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Philosophical Interpretations of. Quantum Mechanics. Outline. Classical “Newtonian” Mechanics Elementary Quantum Mechanics Young’s Double-Slit Experiment Uncertainty Principle due to Heisenberg Schrödinger’s Cat Thought Experiment Interpretations of Quantum Mechanics

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Outline

  • Classical “Newtonian” Mechanics

  • Elementary Quantum Mechanics

    • Young’s Double-Slit Experiment

    • Uncertainty Principle due to Heisenberg

    • Schrödinger’s Cat Thought Experiment

  • Interpretations of Quantum Mechanics

    • The Copenhagen Interpretation

    • The Many-Worlds Interpretation


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Classical Newtonian Mechanics

  • Determinism

    • universe has a starting point (Big Bang?)

    • correct formulations for laws of nature allow histories of all particles to be traced and predicted into the future

    • everything is predictable, universe functions like clockwork

    • Free will?

Sir Isaac Newton


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Young’s Double-Slit Experiment

  • Thomas Young

    • light consists of waves, not particles

    • wave interference

  • electrons, protons

  • wave-particle duality

    • matter sometimes behaves like a wave, sometimes like a particle


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Pauli’s Exclusion Principle

  • particles around an atom are assigned quantum numbers {n, l, ml, ms}, which define their quantum state

  • no two particles can occupy the same quantum state

Wolfgang Pauli (1945)


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Heisenberg’s Uncertainty Principle

  • two properties of a particle are unknowable to arbitrary accuracy

  • momentum (p) and position (x) of a particle cannot be known exactly at the same time

Standard Deviation (Δ) of momentum (p) or position (x) measurement multiplied together are larger than or equal to half the reduced Planck constant (ħ)


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Bohr‘s Complementarity Principle

  • connects to the uncertainty principle

  • characteristics which are uncertain are complementary

  • wave and particle behavior is complementary as well

Niels Bohr and Albert Einstein (1925) during the Bohr-Einstein Debates


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The Copenhagen Interpretation

  • Wavefunction ψ (Psi) describes a quantum mechanical system.

  • The nature of a system can be described by probabilistic values; probability of an event is equal to the square of the amplitude of the wavefunction (|ψ|²).

  • Impossible to know all properties of a system at the same time, each must be given by probabilistic values (uncertainty principle).

  • Matter exhibits wave-particle duality; particles may exhibit both particle and wave properties, but not both at the same time (complementarity principle).

  • Measuring devices are classical devices, and as such do not measure probabilities, but only classical properties.

  • Quantum mechanical descriptions of the system will closely approximate the values of the classical descriptions of the system.


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Schrödinger‘s Cat (1935)

  • Erwin Schrödinger

  • cat in a box with a vial of poison and a Geiger counter

  • possible decay of atom or not

  • if atom decays, cat dies; if not, cat lives

  • cat is both alive AND dead before one checks

Superposition of Quantum States demonstrated by the Schrödinger Cat Thought Experiment


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The EPR Paradox

  • paradox of the CI formulated by Einstein, Boris Podolsky, and Nathan Rosen in reaction to the CI

  • quantum entanglement – connection of two or more particles

  • anti-correlation of e- and e+ spin

  • if spin is measured in one, the wavefunction of the other collapses; superluminal information transfer

  • Copenhagen Interpretation: second observer cannot benefit until results were relayed, at luminal or subluminal speed


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Wavefunction Collapse

  • quantum system interacts with an observer; wavefunction collapses into a single state

  • “opening the box with the cat”

  • quantum systems are holistic; each particle contains information about the whole system

  • only measuring a specific particle causes wavefunction collapse


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The Many-Worlds Interpretation

  • universal wavefunction exists

  • all alternative histories and futures of the wavefunction progression are followed in different parallel “worlds” or “universes”

Schrödinger‘s Cat as a visualization of the Many-Worlds Interpretation of Quantum Mechanics


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The Universal Wavefunction

  • describes the universe in its entirety as a single quantum state

  • does not collapse; worlds split if an event with different possible outcomes occurs

  • interpretation makes no real difference between itself and CI, since observable results are the same for MWI and CI

  • no evidence for it as of now


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Conclusion

  • Arthur Eddington’s View

  • Why describe the world with quantum theories?

  • Connections to Hawking?

  • Scientific determinism?

  • Many worlds?