Transcript Quantum Mechanics

Philosophical Interpretations of
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
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 Young
 light consists of
waves, not particles
 wave 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?