Symmetry Debts: the "Tetrahedron Model" VS
the "Standard Model"
John A. Gowan
(Revised Dec., 2013)
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Both the "Standard" and the "Tetrahedron
Model" rely on symmetry principles to create unified theories
of the "four forces of physics" (in the sense of Emmy Noether's great theorem relating
symmetry and conservation). But in general I use the symmetries of
the "forest", while the standard model uses the symmetries of the
"trees". Obviously, these cannot be mutually exclusive categories;
in most respects the two theories complement each other.
Another major difference is that I use the concept of symmetry
"debts" to solve qualitative "why" or conservation problems (Why gravity? What is the conservation
reason that gravity must exist as a force in the universe?), whereas
the "establishment" uses the concept of symmetry-in-action to solve
quantitative "how" or mechanistic problems (how does gravity produce
its effects and how can we calculate them?). (See: "The 'Tetrahedron Model' VS the 'Standard
Model' of Physics: A Comparison".)
The Electromagnetic Force
Our universe is an electromagnetic universe, composed of bound and
free forms of electromagnetic energy (matter and light), which are
inter-convertible, as demonstrated by the creation and annihilation
of particle-antiparticle pairs in our accelerators and colliders, as
well as numerous astrophysical processes. This relationships is also
theoretically illuminated by such celebrated formulas as E=mcc
(Einstein), E=hv (Planck-Einstein), and hv=mcc (de
Broglie-Planck-Einstein). Therefore, principles of symmetry in the
electromagnetic force (in both its bound and free forms) are of
primary significance for any theory of force unification.
The most fundamental of these electromagnetic phenomena is the
symmetry gauge "velocity c", the velocity of light, the universal
electromagnetic constant. Einstein showed that "velocity c"
characterizes a symmetric state of free energy. The photon, or
quantum of light (the boson, field vector, or force-carrier of the
electromagnetic field), traveling freely in vacuum at "velocity c",
is the most symmetric state of energy known, carrying no charges,
having no mass, producing no
gravitational field, having no time dimension, and having no
spatial dimension in the direction of motion. In short, the photon
has forever to go nowhere, "traveling" with an effectively infinite
velocity. This is the origin of the photon's "non-local" energy
state, a state of pure spatio-temporal symmetry. The loss of this
symmetric non-local energy state (when free electromagnetic energy -
light - is converted into massive, local, immobile forms of bound
electromagnetic energy - matter) is the root cause of the
gravitational "location" charge, and indeed all the other charges of
matter.
The charges of matter are symmetry debts of light (per Noether's theorem). To see this
directly, imagine an electron-positron pair. Now (by some
miracle of the weak force) take the positron away and look at the
remaining electron. The energy of the electron is conserved by its
mass, but what is the electric charge for? It was supposed to
produce an annihilation reaction with the positron, returning the
particle pair to the symmetry of light, but now the charge is
"hung", preserved indefinitely by the symmetry principle of charge
conservation. This charge, isolated from its antimatter complement,
is what I refer to as a symmetry debt. Charges produce forces which
demand repayment of the symmetry debt they represent. And just in
case the electric charge should fail to produce the expected
annihilation, there is a "plan B": the gravitational charge of the
electron's mass. This "fail safe" charge will eventually return the
electron's mass to light, if only via the "Hawking Radiation" of a
black hole. It's all very simple, and it applies directly to our
asymmetric universe because antimatter went missing after the "Big
Bang".
The evolution of the universe is the story of the safeguarding and
conservation of matter's energy and symmetry debts (conserving the
quality as well as the quantity of matter's energy content), and the
ongoing conversion of asymmetric bound electromagnetic energy back
to its original symmetric form of light (free electromagnetic
energy) - as in our Sun, the stars, supernovas, quasars, black
holes, and many other astrophysical processes. This is the "big
picture" of the symmetry of the "forest" (the Cosmos), over
and above the symmetry of the "trees" (the atoms), and it provides a
road map to a theory of force unification. With this overview we
don't get lost working our way through an unconnected maze of atomic
details. Naturally, we need the atomic detail (the puzzle pieces),
but we also need a clear prospect of our goal, or we cannot fit the
pieces together.
