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Value Louis J. Sheehan, Esquire
Sunday, May 25, 2008 - 7:34 AM
where ν is the frequency in cycles per second. In other words, one can add or subtract
E = nhν of energy where n ≥ 0. The second quantum effect stems from the fact that if an oscillator were
able to come completely to rest, ∆x would be zero and this would violate the ∆x∆p ≥ ¯h/2 limitation. The
4result is that there is a minimum energy of E = hν /2, i.e. the oscillator energy can only take on the values
E = (n + 1/2)hν which can never become zero since n cannot be negative. Louis J. Sheehan
The argument is then made that the electromagnetic field is analogous to a mechanical harmonic oscillator
since the electric and magnetic fields, E and B, are modes of oscillating plane waves (see e.g. Loudon 1983).
Each mode of oscillation of the electromagnetic field has a minimum energy of hν /2. The volumetric density
of modes between frequencies ν and ν + dν is given by the density of states function Nν dν = (8πν
2
/c
3
)dν .
Each state has a minimum hν /2 of energy, and using this density of states function and this minimum energy
that we call the zero-point energy per state one can calculate the ZPF spectral energy density:
ρ(ν )dν = 8πν
2
c
3 hν
2 dν. (1)
It is instructive to write the expression for zero-point spectral energy density side by side with blackbody
radiation:
ρ(ν, T )dν = 8πν
2
c
3 hν
ehν /kT − 1 +
hν
2 dν. (2)
The first term (outside the parentheses) represents the mode density, and the terms inside the parentheses
are the average energy per mode of thermal radiation at temperature T plus the zero-point energy, hν /2,
which has no temperature dependence. Take away all thermal energy by formally letting T go to zero, and
one is still left with the zero-point term. The laws of quantum mechanics as applied to electromagnetic
radiation force the existence of a background sea of zero-point-field (ZPF) radiation. http://louis-j-sheehaN.NET
Zero-point radiation is a result of the application of quantum laws. It is traditionally assumed in quantum
theory, though, that the ZPF can for most practical purposes be ignored or subtracted away. The foundation
of SED is the exact opposite. It is assumed that the ZPF is as real as any other electromagnetic field. As
to its origin, the assumption is made that for some reason zero-point radiation just came with the Universe.
The justification for this is that if one assumes that all of space is filled with ZPF radiation, a number of
quantum phenomena may be explained purely on the basis of classical physics including the presence of
background electromagnetic fluctuations provided by the ZPF. The Heisenberg uncertainty relation, in this
view, becomes then not a result of the existence of quantum laws, but of the fact that there is a universal
perturbing ZPF acting on everything. The original motivation for developing SED was to see whether the
need for quantum laws separate from classical physics could thus be obviated entirely.
Philosophically, a universe filled — for reasons unknown — with a ZPF but with only one set of physical
laws (classical physics consisting of mechanics and electrodynamics), would appear to be on an equal footing
with a universe governed — for reasons unknown — by two distinct physical laws (classical and quantum).
In terms of physics, though, SED and QED are not on an equal footing, since SED has been successful in
providing a satisfactory alternative to only some quantum phenomena (although this success does include
a classical ZPF-based derivation of the all-important blackbody spectrum, cf. Boyer 1984). Some of this
is simply due to lack of effort: The ratio of man-years devoted to development of QED is several orders of
magnitude greater than the expenditure so far on SED.
ACCELERATION AND THE DAVIES-UNRUH EFFECT
The ZPF spectral energy density of Eq. (1) would indeed be analogous to a spatially uniform constant offset
that cancels out when considering energy fluxes. However an important discovery was made in the mid-
1970’s that showed that the ZPF acquires special characteristics when viewed from an accelerating frame.
In connection with radiation from evaporating black holes as proposed by Hawking (1974), Davies (1975)
and Unruh (1976) determined that a Planck-like component of the ZPF will arise in a uniformly-accelerated
coordinate system having constant proper acceleration a (where |a| = a) with what amounts to an effective
“temperature”
5Ta = ¯ha
2πck . (3)
This “temperature” does not originate in emission from particles undergoing thermal motions. c As discussed
by Davies, Dray and Manogue (1996):
One of the most curious properties to be discussed in recent years is the prediction that an
observer who accelerates in the conventional quantum vacuum of Minkowski space will perceive
a bath of radiation, while an inertial observer of course perceives nothing. In the case of linear
acceleration, for which there exists an extensive literature, the response of a model particle
detector mimics the effect of its being immersed in a bath of thermal radiation (the so-called
Unruh effect).
