Another possibility of sonoluminescence due to the cherenkov radiation from the ZPF field in a water bubble

doi:10.4236/ns.2011.33031

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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; [email protected]

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].



4π11

2π

111

6π

cavity

in out

kdk ck

cR K























(1)







 





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

~10



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].



8π

EcKRK

cR K























(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







 (3)

where 22 24

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

1pc

amt l





, (5)

from the uncertainty of momentum and energy given by

pl and Epc, respectively, when we let

Emc and tlc .

Then the wave function for the accelerated particle

becomes [16]







exp 1

loglog 1

Cil













 









 













(6.1)







exp 1

loglog 1













 









 













(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



exp1loglog 1















 













(7)

By applying the uncertainty principle to the virtual

superluminal particle, we obtain 2



 [17] and then

Eq.7 becomes



exp3loglog 3

Tl c







 









. (8)

Supposing that l has a size of the Plank length, then

Eq.8 can be approximated by



exp











, (9)

where

l is a Plank length and

3log3 2 3log()5.6210









. (10)

If tachyon pairs created from the ZPF background

have an electric charge, it radiates photons at the angle





cos 1





, where c



is half-angle of the

Chrenkov radiation from the particle moving at the

speed of *





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;

 



2π

expexp 1

2π

kkT

lkT



 





















 

















, (11)

where

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]



6π

NRK

nn nn











 , (12)

then the average energy per emitted photon can be given

EEN cKn. (13)

From which, the temperature inside the collapsing

bubble due to the Casimir effect can be obtained from

3π

EkT





, (14)

where



is a wavelength of ultraviolet cutoff fre-

quency given by 2π





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



exp exp1

3π



 







 









. (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







, where



is an absorption coefficient and



is a density of

gas. Then the total energy radiated by Cherenkov radia-

tion becomes



0min

23 0

0min

exp exp1

3π

81π4,1

EVd RR

cRR

 





 

















 















(16)

where



3π2

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



81 4, 1

32 π

ERK







, (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.





max



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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