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Philosophical Interpretations of
Outline
Classical “Newtonian” Mechanics Elementary Quantum Mechanics
Young’s Double-Slit ExperimentUncertainty Principle due to HeisenbergSchrödinger’s Cat Thought Experiment
Interpretations of Quantum MechanicsThe Copenhagen InterpretationThe Many-Worlds Interpretation
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
Young’s Double-Slit Experiment
Thomas Younglight consists of
waves, not particleswave interference
electrons, protons wave-particle duality
matter sometimes behaves like a wave, sometimes like a particle
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)
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)
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
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.
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
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
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
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
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
Conclusion
Arthur Eddington’s View Why describe the world with
quantum theories? Connections to Hawking? Scientific determinism? Many worlds?