Quantum Gravity 366.4: HUP 3rd Analysis of its Coincidence
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From: OsherD on 24 Apr 2010 20:30 I typed the heading of this post without the "Quantum Gravity" number identifier, so look it up under my name rather than by number, or by keyword "HUP" or "Heisenberg Uncertainty Principle". The basic idea is that Var(X) = E(X - u)^2 where u = E(X) is the mean of X (population mean or expectation) is the minimum of E(X - a)^2 for all real a, but this minimum is NOT for a proper crossection of the distribution of random variable X. If we can show that for a proper crossection, say P(c < = X < = d), that P(c < = X < = d) < k1, and P(c ' < = Y < = d ' ) < k2, then Var(X)Var(Y) > = k = k1k2 > 0 is LESS RELEVANT than the product of the two probabilities being < k1k2! And for X, Y continuous random variables, there always must be such choices of c, d, c ' , d ' by continuity. The "opposition" will undoubtedly try to argue about "discrete" rather than continuous random variables, but regarding position (X) and momentum (Y) as "discrete" rather than continuous has its own anomalies and paradoxes, not to mention that fact that continuous X and Y can approximate their discrete "relatives" rather easily. Osher Doctorow |