265 lines
9.4 KiB
Plaintext
265 lines
9.4 KiB
Plaintext
|
|
|||
|
|
|
|||
|
|
|
|||
|
|
|
|||
|
|
(word processor parameters LM=8, RM=75, TM=2, BM=2)
|
|||
|
|
Taken from KeelyNet BBS (214) 324-3501
|
|||
|
|
Sponsored by Vangard Sciences
|
|||
|
|
PO BOX 1031
|
|||
|
|
Mesquite, TX 75150
|
|||
|
|
|
|||
|
|
There are ABSOLUTELY NO RESTRICTIONS
|
|||
|
|
on duplicating, publishing or distributing the
|
|||
|
|
files on KeelyNet!
|
|||
|
|
|
|||
|
|
August 30, 1991
|
|||
|
|
|
|||
|
|
CPEDOG.ASC
|
|||
|
|
--------------------------------------------------------------------
|
|||
|
|
This file shared with KeelyNet courtesy of Woody Moffitt.
|
|||
|
|
Also see ZPE1, ZPE2, CFG1 on KeelyNet.
|
|||
|
|
--------------------------------------------------------------------
|
|||
|
|
|
|||
|
|
Casimir Potentials,
|
|||
|
|
Electromagnetic Density Oscillations
|
|||
|
|
and Gravitation
|
|||
|
|
by
|
|||
|
|
Darrell Moffitt
|
|||
|
|
|
|||
|
|
Among the less researched topics of classical and quantum physicists
|
|||
|
|
is that of electromagnetic density oscillations (e.d.o.s), i.e.,
|
|||
|
|
acoustic-form longitudinal waves in electromagnetic media.
|
|||
|
|
|
|||
|
|
Though current literature does address phonon interactions, and
|
|||
|
|
their influence on conductivity in solids, longitudinal plasma
|
|||
|
|
waves and their quantum relatives are largely ignored. While
|
|||
|
|
acoustic waves may admit transverse polarities, they are
|
|||
|
|
fundamentally a longitudinal phenomenon.
|
|||
|
|
|
|||
|
|
Plasma oscillations possess up to four longitudinal modes; the
|
|||
|
|
alternating compression and rarefaction zones comprising a wave may
|
|||
|
|
consist of either particles or fields, and the field itself may be
|
|||
|
|
electric or magnetic.
|
|||
|
|
|
|||
|
|
Still another form of e.d.o. results from interacting charge
|
|||
|
|
densities; the square of charge density is dimensionally identical
|
|||
|
|
to that of sound,
|
|||
|
|
|
|||
|
|
(M/(R^3*t^2)),
|
|||
|
|
|
|||
|
|
and van der Waals forces both derive from such couplings and
|
|||
|
|
contribute the restoring force responsible for ordinary sound.
|
|||
|
|
|
|||
|
|
Quantum mechanics describes van der Waals forces via Casimir
|
|||
|
|
potentials, simple, non-relativistic equations which take their name
|
|||
|
|
from Hendrick B. G. Casimir.
|
|||
|
|
|
|||
|
|
Casimir's polar-polar potential, applied to any two polarizable
|
|||
|
|
bodies, is a prototype of quantum-level e.d.o.s. This equation
|
|||
|
|
reads
|
|||
|
|
|
|||
|
|
E=((h/(2pi*c^5))(P1*P2)(w^6/6))(1/R)
|
|||
|
|
|
|||
|
|
|
|||
|
|
Page 1
|
|||
|
|
|
|||
|
|
|
|||
|
|
|
|||
|
|
|
|||
|
|
|
|||
|
|
where (P1,P2) are the respective (volume) polarizations,
|
|||
|
|
"w" is the characteristic frequency,
|
|||
|
|
and "R" is the separation of the bodies in question.
|
|||
|
|
|
|||
|
|
("h" is, of course, Planck's constant,
|
|||
|
|
and "c" is the speed of light..)
|
|||
|
|
|
|||
|
|
The frequency is evaluated over a cut-off determined by the size of
|
|||
|
|
the system, "r", and roughly equal to (c/r).