After "velocity c" and the photon, the second most important
electromagnetic symmetry condition, phenomenon, or symmetry debt to
consider is the electric charge itself (of which the photon is the
"field vector" or force carrier). Electric charge is a major
expression of the symmetry debt of matter, so what is it telling us?
It is (in terms of the "forest") telling us that the entire realm of
antimatter is missing from our universe ("someone has stolen our
tent") - that is, if antimatter were present, charge symmetry would
be restored and the universe of matter and antimatter would dissolve
(explosively) into a universe of perfect symmetry and light. Another
way of looking at this is to recognize that electric charge is
telling us the entire realm of matter is asymmetric, because it
comes with mass, time, gravity, and charge. Electric charge is a
protest against these asymmetric conditions, and is trying to avoid
them by producing annihilation reactions. The electric charge
continues to search for antimatter, and it will be conserved until
it finds antimatter and cancels the electromagnetic debt of matter -
regardless of how long it takes. This search for symmetry, combined
with energy conservation and entropy (the intrinsic motions of
light, time, and gravity), are the fundamental motivating forces of
the universe. Our Cosmos exists because the conservation of symmetry
debts through time - via the principle of charge conservation -
allows it to exist.
There are many other symmetries of the electromagnetic force and of
electromagnetic bound energy that have been known and studied since
the time of Maxwell, beginning of course, with the symmetry between
electric and magnetic fields. There is the global and local "gauge"
symmetry of voltage, phase, and the exchange of photons (field
vectors) between charged particles, the invariance of Maxwell's
equations, the invariance of velocity c, the invariance and
conservation of electric charge, and other effects due to symmetry
at the atomic level of the "trees" which I need not go into because
the "establishment" has already explored it so thoroughly. I'm more
interested in the "forest" symmetries the "establishment" has either
ignored or simply not emphasized, apparently because they tend to be
of a more philosophical, rather than practical, nature (you can't
make money or bombs with them). (For a technical insight into the
connections between the symmetry phenomena of electromagnetism and
spacetime, see the classic text by: Robert Resnick Introduction
to Special Relativity (Chapt. IV) John Wiley and Sons, Inc.
1968.)
Gravity
Another major symmetry debt of matter is expressed through the
gravitational "location" charge. The "location" charge of gravity
derives from the lost "non-local" symmetric energy state of light
when free electromagnetic energy is converted to bound
electromagnetic energy (in any form). Bound energy (atoms, matter)
is massive, immobile, and local, carrying various charges (symmetry
debts) including the gravitational symmetry debt. Bound energy is
4-dimensional, including the asymmetric time dimension, whereas free
energy (light) is 2-dimensional - lacking both a time dimension and
one spatial dimension in the direction of motion. The asymmetric
time dimension fixes the location of bound energy in 3-D space
(because time is one-way, every point in spacetime is unique), and
time itself is the active principle of gravity's "location" charge.
A gravitational field is the spatial consequence of the intrinsic
motion of time. (See: "Introduction
to Gravity".)
Time moves into history at right angles to all three spatial
dimensions, pulling space along with it. But 3-D space cannot enter
the point-like beginning of the one-D time line of history, and so
the spatial dimensions self-annihilate at the center of every mass,
leaving behind a temporal residue, the metric equivalent of the
annihilated space. The intrinsic (entropic) one-way motion of this
temporal residue into history continues this self-feeding process
forever, or until bound energy is completely converted to free
energy (light) - which has no time dimension nor the gravitational
field to produce one. (See: "Does Light
Produce a Gravitational Field?".) Time and history are an
alternative entropic drive and domain to space, replacing the
intrinsic (entropic) motion of the photon - to accommodate the
unique entropic requirements of bound energy (which is causal,
whereas light is acausal). (See: "Spatial vs
Temporal Entropy".)
Gravity will eventually completely convert bound to free energy (via
the nucleosynthetic pathway of stars, supernovas, quasars, and
finally and completely, via "Hawking Radiation" of black holes),
returning the Cosmos to its original state of symmetric free energy
(light). (Note that gravity always tells us exactly where the center
of mass of any form of bound energy is located, and exactly how much
is present. It will also tell us the average density if we know the
size of the gravitating object.)
