The Least Action Consistent Stable Universe and the Mathematics, Section 1

Subject:	The Least Action Consistent Stable Universe and the Mathematics, Section 1
Date:	Mon, 7 Dec 2009 01:12:39 -0800 (PST)

The Least Action Consistent Stable Universe and the Mathematics
Modified June 6, 2009, December 7, 2009
John Lawrence Reed, Jr.
Section 1

The Universe and the Mathematics:
Why They Are So Well Matched
Part 1 of: "Why the Mathematics Works So Well On the Universe"

When I was a boy I suspected that there was a common thread that ran
through all physical systems, and connected all physical laws. The
more I learned, the closer I came to identify it. A recurring thought
of a short lived image. A focused but momentary insight. A sudden and
clear panoramic view, but again and again, it disintegrated and was
gone. Defining this thread, putting my finger on it precisely, was for
a long time, just outside the range of my consciousness.

The most difficult physics problem for me, at that time, was the
conceptual understanding of atomic structure. A mathematics had been
conceived and refined, by Bohr, Heisenberg, Schrodinger, Born, Dirac,
Feynman, and others, developed expressly for the operational, or
scientific analysis of atomic phenomena. My view of atomic structure
remained unclear for a long time [1], with or without the
mathematics. Today the least action consistent, mathematical
descriptions of the universe, on the blackboard, and in the published
papers, are abstract and (to me), devoid of any conceptual connection
to physical reality [2], other than a consistency with least action.

The American physicist, Steven Weinberg, wrote, "... it is always hard
to realize that these numbers and equations we play with at our desks
have something to do with the real world." With the phrase
"...something to do with the real world", Weinberg reveals that the
theoretical physicist mathematician has an unformed idea as to what
many of his or her, quantitative abstractions represent conceptually.
Consider the words of the late Hungarian mathematician and physicist,
Eugene P. Wigner "...the enormous usefulness of mathematics in the
natural sciences is something bordering on the mysterious... there
is no rational explanation for it." Eugene Wigner wrote this in a
1960 essay and continued by noting that, the ease by which the
mathematics applies to the universe is, "a... gift which we neither
understand nor deserve."

While I did not concern myself at the time, with our intellectual
qualifications as the beneficiaries of the gift, I did seek to
understand why it was so effective. Wigner's essay was a major
influence on my early thinking, so it was with special interest that I
read the recent words of Lawrence M. Krauss in his 2005 book titled,
"Hiding in the Mirror". Krauss addresses the ideas presented by Wigner
in the 1960 essay [3]. Krauss writes, "... are our physical theories
unique... do they represent some fundamental underlying reality about
nature... or have we just chosen one of many different, possibly
equally viable mathematical frameworks within which to pose our
questions... in this... case would the physical picture corresponding
to... other mathematical descriptions each be totally different?"

Krauss colors Wigner's concept in a shade perhaps, more reflective of
his own. My coloring of Wigner's concern is slightly different.
Although Wigner questioned the uniqueness of our physical theories,
Wigner did not question that the mathematics reflects a fundamental
aspect of the universe. Rather, Wigner pointed out the "uncanny"
usefulness of mathematics, and expressed some uncertainty with respect
to our reliance on the significance of the massaged and experimentally
supported predictions of our least action consistent mathematics, to
serve as a sole and solid basis on which to verbally formulate our
"unique" conceptual physical theories. Wigner approaches the idea that
the selection of a mathematical model determines the questions that we
ask. He suggests that once we select a mathematical model, both our
questions, and the answer to our questions are preordained. In other
words, because the least action consistent mathematics adapts to the
real world so well, our mathematical model may be easily colored by
any erroneous "a priori" subjective assumptions we include and attach
to the questions that we ask.

Where Wigner noted the "uncanny" usefulness of mathematics, I noted
that the usefulness remains, regardless of the veracity of our a
priori assumptions. As an example, first consider the Ptolemaic, earth
centered model of the solar system. Ptolemy based his model on a
divine notion for symmetry. Perfect circles and perfect motion. A
circle is an efficient enclosure of area. That is, the circle
circumference is the shortest line length to enclose the greatest
area. Equal arc lengths from the same circle will radially enclose
equal areas. When we take this symmetrical efficiency ratio of the
circle as the quotient [circumference/area] or [2pir/pir^2] and reduce
it, we have [2/r]. When we take the quotient of an arc segment length
to its radially enclosed subtended area we also reduce that to [2/r].
This is an efficient area enclosing symmetrical property of the circle
itself (see Take II). This is, on the face, trivial and rather
mundane, as it follows from the perfect symmetry of the circle as an
artifact of the circle.

