Another Possibility of Sonoluminescence Due to the Cherenkov Radiation from the ZPF Field in a Water Bubble

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 obtained in various fluids have shown that; 1) a flash of light emitted from the collapsing bubble with a maxi- Sonoluminescence is the light produced from mum diameter of 100 microns creates a temperature of the collapse of bubbles in water under ultra- 5500˚C with a blackbody spectrum when it rapidly sound. Schwinger proposed a physical mecha- shrinks to less than one micron in radius, 2) light flashes nism for sonoluminescence in terms of photon from the bubbles are extremely short persisted only for production due to changes of quantum elec- 50 picoseconds or shorter with peak intensities of the trodynamic energy contained in a collapsing order of 1~10 mW, which was too brief for the light to dielectric bubble. However there are critics for be produced by some atomic process, 3) bubbles are the Schwinger’s proposal that his estimate of very small when they emit the light with about 1 μm in the Casimir energy involved is inaccurate and diameter depending on the ambient fluid and the gas there are several papers to propose its missing content of the bubble, 4) single-bubble sonolumines- term. In this paper, the author presents another cence pulses have very stable periods and positions and possible component of sonoluminescense which the frequency of light flashes can be more stable than the is due to Cherenkov radiation from tachyon pairs rated frequency stability of the oscillator making the generated in a collapsing bubble. sound waves driving them, and 5) the addition of a small amount of noble gas to the gas in the bubble increases Keywords: Sonoluminscence; Casimir Energy; the intensity of the emitted light. Spectral measurements Cherenkov Radiation; Tachyon; Zero-Point Energy have given bubble temperatures in the range from 2300˚K to 5100˚K, the exact temperatures depending on 1. INTRODUCTION experimental conditions including the composition of the liquid and gas [2]. The mechanism of the phenomenon Cavitation is the formation of vapor bubbles of a of sonoluminescence remains unsettled and theories flowing liquid in a region where the pressure of the liq- those included hotspot, bremsstrahlung radiation, colli- uid falls below its vapor pressure. This is a process in sion-induced radiation and corona discharges, non- which a void or a bubble in a liquid rapidly collapses classical light, proton tunneling, electrodynamic jets, and producing a shock wave to cause a temperature in- fractoluminescent jets, and so forth were presented [3]. crease and emits light. This phenomenon is now referred As the properties of sonoluminescence which releases to as sonoluminescence (SL). Sonoluminescence can too large an amount of energy and releases the energy on occur when a sound wave of sufficient intensity induces too short a time scale are consistent with the vacuum a gaseous cavity within a liquid to collapse quickly. The energy explanation, Schwinger proposed a physical me- bubble reaches a maximum at about ten times its original chanism based on the instantaneous collapse of a bubble size, it completely collapses within a few milliseconds for sonoluminescence in terms of photon production due later. Sonoluminescence observed in the laboratory can to changes of quantum electrodynamic energy contained be made to be stable, so that a single bubble will expand in a collapsing dielectric bubble [4]. and collapse over and over again in a periodic fashion, According to the Schwinger’s theory, the surface of a emitting a burst of light each time it collapses. For this to bubble is supposed to act as the Casimir force plates and occur, a gas filled bubble undergoes repeated growth and an abrupt change of electromagnetic energy is emitted as collapse in response to an acoustic standing wave. As the visible light in sonoluminescent flashes when the bubble radius of the bubble quickly shrinks, the potential energy collapses. But there are some critics for the Schwinger’s is released as heat and light [1]. The experimental results proposal that his estimate of the Casimir energy involved