There are two important (and astonishing) things to recognize about
the time dimension with respect to its gravitational role as the
"location" dimension, the dimension which specifies the spatial
location of bound energy: 1) time is one-way, hence always new,
never repeating (because of its role in causality); 2) the universe
begins with a "Big Bang" at time zero everywhere in space,
simultaneously. Hence a 4-dimensional point ("event") in spacetime
can be absolutely unique.
Using a financial metaphor, we can think of gravity in its low
energy stages (for example, here on planet Earth) as simply paying
the "interest" on the symmetry debt of mass. That is, gravity works
away continuously but no change in the Earth's mass or its
gravitational force ever occurs. However, at higher energy levels,
as on our Sun, gravity begins to "pay down" the "principle" on the
symmetry debt of mass - mass is actually converted to light and the
gravitational field of the Sun is reduced in consequence. This
process goes to completion (eventually but inexorably) via the
"Hawking Radiation" of black holes.
The electromagnetic and gravitational symmetry debts are related in
that both are long-range force debts that are indifferent to the
specific nature of the matter involved. Furthermore, "in the
beginning", the negative energy of gravity exactly balanced the
positive energy of electromagnetic energy, allowing the universe to
be born as a quantum fluctuation of the "multiverse", containing
zero net energy and zero net charge (due to the compensating
presence of antimatter). The ongoing conversion (in stars, etc.) of
bound to free energy continues to reduce the total gravitation
energy of the universe (since light, having no "location", produces no gravitation field),
resulting in the apparent "acceleration" of cosmic expansion (as
recently observed).
The remaining charges of matter (strong and weak) are short-range
force debts which play the major role of converting free to bound
energy in the early universe - and continuing today in such
phenomena as heavy element building in stars and the radioactive
decay of heavy atomic nuclei. These are symmetry debts of the
"trees" rather than the "forest", and here my ideas more closely
follow "establishment" lines. I turn to them next.
The Strong and Weak Nuclear Forces
While the long-range electromagnetic and gravitational forces are
primarily forces concerned with establishing, maintaining, and
conserving the spatio-temporal metric of the Cosmos, the strong and
weak nuclear forces are primarily concerned with breaking the
primordial symmetry of light and its particle-antiparticle pairs,
and creating a matter-only Cosmos of bound electromagnetic energy.
(See: "The Origin of Matter and Information".)
Atomic nuclei contain almost all of the visible, baryonic, bound
electromagnetic energy in the Cosmos, and atomic nuclei are held
together by the strong force. The obvious questions are: 1) how does
the free energy of light become bound into the mass of an atomic
nucleus; and 2) what are the conservation consequence of the
conversion of free to bound energy?
We can only speculate about the first question, as this conversion
takes place at the unthinkable (and unreproducible) energies of the
early micro-moments of the "Big Bang". Briefly, my presumption is
that all four forces participate in the creation of a primordial
"leptoquark" - a heavy lepton (charged particle similar to a very
heavy electron) which splits into three parts (the nascent quarks)
under its own excessive mass and size. The weak force rearranges
these quarks into electrically neutral threesomes (similar to a
heavy neutron), which then decays asymmetrically to produce a
matter-only Universe. The electrical neutrality of the primordial
leptoquarks is essential to allow the weak force enough time to
produce an asymmetric decay - otherwise everything simply vanishes
into photons via matter-antimatter electrical annihilation reactions
(returning to the unbroken symmetry of light and matter-antimatter
particle pairs). Hence the necessity for a primordial particle
composed of quark sub-units that can begin as a charged
leptoquark-anti-leptoquark pair, but undergo an internal
rearrangement of its subunits to become an electrically neutral
leptoquark subject to an asymmetric weak force decay. We insist on
the leptoquark designation (which amounts to an internally fractured
heavy lepton) to establish the link between leptons and baryons
(baryons are derived from primordial, internally fractured heavy
leptons). During the primordial asymmetric weak force decay, a
leptoquark anti-neutrino is emitted, balancing the "hidden" number
charge of the surviving baryon; this heavy anti-neutrino is a prime
candidate for the mysterious "dark matter" of the Cosmos. (See: "The Higgs Boson and the Weak Force IVBs".)
