Harmonic Oscillator Quotes

The career of a young theoretical physicist consists of treating the harmonic oscillator in ever-increasing levels of abstraction.

Quantum mechanics. What a repository, a dump, of human aspiration it was, the borderland where mathematical rigor defeated common sense, and reason and fantasy irrationally merged. Here the mystically inclined could find whatever they required and claim science as their proof. And for these ingenious men in their spare time, what ghostly and beautiful music it must be--spectral asymmetry, resonances, entanglement, quantum harmonic oscillators--beguiling ancient airs, the harmony of the spheres that might transmute a lead wall into gold and bring into being the engine that ran on virtually nothing, on virtual particles, that emitted no harm and would power the human enterprise as well as save it. Beard was stirred by the yearnings of these lonely men. And why should he think they were lonely? It was not, or not only, condescension that made him think them so. They did not know enough, but they knew too much to have anyone to talk to. What mate waiting down the pub or in the British Legion, what hard-pressed wife with job and kids and housework, was going to follow them down these warped funnels in the space-time continuum, into the wormhole, the shortcut to a single, final answer to the global problem of energy?

We go to three parks. We walk nonstop or else she cries. The baby likes moving, especially moving at high speeds, so we go on swings. She opens one eye and looks at me with profound suspicion. What is this contraption? she asks silently, a tiny cyclops in my hands. This is a simple harmonic oscillator, I say, a pendulum; this is periodic motion. Wheeeee is the sound I think her temporal lobe wants to make" (p125)

Quantum mechanics. What a repository, a dump, of human aspiration it was, the borderland where mathematical rigor defeated common sense, and reason and fantasy irrationally merged. Here the mystically inclined could find whatever they required and claim science as their proof. And for these ingenious men in their spare time, what ghostly and beautiful music it must be—spectral asymmetry, resonances, entanglement, quantum harmonic oscillators—beguiling ancient airs, the harmony of the spheres that might transmute a lead wall into gold and bring into being the engine that ran on virtually nothing, on virtual particles, that emitted no harm and would power the human enterprise as well as save it.

We might add here that later on the constructors had an article published in a prominent scientific journal under the title of “Recursive β—Metafunctions in the Special Case of a Bogus Polypolice Transmogrification Conversion on an Oscillating Harmonic Field of Glass Bells and Green Gig, Kerosene Lamp on the Left to Divert Attention, Solved by Beastly Incarceration-Concatenation,

The granite complex inside the Great Pyramid, therefore, is poised ready to convert vibrations from the Earth into electricity. What is lacking is a sufficient amount of energy to drive the beams and activate the piezoelectric properties within them. The ancients, though, had anticipated the need for more energy than what would be collected only within the King's Chamber. They had determined that they needed to tap into the vibrations of the Earth over a larger area inside the pyramid and deliver that energy to the power center—the King's Chamber —thereby substantially increasing the amplitude of the oscillations of the granite. Modern concert halls are designed and built to interact with the instruments performing within. They are huge musical instruments in themselves. The Great Pyramid can be seen as a huge musical instrument with each element designed to enhance the performance of the other. While modern research into architectural acoustics might focus predominantly upon minimizing the reverberation effects of sound in enclosed spaces, there is reason to believe that the ancient pyramid builders were attempting to achieve the opposite. The Grand Gallery, which is considered to be an architectural masterpiece, is an enclosed space in which resonators were installed in the slots along the ledge that runs the length of the gallery. As the Earth's vibration flowed through the Great Pyramid, the resonators converted the vibrational energy to airborne sound. By design, the angles and surfaces of the Grand Gallery walls and ceiling caused reflection of the sound, and its focus into the King's Chamber. Although the King's Chamber also was responding to the energy flowing through the pyramid, much of the energy would flow past it. The specific design and utility of the Grand Gallery was to transfer the energy flowing through a large area of the pyramid into the resonant King's Chamber. This sound was then focused into the granite resonating cavity at sufficient amplitude to drive the granite ceiling beams to oscillation. These beams, in turn, compelled the beams above them to resonate in harmonic sympathy. Thus, with the input of sound and the maximization of resonance, the entire granite complex, in effect, became a vibrating mass of energy.

Emerging Possibilities for Space Propulsion Breakthroughs Originally published in the Interstellar Propulsion Society Newsletter, Vol. I, No. 1, July 1, 1995.  Marc. G. Millis, Space Propulsion Technology Division, NASA Lewis Research Center Cleveland, Ohio “New perspectives on the connection between gravity and electromagnetism have just emerged. A theory published in February 1994 (ref 11) suggests that inertia is nothing but an electromagnetic illusion. This theory builds on an earlier work (ref 12) that asserts that gravity is nothing other than an electromagnetic side-effect. Both of these works rely on the perspective that all matter is fundamentally made up of electrically charged particles, and they rely on the existence of Zero Point Energy. Zero Point Energy (ZPE) is the term used to describe the random electromagnetic oscillations that are left in a vacuum after all other energy has been removed (ref 13). This can be explained in terms of quantum theory, where there exists energy even in the absolute lowest state of a harmonic oscillator. The lowest state of an electromagnetic oscillation is equal to one-half the Planck constant times the frequency. If all the energy for all the possible frequencies is summed up, the result is an enormous energy density, ranging from 1036 to 1070 Joules/m3. In simplistic terms there is enough energy in a cubic centimeter of the empty vacuum to boil away Earth's oceans. First predicted in 1948, ZPE has been linked to a number of experimental observations. Examples include the Casimir effect (ref 14), Van der Waal forces (ref 15), the Lamb-Retherford Shift (ref 10, p. 427), explanations of the Planck blackbody radiation spectrum (ref 16), the stability of the ground state of the hydrogen atom from radiative collapse (ref 17), and the effect of cavities to inhibit or enhance the spontaneous emission from excited atoms (ref 18). Regarding the inertia and gravity theories mentioned earlier, they take the perspective that all matter is fundamentally constructed of electrically charged particles and that these particles are constantly interacting with this ZPE background. From this perspective the property of inertia, the resistance to change of a particle's velocity, is described as a high- frequency electromagnetic drag against the Zero Point Fluctuations. Gravity, the attraction between masses, is described as Van der Waals forces between oscillating dipoles, where these dipoles are the charged particles that have been set into oscillation by the ZPE background. It should be noted that these theories were not written in the context of propulsion and do not yet provide direct clues for how to electromagnetically manipulate inertia or gravity. Also, these theories are still too new to have either been confirmed or discounted. Despite these uncertainties, typical of any fledgling theory, these theories do provide new approaches to search for breakthrough propulsion physics.

