Vol.3, No.3, 249-254 (2011) Natural Science
http://dx.doi.org/10.4236/ns.2011.33031
Another possibility of sonoluminescence due to the
cherenkov radiation from the ZPF field in a water bubble
Takaaki Musha
Advanced Sci.-Tech. Research. Organization, Namiki, Kanazawa-ku, Yokohama, Japan;
Received 13 January 2011; revised 10 February 2011; accepted 15 February 2011.
ABSTRACT
Sonoluminescence is the light produced from
the collapse of bubbles in water under ultra-
sound. Schwinger proposed a physical mecha-
nism for sonoluminescence in terms of photon
production due to changes of quantum elec-
trodynamic energy contained in a collapsing
dielectric bubble. However there are critics for
the Schwinger’s proposal that his estimate of
the Casimir energy involved is inaccurate and
there are several papers to propose its missing
term. In this paper, the author presents another
possible component of sonoluminescense which
is due to Cherenkov radiation from tachyon pairs
generated in a collapsing bubble.
Keywords: Sonoluminscence; Casimir Energy;
Cherenkov Radiation; Tachyon; Zero-Point Energy
1. INTRODUCTION
Cavitation is the formation of vapor bubbles of a
flowing liquid in a region where the pressure of the liq-
uid falls below its vapor pressure. This is a process in
which a void or a bubble in a liquid rapidly collapses
and producing a shock wave to cause a temperature in-
crease and emits light. This phenomenon is now referred
to as sonoluminescence (SL). Sonoluminescence can
occur when a sound wave of sufficient intensity induces
a gaseous cavity within a liquid to collapse quickly. The
bubble reaches a maximum at about ten times its original
size, it completely collapses within a few milliseconds
later. Sonoluminescence observed in the laboratory can
be made to be stable, so that a single bubble will expand
and collapse over and over again in a periodic fashion,
emitting a burst of light each time it collapses. For this to
occur, a gas filled bubble undergoes repeated growth and
collapse in response to an acoustic standing wave. As the
radius of the bubble quickly shrinks, the potential energy
is released as heat and light [1]. The experimental results
obtained in various fluids have shown that; 1) a flash of
light emitted from the collapsing bubble with a maxi-
mum diameter of 100 microns creates a temperature of
5500˚C with a blackbody spectrum when it rapidly
shrinks to less than one micron in radius, 2) light flashes
from the bubbles are extremely short persisted only for
50 picoseconds or shorter with peak intensities of the
order of 1~10 mW, which was too brief for the light to
be produced by some atomic process, 3) bubbles are
very small when they emit the light with about 1 μm in
diameter depending on the ambient fluid and the gas
content of the bubble, 4) single-bubble sonolumines-
cence pulses have very stable periods and positions and
the frequency of light flashes can be more stable than the
rated frequency stability of the oscillator making the
sound waves driving them, and 5) the addition of a small
amount of noble gas to the gas in the bubble increases
the intensity of the emitted light. Spectral measurements
have given bubble temperatures in the range from
2300˚K to 5100˚K, the exact temperatures depending on
experimental conditions including the composition of the
liquid and gas [2]. The mechanism of the phenomenon
of sonoluminescence remains unsettled and theories
those included hotspot, bremsstrahlung radiation, colli-
sion-induced radiation and corona discharges, non-
classical light, proton tunneling, electrodynamic jets,
fractoluminescent jets, and so forth were presented [3].
As the properties of sonoluminescence which releases
too large an amount of energy and releases the energy on
too short a time scale are consistent with the vacuum
energy explanation, Schwinger proposed a physical me-
chanism based on the instantaneous collapse of a bubble
for sonoluminescence in terms of photon production due
to changes of quantum electrodynamic energy contained
in a collapsing dielectric bubble [4].
According to the Schwinger’s theory, the surface of a
bubble is supposed to act as the Casimir force plates and
an abrupt change of electromagnetic energy is emitted as
visible light in sonoluminescent flashes when the bubble
collapses. But there are some critics for the Schwinger’s
proposal that his estimate of the Casimir energy involved

