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?

Robert,

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

framework.

Best regards,

Ralph Frost

Some images at:

http://magnetictetrahedra.com/

With joy you will draw water

from the wells of salvation. Isaiah 12:3

> 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?

Robert,

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

framework.

Best regards,

Ralph Frost

Some images at:

http://magnetictetrahedra.com/

With joy you will draw water

from the wells of salvation. Isaiah 12:3

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