By H. Pierre Noyes
Lets be at the threshold of a systematic revolution. Quantum mechanics relies on distinctive, finite and discrete occasions. basic relativity assumes a continuing, curved space-time. Reconciling the 2 continues to be the main basic unsolved clinical challenge left over from the final century. The papers of H. Pierre Noyes accumulated during this quantity replicate one try to in achieving that unification via changing the continuum with the bit-string occasions of desktop technological know-how. 3 rules are used: physics can confirm no matter if amounts are an analogous or various; size can inform whatever from not anything; this constitution (modelled via binary addition and multiplication) can depart a ancient list including a transforming into universe of bit-strings. This ebook is particularly addressed to these drawn to the principles of particle physics, relativity, quantum mechanics, actual cosmology and the philosophy of technological know-how.
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Additional resources for Bit-string physics: A finite and discrete approach to natural philosophy
Let us take half of the sum of four pseudo-random variables uniformly distributed over [—\/3, \/3]. The first three moments are the same as for the normal law and the fourth one is 10% off the normal value. 2. 2 13 Stable laws for sum of uncorrelated variables We return now to the additive unsealed case : MN = Y,Xi (2-6) • The quest for a statistical investigation of large objects corresponds to the characterization of the limiting distribution of such variable as M/v, with N the (large) number of subunits of the system.
J. Gumbel (1958)]. This is achieved equating to 0 the first derivative of fyN(y)- This leads to the equation : /»oo dfyjy) dy / fx(x)dx = (N-l)fY(y) Jy which admits a negative solution for the unimodal distributions fy- Let y* denotes this most probable value. Then one considers the scaled variable Wjv = (YN — y*)/-Bj\r. 42) converges towards a limit distribution when N —> oo. Three universality classes are known. The first one is when fx decreases faster than any power law for x —> — oo. A generic example from this class is the distribution : with the positive parameters b and /3.
Hence, in the following, this index j will be considered as the location in an appropriate metric space whose dimensionality is equal to the dimensionality of the index. This is the general case and the underlying metrics is not difficult to find in any particular application *. *For example, this could be an ordinary space for the renormalization for random tossing of a coin.
Bit-string physics: A finite and discrete approach to natural philosophy by H. Pierre Noyes