海森堡不确定性原理

The Heisenberg Uncertainty Principle is a fundamental tenet of quantum mechanics, not a statement about the limitations of measurement technology. It reflects an inherent property of quantum systems. The principle arises from the wave-like nature of all quantum objects. A particle’s position and momentum are described by its wavefunction. A wavefunction that is highly localized in space (small [latex]\Delta x[/latex]) is necessarily composed of a wide superposition of many different momentum waves, resulting in a large uncertainty in momentum (large [latex]\Delta p[/latex]). Conversely, a wavefunction with a well-defined momentum (small [latex]\Delta p[/latex]) must be a spatially spread-out wave, leading to a large uncertainty in position (large [latex]\Delta x[/latex]).

The principle applies to any pair of ‘conjugate variables,’ which are related through 傅立叶 transforms in the mathematical formalism of quantum mechanics. Another important pair is energy ([latex]E[/latex]) and time ([latex]t[/latex]), with the relation [latex]\Delta E \Delta t \ge \frac{\hbar}{2}[/latex]. This implies that the energy of a state that exists for only a short time cannot be precisely determined. This has profound consequences, such as allowing for the temporary creation of ‘virtual particles’ in quantum field theory, which mediate fundamental forces. The uncertainty principle fundamentally limits the determinism envisioned by classical physics, replacing it with a probabilistic description of nature at the smallest scales.