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?