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In an opera, the scenery and costumes are unmistakably artificial. We
know so
and play along with the theatrics in hopes that we will be moved towards
a deeper
understanding and appreciation of life. The actors and scenery are
conjurors to help
us enter into the mystery of life. Spirit can be emphasized through
operatic extravagance
or bare ascetic essentials. However, what really exists cannot be mapped
onto any single
scene, no matter how grand or clever. To show what is true, one strives
for an ingenious
interplay of seemingly irreconcilable elements, none of which directly
corresponds to
what actually exists. No one likes to be pinned down with a label.
' Tis better to be an
enigma, than a number in someone's book. Reality cannot be boxed in
with dogma
anymore than it can be captured with a handful of equations. We do
not consequently
have to be mute. In fact, it is man's peculiar challenge to give form
and expression to
ultimate reality. If part of that reality is Love, then of course we
must love one another
and reconcile our differences.
In the world we perceive, there are certain pairs of opposites that
can be reconciled into a
whole that is beyond them. In several historic "debates" with Albert
Einstein, Niels Bohr
rigorously demonstrated how energy and time in classical physics are
complementary
opposites. Bohr went further and explained how conflicting viewpoints
of life itself are
special cases of complementary opposites. He developed a deep understanding
of the
meaning of symbols and of the proper use of language (semantics). He
sensed that the
lesson of complementarity had been with wise men through the ages.
But he also felt
that we are in a better position today to understand it than ever before.
He died in 1962
with the hope that the wisdom of complementarity would help create
for us an open
and harmonious world.*
To move forward, you must bring with you the virtue in Galileo and the
virtue in Einstein.
They knew that the laws of physics must be covariant,
that is, independent of the observer.
They knew that there is a breathtakingly beautiful reality "out there"
for which we should reach
without contaminating it with our provincial minds. Their science was
an art of purification
and preparation for going behind the veils to the holy of holies. Physics,
undefiled by man,
was their humble quest. It involves a search for high dimensional symmetries
and it has been
an exceedingly successful program and continues today in high energy
particle physics,
in string theories and in quantum cosmology.
March 30, 1998: Note to reader: deep connections to the humanities
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levels ahead (and behind). Please be patient. Our web logs show
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clearing of the air
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In his search for the right field equations for general relativity,
Einstein struck upon a
number of promising candidates. The way he winnowed the false from
the true was by
testing for covariance. Mathematicians (e.g. Grossman)
helped him do the advanced
calculus. The true equations would be those that are transformable
from one coordinate
system to another, from one arbitrary observer to another, without
causing any change
in the laws of motion or any violation of the conservation of energy
and momentum.
Einstein's covariant science rose above our feeble minds by discovering
ways of
making our minds irrelevant.
Einstein's triumphs in covariant mathematics made quantum theory's dependence
on the
observer or environment extremely perplexing. At the end of his life,
before a class of
students learning special relativity at Princeton he implored, "When
a person such as a
mouse observes the universe, does that change the universe?" Quantum
mechanics
perniciously slips in this observer-dependency while retaining the
best of classical physics.
It's a conundrum. Niels Bohr tried to resolve the dilemma by trying
to show that quantum
theory demanded a higher form of covariance. He knew from hard laboratory
experience
that there was a world of atoms and nuclei out there manifest in the
periodic table of elements
and in tables of isotopes. Planck's quantum of action is the keystone
to these charts; without it,
there could be any number of fundamental elements and nothing would
be repeatable with any
sort of assurance. With his higher form of covariance, complementarity,
Bohr tried to explain
that each of Heisenberg's "conjugate variables" momentum & position
(or energy & time, etc)
were like distinct coordinate systems. (Hamiltonian mechanics had already
laid the ground
work for this independence.) Each variable's images were no more fundamental
than is the
shape of Greenland on a flat map. What we see depends on how we choose
to coordinate
our experiences. With quantum mechanics, one cannot switch from one
mapping system to
another and back again without "Greenland" being uncontrollably changed.
The order in
which one makes one's observations is not reversible. However, this
shape changing has
no effect on what quantum mechanics proves are the fundamental properties
of atoms.
Regardless of all of the apparent observer-dependency inherent in quantum
mechanics,
the periodical table lives on unchanged. Its patterned rows are covariant
in a higher sense
than are the field equations of electromagnetism or Einstein's symmetry
relations between
matter and space-time.
Covariance relates distinct "cross sections" of space-time. Complementarity
relates
distinct "cross sections" of an interaction. Each cross section involves
choices in
how an event is to be observed. Bohr enlarged Einstein's coordination
of reference
frames by including changes in one’s experimental setup. Appearances
were shown
to be contingent on the whole environment in which they occur. "No
sharp separation
can be made between an independent behaviour of the objects and their
interaction
with the measuring instruments which define the frame." (Bohr
in 1935 & 1949)
Using complementarity, Bohr was able to coordinate the observer-dependencies
into a higher noumenal framework that explained why matter has certain
properties
completely independent of us.
In dense prose, Bohr stated his case for the high covariance of quantum
mechanics.
He was not able to prove it rigorously using mathematics with which
Einstein was
familiar. To solve the debate between Einstein and Bohr one has to
forge a new alloy
using the gold of the enlightenment and the silver of the romantics.
Alchemists have
already tried to do this literally. All they got was a weak white gold,
hardly the
Holy Grail of physics. Unified field theories have similarly been disappointing;
they are less functional than General Relativity and Quantum Mechanics
in their
separate and pure forms.
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