bell curve and uncertainty

the lowest propobilities comes up with everybody in different ways and aspects. nobody knows when , how, why. when the bell rings, it's know that we are out of 3 sigma.



This excerpt from Heisenberg's original paper shows his derivation of the uncertainty relation for momentum and position.

Here Heisenberg transforms the "bell curve" in quantum theory for the imprecision in the measurement of the position q of a moving electron to the corresponding bell curve of the measured momentum p. The uncertainty, or standard deviation, of each curve is Dp=p1 and Dq=q1. Heisenberg obtains an equal sign for the minimum uncertainty. He later included the possibility of even greater uncertainty by using the sign for "greater than or equal to."


Heisenberg's uncertainty paper has been translated into English by John Archibald Wheeler and Hubert Zurek, in Quantum Theory and Measurement, Wheeler and Zurek, eds.

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Triumph of the Copenhagen Interpretation
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The Uncertainty Relations
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Heisenberg Speaking on the Origins of Uncertainty