The Strong Force
The strong force arises completely naturally to hold the three
fractured parts of the leptoquark together. (See: "The Strong Force: Two Expressions".) This
fractional elementary charge of the quarks has also been seen in the
"fractional quantum Hall effect", for which the 1998 Nobel Prize was
awarded (See: Robert B. Laughlin A Different Universe Basic
Books 2005). The strong force also naturally grows stronger as the
quarks try to separate, since a free fractionally charged particle
would threaten the quantum rules of symmetry conservation - only
whole quantum unit charges are allowed. Fractional charges are
allowed only if they remain permanently confined within whole
quantum-unit charged entities - that is, as "virtual" fractional
charges inside baryons. By the same token, the strong force grows
weaker as the quarks move closer together, since the threat to
symmetry conservation posed by their fractional charges is thereby
reduced. This is the celebrated effect of "asymptotic freedom" -
also awarded a Nobel Prize (Gross, Politzer, Wilczek, 2004 - see: Science
15 Oct. 2004 page 400). The strong force is perfectly understandable
from the point of view of symmetry conservation, and the gluon field
is a perfectly composed invariant "gauge" field of local symmetry.
Just as the quarks appear to be the massive fractured parts of an
elementary lepton, so the gluons seem to be fractional parts of
photons - fractured field vectors of the lepton's fractured electric
charge (reminiscent of the fractional quantum Hall effect). The
actual mass of the nucleus is not contained in the quarks
themselves, but rather in the huge energy of the gluon field which
binds them together. (For a discussion of gravitational VS inertial
mass, see: "The Higgs Boson VS the Spacetime
Metric". Further discussions of the role of the Higgs boson as
a gauge of particle mass may be found in: "The
Higgs Boson and the Weak Force IVBs"; see also "Table of the Higgs Cascade".)
Conservation Consequences of the Conversion
of Free Electromagnetic Energy (light) to Bound Electromagnetic
Energy (matter)
Light is the most symmetric form of electromagnetic energy, and when
it is converted to any form of bound electromagnetic energy, the
loss of light's non-local symmetric energy state must have
consequences - according to Noether's Theorem. The "quality" of
light's energy content is conserved no less than its quantity.
Light's energy is conserved in bound form as mass (hv=mcc),
while light's symmetry is conserved in the form of charge. The
charges of matter are symmetry debts of light. Electric charge
and gravity are the two most general forms of these symmetry debts.
Both are long-range forces and both have a single ultimate purpose
and conservation role - to return bound energy to its original
symmetric form. The electric charge does this through
matter-antimatter annihilation, the gravitational charge does this
through astrophysical processes such as stars, supernovas, quasars,
and finally and completely, through Hawking's "quantum radiance" of
black holes. (See: "Symmetry Principles of
the Unified Field Theory"; see: "A
Description of Gravity".) Gravity and the electromagnetic
force are related through time, velocity c, and the spacetime
metric. Time is the asymmetric dimension which electric charge is
trying to avoid in its annihilation reactions (light has no time
dimension but matter does), but once matter is formed, time itself
becomes the active or motivating principle of the gravitational
"location" charge. Time and gravity modify the spatial metric
established by light, and in the extreme case of the black hole, the
spatial electromagnetic metric is completely converted to a
gravitational temporal metric, in which matter moves at velocity c
while light stands still (g = c). Time and gravity create history,
which functions as an alternative entropy domain for matter's causal
information field, replacing the acausal spatial entropy domain of
light. (See: "Spatial VS Temporal Entropy".)
The intrinsic motion of light is the spatial entropy drive of free
energy, the intrinsic motion of time is the historical entropy drive
of bound energy. The intrinsic motion of gravity connects these two
entropy drives by converting space into time (as on planet Earth) or
vice versa (as in the stars).
Weak Force
Whereas the strong force holds atomic nuclei together, the weak
force tears them apart. Acting together, the strong and weak forces
create matter both De Novo in the "Big Bang", and produce
all the heavy elements of the periodic table - in stars and
supernovas, as well as during the later stages of the "Big Bang ".
The weak force produces the asymmetric decay of electrically neutral
leptoquarks during the early moments of the "Big Bang", creating
matter-only baryons (heavy particles containing 3 quarks) that fuse
together to produce all the atomic elements of our cosmos. The weak
force is the only force that can produce asymmetric decays, and it
is likewise the only force that can produce and/or transform the
identity of a single elementary particle - other forces
produce only particle-antiparticle pairs (excepting only gravity in
the extreme case of "Hawking Radiation" in black holes). It is
precisely the capability of the weak force to produce elementary
particle "singlets" that requires the bizarre form/mechanism of this
force, with its massive "IVBs" ( "Intermediate Vector Bosons").
