Thread: random walk
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AntonioLao
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06-01-2007, 12:59 PM
random walk

In one dimensional random walk the probability of axial motion in either of two directions is ½. In two dimensions having two axes of motion the probability is ¼. In three dimensions with three axes of motion the probability is 1/8. In four dimensions with four axes of motion the probability is 1/16. For n dimensions with n axes of motion the probability is ½ raised to the nth power. As n approaches infinity the probability of any axial motion approaches zero. When n is exactly infinity then all random walks stop. Since different states of motion exist n never actually reach infinity and consequently absolute rest is impossible. Therefore singularity is not real and big bang never happened in the past or in any other time. This logical sequence would then correctly invalidate the existence of relativistic light-cones and their empty graticules at (0, 0, 0, 0).

Note that the general expression for finding the probability of n-dimensional random walk is equivalent to the multiplicative factor for finding the amount of remaining radioisotopes using half-lives of radioactive decay. The varying half-lives of radioisotopes, some lasting billions of years, are also a good indication that absolute rest is impossible. Therefore life or death is just varying rates and directions of continuous random walks. It is natural to keep walking. To live forever is to keep walking along a straight (or curved) line. To die is to walk in the opposite direction. Since there are infinite number of lines and directions there are infinite ways to live or to die.
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Time independence: [∂E(g)]²=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: a(tr(t)=c²
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