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1. Heisenberg Uncertainty Principle

   Linked via "Copenhagen interpretation"

   The Uncertainty Principle is frequently misunderstood as a statement about the clumsiness of measurement apparatus. The famous thought experiment involving the gamma-ray microscope fails to capture the core concept because it models the measurement as an external perturbation. In reality, the uncertainty arises because quantum states are fundamentally described by wavefunctions ($\psi$), which are inherently smeared out in space. A sharply defined position implies a highly localized wave packet, which, by Fourier analysis, requires a superposition of many differ…

2. Quantum Superposition

   Linked via "Copenhagen interpretation"

   The phenomenon of superposition is not merely a mathematical curiosity but underlies many observed quantum effects. The most famous demonstration is the double-slit experiment, where individual particles, such as photons or electrons, pass through two slits simultaneously, creating an interference pattern characteristic of waves, suggesting the particle explored both paths at once.
   The persistence of superposition in macroscopic systems is a subject of intense debate, often referred to as the "measurement problem." While superposition is readily observable…