from a discussion by New Alexandria and Otto van Nieuwenhuijze
Sonoluminescence is the emission of light in materials that are rhythmically pulsed. Most sonoluminescence scenarios involve water in a vessel, which is connected to loudspeakers that induce their vibrations directly into the vessel, and the water within it. Once the system is brought to resonance (i.e. operating at the eigen frequencies of the system), a bubble of air is introduced into the middle of the vessel. This cavity must now be accounted for, and the system retuned to the eigen resonance of the system. When this resonance is reached the system begins to emit light in regular pulses, occurring in phase with the compression of the cavity. This can be compared to the principle that is used in Masers and Lasers.
The following describes a hypothesis based on known physical principles as well as experimental data from a variety of sources. It is known that a superposition of waves will introduce both a higher and lower frequency, which is composed of the sum and difference of the given frequencies. Index of refraction also comes into play at the surface between materials, changing the shape of the wave (cf. a straw appearing as 'bent', when seen in a glass of water).
These principles inter-operate with field wave and surface wave coupling between the water/air medium and the air/water interface. At the wave envelope, the four wave systems (in the air, on the air, in the water, on the water) must all be coupled. This system can be calculated via the 'Green Integral,' a loop integral around a singularity (in this case: the bubble of air in the center of the system).
Together these principles evoke the image of atomic oscillation models. Atomic systems can be understood as rotational and translational vibrations around a point. These standing waveforms will have lengths that are multiples of N, as fitting in/on certain 'geodesics', determining distances within the system.
The hypothesis links all these physical and mathematical principles as follows:
Take as given, that there is a stable, resonant system in which degassed water is contained in a vial, pulsed by sound waves - a masing effect. The system can be attuned, via frequency sweeping, to the system's eigen-frequency. By doing so, the frequency imparted (generally an ultrasonic wave) can be made to match the system-characteristic wavelength, which consists of both the material object sizes and the wave velocities of the medium. This has been described as the Stradivarius Principle (van Nieuwenhuijze). The frequencies of oscillation will stabilize into those wavelengths that fit the system's eigen wavelength and inner processing speed (the speed of sound).
Once attuned, the water and container elements of the system operate as coupled dynamic oscillators, in which each vibrate harmonically. As soon as a bubble of air is introduced into this system, however, the established frequency attunement will no longer be resonant. The waves, fitting the length of the water in the sphere, now break on the water-air surface (interface) of a bubble of air in the system.
By the geometry of the vibrations in the system, it is possible to 'capture' a bubble of air in the middle of the chamber. This generally happens at the center of the vessel because the waves fitting the chamber will introduce a standing wave node in that location. Wave vibrations stretch and compress the air bubble by orbital motion, which may dissolve the bubble into the water as the surface tension of the air-water interface is surpassed. A sufficient driving force is required to capture the bubble yet not exceed the surface tension, and this is most easily determined via range sweeping.
With an air bubble harmonically 'caught' in the center of the vessel, the system can be re-attuned to the eigen-wavelengths of the newly formed system, which now includes a water-air interface. The material densities and eigen-velocities of both air and water mediums is involved. By sweeping for attunement, the eigen-frequencies of this new system of coupled oscillators can be determined.
It is presumed that these frequencies and wavelength can also be determined by calculation: the main characteristic wavelengths are those of the vessel wall, the radius length from the vessel wall to the bubble of air in the center, as measured though the water, and the size of the air cavity (bubble). The material densities of the vessel, water, and air determine the main eigen-velocities. It is also likely that these factors can be used to determine properties of water (e.g. homeopathic information 'doping', gasses, etc.) It also opens realms of further investigation, such as creating a multiple interface systems, as with a vessel within a vessel.
In this attuned setup, the acoustic pressure from the loudspeakers is the driving force; it essentially 'clamps' the system and introduces a determined, and thus determinable, frequency into the system. These frequencies will follow standard principles of diffraction and refraction at any and every interface within the system. As a result, the speeds of propagation, and corresponding wavelengths of oscillation, are different for the material of the vessel, the liquid water, and the gaseous air in the center. These slower eigen-frequencies in the air, the faster eigen-frequencies in the water, and those in the material of the vessel, will all interact and produce sum-and-difference frequencies.
Once the full system is attuned, light is emitted; this happens either from within the volume of air, or from the air/water interface. The pulses of light increase in frequencies and intensity in synchronization with a reduction in bubble size. This reduction in size is due to the pressures created by vibrations in the core of the system. The collapse of the bubble of air is a rhythmic process, always followed by its re-emergence and successive collapse.
Each regular re-emergence of the bubble is of lesser radius than the previous oscillation. This happens to a point where collapse and expansion are not measurable - a point around which the bubble experiences a uniform expansion to its maximum radius. It then repeats these collapse/expansion cycles again to non-measurability, a process that will continue as long as the system is maintained.
