Tuesday, August 9, 2016

Can Gauge Symmetry Be Understood Conceptually?

On Sunday, December 13, 2015 at 3:56:58 AM UTC-5, Robert L. Oldershaw wrote:
> Is there a way to explain gauge symmetry/gauge invariance conceptually,
> i.e., without mathematics or any abstract constructs.
> This would require a pictorial representation involving known physical
> objects, their observable motions, and non-abstract dynamic/geometric
> reasoning.
> Is this possible?


Others may disagree, but I think
that expression  is actually
a fairly straightforward thing
to put on the table. Doing so
though, involves expanding
the problem statement or
expression so as to also
illustrate (approximately)
the symmetry/invariance
with abstract mathematics.
(That is, to also show the
symmetry that accounts,
albeit, perhaps only intuitively,
for the unreasonable
effectiveness of mathematics.)

The "equation", typically is best
scribbled out in analog math. In
one sense, it could be done with
ANY physical artifact since every
artifact is an instance of
~quantum gravity, and thus is an
exemplar of  that which is sought.
The useful instance, though is
the first one which is oddly
written enough to spark and
convey a substantial amount
of physical intuition (what
abstract mathematics is
supposed to provide) on the
more unified ~quantum
gravity and/or, let's say,
the larger, overall, non-
abstract gauge symmetry.

The analog math 'equation' that I
advocate is any of those which
answer the question: what do you
get when you build a polyhedron
out of magnets?

Solving that with the five ways
to align four rod magnets along
the radii of a tetrahedron, and
then repulsing one ~vertex
above a like poled support
magnet and probing it with a
hand-held magnet, what one gets
is a variable mass density,
multiple state artifact that
provides tactile impressions
of field-field interactions,
damped anharmonic motion, plus
collapse and entanglement, etc.,
at the hand-held gauge/scale.
With just two magnets a person
can experience the symmetry that
there are two different field
arrangements that give the same
tactile (repulsive) result.

Scale-wise, the five primary
states of this artifact:
n4, n3s, n2s2, ns3, s4;
echo the angle,  look and
feel of the five Debye
electronegativity patterns of
sp^3 hybridized molecular
bonds found at the atomic-
molecular scale, in  ourselves
and throughout our
surroundings -- in water,
organic carbon and organic
nitrogen compounds,
silicates, etc.

And, yes, like I said, this
expression is approximate.
However, it fits the bill
and does the trick: Can Gauge
Symmetry Be Understood
Conceptually (without
abstract mathematics)?

~Proof is in the physical
experience and experimentation.

To grasp how this same pattern
accounts for the unreasonable
effectiveness of mathematics,
one  needs to acknowledge
the symmetry with the five Debye
electronegativity patterns and
with the fact that in our
respiring 160 kg oxygen per year,
we are also generating 10^20
(tetrahedral) water molecules
per second which can orient
in 6 to 12 ways within an
enfolding field, thus
providing us with a 6^n
analog (hydrogen-bonding)
language providing an
internal representation
of our surroundings as well
as means, via influences
on protein folding, for
all expression  and for (gauge
symmetric) theory building.

Readers will please note
this simplified, approximate,
physically intuitive model
comes after development
of the more complete, more
detailed concepts via the
abstract math developed
from within the XYZ-cubic

Best regards,
Ralph Frost

Some images at:

With joy you will draw water
from the wells of salvation. Isaiah 12:3

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