Zero Point Field (ZPF) effects
Zero Point Field (ZPF) effects
in the interaction of the ultrashort laser pulses with matter
Miroslaw Kozlowski^{a}, Janina MarciakKozlowska^{b,c}
^{a}Institute of Experimental Physics and
Science Teacher's College, Warsaw University,
Hoza 69, 00681 Warsaw, Poland
mirkoz@ids.pl
M. Kozlowski's Home Page
^{b}Institute of Electron Technology,
Al. Lotników 32/46, 02668 Warsaw, Poland
^{c}Author to whom correspondence should be addressed.
Abstract
In this paper the effects of zeropoint energy (ZPE) on the heat
transport induced by ultrashort laser pulses is investigated. It will be
shown that the existence of the zeropoint energy in the physical
vacuum influence the heat transport on the atomic level. The interaction
of the building blocks of matteratoms with the zeropoint
fields (ZPF), which generate the ZPE guarantees the stability of matter.
The interaction of the ultrashort laser pulses (Dt ~ 1 as) with
matter can be used as the source of the information on the ZPF.
Key words: Ultrashort laser pulses; Quantum heat transport;
Zeropoint energy; Zeropoint fields.
1 Introduction
During the 20th century, our knowledge regarding space and the properties
of the vacuum has taken a considerable progress. In the popular meaning
the vacuum is considered to be a void or ``nothingness''. This is the
definition of a bare vacuum. However, with the progress of
science, a new and contrasting description has arisen, which physicist
call the physical vacuum. The physical vacuum contains
measurable energy. This energy is called the zeropoint
energy (ZPE) because it exists even at absolute zero. The very fruitful
theoretical framework in which we can describe the zeropoint
energy is the stochastic electrodynamics (SED) [1,2,3,4]. In the SED approach the physical vacuum at the atomic or
subatomic level may be considered to be inherently comprised of a
turbulent sea of randomly fluctuating electromagnetic field.
These fields exist at all wavelengths longer than the Planck length. At
the macroscopic level these zeropoint fields (ZPF) are homogenous
and isotropic.
The atomic building blocks of matter are dependent upon the ZPF for their
very existence. This was demonstrated by H. Puthoff [3,4].
Puthoff started by pointing out the anomaly. According to classical
concepts an electron in orbit around the proton should be radiating
energy. As a consequence, as it losses energy, it should spiral into the
atomic nucleus. But that does not happen. In quantum mechanics it is
explained by the Bohr's quantum conditions. Instead of the Bohr
model of the atom, Puthoff approached this problem with the assumption
that the classical laws of electrodynamics were valid and that the
electron is therefore losing energy and the loss was exactly balanced by
energy gain from the ZPF.
In this paper we adapted the Puthoff's results to the study the heat
transport on the atomic level. To that aim we consider the quantum heat
transport (QHT) equation [5]. It will be shown that at the
atomic level the structure of the QHT is dependent upon the ZPF. The
condition for the quantum heat transport limit [5] guarantees
the balance of the lossgain energy on the atomic level. This open new
field of investigation for laser scientists and engineers. The
interaction of the ultrashort laser pulses (D t ~ attosecond)
with matter can be used as the source of the information on the ZPF.
Maybe that the future engineers will be specialized in ``vacuum
engineering''.
2 The physical vacuum
In the stochastic electrodynamics (SED) [1,2,3,4] the
physical vacuum is assumed to be filled with random classical zeropoint
electrodynamic radiation which is homogenous, isotropic and Lorentz
invariant. Writing as a sum over plane waves, the random radiation can be
expressed as [3]


Re 
2 å
d = 1


ó õ

d^{3}k 
^ e


æ ç
è

(^{h}/_{2p})w 8p^{3}e_{0}

ö ÷
ø

1/2

× e^{(i®k®riwt+iQ(k,d))}, 
 (1)  

Re 
2 å
d = 1


ó õ

d^{3}k( 
^ k

× 
^ e

) 
æ ç
è

(^{h}/_{2p}) w 8p^{3}m_{0}

ö ÷
ø

1/2

× e^{(i®k®riwt+iQ(k,d))}, 


where d = 1,2 denote orthogonal polarizations, Ùe and
Ùk are orthogonal unit vectors in the direction of the electric
field polarization and wave propagation. Vectors, respectivately,
Q(®k, d) are random phases distributed uniformly on the
interval 0 to 2p (independently distributed for each ®k,d) and w = kc. It must be stressed that in the SED the
zeropoint field is treated in every way as a real, physical
field.
In the subsequent we will approximate the matter as the ensemble of the
one dimensional charged harmonic oscillators of natural frequency
w_{0} immersed in the zeropoint field. For orientation along
the x axis the (nonrelativistic) equation of motion for a particle of
mass m and charge e, including damping is given by [3]
m 
d^{2}x dt^{2}