|
|||
|
|
|
|||
|
|
Here, the factor (1/6) represents an integral over w^5, and r may be
|
|||
|
|
taken as an average atomic radius. This equation is accurate over a
|
|||
|
|
wide range of scales, with corrections on the order of unity being
|
|||
|
|
found in most situations of interest.
|
|||
|
|
|
|||
|
|
The factor
|
|||
|
|
|
|||
|
|
(hw^6/(12pi*c^5))
|
|||
|
|
|
|||
|
|
is the e.d.o. term, and yields large exponents in the case of
|
|||
|
|
molecular or atomic systems. These large exponents are deceptive
|
|||
|
|
however, as average polarization in an atomic system is on the order
|
|||
|
|
of
|
|||
|
|
|
|||
|
|
((10^-27)cm^3) or less.
|
|||
|
|
|
|||
|
|
Polar-polar potentials thus tend to produce energies which are small
|
|||
|
|
compared to the total energy of a given system. This low-energy
|
|||
|
|
behavior suggests some resemblance to gravitation, which a sample
|
|||
|
|
calculation will make more evident.
|
|||
|
|
|
|||
|
|
Consider first the physical dimensions of Newton's constant,
|
|||
|
|
|
|||
|
|
(R^3/(M*t^2)).
|
|||
|
|
|
|||
|
|
It can be written
|
|||
|
|
|
|||
|
|
(w^2/d),
|
|||
|
|
|
|||
|
|
where "d" is a volume mass density, and could as well be written
|
|||
|
|
|
|||
|
|
((M/(R^3*t^2))(1/d)^2,
|
|||
|
|
|
|||
|
|
the ratio of an e.d.o.divided by the square of a density.
|
|||
|
|
|
|||
|
|
The Casimir interpretation of this expression takes the form
|
|||
|
|
|
|||
|
|
(hw^6/(2pi*c^5))(1/d)^2.<2E>
|
|||
|
|
|
|||
|
|
To get an estimate of the frequency-to-density ratios which are
|
|||
|
|
relevant, one should look at a simple system with well-known
|
|||
|
|
parameters.
|
|||
|
|
|
|||
|
|
Monoatomic hydrogen is just such a system. Assume that the atom in
|
|||
|
|
question is in its ground state, with a minimal volume polarization
|
|||
|
|
equal roughly to one electron volume
|
|||
|
|
|
|||
|
|
(approx.(2.818*10^-13)^3).
|
|||
|
|
|
|||
|
|
|
|||
|
|
Page 2
|
|||
|
|
|
|||
|
|
|
|||
|
|
|
|||
|
|
|
|||
|
|
|
|||
|
|
Then, the polar-polar potential of this system will be proportional
|
|||
|
|
to the orbital frequency of the electron
|
|||
|
|
|
|||
|
|
(a^3*c/4pi*r#)
|
|||
|
|
|
|||
|
|
where "a" is the electromagnetic coupling constant (1/137.036),
|
|||
|
|
and"r#" is the electron radius.
|
|||
|
|
|
|||
|
|
The e.d.o. of this system
|
|||
|
|
|
|||
|
|
((h/(2pi*c^5))(a^3*c/(4pi*r#)^6)
|
|||
|
|
|
|||
|
|
is
|
|||
|
|
|
|||
|
|
5.52107*10^13(gm/(cm^3*t^2)),
|
|||
|
|
(factor of (1/6) suppressed).
|
|||
|
|
|
|||
|
|
When this quantity is multiplied by the electron volume squared, the
|
|||
|
|
result,
|
|||
|
|
|
|||
|
|
2.76449*10^-62(gm*cm^3/t^2),
|
|||
|
|
|
|||
|
|
is a tiny value indeed.
|
|||
|
|
|
|||
|
|
Herein lies a surprise. Recall that Newton's constant has multiple
|
|||
|
|
definitions in dimensional analysis.
|
|||
|
|
|
|||
|
|
In this case, dividing the Casimir potential value just given by the
|
|||
|
|
electron mass squared creates a fascinating "coincidence", namely, a
|
|||
|
|
figure which is just shy of one-half Newton's constant.
|
|||
|
|
|
|||
|
|
Properly reduced, and doubled to account for two interacting
|
|||
|
|
systems, the full expression will read
|
|||
|
|
|
|||
|
|
G=((hc/(pi*m#^2))(a^3/4pi)^6)
|
|||
|
|
|
|||
|
|
which equals Newton's constant to within 99.85%("m#"=electron mass).