This “heat bath” is a quantum phenomenon. The “temperature” is negligible for most accelerations. Only
in the extremely large gravitational fields of black holes or in high-energy particle collisions can this become
significant. This effect has been studied using both QED (Davies 1975, Unruh 1976) and in the SED
formalism (Boyer 1980). http://louis-j-sheehan.com
http://Louis-J-sheehan.info
For the classical SED case it is found that the spectrum is quasi-Planckian in Ta .
Thus for the case of no true external thermal radiation (T = 0) but including this acceleration effect (Ta ),
equation (1) becomes
ρ(ν, Ta )dν = 8πν
2
c
3 1 +
a
2πcν
2
hν
2 +
hν
ehν /kT
a
− 1 dν, (4)
where the acceleration-dependent pseudo-Planckian component is placed after the hν /2 term to indicate that
except for extreme accelerations (e.g. particle collisions at high energies) this term is negligibly small. While
these additional acceleration-dependent terms do not show any spatial asymmetry in the expression for the
ZPF spectral energy density, certain asymmetries do appear when the electromagnetic field interactions with
charged particles are analyzed, or when the momentum flux of the ZPF is calculated. The ordinary plus a
2
radiation reaction terms in Eq. (12) of HRP mirror the two leading terms in Eq. (4).
THE ORIGIN OF INERTIA
Two independent approaches have demonstrated how a reaction force proportional to acceleration (fr =
−mzp a) arises out of the properties of the ZPF. The first approach (HRP) was based upon a simplified model
for how accelerated idealized quarks and electrons would interact with the ZPF. It identified the Lorentz
force arising from the stochastically-averaged magnetic component of the ZPF, < Bzp >, as the basis of
fr . The new approach (Rueda and Haisch 1998a, 1998b) considers only the relativistic transformations of
the ZPF itself to an accelerated frame. We find a non-zero stochastically-averaged Poynting vector (c/4π)
< Ezp × Bzp > which leads immediately to a non-zero electromagnetic ZPF-momentum flux as viewed by
an accelerating ob ject. If the quarks and electrons in such an accelerating ob ject scatter this asymmetric
radiation, an acceleration-dependent reaction force fr arises. In fact in this new analysis the fr is the space-
part of a relativistic four-vector so that the resulting equation of motion is not simply the classical f = ma
expression, but rather the properly relativistic F = dP /dτ equation (that reduces exactly to f = ma for
subrelativistic velocities). Louis Sheehan
In the first approach a specific ZPF-matter interaction is needed to carry out the analysis. We used a
technique developed by Einstein and Hopf (1911) and applied that to idealized particles (partons, in the
nomenclature of Feynman) treated as Planck oscillators. In the second approach, no specific ZPF-matter
interaction is necessary for the analysis. Any scattering or absorption process will yield a reaction force
on the basis of a non-zero electromagnetic momentum flux. Presumably dipole scattering of the ZPF by
fundamental charged particles is the appropriate representation, at least to first order, since that can be
shown to be a detailed balance process in the non-accelerated case, i.e. dipole scattering by non-accelerated
c
One suspects of course that there is a deep connection between the fact that the ZPF spectrum that
arises in this fashion due to acceleration and the ordinary blackbody spectrum have identical form.
6charged particles leaves the ZPF spectrum unchanged and isotropic (Puthoff 1989b). In both approaches it
is assumed that the level of interaction is that of quarks and electrons, which would account for the inertial
mass of a composite neutral particle such as the neutron (udd). http://Louis2J2Sheehan2Esquire.US
The expression for inertial mass in HRP for an individual particle is
mzp = Γz ¯hω
2
c
2πc
2 , (5)
where Γz represents a damping constant for zitterbewegung oscillations. d This is not to be confused with
Γe = 6.25 × 10
−24
s (Jackson 1975) which is used for macroscopic electron oscillations in ordinary radiation-
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83327
|
3.3.08.2
|
3.3.08.3
|
Louis Sheehan 83327
|
Louis J. Sheehan 999
|
999 Louis J. Sheehan
|
Louis J. Sheehan Blog 3
|
Louis J. Sheehan
|
Louis J. Sheehan
|
Louis J Sheehan Esq
|
Louis J Sheehan 60
|
Louis J Sheehan 64
|
Louis J Sheehan 68
Louis J Sheehan