Position & Momentum: Detectors, Measurements & Identifiers

In summary, the uncertainty principle states that the position and momentum of a particle cannot be measured simultaneously with unlimited precision. This is due to the fact that the standard deviations of position and momentum have a minimum value as expressed in the equation \Delta x \Delta p \ge \hbar / 2. This principle is not a limitation of detectors, but rather a fundamental property of quantum mechanics. Attempts to measure both properties simultaneously can result in different values each time, and this extends to entangled particles as well. Additionally, the Bekenstein bound places a limit on the amount of information that can be stored in a volume, dependent on the energy used and the mass of the particle.
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