T. Musha / Natural Science 3 (2011) 249-254 250
is inaccurate and several papers were presented to con-
sider the missing terms [5-8]. One of them was a propo-
sition given by Claudia Eberlein [9,10] that sonolumi-
nescence could be explained in terms of quantum vac-
uum radiation by moving interfaces between media of
different polarization, which might be alike to the Unruh
effect. Instead of their conventional quantum electrody-
namic (QED) ideas for the explanation of sonolumines-
cence, the author tries to present another component of
sonoluminescense, which is due to the Cherenkov radia-
tion from tachyon pairs created from the zero-point
fluctuations of electromagnetic field (ZPF field) con-
tained in a collapsing bubble.
2. THEORETICAL ANALYSIS FROM THE
STANDPOINT OF ZPF THEORY
2.1. ZPF Radiation Due to Casimir Energy
As shown in Figure 1, the vacuum constitutes an ex-
tremely energetic physical state.
The premier example for considering the possibility of
extracting energy from the vacuum has already appeared
in a paper by R.L.Forward by applying the Casimir ef-
fect [11]. Schwinger wrote papers wherein the Casimir
energy released in the collapse of a spherically symmet-
ric bubble or a cavity with a volume V in a dielectric
fluid can be given by [4].

2
3
0
34
4π11
22
2π
111
6π
K
cavity
in out
in out
kdk ck
EV
cR K



 









(1)

3
23
2
dd
c


 


Figure 1. Zero point energy which fills the space.
where V is the volume of a bubble, R is its radius, K is a
high wavenumber cutoff that characterizes the waven-
imber at which the dielectric constants drop to their
vacuum values,  is a Plank’s constant divided by 2π,
c is a light speed and in

and out

are dielectric con-
stants for outside the bubble and inside it respectively.
However the possible relevance of the Casimir effects to
sonoluminescence was considered to be controversy
because the corresponding Casimir energy was only
22
~10
c
E

J for a rapidly collapsing bubble [12], which
was about 10 ordered of magnitude too small to be rele-
vant to sonoluminescence from the experimental results.
Instead of Schwinger’s idea to explain the sonolumi-
nescense, Liberati, Visser, Belgiorno and Sciama derived
the equation in the framework of the dynamical Casimir
effect to give reasonable agreement with observations,
which included the contribution of dynamical Casimir
effect shown as [13].

2
3
2
2
34
2
1
8π
11
1
8π
nn
EcKRK
nn nn
cR K
n n












(2)
where n is a refractive index of liquid and n

is a re-
fractive index of gas inside the bubble. However this
mechanism can not explain impossibly short time scales
of SL radiation because it is required that the overall
collapse time of a bubble is 4
10 sec instead of the im-
possible short time scale on the order of 15 10  sec [14].
Thus I have proposed another missing component of
sonolumenescence due to Cherenkov radiation from
tachyon pairs generated from the ZPF field contained in
a collapsing bubble instead of a conventional theory for
explaining sonolumenescence as a QED vacuum effect,
given as follows.
2.2. Cherenkov Radiation from Tachyon
Pairs Generated in a ZPF Field in a
Space
The author proposed the possibility in his paper that
the Cherenkov radiation can be generated from tachyon
pairs created in a collapsing bubble shown as follows;
From the wave equation taking account of the special
relativity (i.e. Klein-Gordon equation) given by
iH
t




 (3)
where 22 24
H
pcM c (p: momentum of the parti-
cle, M: effective mass) and

is a wave function for
the particle, the following equation can be obtained for
the accelerated particle [15];

T. Musha / Natural Science 3 (2011) 249-254
251251
22 24
ipcM c
pMa


 
 (4)
where a is a proper acceleration of the virtual elementary
particle generated from a ZPF field. If the photon is
generated in a quantum region, which size is l, the
proper acceleration of the photon becomes
2
1pc
amt l


, (5)
from the uncertainty of momentum and energy given by
pl and Epc, respectively, when we let
2
Emc and tlc .
Then the wave function for the accelerated particle
becomes [16]