With the Ptolemaic model of the universe the efficient enclosure of
area falls out of each contrived orbit as a property of the perfect
circle and its perfect motion. With the real world orbits this
efficiency is retained in terms of time and space. We have the
efficiency ratio as the quotient [the period/the area enclosed by the
orbit]. The analogous reduced quotient here when we take [r] as the
average distance, of the planets from the sun (as is done in college
physics texts), is [2/rv]. In Ptolemy=92s model it is the least action
consistent time-space efficiency of the orbits that enable the model
to be as useful as it is. The sole quantitative connection to the real
universe in this "still useful" model, is the efficient, least action
consistent, time-space property, attendant to each of the otherwise
contrived, circular, cyclic and epi-cyclic orbits.

The Ptolemaic model shows that accurate least action consistent,
mathematical time-space predictions serve us to a limited operational
extent, but provide no absolute basis for an accurate dynamic
conceptual view. Viewed through the clear lens of hindsight here, we
can see that our conceptual questions must be framed correctly, prior
to applying the mathematical model beyond its operational context.
Must we frame our conceptual questions any less correctly today?

Krauss continues: "... because we have made huge strides in our
understanding of the nature of scientific theories... since Wigner
penned his essay... I believe we can safely say that the question he
poses is no longer of any great concern to scientists." During the
course of my life, my wide ranging research has included the study of
every publication in English print, that I have found, that seeks to
present a popularized view of theoretical physics and the attendant
mathematics. In my many years at this endeavor Krauss, to his credit,
is the only author I have read that directly entertains Wigner's
essay. Further, the cutting edge of science is focused on
technological progress. Consequently, the focus of Wigner's concern is
not seen as a subject that qualifies for research grants. Therefore,
as near as I can determine, the question posed by Wigner was never of
any great concern to other scientists. Although Wigner's concern is
clearly restated as a question, and the answer to that question
resides within obtainable bounds, we have been content to leave the
question unanswered, and use the least action consistent mathematics
as though the mathematics is a crystal ball, enabling us a near
mystical means by which we decipher our least action universe. I am
reminded of the quote by Dirac, "... my equations are smarter than
me." (paraphrased).

Wigner's concern, together with many other concerns [4], did
represent a significant problem to me. Even to the extent that my
intent to pursue a professional career in theoretical physics was
eventually derailed [5]. Now, much to my surprise, Krauss indicates
that the question has been answered as the result of "huge strides we
have made in our understanding of scientific theories..." Krauss
continues: "We understand precisely how different mathematical
theories can lead to equivalent predictions of physical phenomena
because some aspects of the theory will be mathematically irrelevant
at some physical scales and not at others."

The word "precisely" as used with the scientifically represented,
quoted word stream above, is a loosely chosen, unclear and misleading,
application of the English language. Many theoretical physicist
mathematicians today, regard any spoken language as inadequate, even
trivial, when compared to the more rigorous and more intellectually
forgiving mathematics. The initial difficulty of learning the
mathematics, combined with its operational effectiveness when applied
to least action consistent, natural physical processes, provide to the
physicist mathematician; the academic humanist; and to educated
humanity at large; the =91illusion=92 that a "deep" intellectual
connection to physical reality exists, that is revealed through the
mathematics, and accessible only to the theoretical physicist
mathematician. This mindset provides an unquestioned and largely
unchallenged world academic platform that enables the theoretical
physicist mathematician to put forward any sort of theoretical
fantasy, so long as the fantasy retains a least action mathematical
consistency with respect to experimental prediction. To the
theoretical physicist mathematician, =93any=94 notion that is not
"outlawed" by the applied least action consistent mathematics, say
quantum mechanics or general relativity, is viable.

As a clear and representative example of the extent of this view,
consider the following quote from Stephen Hawking, in response to a
question on the conceptual validity of an extra-dimensional universe.
The question: =93Do extra dimensions really exist has no meaning. All
one can ask is whether mathematical models with extra dimensions
provide a good description of the universe.=94 And =93=85one cannot
determine what is real. All one can do is find which mathematical
models describe the universe we live in.=94

Extra dimensions are obvious =93artifacts=94 of the mathematics. These are
theoretically brought to the real world conceptual table here by
Hawking, with a proclamation that I find uncomfortably similar to:
=91Verily, verily, I say unto you =93All we can ask=85=94 and =93All we can=
do=85=94
will be revealed by our crystal ball.=92 Hawking, one of the high
priests in the field, speaks for most all theoretical physicist
mathematicians.

God like pronouncements on the limitations of our capacity for
knowledge, coupled with the ineffectual (See Brian Greene=92s PBS,
offering: The Elegant Universe) disclaimers as quoted above, together
with the unbridled faith, humanity at large places in the conceptual
views attendant to the mathematics, are other factors that caused me
to engage in, what has turned out to be a lifelong quest, one purpose
of which was to understand why the crystal ball extends the =93decreed=94
limits so effectively. I believe that the mathematics is a present key
to understanding the universe. I believe that today, it is a master
key, capable of opening many locks. The key must be ground so all the
locks open. To accomplish this we must understand the focus and
limitations of the lock and key.

