The Isenberg Uncertainty Principle (“IUF”) is a simple, somewhat flawed analogy of the very complex (Heisenberg Uncertainty Principle – see below). The IUF is attributed to Dr. Andrew Isenberg, trauma surgeon and my cousin.
“If you know where I am, you won’t know what I’m doing. Conversely, if you know what I’m doing, you won’t know where I am.”
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Excerpt from Wikipedia on Werner Heisenberg’s (1901-1974) Uncertainty Principle:
The uncertainty principle is stated in popular culture in many ways, for example, by some stating that it is impossible to know both where an electron is and where it is going at the same time. This is roughly correct, although it fails to mention an important part of the Heisenberg principle, which is the quantitative bounds on the uncertainties. Heisenberg stated that it is impossible to determine simultaneously and with unlimited accuracy the position and momentum of a particle, but due to Planck’s Constant being so small, the Uncertainty Principle was intended to apply only to the motion of atomic particles. However, culture often misinterprets this to mean that it is impossible to make a completely accurate measurement.
Reference:
http://en.wikipedia.org/wiki/Heisenberg_uncertainty_principle#History_and_interpretations
Heisenberg uncertainty inequality. [Quantum Mechanics derivation]
Defining concentration in terms of standard deviation leads to the Heisenberg uncertainty inequality. If 
and 
, the quantity 
is a measure of the concentration of 
around 
. Roughly speaking, the more concentrated 
is around 
, the smaller will this quantity be. If one normalizes 
such that 
, then by the Plancherel theorem 
. Here, 
is the Fourier transform of 
, defined by
 |
the convergence of the integral being interpreted suitably. Then, for 
one has the Heisenberg inequality
 |
 |
Thus, the above says that if 
is concentrated around 
, then no matter what 
is chosen, 
cannot be concentrated around 
. Equality is attained in the above if and only if 
is, modulo translation and multiplication by a phase factor, a Gaussian function (i.e. of the form 
).
Reference:
