Misner, Thorne and Wheeler: 11.4 Parallel Transport Around aClosed Curve

On Apr 16, 7:19 pm, Hetware wrote:

http://www.speakeasy.org/~hattons/mtw/

They construct a small deviant quadrilateral from elements of two
arbitrary vector fields u and v by first by displacing by u da and
evaluating v db at the tip of u da. Then they displace by v db and
evaluate u da at the tip of v db. That produces a quadrilateral that
isn't quite closed. They close it with [v,u]da db.

All good and well. Then they transport a vector A around the curve.

"With the route now specified, the vector A is to be transported around
it. One way to do this, "geometrical construction" by the method of
Schild's ladder applied over and over, is the foundation for planning a
possible experiment. For planning an abstract and coordinate-free
calculation (the present line of action), introduce a "fiducial field,"
only to take it away at the end of the calculation. Plan: conceive of
A, not as a localized vector, defined solely at the start of the trip,
but as a vector field (defined throughout the trip). Purpose: To provide
a standard of referenc (comparison of A transported from the origin with
A at the place in question.)..."

They then give a longish description of the steps which might be
summarized as:

delta A =
A(u da)_;v db
- A_;v db
- A(v db)_;u da
+ A_;u da
+ A_;[v,u] da db

where A on the rhs of this expression is the A field.

Yes, all these parallel transport things came during the so-called
golden age of GR where self-styled physicists were trying to create
something that will finally make themselves to be the elitists of
science just like the ancient Egyptian priests able to maintain their
status quo as social elites among a bunch of working people. In
reality, the self-styled physicists actually have not understood much,
and the name of the game is image that is how the rest would think how
smart the self-styled physicists are. It is truly fvcking pathetic.
shrug

A few years ago, Koobee Wublee was just like you combing through
literatures about GR trying to understand the supposed to be the most
complicated theoretical creation of mankind. After sensing bull****
after bull****, Koobee Wublee then decided to bypass the golden age of
GR charade and examine the raw materials that came out of the founding
fathers of differential geometry and then finally GR. Over there, you
will understand the entire hypothesis crystal clear and the very
reasons why some of the founding fathers decided to walk away from
it. You will then realize the majority of the self-styled physicists
do not even understand the crap they are worshipping. That, of
course, included Wheeler who did not really have understood Weyl.
When someone has hinted at you that he always finds something new
rereading the same book decade after decade, that is a tell-tale sign
of not understanding a single fvckig thing in the first place. Don’t
be so fvcking gullible. shrug

So, keep up with your quest. It depends on your intelligence. Some
will see the crap earlier while some will be indulged in the cesspool
of bull**** for quite some time before realizing they are swimming in
crap, but most will succumb to peer pressures fantasizing about the
Emperor’s non-existing clothes. If your id allows you to steer away
from peer pressure, you can reach out to Koobee Wublee, and Koobee
Wublee will be happy to give you better guidance in understanding GR
according to the founding fathers of this great and fun-to-study
hypothesis but at the end --- no cigar. shrug