An alternate statement of this rule is that a function and its Fourier transform cannot both be compactly supported.  Local hidden variable theories tried to explain it in the context of the EPR Paradox, but Bell's Theorem disproved that explanation. Its derivation makes use of the Cauchy-Schwarz Inequality, and it is most accurately understood in terms of wave-particle duality, whereby the product of the widths of two different wavefunction collapses must be greater than Planck's constant over 4 pi.  Describing the non
An alternate statement of this rule is that a function and its Fourier transform cannot both be compactly supported.  Local hidden variable theories tried to explain it in the context of the EPR Paradox, but Bell's Theorem disproved that explanation. Its derivation makes use of the Cauchy-Schwarz Inequality, and it is most accurately understood in terms of wave-particle duality, whereby the product of the widths of two different wavefunction collapses must be greater than Planck's constant over 4 pi.  Describing the non-commutability of the operators for pairs of observables, FTP name this principle whose most famous example relates the inability to determine the exact momentum and position of a particle simultaneously.
An alternate statement of this rule is that a function and its Fourier transform cannot both be compactly supported.  
Heisenberg uncertainty principle