It is a universal fact (a "global" symmetry) that every electron is
absolutely identical to every other electron in the Cosmos - and
must be, if energy, charge, and symmetry are to be conserved. And
it's not only electrons: every elementary particle must be
absolutely identical to every other (of its type) no matter when or
where it was, is, or will be created. It is the task of the weak
force (and only the weak force) to produce these particles as
"singlets", that is, as individual particles, not as
particle-antiparticle pairs. The method used by the weak force
involves the very massive IVBs, which recreate the original
primordial conditions of energy-density in which these particles
were first produced. Every weak force transformation involving an
IVB is therefore a mini "Big Bang", a recreation of the birth trauma
of the Cosmos but reduced to the scale of an individual elementary
particle. (See: "The 'W' IVBs and the Weak
Force Mechanism"; see: "Introduction to
the Weak Force".)
The weak force charge is "identity" charge, also known as lepton
"number" (or "flavor") charge. (See: "Identity
Charge and the Weak Force".) The (nearly) massless neutrinos
carry this charge in its explicit form, while the massive leptons
(the electron, muon, tau) carry this charge in "hidden" form
("hidden" because the identity charge involves handedness, which
cannot be strictly conserved by a massive particle). The neutrino's
explicit identity charge nevertheless balances the hidden identity
charge of the heavy leptons. Any newly created (single) massive
lepton must be accompanied by the appropriate neutrino to balance
its identity charge; hence the neutrino functions as a sort of
certificate which guarantees the mass, charge, spin, etc., of the
newly minted elementary particle conforms to the universal standard.
Neutrinos must also be emitted when leptons are destroyed - the
relationship between the massive lepton and its paired neutrino is
curiously analogous to the commonly presumed relationship between
the human body and soul.
Only elementary particles are paired with neutrinos; quarks have
none, as they are sub-elementary particles with fractional charges.
Their identity charges, like their fractional electric charges, are
conserved by the composite baryons which comprise them ("baryon
number" charge, which as we have seen is balanced by a leptoquark
anti-neutrino). In the modern universe, the baryon neutrino can only
be seen during proton decay - which (fortunately) I presume commonly
occurs only inside black holes (if anything occurs there at all).
The symmetry constraining the weak force is just the global symmetry
of identity (within type) among all elementary particles ever
created. An electron created during the "Big Bang" can be "swapped
out" with an electron created today and no one can tell the
difference. It should be obvious that this symmetry is completely
necessary for energy and charge conservation and hence the orderly
functioning of the Cosmos.
For the role of the Higgs boson in all this, see: "The Higgs Boson and the Weak Force IVBs";
see also "Table of the Higgs Cascade";
see also "Introduction to the Higgs Boson
Papers". For a discussion of the Life Force
(Information Force) and the Information Pathway see: "The Information Pathway"; "The Information Ladder"; "The Human Connection"; "The Fractal Organization of Nature".
For a discussion of cosmological issues, see: "A Spacetime Map of the Universe".
The Maintenance of Charge Values Through
Time
Closely related to symmetry conservation via absolute charge
conservation (charge annihilation) is the phenomenon of charge
maintenance - the safeguarding of the value, magnitude, quality and
quantity of charge for an indefinite period of time until full
conservation (as via antimatter annihilation) can be accomplished.
The great and significant difference between energy debts and
symmetry debts is that the latter, as carried by
charge/spin/handedness, may be carried undamaged through an
indefinite duration of time until they are paid, whereas the former
must be paid immediately. Hence the mechanism of symmetry debts as
carried by absolutely conserved charges through time is essential to
a Cosmos such as ours that enjoys an evolutionary development
through an extended historical dimension.