Krauss continues =93Moreover, we now tend to think in terms of=94
symmetries =93of nature... reflected in the underlying mathematics."
Krauss is not the first author I have encountered that sets great
importance to the near mystical notion for symmetry in nature. He is
however, the first to place the notion directly at Wigner's door. Nor
is he the only physicist mathematician that considers the mathematics
as an "underlying" and therefore controlling aspect of nature, however
contrived the mathematics may, or may not be. Krauss perhaps offers
that the symmetries in nature are the reason that the mathematics
applies so well to the universe. I can agree with this to the extent
of its conceptual clarity. However, the idea for symmetry in nature is
not new. The idea was held by the Ancient Greeks some thousands of
years ago. The Greeks believed in a divine, therefore perfect symmetry
for the motion in the heavens. The Greeks conjectured that perfect
circles represented the symmetry. Have we progressed, as Krauss
indicates, only to the point of recognizing that the symmetry need not
manifest as a perfect circle?

Following my analysis of the Ptolemaic model of the solar system, I
considered our limited perceptive ability. I concluded that the ease
of application of the least action consistent mathematics to the least
action universe, in terms of time and space, is for us, both a
weakness and a strength. We cannot allow the easily applied least
action consistent mathematics, to lead us into otherwise (outside the
operational limits of the mathematical model) incomprehensible
conceptual ideas, that we validate intellectually, solely on the basis
of our limited perceptive abilities. We cannot include quantities
within our mathematical models that are loosely defined by the words
of the language we think in terms of, and expect the rigor of a least
action consistent mathematical model to clarify and compensate for,
our laziness in conceptual thought. As evidenced by the Ptolemaic
model of the solar system, our reliance on perceived events to build
the conceptual model, requires that our conceptual foundation for the
mathematical model, be error free. If we carry any erroneous a priori
assumptive baggage into the mathematical model, that mathematical
model will eventually be shown to be a new age Ptolemaic mathematical
model (if we are fortunate). We require circumspect conceptual
reasoning [6] concurrent with our use of the mathematics. As a place
to begin, we must precisely answer the comparatively simple, fairly
straight forward question: "Why does the least action consistent
mathematics work so well on the =93stable=94 least action universe?", if
we wish to obtain a non-mystical, non-fantasy based (non-new age
Ptolemaic), rationally comprehensible understanding of natural
phenomena. I have indicated an answer to that question in this post
and I will support this answer within the five parts of this post.

Endnotes to Part 1:
[1] Eleven years passed before the results I obtained from my study of
atomic structure, forced me to turn my focus toward gravity. A topic
that until then, represented a solid, unassailable pillar, in my
worldview. The wave nature of particles is a clue to the structure of
the atom. I have briefly applied this clue in Take 6, and have
recently expanded on this in Take 25.

[2] Except as noted herein.

[3] Actually the Krauss books are informative and entertaining. The
subject complexity is daunting. My kudos to the author. However,
Eugene Wigner's 1960 essay is seldom seriously entertained by anyone
but me. I graduated from high school in 1961. Consequently, Wigner's
essay was a major and continued influence on my subsequent thinking.

[4] As one example, consider Einstein's postulate that all inertial
observers measure the same speed of light, regardless the velocity of
the observer and the light source. Note that light comes in one speed.
It has no acceleration one way or another. It has many frequencies and
many corresponding wavelengths. The discrepancy of velocity with
respect to the observer and source is accounted for by the difference
in frequency and wavelength measured by each observer. Therefore, if
we require the Fitzgerald-Lorentz modification, originally proposed in
response to the missing (and not necessary) "ether" left undiscovered
by Michelson and Morley, it "may" have something to do with a time of
arrival, in that the light may have to reach us for us to see its
source, initially (I question this today 12/7/2009), but it has
nothing to do with the measure of light speed. As another example:
Take 6 together with Take 1D provides an alternative view that
eliminates the gravitationally predicted "black hole". The black hole
eventually became another major concern in my thinking. I believe that
Take 23 expands on this.

[5] As I continued my education, the physical descriptions of reality
that were presented as science left me incredulous. I set out to make
sense out of the nonsense.

[6] In Take 1D, "Mass: The Emergent Quantity", I put forward a viable,
rationally consistent, conceptual alternative, to our theory for a
mass derived gravitational force. Through the "present-sight", more
finely ground conceptual lens, provided by Take1D, we can, with some
unexpected amplification, again see the importance of succinctly
defining the quantities we use within our mathematical model, prior to
using the accurate time-space predictions provided by the mathematical
model, to point toward an investigative direction, and prior to
describing the universe in conceptual terms. In Take 1D, I define, and
so limit, the extent to which our perception applies within the
mathematical model, and a clarity falls out of the conceptual model.
Compare this to the many mathematical models today that exploit our
limited perception, in order to provide the foundational basis for the
veracity of the mathematical model, while abandoning any requirement
for conceptual contiguity. See my more recent work titled: The
Principle of Equivalence Explained.
johnreed