Uncertainty is not the instrument’s fault. A wave packet narrow in space must be assembled from many different wavelengths, so its momentum is intrinsically smeared — that is Fourier mathematics, not clumsy experimenting. The tighter the packet is squeezed, the wider its momentum spectrum bulges, and the product Δx·Δp never dips below ħ/2, a floor only a Gaussian packet actually touches. For the same reason a particle can never sit perfectly still: it always keeps its zero-point energy.
Uncertainty is not the instrument’s fault. A wave packet narrow in space must be assembled from many different wavelengths, so its momentum is intrinsically smeared — that is Fourier mathematics, not clumsy experimenting. The tighter the packet is squeezed, the wider its momentum spectrum bulges, and the product Δx·Δp never dips below ħ/2, a floor only a Gaussian packet actually touches. For the same reason a particle can never sit perfectly still: it always keeps its zero-point energy.
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