The Pauli Exclusion Principle states that no two identical fermions (particles with half-integer spin) can occupy the same quantum state simultaneously. This means that two fermions cannot have the same set of quantum numbers, such as energy level, spin, and orbital angular momentum, in an atom or molecule.
The Pauli Exclusion Principle dictates that electrons must occupy different energy levels and have different spins within an atom. This leads to the formation of electron shells and subshells, which determine the chemical and physical properties of elements.
Entanglement is a phenomenon in quantum mechanics where two or more particles become correlated in such a way that the quantum state of one particle cannot be described independently of the other(s). This means that measuring the state of one entangled particle will instantly affect the state of the other(s), regardless of the distance between them.
The Pauli Exclusion Principle states that two particles cannot occupy the same quantum state. However, in entangled particles, their quantum states are linked and cannot be described separately. This means that entangled particles can have the same quantum numbers, violating the principle.
Entanglement has significant implications for quantum computing, cryptography, and teleportation. It also challenges our understanding of reality and the classical laws of physics, leading to ongoing research and discussions in the field of quantum mechanics.