|
|||
|
|
|
|||
|
|
A more accurate derivation requires evaluation of the Lambshift
|
|||
|
|
contribution, and estimates of such factors as vacuum polarization,
|
|||
|
|
charge screening, relativistic corrections (long-range) and higher
|
|||
|
|
order interactions.
|
|||
|
|
|
|||
|
|
The model just presented is not, arguably, an accurate "definition"
|
|||
|
|
of gravitation, as other models are much more precise and detailed.
|
|||
|
|
|
|||
|
|
It does, however, illustrate the utility of alternative
|
|||
|
|
conceptualization made feasible by the use of e.d.o.s and Casimir
|
|||
|
|
potentials.
|
|||
|
|
|
|||
|
|
The value of this approach lies in its ability to reveal new
|
|||
|
|
phenomena and relationships between seemingly well-known processes.
|
|||
|
|
|
|||
|
|
A similar treatment might have been performed on quark-gluon
|
|||
|
|
coupling, say, where longitudinal virtuals have been found to play
|
|||
|
|
an active role.
|
|||
|
|
|
|||
|
|
What is more important is that consideration be given to a broader
|
|||
|
|
range of qualitative issues in physics. Quantitative methods are
|
|||
|
|
|
|||
|
|
Page 3
|
|||
|
|
|
|||
|
|
|
|||
|
|
|
|||
|
|
|
|||
|
|
|
|||
|
|
only as good as the qualitative concepts they address, for one
|
|||
|
|
cannot calculate our planet's circumference without first asking if
|
|||
|
|
it is round.
|
|||
|
|
|
|||
|
|
Add 1: A good introduction to Casimir potentials will be found
|
|||
|
|
in
|
|||
|
|
"Physics Today", 11/86, p.p.37-45,
|
|||
|
|
titled "Retarded, or long-range, Casimir potentials",
|
|||
|
|
by Larry Spruch, which contains a very complete
|
|||
|
|
bibliography.
|
|||
|
|
|
|||
|
|
Note also the bibliography contained in the
|
|||
|
|
KeelyNet file "ZPE1", especially the papers of
|
|||
|
|
Timothy Boyer, H.E. Puthoff, and A.E. Sakharov, which
|
|||
|
|
detail matters related to quantum fluctuations in
|
|||
|
|
vacuum.
|
|||
|
|
|
|||
|
|
--------------------------------------------------------------------
|
|||
|
|
E-mail may be directed to the author of this paper through Woody
|
|||
|
|
Moffitt on KeelyNet/Dallas. Thank you for your comments.
|
|||
|
|
--------------------------------------------------------------------
|
|||
|
|
|
|||
|
|
If you have comments or other information relating to such topics
|
|||
|
|
as this paper covers, please upload to KeelyNet or send to the
|
|||
|
|
Vangard Sciences address as listed on the first page.
|
|||
|
|
Thank you for your consideration, interest and support.
|
|||
|
|
|
|||
|
|
Jerry W. Decker.........Ron Barker...........Chuck Henderson
|
|||
|
|
Vangard Sciences/KeelyNet
|
|||
|
|
|
|||
|
|
--------------------------------------------------------------------
|
|||
|
|
If we can be of service, you may contact
|
|||
|
|
Jerry at (214) 324-8741 or Ron at (214) 242-9346
|
|||
|
|
--------------------------------------------------------------------
|
|||
|
|
|
|||
|
|
|
|||
|
|
|
|||
|
|
|
|||
|
|
|
|||
|
|
|
|||
|
|
|
|||
|
|
|
|||
|
|
|
|||
|
|
|
|||
|
|
|
|||
|
|
|
|||
|
|
|
|||
|
|
|
|||
|
|
|
|||
|
|
|
|||
|
|
|
|||
|
|
|
|||
|
|
|
|||
|
|
|
|||
|
|
|
|||
|
|
|
|||
|
|
|
|||
|
|
|
|||
|
|
|
|||
|
|
|
|||
|
|
Page 4
|
|||
|
|
|
|||
|
|
|