Declaration For Greater Independence

Molecular Vibrations

When atoms join together in molecules, they can enter into characteristic vibrations and rotations. Just as an atom has a set of energy states associated primarily with the possible configurations of its electrons, so molecules have sets of energy states associated with their vibrations and rotations, as well as a set of electronic states. Light of the correct energy will induce changes from one vibrational (and/or rotational) state to another. Two ways in which isotopy relates to molecular vibrations, in particular, can be illustrated with the simplest of all molecules—diatomic molecules, which consist of only two atoms. Vibrational spectroscopy shows that isotopically heavier diatomic molecules have higher bond energies. (Bond energy is the amount of energy needed to separate the two atoms.) Quantum mechanical theory makes it possible to calculate from vibrational spectra just how much stronger the bond to the heavier isotope is. The differences between the chemical bond energies of isotopes help to explain why the isotopes do not behave identically in chemical reactions. The second relation concerns the spacing between vibrational energy levels: the vibrational energy levels of an isotopically heavier molecule lie closer together. Consequently, it takes less energy to excite ¹⁸O—¹⁸O from one vibrational level to the next than it does ¹⁶O—¹⁶O. Spectroscopists made good use of this fact when they inferred from the spectra of isotopically mixed diatoms the existence of previously unknown isotopes. Oxygen-18 was discovered in this way.

Importance in the study of polyatomic molecules

This second point, the distinguishability of the vibrational spectra of isotopically different molecules, is of great importance in the study of polyatomic molecules (molecules that contain three or more atoms). One key issue for chemists is the nature of the vibrations in polyatomic molecules: How do the nuclei of the atoms oscillate in relation to each other? The answer to this question bears strongly on what transient shapes the molecule may assume, how it will react with other molecules, and the rate at which it will do so. It is usually impossible to obtain this information from a study of the vibrational spectra of molecules made from atoms at natural abundance levels. Fortunately, the systematic substitution of heavier isotopes at known points in polyatomic molecules gives rise to new sets of vibrational spectra that clarify the nature of the atomic motions.

There is a second, fundamental reason for investigating the vibrational spectra of isotopically substituted, or "labeled," molecules. In interpreting spectra, spectroscopists rely on the mathematical results of quantum theory. Often, a close analysis of vibrational spectra of labeled molecules offers the best means for testing the soundness of the prevailing theoretical understanding of molecules.

Phosphorescence

Phosphorescence is related to fluorescence in terms of its general mechanism but involves a slower decay. It occurs when a molecule whose normal ground state is a singlet is excited to a higher singlet state, goes to a vibrationally excited triplet state via either an intersystem crossing or a molecular collision, and subsequently, following vibrational relaxation, decays back to the singlet ground state by means of a forbidden transition. The result is the occurrence of a long lifetime for the excited triplet state; several seconds up to several hours are not uncommon. These long lifetimes can be related to interactions between the intrinsic (spin) magnetic moments of the electrons and magnetic moments resulting from the orbital motion of the electrons.

Molecules in singlet and triplet states react chemically in different manners. It is possible to affect chemical reactions by the transfer of electronic energy from one molecule to another in the reacting system. Thus the study of fluorescence and phosphorescence provides information related to chemical reactivity.

Vibration reception

Adaptation and recovery occur most rapidly among touch receptors, and they tend to respond well to repeated stimulation, even of relatively high frequency. Thus, a person can feel whether an object is vibrating; above a threshold frequency of about 15 cycles per second (cps), discretely perceived tactual stimuli seem to fuse into a quite new and distinct vibratory sensation. The upper frequency limit of this vibration sense is found at several thousand cps among normal individuals, with sensitivity being maximal in the range of 200 cps (above a threshold amplitude of about 100 millimicrons). Just as pitch is discriminated in hearing, differences of about 12 to 15 percent in vibration frequencies can be distinguished by most people.

Vibration sensitivity is not limited to man; fish, for instance, also may respond to low-frequency water vibrations with tactile receptors. In addition, several kinds of animals have special vibration receptors. In some insects, a group of specialized structures (chordotonal sensilla) in the upper part of each tibial segment of the leg signal vibrations from the ground below. In the cockroach, the threshold amplitude for vibrational stimuli of this kind has been found to be less than 0.1 millimicron. Birds have special receptors (corpuscles of Herbst in the tibiotarsal bone of the leg) with which they can detect slight vibrations of the twig or branch on which they sit. Perhaps birds are alerted at night in this way to approaching predators; maximal sensitivity is at about 800 cps, and the threshold amplitude is close to 20 millimicrons. Spiders also use their vibration sense to locate prey in the web.

