Strange Paths

Timelapse photo of the total lunar eclipse of October 27, 2004.¹ Celestial bodies orbiting around a star cast shadows, which may partially or totally obscure other bodies aligned behind them, “eclipsing” the star from their viewpoint (from Greek ekleipein, “failing to appear”).

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Given their short duration, eclipses are amongst the phenomena where cosmic scale dynamics may be perceived most dramatically. In the picture, the moon’s curved path is primarily due to Earth’s rotation, and to a small extent to the lunar motion in its elliptical orbit around the Earth. During the totality stage the Moon appears red, because Earth’s atmosphere scatters sunlight and only red wavelengths are refracted into the shadow. An observer on the moon would see a bright ring of red light, coming from all simultaneous Earth’s sunrises and sunsets.²

A total lunar eclipse will happen Saturday, March 3, 2007, and will be visible from Europe, Africa, Western Asia and Eastern America.

1. Picture © Forrest J. Egan, Digital Astro [↩]
2. Eclipse seen from the moon, Surveyor 3 mission, 24 April 1967 (artificial color) © NASA [↩]

Caustics (from the Greek kaustikos, kaiein, ‘to burn’) are geometrical entities formed by the singular concentration of curves, which model approximately the behavior of light rays focused by lenses or curved mirrors, leading to very bright regions when they encounter a surface. The light patterns at the bottom of swimming pools are examples of caustics, produced by the refraction on the wavy surface of water. In this computer image are discovered light caustics produced by two consecutive wavy surfaces, as if light was entering a second sea under the sea.

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1. Digital Artwork © Eric J. Heller, Resonance Fine Art [↩]

The concept of star travel, from planetary system to planetary system, is at the same time completely familiar and completely uncharted. Familiar, as we have certainly all heard of science fiction stories set on a far galaxy, where planets are nations or provinces of an empire. The characters usually move from one planet to another during intervals of time consistent with the story. The actual travel appears just like a formality, which the future advancements of a Triumphant Physics will put within reach.

This is what I’ll call the “strategy zero” (S0) : here travel is “instantaneous” or at the very least quicker than one year, eg. comparable to the durations of terrestrial travels or manned missions to the moon or other solar system’s bodies.

The way toward stars becomes however quite unfamiliar if we consider that such Triumph of Physics could possibly not happen, and that the famous constant of Einstein c, the speed of light (3E8 m/s), represents an horizon speed which is impossible to exceed and which is even extraordinarily difficult to approach, so that we would begin to see outer space like it is seen by astronomers: a vastness compared to which that of terrestrial oceans is nothing.

It is not without reserve that our mind adapts to the true dimensions of interstellar space. The insanity of these distances is not the only reason: in a sense, one could say that the “strategy zero” is enracined in a child’s desire of space. Not of a space-distance, of a horridly naked space, speechless and fearless, but of a space-treasure, and of the worlds which roll within its vastness. All these worlds whose reach should not suffer any delay and whose discovery turns on our imagination.
Realism helping, we leave with some regret the green paradise of “strategy zero”, but we can still consider a little more “teenager” strategy, within the framework of Special Relativity, which we will name “short strategy” or SI, which promises a travel duration within a man’s lifetime.

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Computer simulation of classical paths of electrons within a two-dimensional electron gas.¹ Transistors, the most common electronic devices, contain layered structures constraining the motion of electrons, so that they are free to move in the x-y plane but are completely confined in the z direction, forming a so-called two-dimensional electron gas (2DEG). The details of the electrons motion in a 2DEG flow were unknown until recently, when newly developed microscopy techniques made possible the observation of the actual electron paths. ²

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Instead of a smooth flow, unexpected chaotic channeling was observed, with continuous branching of classical paths reminiscent of familiar natural forms. It has been found through simulation that these patterns are not due to preferred-energy paths in the background, like for the path of a river on a valley, but to the cumulative chaotic effect of encountering random positive “bumps” in the atomic landscape.

1. Digital Artwork © Eric J. Heller, Resonance Fine Art [↩]
2. M. A.Topinka, B. J. LeRoy, R. M. Westervelt, S. E. J. Shaw, R. Fleischmann, E. J. Heller, K. D. Maranowski, A. C. Gossard, “Coherent Branched Flow in a Two-Dimensional Electron Gas“, Nature, 410, 183 (2001) [↩]

Optical microscope photographs of snow crystals.¹ Their characteristic 6-fold symmetry is related to the molecular structure of water, which stabilizes in hexagonal lattices at earth temperature and pressure.² Each crystal has about 10¹⁸ molecules of water, and its very specific shape is due to a complex dependence on temperature and humidity change, and to nonlinear diffusion leading to structural branching instabilities and dendritic patterns. Each snowflake registers a history of interactions with the environment, like “a hyeroglyph sent from the sky”.³

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1. © Kenneth G. Libbrecht (Caltech) [↩]
2. Water has several other possible solid phases, depending on pressure and temperature, with different crystal symmetry. Eg. ice-Ic forming at earth pressure and temperature lower than -80°C has cubic symmetry. [↩]
3. U. Nakaya, “Snow Crystals: Natural and Artificial”, Harvard University Press (1954) [↩]