gauge vs. directional invariance

[AntonioLao]

Reading portions of Terence W Barrett’s Topological Foundations of Electromagnetism, Volume 26 of World Scientific Series in Contemporary Chemical Physics gives the decision to compare two physical concepts: gauge invariance and directional invariance. Barrett’s idea can be found starting on Page 16 with the following slightly edited introductory quote:

In 1918 Weyl…treated Einstein’s general relativity as if Lorentz symmetry were an example of global symmetry but only local coordinates defineable, i.e. the general theory was considered as a local theory. A consequence of Weyl’s theory is that the absolute magnitude or norm of a physical vector is not treated as an absolute quantity but depends on its location in space-time. This notion was called gauge invariance.

From this brief quotation, the topological characteristic is not clearly described except that the scalar and the vector potentials are invariance under certain additive or subtractive differential gauge transformations. On the other hand, a descriptive topology of directional invariance is the non-orientable Möbius surface such that a complete circuit would allow a left transformed to a right, or a top to a bottom, or a forward to a backward. All these are irreducible characteristics of the 8 directional invariance properties discussed in other threads. Regarding local and global characteristics, Barrett asserted that the gauge is truly a physical quantity that can be determined by setting boundary conditions to the experiments that cannot be derived from Maxwell’s equations. On the other hand, directional invariance is locally attributed to the Hadamard matrices embedded in a global infinity matrix of a sieve of Diophantus.

[mkirkpatrick]

Which way to go G or DI ??




regards michael.

[AntonioLao]

For a complete theory of quantized spacetime I strongly believed going with a DI. But where and when browsing thru the academic libraries at the universities nearby all I can find are more G's with no DI except of course in my personal library.

[mkirkpatrick]

For a complete theory of quantized spacetime I strongly believed going with a DI. But where and when browsing thru the academic libraries at the universities nearby all I can find are more G's with no DI except of course in my personal library.

Well then,one must follow your gut feeling.



regards michael.

[AntonioLao]

But a Moebius topology gutted out the common sense out of most people.

[mkirkpatrick]

But a Moebius topology gutted out the common sense out of most people.

Yes,I can understand that.



regards michael.

[AntonioLao]

I am just hoping not to become gutless or clueless sticking all my marbles on the principle of directional invariance.

[Profpat]

I am just hoping not to become gutless or clueless sticking all my marbles on the principle of directional invariance.

Speaking of which could you look at my post # 3548 at my An Idea thread Antonio, and comment please. Thank you.

[mkirkpatrick]

I am just hoping not to become gutless or clueless sticking all my marbles on the principle of directional invariance.

Just be true to your own inner promtings and you will
not go wrong.




regards michael.

[Profpat]

I did a search on google for directional invariances and the 1st hit is this.

Google

Advanced Search
Preferences
Web Books
Results 1 - 10 of about 482,000 for 8 directional invariances. (0.32 seconds)

Search Results

1. gauge vs. directional invariance - ToeQuest
   
   6 posts - 2 authors
   All these are irreducible characteristics of the 8 directional invariance properties discussed in other threads. Regarding local and global characteristics, ...
   www.toequest.com/forum/mathematics/4481-gauge-vs-directional-invariance.html -

Congratulations Antonio I guess you are the expert on the subject.