Vibration (Occupational disease)

Whole-body vibration is experienced in surface and air transport, with motion sickness its most familiar effect. A more serious disorder, known as Raynaud's syndrome or vibration white finger (VWF), can result from the extensive use of vibratory hand tools, especially in cold weather. The condition is seen most frequently among workers who handle chain saws, grinders, pneumatic drills, hammers, and chisels. Forestry workers in cold climates are particularly at risk. Initial signs of VWF are tingling and numbness of the fingers, followed by intermittent blanching; redness and pain occur in the recovery stage. In a minority of cases the tissues, bones, and joints affected by the vibration may develop abnormalities; even gangrene may develop. VWF can be prevented by using properly designed tools, avoiding prolonged use of vibrating tools, and keeping the hands warm in cold weather.

Other mechanical stresses

Muscle cramps often afflict workers engaged in heavy manual labour as well as typists, pianists, and others who frequently use rapid, repetitive movements of the hand or forearm. Tenosynovitis, a condition in which the sheath enclosing a tendon to the wrist or to one of the fingers becomes inflamed, causing pain and temporary disability, can also result from prolonged repetitive movement. When the movement involves the rotation of the forearm, the extensor tendon attached to the point of the elbow becomes inflamed, a condition commonly known as tennis elbow.

From Britannica article on String Theory:

Predictions and theoretical difficulties

String theory was an intuitively attractive proposal, but by the mid-1970s more-refined measurements of the strong force had deviated from its predictions, leading most researchers to conclude that string theory had no relevance to the physical universe, no matter how elegant the mathematical theory. Nevertheless, a small number of physicists continued to pursue string theory. In 1974 John Schwarz of the California Institute of Technology and Joel Scherk of the École Normale Supérieure and, independently, Tamiaki Yoneya of Hokkaido University came to a radical conclusion. They suggested that one of the supposedly failed predictions of string theory—the existence of a particular massless particle that no experiment studying the strong force had ever encountered—was actually evidence of the very unification Einstein had anticipated.

Although no one had succeeded in merging general relativity and quantum mechanics, preliminary work had established that such a union would require precisely the massless particle predicted by string theory. A few physicists argued that string theory, by having this particle built into its fundamental structure, had united the laws of the large (general relativity) and the laws of the small (quantum mechanics). Rather than merely being a description of the strong force, these physicists contended, string theory required reinterpretation as a critical step toward Einstein's unified theory.

The announcement was universally ignored. String theory had already failed in its first incarnation as a description of the strong force, and many felt it was unlikely that it would now prevail as the solution to an even more difficult problem. This view was bolstered by string theory's suffering from its own theoretical problems. For one, some of its equations showed signs of being inconsistent; for another, the mathematics of the theory demanded the universe have not just the three spatial dimensions of common experience but six others (for a total of nine spatial dimensions, or a total of ten space-time dimensions).

Dimensions and vibrations

Because of these obstacles, the number of physicists working on the theory had dropped to two— Schwarz and Michael Green, of Queen Mary College, London—by the mid-1980s. But in 1984 these two die-hard string theorists achieved a major breakthrough. Through a remarkable calculation, they proved that the equations of string theory were consistent after all. By the time word of this result had spread throughout the physics community, hundreds of researchers had dropped what they were working on and turned their full attention to string theory.

Within a few months, string theory's unified framework took shape. Much as different vibrational patterns of a violin string play different musical notes, the different vibrations of the tiny strands in string theory were imagined to yield different particles of nature. According to the theory, the strings are so small that they appear to be points—as particles had long been thought to be—but in reality they have length (about 10-33 cm); the mass and charge of a particle is determined by how a string vibrates. For example, string theory posits that an electron is a string undergoing one particular vibrational pattern; a quark is imagined as a string undergoing a different vibrational pattern. Crucially, among the vibrational patterns, physicists argued, would also be the particles found by experiment to communicate nature's forces. Thus, string theory was proposed as the sought-for unification of all forces and all matter.

What of the six extra spatial dimensions required by string theory? Following a suggestion made in the 1920s by Theodor Kaluza of Germany and Oskar Klein of Sweden, string theorists envisioned that dimensions come in two distinct varieties. Like the unfurled length of a long garden hose, dimensions can be big and easy to see. But like the shorter, circular girth of the garden hose, dimensions can also be far smaller and more difficult to detect. This becomes more apparent by imagining that the circular cross section of the garden hose is shrunk ever smaller, below what can be seen with the naked eye, thereby misleading a casual observer into thinking the garden hose has only one dimension, its length. Similarly, according to string theory, the three dimensions of common experience are large and hence manifest, while the other six dimensions are crumpled so small that they have so far evaded detection.

During the decade from 1984 to 1994, many theoretical physicists strove to fulfill string theory's promise by developing this abstract, wholly mathematical framework into a concrete, predictive theory of nature. Because the infinitesimal size of strings has precluded their direct detection, theorists have sought to extract indirect implications of the theory that might be testable. In this regard, the extra dimensions of string theory have proved a major hurdle. Imagining these extra dimensions as small and hidden is a reasonable explanation for their apparent absence. However, also because strings are so small, they would vibrate in every dimension, not just in the usual three dimensions. Studies showed that, much as the shape and size of a French horn affect the vibrational patterns of air-streams coursing through the instrument, the exact shape and size of the extra dimensions would affect how strings vibrate. And since the strings' vibrations determine quantities such as particle masses and charges, predictivity requires knowledge of the geometrical form of the extra dimensions. Unfortunately, the equations of string theory allow the extra dimensions to take many different geometric forms, making it difficult to extract definitive testable predictions.