Think of the difference between the electron's charge (a symmetry
debt) and its mass (an energy debt). The electron's mass is an
actual alternative form of the energy of light from which the
electron was made (bound electromagnetic energy VS free
electromagnetic energy - mcc = hv), whereas the electron's
charge just produces a blind force seeking its anti-charge, and is
not in any sense an alternative form of the symmetry debt it
actually represents - the lost dimensional symmetry of light
(acausal light has no asymmetric time dimension, whereas causal
matter does). While the rest mass of the electron cannot vary,
nevertheless because mass is an actual alternative (bound) form of
electromagnetic energy, the electron's effective mass can
vary to represent or accommodate additional energy inputs to the
electron, as for example energy inputs due to acceleration. The
election's charge however, cannot vary and accelerated charges
produce instead magnetic fields and radiation (synchrotron
radiation, Cherenkov radiation, radio and TV waves, etc.),
shunting the excess energy into alternative electromagnetic forms
without changing the actual magnitude of the electric charge. Such
"local gauge symmetry" effects are further discussed below.
But how are these charges (symmetry debts) carried unchanged through
aeons of time - from the "Big Bang" to the present? While this is a
much more complex function than simple charge conservation via
annihilation, it is nevertheless the specific and daily task of each
of the field vectors of the four forces. Our universe is built to
deal with this problem from the outset, or it could not function -
it could not conserve energy. It is why we have such dualities as
spacetime and electromagnetism, and why the field vectors all seem
to have one foot in the universe of matter and the other in the
universe of antimatter. The photon of electromagnetism is its own
antiparticle; likewise the graviton (a quantum unit of time or
negative entropy); also the IVBs and the Higgs boson of the weak
force, taken together; and again as seen in the gluon field of the
strong force, which is composed of color-anticolor charges in all
combinations (Gell-Mann's strong force), even including the meson
field of quark-antiquark pairs (Yukawa's strong force). These are
the "gauge" fields of local symmetry, which all act to maintain
invariant the particular symmetry they represent despite the
uncertain and changing environment in our realm of warped/curved
metric and relative (rather than absolute) motion, massive (rather
than massless) particles, and our "real" (historical) world of 4
dimensional spacetime and causal (rather than acausal) relations
among particles.
We have seen how the massive IVB field vectors of the weak force
accomplish their task of safeguarding the identity charge and
invariant mass of elementary particles through the recreation of the
primordial environment of the "Big Bang"; other field vectors have
analogous compensatory effects and actions. The exchange of the
strong force gluon field permanently confines the fractionally
charged quarks to whole quantum-unit charge "packages" - the
baryons; the co-variance of time and space in relative motion
produces magnetic effects which compensate moving electrical
charges, while "warped" gravitational metrics maintain the
invariance of velocity "c", the "Interval", and causality via
similar mechanisms ("Lorentz Invariance" of Special and General
Relativity).
All the field vectors operate by exchanging force carriers or bosons
of their particular field, and all can be represented by simple
Feynman diagrams as well as complex mathematical equations. Thus
electrically charged particles exchange photons, massive particles
exchange gravitons (time quanta) with spacetime, quarks exchange
gluons, IVBs are exchanged between weakly interacting (decaying,
transforming) particles. All these activities of the field vectors
have a simple function: to maintain the magnitude, quantity, and
integrity of charges and the symmetry debts they represent through
time, including such fundamental gauges of charge as "velocity c",
the final arbiter of both causality and symmetry.
But these "local gauge symmetries" - the symmetries of the "trees" -
have been extensively studied and formalized by the "establishment".
The reader should consult standard textbooks (or Wikipedia -
Google-search "local gauge symmetry") on these subjects for further
and more detailed mathematical information regarding the action of
the field vectors of the four forces with regard to "Yang-Mills"
theories of "local gauge symmetry", "renormalized" force fields, and
their crucial role in the maintenance of charge and gauge magnitudes
through time. This is where physics gets complicated - as perfectly
invariant charges and particles derived from the ideal realm of
light (as symmetry/energy debts) are thrust into an imperfect realm
of relative motion, one-way time, and varying gravitational metrics,
in which they must nevertheless maintain the integrity and value of
their primal charges.
Links
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References
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Non-Abelian Gauge Theories. Phys. Rev. Lett. 30: 1343.
H. D. Politzer. 1973. Phys. Rev. Lett. 30: 1346.
Gross, Politzer, Wilczek: Science: 15
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Blackwell Publishers
Zee, A. "Fearful Symmetry". 1999, Princeton Univ. Press
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