Copyright © 2011 SciRes. OPEN ACCESS 250 T. Musha / Natural Science 3 (2011) 249-254 is inaccurate and several papers were presented to con- where V is the volume of a bubble, R is its radius, K is a sider the missing terms [5-8]. One of them was a propo- high wavenumber cutoff that characterizes the waven- sition given by Claudia Eberlein [9,10] that sonolumi- imber at which the dielectric constants drop to their nescence could be explained in terms of quantum vac- vacuum values,  is a Plank’s constant divided by 2π , uum radiation by moving interfaces between media of c is a light speed and in and out are dielectric con- different polarization, which might be alike to the Unruh stants for outside the bubble and inside it respectively. effect. Instead of their conventional quantum electrody- However the possible relevance of the Casimir effects to namic (QED) ideas for the explanation of sonolumines- sonoluminescence was considered to be controversy cence, the author tries to present another component of because the corresponding Casimir energy was only 22 sonoluminescense, which is due to the Cherenkov radia- Ec ~10 J for a rapidly collapsing bubble [12], which tion from tachyon pairs created from the zero-point was about 10 ordered of magnitude too small to be rele- fluctuations of electromagnetic field (ZPF field) con- vant to sonoluminescence from the experimental results. tained in a collapsing bubble. Instead of Schwinger’s idea to explain the sonoluminescense, Liberati, Visser, Belgiorno and Sciama derived 2. THEORETICAL ANALYSIS FROM THE the equation in the framework of the dynamical Casimir STANDPOINT OF ZPF THEORY effect to give reasonable agreement with observations, which included the contribution of dynamical Casimir 2.1. ZPF Radiation Due to Casimir Energy effect shown as [13]. 2 As shown in Figure 1, the vacuum constitutes an ex- 1 nn  3 EcKRK 2   tremely energetic physical state. 8πnn nn (2) The premier example for considering the possibility of 2 11 extracting energy from the vacuum has already appeared 34 2 1 cR K in a paper by R.L.Forward by applying the Casimir ef- 8πn n fect [11]. Schwinger wrote papers wherein the Casimir where n is a refractive index of liquid and n is a re- energy released in the collapse of a spherically symmet- fractive index of gas inside the bubble. However this ric bubble or a cavity with a volume V in a dielectric mechanism can not explain impossibly short time scales fluid can be given by [4]. of SL radiation because it is required that the overall 2 4 K 4πkdkck 11 collapse time of a bubble is 10 sec instead of the im- EV2  15 cavity 0 3 2  possible short time scale on the order of 10 sec [14]. 2π in out (1) Thus I have proposed another missing component of  sonolumenescence due to Cherenkov radiation from 11134 cR K  tachyon pairs generated from the ZPF field contained in 6π  in out 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   (3) t where H pc22 M 24 c (p: momentum of the parti-  3  dd  cle, M: effective mass) and  is a wave function for 2 23c the particle, the following equation can be obtained for Figure 1. Zero point energy which fills the space. the accelerated particle [15];

