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4 years ago in Philosophy of Science , Physics , Quantum Mechanics By Saravanan

Why can position and momentum not be known simultaneously?

The Heisenberg principle is often stated, but in my quantum foundations reading, the explanations vary from wave-like nature to measurement disturbance. I'm seeking a clear, foundational reason rooted in the theory's axioms.

QuantumFoundations Wave-ParticleDuality MomentumSimulator

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By Sneha Answered 3 years ago

This gets to the heart of quantum theory. Based on my study of its foundations, it's not merely a measurement problem. The core reason is that in quantum mechanics, position and momentum are represented by mathematical operators that do not "commute." This non-commutativity is built into the theory's structure. I have seen this interpreted as stemming from the wave-like description of particles a pure wave has a well-defined wavelength (momentum) but is spread out everywhere (position), and vice-versa. I would recommend focusing on the wavefunction's properties; precise knowledge of one variable mathematically forces the conjugate variable into a state of inherent uncertainty.

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