Particle theory explains that all matter is made of many small particles that are always moving. There are particles in solids, liquids, and gases, and all of them continually vibrate, in varying directions, speeds, and intensities.17 Particles can only interact with matter by transferring energy. Waves are the counterpart to particles. There are three ways to regard waves: •​A disturbance in a medium through which energy is transferred from one particle within the medium to another, without making a change in the medium. •​A picture of this disturbance over time. •​A single cycle representing this disturbance. Waves have a constructive influence on matter when they superimpose or interact by creating other waves. They have a destructive influence when reflected waves cancel each other out. Scientists used to believe that particles were different from waves, but this is not always true, as you will see in the definition of wave-particle duality in this section. Waves, or particles operating in wave mode, oscillate, or swing between two points in a rhythmic motion. These oscillations create fields, which can in turn create more fields. For instance, oscillating charged electrons form an electrical field, which generates a magnetic field, which in turn creates an electrical field. Superposition in relation to waves means that a field can create effects in other objects, and in turn be affected itself. Imagine that a field stimulates oscillations in an atom. In turn, this atom makes its own waves and fields. This new movement can force a change in the wave that started it all. This principle allows us to combine waves; the result is the superposition. We can also subtract waves from each other. Energy healing often involves the conscious or inadvertent addition or subtraction of waves. In addition, this principle helps explain the influence of music, which often involves combining two or more frequencies to form a chord or another harmonic. A harmonic is an important concept in healing, as each person operates at a unique harmonic or set of frequencies. A harmonic is defined as an integer multiple of a fundamental frequency. This means that a fundamental tone generates higher-frequency tones called overtones. These shorter, faster waves oscillate between two ends of a string or air column. As these reflected waves interact, the frequencies of wavelengths that do not divide into even proportions are suppressed, and the remaining vibrations are called the harmonics. Energy healing is often a matter of suppressing the “bad tones” and lifting the “good tones.” But all healing starts with oscillation, which is the basis of frequency. Frequency is the periodic speed at which something vibrates. It is measured in hertz (Hz), or cycles per second. Vibration occurs when something is moving back and forth. More formally, it is defined as a continuing period oscillation relative to a fixed point—or one full oscillation.

You can literally re-code your being; repair, animate and activate your 12-Strand DNA; heal (emotional and etheric) trauma; and cure cancer and other illnesses; all through the use of sound frequencies, the harmonic science of the ancients. For sound is vibration, the oscillating motion of molecules in the atmosphere. All dimensions exist in states of vibration.

All manner of physical systems,” wrote Robert G. Jahn, “whether mechanical, electromagnetic, fluid dynamical, quantum mechanical, or nuclear, display capacities for synergistically interactive vibrations with similar systems, or with their environment. Coupled harmonic oscillators, all common musical instruments, radio and television circuitry, atomic components of molecules, all involve this ‘sympathetic’ resonance, from which strikingly different properties emerge than those that characterize their isolated components.”21

In order to draw mechanical vibrations and relieve the stresses that build up within the Earth, we would need an object that would respond sympathetically with the Earth's fundamental frequency. This object would need to be designed in such a way that its own resonant frequency was the same as, or a harmonic of, the Earth's. In this manner, energy transfer from the source would be at maximum load. In harmony with the Earth's vibrations, this object would have the potential to become a coupled oscillator. (A coupled oscillator is an object that is in harmonic resonance with another, usually larger, vibrating object. When set into motion, the coupled oscillator will draw energy from the source and vibrate in sympathy as long as the source continues to vibrate.) Because the Earth constantly generates a broad spectrum of vibration, we could utilize vibration as a source of energy if we developed suitable technology. Naturally, any device that attracted greater amounts of this energy than is normally being radiated from the Earth would greatly improve the efficiency of the equipment. Because energy will inherently follow the path of least resistance, it follows that any device offering less resistance to this energy than the surrounding medium through which it passes would have a greater amount of energy channeled through it. Keeping all of this in mind and knowing that the Great Pyramid is a mathematical integer of the Earth, it may not be so outlandish to propose that the pyramid is capable of vibrating at a harmonic frequency of the Earth's fundamental frequency.

In the presence of a quadratic nonlinearity, a damped harmonic oscillator with a sum of two sinusoidal forcing terms of different frequencies will vibrate with not only the two incoming frequencies but also with components at twice these frequencies and at the sum and difference of the frequencies. Intuitively, this is because