Particle-Like Behavior

In fact, following a small initial transient period, temporal sections of the space-time pattern are always of the form 

Class c4 Rules, T20 (r=2) and T88 (r=3) It has been conjectured that all generic class c4 CA are capable of universal computation [wolf85e]. With initial configurations specifying arbitrary algorithmic procedures, such systems can effectively evaluate any computable function and therefore mimic the action of any general purpose computer. 

The simplest binary valued CA proven to be computation universal is John Conway s two-dimensional Life rule, about which we will have much to say later in this chapter. Many of the key ingredients necessary to prove universality, however, such as sets of propagating structures out of which analogs of conventional hardware components (i.e., wires, gates and memory) may be explicitly constructed, appear, at least in principle, to be supported by certain one-dimensional rules as well. The most basic component required is a mechanism for transporting localized packets of information from one part of the lattice to another i.e., particle-like persistent propagating patterns, whose presence is usually indicative of class c4 behavior. 

Examination of the evolution of all configurations with nonzero sites confined to a some finite region of N sites, reveals that the fraction of such configurations that generate persistent structures approaches 7% for large N and t (see figure 3.35). 

Note also that the curves appear to approach a fixed, possibly universal, form for large N. Wolfram [wolf85e] speculates that at least some aspects of such curves may in fact be universal to all computationally universal systems. 

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Analogous experiments using electrons instead of photons have been carried out with the same results. Electrons passing through a system with double slits produce an interference pattern. If a detector determines through which slit each electron passes, then the interference pattern is not observed. As with the photon, the electron exhibits both wave-like and particle-like behavior and its location on a detection screen is randomly determined by a probability distribution. 

The Duality. Hence, if the photon is a wave, what is the origin of the particle-like behavior ... 

Probably the most dramatic difference in the behavior of particles and waves is the possibility of interference for waves when multiple sources are present. Figure 3.6 illustrates the differences. The top of Figure 3.6 illustrates purely particle-like behavior (for instance, firing two shotguns simultaneously). The particles from each shotgun... 

During this same period de Broglie s brother Maurice was studying experimental physics, and he was particularly interested in x rays. The brothers frequently discussed x rays, and their dual nature (both wavelike and particle-like behavior) suggested to Louis that this same particle-wave duality might also apply to particles such as electrons. 

Beginning less than 10 years ago, the independent-particle model for atoms was challenged, first for a specific set of rather exotic states of helium and, more recently, for the ground and ordinary excited states of the alkaline earth atoms Be, Mg, Ca, Sr, and Ba. Evidence has been building that the quantization in these two-electron and quasi-two-electron atoms corresponds to collective, moleculelike behavior, rather than to independent-particle-like behavior. 

Soon afterward, other phenomena such as Compton scattering. X-ray production, pair creation and annihilation could be interpreted successfully using a photon picture of light. Light still retains its wavelike properties as it travels through space. It assumes its photon or particle-like behavior only when it interacts with matter in a detector or at a target. 

Having observed that light could exhibit particle-like behavior, de Broglie proposed that matter might also exhibit wavelike behavior. 

Since the electron s mass turns out to be 1/2000 that of the proton or neutron, its wavelength is on the order of atomic dimensions and its wave-like nature becomes dominant whereas protons and neutrons with heavier masses and much shorter wavelengths exhibit more particle-like behavior. (Neutron diffraction, a powerful tool for analyzing the structure of crystals, takes advantage of the short wave-like properties of the neutron which allows the positions of the lighter elements such as hydrogen, which are not seen by x-rays, to be determined.)... 

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