2
2
exp 1
2
loglog 1
1
vc
Cil
c
c






 




 
 




(6.1)



*2
2
exp 1
2
loglog 1
1
vc
Cl
c
c






 




 
 




(6.2)
From these equations, it can be seen that the wave
function continues beyond the light barrier and we can
see that there is a possible existence of virtual superlu-
minal particles created from the ZPF field.
According to the WKB approximation, the penetration
probability through the light barrier of the tunneling
photon can be estimated by

22
*
2
2
exp1loglog 1
1
p
T
lc
c







 
 




(7)
By applying the uncertainty principle to the virtual
superluminal particle, we obtain 2

 [17] and then
Eq.7 becomes

2
exp3loglog 3
3
p
Tl c
c
 

 
 


. (8)
Supposing that l has a size of the Plank length, then
Eq.8 can be approximated by

exp
pp
Tl





, (9)
where
p
l is a Plank length and
7
3log3 2 3log()5.6210
3
c
c




. (10)
If tachyon pairs created from the ZPF background
have an electric charge, it radiates photons at the angle
of


1
cos 1
cn


, where c

is half-angle of the
Chrenkov radiation from the particle moving at the
speed of * vc


and n is the index of refraction
which equals to unity in a vacuum.
As the radiation field by the Cherenkov effect can be
regarded as a thermal equilibrium system filled with
non-radiating electromagnetic waves, it is permitted that
small fraction of energy from non-radiating electromag-
netic field can be radiated as blackbody radiation ac-
cording to the SED theory shown as follows;
 

3
0
3
0
1
3
23
2π
expexp 1
2π
B
B
kkT
k
Ep
kkT
k
p
B
ke
T
ce
lkT
c



 










 











, (11)
where
B
k is the Boltzmann constant and T is the abso-
lute temperature of radiation.
From the calculation by Liberati et al, the total num-
ber of created photons by Casimir effect becomes [13]

2
3
1
6π
nn
NRK
nn nn





 , (12)
then the average energy per emitted photon can be given
by
3
4
EEN cKn. (13)
From which, the temperature inside the collapsing
bubble due to the Casimir effect can be obtained from
3π
2B
c
EkT
n 

, (14)
where

is a wavelength of ultraviolet cutoff fre-
quency given by 2π
K


.
By inserting this formula to Eq.11, the energy density
of sonoluminesence due to the Cherenkov radiation from
tachyon pairs at the temperature generated by the
Casimir effect becomes
 
1
3
23
2
exp exp1
3π π
Ep
n
lc
c

 



 
 


. (15)
3. ZPF RADIATION FROM THE
COLLAPSING BUBBLE
From the assumption that the collapsing bubble is

T. Musha / Natural Science 3 (2011) 249-254 252
black, i.e. it perfectly absorbs all wavelength of electro-
magnetic radiation that requires the mean free path of
photons be much smaller than the size of the bubble [2],
the bubble radiates all electromagnetic energy confined
inside it when it shrinks to the size less than the mean
free path, which can be defined by

1
l 

, where
 is an absorption coefficient and

is a density of
gas. Then the total energy radiated by Cherenkov radia-
tion becomes





33
0min
0
1
3
23 0
3
33
0min
44
4
3
2
exp exp1
3π π
81π4,1
2
cE
p
EVd RR
n
ld
c c
cRR
n
 


 








 
 







(16)
where

3π2
p
lc n

 , 0 R is the radius of a bubble
which is at the beginning of a rapid collapse phase,
min
R is a radius of the bubble when it radiated electro-
magnetic energy, and

,mn  is a Hurwitz zeta func-
tion. Inside the collapsing bubble, the temperature rises
precipitously, then atoms and molecules collides with
high energy particles to create a hot plasma which makes
the mean free path of photons shorter.
Thus the maximum energy emitted by the Cherenkov
radiation from virtual tachyon pairs in a bubble can be
roughly estimated as