At each of the bubble radii, the characteristic of the light emission is the same, and these emissions are at their brightest when the water is maintained at its triple-point. The collapsed, light-emitting bubble has been measured to have a pressure of 14 million atmospheres, and near-solar temperatures.
As the system is induced to vibration, the oscillations will accumulate at the air-water interface. At that interface, the density of the water and the density of the air produce a sum-and-difference measure of the medium boundary, which determines the eigen-frequency of the surface involved. This is the principle of 'density waves,' and is at work in the system.
Due to the continued oscillations by sound (cf. the 'pumping effect' of a maser), the waves emerging on the air-water interface will increase in amplitude, but not in frequency. This 'pendulum effect' is characteristic to the radius length of the bubble, which determines the path length along the surface, and thus the wave-lengths which can 'ride' on the bubble.
This corresponds with the principle of wave-length matching described by de Broglie: along any surface, waves will 'self-sort,' allowing wavelengths that are a multiple of the available path length to continue to exist as standing waves. All other (transient) wave-lengths, will mutually cancel out. Any oscillating is thereby a selective tuning device; i.e. a filter.
As the surface wave at the water/air interface increases in amplitude, its wave length will be maintained -i.e. the wave becomes more peaked. There is a maximum to the steepness of those peaks, determined by the accelerative (shear) forces in the medium. In the case of the water there is only limited tensile strength, which is coupled by a 'pretension' - the presence of a counter-pressure from the air. This tensile strength is a function of the critical borders and the material characteristics of the medium, and thus the structuring of molecules in the water.
Dimensional Analysis defines similar critical system limits. The work of Thom and Seeman on the topological system constraints of Catastrophe Theory also relates to the material/surface critical behavior.
As the frequencies build to resonance, the eigen wave-length and speed of propagation for the air-water interface becomes established. This 'Pushing the Swing' builds up to the critical limits set by the topology of the water surface, the molecular density of the material, and even the ordering of atoms and molecules with respect to wave peaks in the water. The process of wave-forms building to higher amplitudes, and higher harmonics, brings atomic properties into play as the repeated reverberations require a molecular alignment at the air-water surface. Because of the geometry of the system, all these principles interrelate.
There is a principle at play here, which in the interest of clarity, must be directly addressed. The material properties will determine ratios for the emergence of higher eigen-frequency harmonics at the water-air interface. As described above, this is a selective filter for frequency matching, and thus wave-length matching.
The wave-lengths that are longer, are more easily established; the wave-lengths that are of a higher amplitude, allow for better containment of the energy of vibrations. It is the relationship between the material, molecular and atomic characteristics of the medium itself (this includes the underlying 'sub-atomic' phase field characteristics) that will determine at which moment, and to what extent, the higher harmonics emerge within the system.
The emergence of higher harmonics results in a 'smoothing function,' allowing the same amount of energy to be accommodated, but at lower amplitude. This means that the peaks of the wave can be smaller, thus, criticality of the wave-form geometry, molecular alignment, and orientation of atoms as the wave crests, will take place at more points along the surface.
How the higher frequency emergence (frequency 'split') is introduced, and at which moment, needs a more detailed description. Material properties and levels of organization (sub-atomic, atomic, molecular and material) must all be accounted for, especially in the production of light. As a result of induced frequency patterns and their harmonics, electrons within the materials are oriented and accelerated. This occurs within the oscillating wave crests, whose amplitudes and frequencies (wave-lengths) are determined by the geometry and materials of this system. The light emission of this vibrational system is related to these electron accelerations, and interference pattern harmonics from ordered molecular arrays. This relationship needs further investigation.
It is found that the light pulses are emitted in a 'star blue' frequency range � that is, the visible light looks like a star.
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A typical behaviour is observed: the air bubble decreases in size while the light is emitted; this 'collapse' is followed by a restoration of its original size. This hypothesis presents three thoughts, which argue why this takes place:
1) The increase of resonance in the system (via masing) accelerates the water at the tip of the wave on the water-air interface. This causes a lasing effect: the wave crests become more peaked, the water molecules will need to be more ordered, and the atoms themselves will be arrayed. As this lasing effect takes place at increasingly higher velocities (within limits) the amplitude also grows. Amplitude growth causes the surface of the bubble to become 'thicker', i.e. more ordered. The bubble may appear to become smaller as a result of this change in density. The system 'counter-weights' this shift by frequency-doubling and storing of the vibrations as higher frequency harmonics.
2) Also, as the light is emitted and material is lost from the bubble of air, its radius reduces: the characteristic eigen-frequency length is thereby reduced, and the eigen-frequency of the bubble increases. In increasing the frequencies, all above mentioned principles apply still (amplitude increase, peaking wave, molecular/atomic array super-organisation, and limit velocities of material coherence). This introduces a shift of the emitter frequency of light, and a measure of the reduction of curvature of the air bubble.
