the other on "Q".

I'll denote components "q^u" and "Q^v" as finite lengths
or time that relate charges "q" and "Q".

For example, a common axis connects "q" and "Q"
spatially, and by the definition a length uses time
x=ct to obtain the magnitude but ct has no direction.

The distinction spatially is q^1 = - Q^1 as the charges
are certainly in relatively opposite spatial directions,
but the times upon which those spatial components
are based are magnitudinally q^0 = Q^0.

These definitions permit the qQ = Fx^2 from above to
be written in a Generally Covariant fashion as,

2qQ = q*F_uv q^u Q^v .

Set and define,

F_01=Q/x^2 = - F_10 ,

q^1=-Q^1 , q^0 = Q^0

and find that a resulting "2qQ" from the torsion
that relates charges "q" and "Q", is invariant.

That relates to units of action "Plancks h" by

h =qQ  (neglecting the scalars for units), giving

2h = q*F_uv q^u Q^v

from above.

g_uv = s_uv + a_uv

and using

a_uv = q*F_uv

we can "surmise"  s^2 to be

s^2 = g_uv q^u Q^v

to represent the invariant spacetime difference
between charges "q" and "Q".

Splitting g_uv into symmetric and antisymmetric

= (s_uv + a_uv) q^u Q^v

= s_uv q^u Q^v + 2h .

Classically the "s_uv" are the metrics used in GR,
but over a length instead of at a point.

Of course the above is superficial, it shows how
torsion, (EM), QT's "h" and GR can relate tightly,
when the continuum definition of g_uv is dispensed,
and then the invariant "2h" emerges naturally.

Regards
Ken S. Tucker