34
0
4
81 4, 1
32 π
c
ERK
n

 
, (17)
which is due to the thermal radiation of electromagnetic
waves created by the Casimir effect for the collapsing
bubble.
From the uncertainty principle, the path of FTL pho-
tons created from the ZPF of electromagnetic field can
be estimated by lc

, from which we have
0.4~ 0.8lm

 for the visible spectrum of the light.
Assuming that the path of the FTL photon almost
equals to the free pass of photons generated inside the
bubble, it is considered that energy confined in a col-
lapsing bubble is radiated when it reaches the size less
than one micron, which can explain the addition of small
amount of noble gas increases the intensity of emitted
light because the free pass of photons becomes shorter
by the formation of hot plasma, that almost coincides
with the experimental result. This mechanism of creating
photons can also explain the short time scale of the ra-
diation from the bubble because the heat can no longer
escape from the bubble until it reaches the size of the
path of FTL photons.
Figure 2 shows the process of a collapsing bubble,
which consists of phases such as; 1) slow expansion, 2)
turnaround at maximum radius, 3) collapse with moder-
ate speed, 4) rapid collapse that the heat can no longer
escape from the bubble, and 5) emission of light. Table
1 shows the experimental results for a collapsing bubble
[18-21], where max
R is a maximum radius of the bub-
ble and E is a energy radiated from the bubble which is
calculated from 400 nm


.
From Eq.17, the energy radiated from the collapsing
bubble can be estimated shown as a real line in Figure 3,
when we set


2π400 nmK, which corresponds to
the upper wavelength of the light spectrum.
Figure 2. Collapsing bubble and Cherenkov radiation.
Table 1. Energy of flash emitted from the collapsing bubble.
No


max
R
m 
Number of
photons

EJ Ref.
1 40 6
110 13 510

 [18]
2 45 – 11
2.5 10  [19]
3 48 6 210 13 9.9 10  [20]
4 50 6 1.6 10 13 810

 [21]
Figure 3. Radiated energy vs. radius of the bubble.

T. Musha / Natural Science 3 (2011) 249-254
253253
Figure 4. Schematic diagram of the fusion reactor by sonolu-
minescence.
The dashed line is the calculation result obtained by
Eq.2 proposed by Liberati et al., which includes the con-
tribution of dynamical Casimir effect. Assuming that
0max
2RR [20], where 0 R is the radius of the bub-
ble at the beginning of rapid collapse, the calculation
result by Eq.17 can be shown as a solid line. In this fig-
ure, the horizontal axis is for the radius of a bubble and
the vertical axis is for the emitted energy from the col-
lapsing bubble in a log scale.
By comparing calculation results with the experimen-
tal results over plotted in this figure, we can see that en-
ergy radiation by the Cherenkov radiation becomes
about 100 times the estimation by dynamical Casimir
energy calculations, which almost coincides with the
experimental results. Thus it can be considered that
vacuum energy generated by the sonoluminescence can
create heat over than 107 ˚K, which is a temperature
enough to induce a nuclear fusion by its large amount of
heat during cavitation.
Thus it can be considered that the fusion temperature
might be obtained by Cherenkov radiation created from
ZPF field inside the collapsing bubbles by the apparatus
as shown in Figure 4. R.P. Taleyarkhan and his col-
leagues at the Oak Ridge National Laboratory (ORNL)
conducted acoustic cavitation experiments with deuter-
ated acetone and they reported an observation of tritium
and neutron output that were consistent with the occur-
rence of fusion at their experiment [22]. The neutron
emission was also reported to be coincident with the
sonoluminescence pulse, which suggests that its source
was fusion caused by the sonoluminescence.
4. COMCLUSIONS
From the theoretical analysis, it can be seen that the
Cherenkov radiation from the ZPF field in a bubble,
which becomes larger than the energy radiated by the
dynamical Casimir effect. By comparing them with the
experimental results, it is considered that another miss-
ing component of the sonoluminescense may attribute to
the Cherenkov radiation from tachyon pairs created from
the ZPF field contained in a collapsing bubble, which
may lead to the possible source of unlimited energy in
the future.
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