Transduction of mechanical vibrations (From "Human Ear" article)

The hair cells located in the organ of Corti transduce mechanical sound vibrations into nerve impulses. They are stimulated when the basilar membrane, on which the organ of Corti rests, vibrates. The hair cells are held in place by the reticular lamina, a rigid structure supported by the pillar cells, or rods of Corti, which are attached to the basilar fibres. At the base of the hair cells is a network of cochlear nerve endings, which lead to the spiral ganglion of Corti in the modiolus of the cochlea. The spiral ganglion sends axons into the cochlear nerve. At the top of the hair cell is a hair bundle containing stereocilia, or sensory hairs, that project upward into the tectorial membrane, which lies above the stereocilia in the cochlear duct. (The single kinocilium, which is found on the hair cells of the vestibular system, is not found on the receptor cells of the cochlea.) When the basilar membrane moves upward, the reticular lamina moves upward and inward; when the membrane moves downward, the reticular lamina moves downward and outward. The resultant shearing forces between the reticular lamina and the tectorial membrane displace or bend the longest of the stereocilia, exciting the nerve fibres at the base of the hair cells.

The mechanism the hair cell uses to convert sound into an electrical stimulus is not completely understood, but certain key features are known. One of the most important aspects of this process is the endocochlear potential, which exists between the endolymph and perilymph. This direct current potential difference is about +80 millivolts and results from the difference in potassium content between the two fluids. It is thought to be maintained by the continual transport of potassium ions from the perilymph into the cochlear duct by the stria vascularis. The endolymph, which has a high potassium level and a positive potential, is contained in the cochlear duct and thus bathes the tops of the hair cells. The perilymph, which has a low potassium level and a negative potential, is contained in the scala vestibuli and scala tympani and bathes the lower parts of the hair cells. The inside of the hair cell has a negative intracellular potential of -60 millivolts with respect to the perilymph and -140 millivolts with respect to the endolymph. This rather steep gradient, especially at the tip of the cell, is thought to sensitize the cell to the slightest sound.

The stereocilia are graded in height, becoming longer on the side away from the modiolus. All the stereocilia are interlinked so that, when the taller ones are moved against the tectorial membrane, the shorter ones move as well. The mechanical movement of this hair bundle generates an alternating hair cell receptor potential. This occurs in the following manner. When the stereocilia are bent in the direction of increasing stereocilia length, ion channels in the membrane open, allowing potassium ions to move into the cell. The influx of potassium ions excites, or depolarizes, the hair cell. However, when the stereocilia are deflected in the opposite direction, the ion channels are shut and the hair cell is inhibited, or hyperpolarized. The depolarization of the cell stimulates the release of chemicals called neuro-transmitters from the base of the hair cell. The neuro-transmitters are absorbed by the nerve fibres located at the basal end of the hair cell, stimulating them to send an electrical signal along the cochlear nerve.

The outer hair cells contain both actin and myosin, the same contractile proteins that make up muscles, and this allows the cells to contract rhythmically in response to tonal stimuli. Recent studies suggest that the cells themselves may be tuned structures. The ability of an outer hair cell to respond to a particular frequency may depend not only on its position along the length of the basilar membrane but also on its mechanical resonance, which probably varies with the length of its bundle of stereocilia and with that of its cell body. The inner hair cells are much more uniform in size. Local groups of outer hair cells act not only as detectors of low-level sound stimuli, but, because they can act as mechanical-electrical stimulators and feedback elements, they are believed to modify and enhance the discriminatory responses of the inner hair cells. How they do this is not understood. Because the inner hair cells rest on the bony shelf of the osseous spiral lamina rather than on the basilar membrane, they are presumably less readily stimulated by the traveling wave. Help from the outer hair cells may be required to generate the signal that the inner cells transmit synaptically to the fibres of the cochlear nerve. Experiments in animals have shown that, when the outer hair cells of the basal turn have been destroyed by the ototoxic action of the antibiotic kanamycin, the inner hair cells in the same region can still respond to sound, but their thresholds are elevated by about 40 decibels.

Remarkably, the cochlea itself actually produces sounds. Its otacoustic emissions can be spontaneous or evoked by external acoustic stimulation. These emissions are thought to be produced by rhythmical contractions of the cochlear hair cells. Although faint, they can be recorded with a small microphone placed in the external canal; they are absent when there has been extensive loss of hair cells from the basal turn, as in cases of presbycusis or ototoxicity. While these emissions challenge some earlier concepts of the micro-mechanisms of cochlear function, they are proving increasingly useful in the audiological evaluation of impaired hearing, in adults as well as infants.