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265 lines
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(word processor parameters LM=8, RM=75, TM=2, BM=2)
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Taken from KeelyNet BBS (214) 324-3501
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Sponsored by Vangard Sciences
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There are ABSOLUTELY NO RESTRICTIONS
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on duplicating, publishing or distributing the
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August 30, 1991
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CPEDOG.ASC
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--------------------------------------------------------------------
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This file shared with KeelyNet courtesy of Woody Moffitt.
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Also see ZPE1, ZPE2, CFG1 on KeelyNet.
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--------------------------------------------------------------------
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Casimir Potentials,
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Electromagnetic Density Oscillations
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and Gravitation
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by
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Darrell Moffitt
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Among the less researched topics of classical and quantum physicists
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is that of electromagnetic density oscillations (e.d.o.s), i.e.,
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acoustic-form longitudinal waves in electromagnetic media.
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Though current literature does address phonon interactions, and
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their influence on conductivity in solids, longitudinal plasma
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waves and their quantum relatives are largely ignored. While
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acoustic waves may admit transverse polarities, they are
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fundamentally a longitudinal phenomenon.
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Plasma oscillations possess up to four longitudinal modes; the
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alternating compression and rarefaction zones comprising a wave may
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consist of either particles or fields, and the field itself may be
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electric or magnetic.
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Still another form of e.d.o. results from interacting charge
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densities; the square of charge density is dimensionally identical
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to that of sound,
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(M/(R^3*t^2)),
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and van der Waals forces both derive from such couplings and
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contribute the restoring force responsible for ordinary sound.
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Quantum mechanics describes van der Waals forces via Casimir
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potentials, simple, non-relativistic equations which take their name
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from Hendrick B. G. Casimir.
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Casimir's polar-polar potential, applied to any two polarizable
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bodies, is a prototype of quantum-level e.d.o.s. This equation
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reads
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E=((h/(2pi*c^5))(P1*P2)(w^6/6))(1/R)
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Page 1
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where (P1,P2) are the respective (volume) polarizations,
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"w" is the characteristic frequency,
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and "R" is the separation of the bodies in question.
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("h" is, of course, Planck's constant,
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and "c" is the speed of light..)
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The frequency is evaluated over a cut-off determined by the size of
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the system, "r", and roughly equal to (c/r).
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Here, the factor (1/6) represents an integral over w^5, and r may be
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taken as an average atomic radius. This equation is accurate over a
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wide range of scales, with corrections on the order of unity being
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found in most situations of interest.
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The factor
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(hw^6/(12pi*c^5))
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is the e.d.o. term, and yields large exponents in the case of
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molecular or atomic systems. These large exponents are deceptive
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however, as average polarization in an atomic system is on the order
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of
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((10^-27)cm^3) or less.
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Polar-polar potentials thus tend to produce energies which are small
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compared to the total energy of a given system. This low-energy
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behavior suggests some resemblance to gravitation, which a sample
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calculation will make more evident.
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Consider first the physical dimensions of Newton's constant,
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(R^3/(M*t^2)).
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It can be written
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(w^2/d),
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where "d" is a volume mass density, and could as well be written
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((M/(R^3*t^2))(1/d)^2,
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the ratio of an e.d.o.divided by the square of a density.
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The Casimir interpretation of this expression takes the form
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(hw^6/(2pi*c^5))(1/d)^2.<2E>
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To get an estimate of the frequency-to-density ratios which are
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relevant, one should look at a simple system with well-known
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parameters.
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Monoatomic hydrogen is just such a system. Assume that the atom in
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question is in its ground state, with a minimal volume polarization
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equal roughly to one electron volume
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(approx.(2.818*10^-13)^3).
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Page 2
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Then, the polar-polar potential of this system will be proportional
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to the orbital frequency of the electron
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(a^3*c/4pi*r#)
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where "a" is the electromagnetic coupling constant (1/137.036),
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and"r#" is the electron radius.
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The e.d.o. of this system
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((h/(2pi*c^5))(a^3*c/(4pi*r#)^6)
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is
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5.52107*10^13(gm/(cm^3*t^2)),
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(factor of (1/6) suppressed).
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When this quantity is multiplied by the electron volume squared, the
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result,
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2.76449*10^-62(gm*cm^3/t^2),
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is a tiny value indeed.
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Herein lies a surprise. Recall that Newton's constant has multiple
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definitions in dimensional analysis.
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In this case, dividing the Casimir potential value just given by the
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electron mass squared creates a fascinating "coincidence", namely, a
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figure which is just shy of one-half Newton's constant.
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Properly reduced, and doubled to account for two interacting
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systems, the full expression will read
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G=((hc/(pi*m#^2))(a^3/4pi)^6)
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which equals Newton's constant to within 99.85%("m#"=electron mass).
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A more accurate derivation requires evaluation of the Lambshift
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contribution, and estimates of such factors as vacuum polarization,
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charge screening, relativistic corrections (long-range) and higher
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order interactions.
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The model just presented is not, arguably, an accurate "definition"
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of gravitation, as other models are much more precise and detailed.
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It does, however, illustrate the utility of alternative
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conceptualization made feasible by the use of e.d.o.s and Casimir
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potentials.
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The value of this approach lies in its ability to reveal new
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phenomena and relationships between seemingly well-known processes.
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A similar treatment might have been performed on quark-gluon
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coupling, say, where longitudinal virtuals have been found to play
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an active role.
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What is more important is that consideration be given to a broader
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range of qualitative issues in physics. Quantitative methods are
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Page 3
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only as good as the qualitative concepts they address, for one
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cannot calculate our planet's circumference without first asking if
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it is round.
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Add 1: A good introduction to Casimir potentials will be found
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in
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"Physics Today", 11/86, p.p.37-45,
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titled "Retarded, or long-range, Casimir potentials",
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by Larry Spruch, which contains a very complete
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bibliography.
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Note also the bibliography contained in the
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KeelyNet file "ZPE1", especially the papers of
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Timothy Boyer, H.E. Puthoff, and A.E. Sakharov, which
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detail matters related to quantum fluctuations in
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vacuum.
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--------------------------------------------------------------------
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E-mail may be directed to the author of this paper through Woody
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Moffitt on KeelyNet/Dallas. Thank you for your comments.
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--------------------------------------------------------------------
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If you have comments or other information relating to such topics
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as this paper covers, please upload to KeelyNet or send to the
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Vangard Sciences address as listed on the first page.
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Thank you for your consideration, interest and support.
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Jerry W. Decker.........Ron Barker...........Chuck Henderson
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Vangard Sciences/KeelyNet
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If we can be of service, you may contact
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Jerry at (214) 324-8741 or Ron at (214) 242-9346
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Page 4
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