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What are the implications of the Copenhagen interpretation of quantum mechanics, particularly in relation to the idea that there is no governing law for the decay of a single given atom and that quantum mechanics is considered a complete theory with only statistical predictions about the outcomes of experiments with single particles?

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The Copenhagen interpretation suggests that quantum mechanics is a complete theory capable of only making statistical predictions, where particles like atoms exist in a superposition state until measured. This contrasts with deterministic classical mechanics, with the correspondence principle reconciling quantum and classical physics at higher energy scales. Schrödinger's cat thought experiment highlights the paradoxes born from this interpretation.

Step-by-step explanation:

Implications of the Copenhagen Interpretation of Quantum Mechanics

The Copenhagen interpretation of quantum mechanics implies that, at the quantum level, such as the decay of a single atom, we can only make statistical predictions. Without observation, particles exist in a state of superposition, embodying all possible states at once. This became famously illustrated by Schrödinger's cat thought experiment, wherein a cat is paradoxically considered both alive and dead until observed. This interpretation posits that quantum mechanics is a complete theory despite its probabilistic nature, standing in contrast with deterministic classical laws.

Classical Mechanics and Quantum Mechanics

Niels Bohr's correspondence principle suggests that classical mechanics is an approximation of quantum mechanics for systems with large energies. Werner Heisenberg’s uncertainty principle further distinguishes quantum mechanics by pointing out the fundamental limits of measuring quantum properties. This dual nature of particles as both waves and particles rejects classical mechanics' adequacy at explaining quantum phenomena, making quantum mechanics essential for understanding the micro-world and informing the macro-world.

In essence, quantum mechanics reshaped our understanding of matter, replacing the predictable 'billiard ball' atoms with a wave-particle duality concept and inherent uncertainties, shifting the philosophy of science from absolute predictions to probabilities.

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