+mw^{2}_{0}x= 
æ ç
è

e^{2} 6pe_{0}c^{3}

ö ÷
ø


d^{3}x dt^{3}

+eE^{zt}_{x}(0,t), 
 (2) 
where e is the charge on electron, c is the light velocity and
e_{0} is the electrical permittivity of the vacuum.
Substitution of formula (1) to formula (2) gives the
following expression for displacement and velocity:



e m

Re 
2 å
d = 1


ó õ

d^{3}k( 
^ e

· 
^ x

) 
æ ç
è

(^{h}/_{2p})w 8p^{3}e_{0}

ö ÷
ø

1/2


1 D

×e^{(i®k®riwt+iQ(k,d))}, 
 (3)  


dx dt

= 
e m

Re 
2 å
d = 1


ó õ

d^{3}k( 
^ e

· 
^ x

) 
æ ç
è

(^{h}/_{2p})w 8p^{3}e_{0}

ö ÷
ø

1/2

× 
æ ç
è

 
iw D

ö ÷
ø

e^{(i®k®riw t+iQ(k,d))}, 


where


w^{2}+w^{2}_{0}iGw^{3}, 
 (4)  



From (1) and (3) the average power absorbed by oscillator
from ZPF can be calculated [3], viz.:
áP^{abs}ñ = áeE^{zp}· 
® v

ñ = 
e^{2}(^{h}/_{2p})w^{3}_{0} 12pe_{0}mc^{3}

. 
 (5) 
We now recognize that for ``planetary'' motion of electrons in the atom
the ground state circular orbit of radius r_{0} constitutes a pair of one
dimensional harmonic oscillator in a plane
Therefore the power absorbed from the background by the electron in
circular orbit is double of (5) or
áP^{abs}ñ_{circ} = 
e^{2}(^{h}/_{2p})w^{3}_{0} 6pe_{0}mc^{3}

. 
 (7) 
The power radiated by charged particle in circular orbit with
acceleration A is given by the expression [6]
áP^{rad}ñ_{circ}= 
e^{2}A^{2} 6pe_{0}c^{3}

= 
e^{2}r^{2}_{0}w^{4}_{0} 6pe_{0}c^{3}

. 
 (8) 
3 Quantum heat transport equation in the presence of ZPF
In monograph [5] the quantum heat transport equation for
electrons in matter was formulated:

l_{B} v_{h}


¶^{2} T^{e} ¶t^{2}

+ 
l_{B} l_{m}


¶T ¶ t

= 
(^{h}/_{2p}) m_{e}

Ñ^{2} T. 
 (9) 
In Eq. (9) T is the temperature, l_{B} and l_{m}
are the reduced de Broglie wavelength and mean free path (for electron)
respectively
l_{B}= 
(^{h}/_{2p}) p

, l_{m}=vt, 
 (10) 
where v is the electron velocity and t is the relaxation time for
electrons.
In the following we will study the quantum limit of the heat transport in
the fermionic system [5]. We define the quantum heat transport
limit as follows
In that case Eq. (9) have the form
t 
¶^{2} T ¶t^{2}

+ 
¶T ¶t

= 
(^{h}/_{2p}) m

Ñ^{2} T, 
 (12) 
where
t = 
(^{h}/_{2p}) m_{e}v^{2}

. 
 (13) 
Having the relaxation time t one can define the pulsation
w [5]
w = t^{1}= 
mv^{2} (^{h}/_{2p})

. 
 (14) 
For an electron in atom, w = w_{0} (formula (6)) i.e.
w_{0}= 
mv^{2} (^{h}/_{2p})

. 
 (15) 
Considering that for circular orbit v=w_{0}r_{0}, formula (15)
gives
r^{2}_{0}= 
(^{h}/_{2p}) mw_{0}

. 
 (16) 
Substituting formula (16) to formula (8) one obtains
áP^{rad}ñ_{circ}= 
e^{2}(^{h}/_{2p})w^{3}_{0} 6pe_{0}mc^{3}

=áP^{abs}ñ_{circ}. 
 (17) 
We conclude that in the SED framework the QHT equation (12)
describes the heat transport on the atomic level where the t is the
relaxation time for the electronzero point field interaction. It
is quite interesting to observe that formula (15) is the Bohr
formula for the ground state of hydrogen atom. It means that the ground
state of the hydrogen atom is the result of the balance between radiation
emitted due to acceleration of the electron and radiation absorbed from
the zeropoint background. For the first time the balance between two
forms of radiation in hydrogen atom was hypothesed by Boyer [7].
4 Conclusion
In this paper, the quantum heat transport (QHT), formulated in our
monograph, was considered in the framework of stochastic
electrodynamics (SED). It was shown that the structure of QHT on the
atomic level reflects the fact that the energy radiated by the
accelerated charged particle in circular motion equals the energy
absorbed from the zeropoint field. It means that hypothetical ZPF
is as real as the real are atoms, i.e. matter.
Acknowledgement
This study was made possible by financial support
from the Polish Committee for Science Research under grant 7 T11 B 024
21.
References
 [1]

L. de la Peña and M. Cetto.
The Quantum Dice: An Introduction to Stochastic
Electrodynamics.
Kluwer, 1996.
 [2]

B. Haisch and A. Rueda.
Phys. Lett., A268, 2000.
 [3]

H. E. Puthoff.
Phys. Rev., D35:3266, 1987.
 [4]

H. E. Puthoff.
Phys. Rev., A39:2333, 1989.
 [5]

Miros³aw Koz³owski and Janina MarciakKoz³owska.
From Quarks to Bulk Matter.
Hadronic Press, 2001.
 [6]

R. P. Feynman, R. B. Leighton, and M. Sands.
The Feynman Lecture on Physics.
AdisonWesley, Reading, MA, 1963.
 [7]

T. H. Boyer.
Phys. Rev., D11:790, 809, 1975.
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