 i 3log3 2 3log( c ) pc22  M 24 c (4)  5.62 107 . (10) pMa 3c where a is a proper acceleration of the virtual elementary If tachyon pairs created from the ZPF background particle generated from a ZPF field. If the photon is have an electric charge, it radiates photons at the angle generated in a quantum region, which size is l, the 1 of c  cos 1 n , where c is half-angle of the proper acceleration of the photon becomes Chrenkov radiation from the particle moving at the 1 pc2 speed of   vc* and n is the index of refraction a , (5) which equals to unity in a vacuum. mt l As the radiation field by the Cherenkov effect can be from the uncertainty of momentum and energy given by regarded as a thermal equilibrium system filled with pl  and Epc, respectively, when we let non-radiating electromagnetic waves, it is permitted that Emc2 and tlc. small fraction of energy from non-radiating electromag- Then the wave function for the accelerated particle netic field can be radiated as blackbody radiation ac- becomes [16] cording to the SED theory shown as follows;  vc kkT   ke B 3    2  T k 0 Cilexp  1  Ep 3   2c (6.1) 2πc kkT B  e , (11)   k 0 2 logc  log 1  1 1   3  23explp  exp  1 2π c kTB vc  where kB is the Boltzmann constant and T is the abso- *2  (6.2) lute temperature of radiation. Clexp   1  2c From the calculation by Liberati et al, the total num-   ber of created photons by Casimir effect becomes [13] logc  log 1   2 1 2  1 nn  3 NRK , (12) From these equations, it can be seen that the wave 6πnn nn function continues beyond the light barrier and we can then the average energy per emitted photon can be given see that there is a possible existence of virtual superlu- by minal particles created from the ZPF field. 3 According to the WKB approximation, the penetration EENcKn . (13) probability through the light barrier of the tunneling 4 photon can be estimated by From which, the temperature inside the collapsing bubble due to the Casimir effect can be obtained from T  22 p * 3π c  EkTB , (14) 2  2 n exp lc 1  log  log 1   c  2 1 where  is a wavelength of ultraviolet cutoff fre- (7) quency given by   2π K . By applying the uncertainty principle to the virtual By inserting this formula to Eq.11, the energy density superluminal particle, we obtain   2 [17] and then of sonoluminesence due to the Cherenkov radiation from Eq.7 becomes tachyon pairs at the temperature generated by the Casimir effect becomes  2 Tlp exp 3  log c  log3 . (8) 3 1 c 3 2n Ep23exp l  exp  1 . (15) Supposing that l has a size of the Plank length, then π c 3πc Eq.8 can be approximated by 3. ZPF RADIATION FROM THE Tlexp  , (9) pp  COLLAPSING BUBBLE where lp is a Plank length and From the assumption that the collapsing bubble is

Copyright © 2011 SciRes. OPEN ACCESS 252 T. Musha / Natural Science 3 (2011) 249-254 black, i.e. it perfectly absorbs all wavelength of electro- which consists of phases such as; 1) slow expansion, 2) magnetic radiation that requires the mean free path of turnaround at maximum radius, 3) collapse with moder- photons be much smaller than the size of the bubble [2], ate speed, 4) rapid collapse that the heat can no longer the bubble radiates all electromagnetic energy confined escape from the bubble, and 5) emission of light. Table inside it when it shrinks to the size less than the mean 1 shows the experimental results for a collapsing bubble 1 free path, which can be defined by l   , where [18-21], where Rmax is a maximum radius of the bub-  is an absorption coefficient and  is a density of ble and E is a energy radiated from the bubble which is gas. Then the total energy radiated by Cherenkov radia- calculated from   400 nm . tion becomes From Eq.17, the energy radiated from the collapsing bubble can be estimated shown as a real line in Figure 3,  4 EV d  RR33 when we set K  2π 400 nm , which corresponds to cE0  0min 3 the upper wavelength of the light spectrum. 1   2n 3 expld exp   1  23 p  π c 0 3πc 3 81π c 33 44RR0min4,1 2 n  (16) where   3πlcp2 n , R0 is the radius of a bubble which is at the beginning of a rapid collapse phase,

Rmin is a radius of the bubble when it radiated electromagnetic energy, and  mn, is a Hurwitz zeta function. 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 Figure 2. Collapsing bubble and Cherenkov radiation. radiation from virtual tachyon pairs in a bubble can be roughly estimated as Table 1. Energy of flash emitted from the collapsing bubble. Number of 81 c No Rmax m EJ Ref. ERK34 4,1  , (17) photons 32π n4 0 1 40 110 6 510 13 [18] which is due to the thermal radiation of electromagnetic 2 45 – 2.5 1011 [19] waves created by the Casimir effect for the collapsing 6 13 bubble. 3 48 210 9.9 10 [20] From the uncertainty principle, the path of FTL pho- 4 50 1.6 106 810 13 [21] tons created from the ZPF of electromagnetic field can be estimated by lc  , from which we have lm 0.4 ~ 0.8 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 collapsing 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 radiation 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, Figure 3. Radiated energy vs. radius of the bubble.

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 missing 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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