3) Another plausible cause for the air bubble to lose radius would be out of a cooling effect. Cooling of this kind is found with instances of super-conduction; as the organization of materials is increased, energy communication (including heat) is more rapid. The bubble can shrink simply by cooling.
At the moment that the air bubble reduces to a minimal size, the material motion is coupled to a molecular array dynamic. These molecular dynamics are, again, connected to the atomic dynamics, by which electrons are perceived to emit [as] electrons. As the frequencies increase, so do their higher and lower harmonics; a coherent fabric of interlaced frequencies is the result. The interference patterns result in coherence domains of stable phase arrays - a property of holographic systems.
In the organisation of this resonant wave system, all frequencies interact, and at all times are interlocked. This interlocking includes the material waves in the medium, the surface waves and density waves that are formed, and the molecular and atomic resonance that is induced. The vibrations of motion, sound and light are 'linked' by radio waves, and each of these wave types is characteristic to the material-molecular-atomic phase arrays that occur within the system.
Further, the minimum compression size may be a result of a kind of 'Eddinton Limit,' where matter in the system is being 'accreted' into the linked material-molecular-atomic organizational lattice to the point where energies, conducted by this lattice, exceed the masing pressure of the driving frequencies.
This linking effect is the result of dynamic wave reorganization, which facilitates the emission of electrons as photons. It also facilitates a 'regrouping' of the system frequencies at the moment that the material/mass ratios of the air-water interface are shifted. When the bubble radius reduces toward zero, the rising frequencies will shift from predominantly material, to increasingly molecular, and even atomic. This causes the organizational lattice of the materials to be extend to these levels.
The predominance of vibrations shift from material, through sound waves, to the range of radio waves and heat, at which point molecular bonds become affected. Thermal radiation, which is vibrations at the molecular-material level, changes the structural organization of molecules in the system.
Stable bonds are then broken as the vibrations at the air-water interface transform from field waves, to surface waves (and density waves), to material waves. The physical chemistry of the materials is thus affected; water is converted to vapor as bonds are released, and the air bubble (composed of water vapor; or perhaps even hydrogen and oxygen) is (re)formed.
This effect would be most pronounced when the water in the vial is nearest its triple point. At that moment the transition from crystalline, to fluid, to vapor state would involve a least energy conversion - making use of the maximum heat storage capacity of the water.
What is seen in Sonoluminescence is a normal wave phenomenon. Waves, in this instance, operate along a surface of gradating density. The principle of wave organization is the same as that seen in atoms: layers of harmonic eigen frequencies, which correspond with the radius curvature of the air-water surface geometry.
As energy is radiated outward, the spherical air bubble is reduced, causing allowable frequencies and harmonics to increase. The increase happens to the level where the material, molecular and atomic properties are 'fused.' This happens while the wave patterns impose a regular dynamic organization array via high frequency oscillations.
As energy is emitted, the temperature of the air bubble changes, which causes the radius to reduce due to the inter-relationship of temperature to pressure.The radius of the air bubble, the temperature, emitted light, and operant material (sound frequencies) can all be monitored and measured. By these measurements the actual relationships between induced and responsive frequencies can be established, and the patterns of perceived oscillations, in light emission and size of the bubble, understood.
The proposed model for sonoluminescence involves harmonic system oscillations which interoperate to the atomic level. These wave topologies are generally modeled as three-dimensional. However, the functions of these waves is described under the equations of James Maxwell's, whose description of Electro-Magnetics encompassed three, four, and N-dimensional operation.
It can be assumed that N-dimensional functions may also be at work in the systemic oscillatons of sonoluminescence. These higher-order dimensions may be the origin of energy phenomenon that remains unexplained in most sonoluminescent theory. If the systemic oscillations are only harmonic in a finite N-dimensions, then the presence of non-harmonic waves existing only in limited, higher-order dimensions would induce a beat pattern, or other form of superposition, within the system.
The investigaton of sonoluminescent systems also generates intriguing questions about relativity. Sonoluminescent systems can be seen as the compression and expansion of uniform fractal geometries. These systems lend insights into the formation and operation of the universe - implying not 'big bang/big crunch' scenarios terminating in equilibrium, but rather continual oscillation and inversion.
In a relative system, an accelerated reference frame and an inertial reference frame are indistinguishable. This indeterminability may make it impossible to distinguish if the universe was in a state of expansion or contraction. A 'rhythmic' reference frame is created by the sequence of oscillations between critical points ('fullness' and 'emptiness'). However, 'previous' wave-states of the same amplitude will appear identical due to the system functioning at a uniform eigen-resonance.
Non-harmonic higher-order wave functions, if existant, would allow for a kind of measurement since their 'disonance' would create a frame of reference. The 'disonance' of these wave function would have a developmental quality - growing and changing. This may imply that wave functions of this nature must remain within a relative 'pressure' threshold until they reach system eigen-resonance, otherwise they would disrupt it. Reaching this threshold harmonically would complement the function of the system, and may yield further higher-order functioning.