Tuesday, November 01, 2005

Harmonic Oscillation

This "math sense" has to become part of one's makeup? An inductive process. Experimentally challenged. Deductive.

If such a idea is held from weak to strong idealizations in terms of comological views, then you get this sense of "energy valuations" as well. If you calculate when the binary pulsar distances around each other, the value of that information has been released in the bulk. This information should become weaker, as the orbits get closer?

The theory of relativity predicts that, as it orbits the Sun, Mercury does not exactly retrace the same path each time, but rather swings around over time. We say therefore that the perihelion -- the point on its orbit when Mercury is closest to the Sun -- advances.

I would think this penduum exercise would make a deeper impression if held in concert with the way one might have look at Mercuries orbit.

Or, binary pulsar PSR 1913+16 of Taylor and Hulse. These are macroscopic valutions in what the pendulum means. Would this not be true?

Part of the Randall/Sundrum picture Sean supplied of the brane world perspectives needed for how we look at that bulk view. If you are to asume that space is not indeed empty, then what is it filled with? Gravitonic perception would make this idea of the quantum harmonic oscillator intriguing to me in the sense that "zero point", would be flat space time. Any curvature parameters would have indeed signalled simple harmonic initiations?

Omega valutions in regard to the what state the universe is in, would have been defined in relation to a triangulation.

The quantum harmonic oscillator has implications far beyond the simple diatomic molecule. It is the foundation for the understanding of complex modes of vibration in larger molecules, the motion of atoms in a solid lattice, the theory of heat capacity, etc. In real systems, energy spacings are equal only for the lowest levels where the potential is a good approximation of the "mass on a spring" type harmonic potential. The anharmonic terms which appear in the potential for a diatomic molecule are useful for mapping the detailed potential of such systems.

But indeed while we understand this large oscillatory factor in our orbits, does it not make sense to wonder how simple that harmonic oscillator can become when we are looking for extra dimensions?

I had a picture the other day of a music instrument of a wire stretched, and weights being applied respectfully. The string when strummed gave certain frequencies accordingly to different mass valuations. This is the early pythagorean instrument I had see a few years ago, that would have similarities with "gourds of water" as weight and levels changed.

Here we seen a torsion pendulum. The way the wire twists and it's resulting valuation.

So you see how simple experimental processes help to correct our views on the way we see things.

From a historical perspective views of scientists with this explanation support the harmonic oscillators as follows:

Let us see how these great physicists used harmonic oscillators to establish beachheads to new physics.

Albert Einstein used harmonic oscillators to understand specific heats of solids and found that energy levels are quantized. This formed one of the key bridges between classical and quantum mechanics.

Werner Heisenberg and Erwin Schrödinger formulated quantum mechanics. The role of harmonic oscillators in this process is well known.

Paul A. M. Dirac was quite fond of harmonic oscillators. He used oscillator states to construct Fock space. He was the first one to consider harmonic oscillator wave functions normalizable in the time variable. In 1963, Dirac used coupled harmonic oscillators to construct a representation of the O(3,2) de Sitter group which is the basic scientific language for two-mode squeezed states.

Hediki Yukawa was the first one to consider a Lorentz-invariant differential equation, with momentum-dependent solutions which are Lorentz-covariant but not Lorentz-invariant. He proposed harmonic oscillators for relativistic extended particles five years before Hofstadter observed that protons are not point particles in 1955. Some people say he invented a string-model approach to particle physics.

Richard Feynman was also fond of harmonic oscillators. When he gave a talk at the 1970 Washington meeting of the American Physical Society, he stunned the audience by telling us not to use Feynman diagrams, but harmonic oscillators for quantum bound states. This figure illustrates what he said in 1970.

We are still allowed to use Feynman diagrams for running waves. Feynman diagrams applicable to running waves in Einstein's Lorentz-covariant world. Are Feynman's oscillators Lorentz-covariant? Yes in spirit, but there are many technical problems. Then can those problems be fixed. This is the question. You may be interested in reading about this subject: Lorentz group in Feynman's world.

Can harmonic oscillators serve as a bridge between quantum mechanics and special relativity?

Lee Smolin saids no to this?