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QUANTUM MECHANICS Probability & Uncertainty

QUANTUM MECHANICS Probability & Uncertainty. Probability Uncertainty Double-slit photons. P( S ) = Probability of getting sum S. Probability. EXPERIMENT. THEORY. # times S occurs # all throws. # ways to get S # all possible outcomes.

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QUANTUM MECHANICS Probability & Uncertainty

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  1. QUANTUM MECHANICS Probability & Uncertainty • Probability • Uncertainty • Double-slit photons

  2. P(S) = Probability of getting sum S Probability EXPERIMENT THEORY # times S occurs # all throws # ways to get S # all possible outcomes Experiment approaches Theory after more & more throws, but always fluctuates.

  3. Wave represents probability of particle detection at a particular place and time (Max Born) Quantum Mechanics Big Idea Solves wave-particle duality paradox Wave = THEORY Particle = EXPERIMENT (compare to dice) Quantum Waves: P = h2 Wave Height h Intensity => Probability P Double Slits – Location of bright bands has high probability of photon hits

  4. New kind of scientific model Probability : Cannot predict result of anyone detection Detection : No objective reality before measurement U C N E R T A Y I N T • Classical physics deterministic • Can predict future position & speed • with arbitrary precision • Quantum physics probabilistic • Can predict only probability of observing certain • future speed or position

  5. X ? How is position of an object detected? Observe (e.g. with light) Increasing certainty of position X, decreases certainty of momentum P (momentum = mass times velocity ) A photon bounces off (detection) Object gets an uncertain `kick’ (changes velocity) Observe

  6. Measure X ± ΔX Measure P ± ΔP QM says can make either ΔX or ΔP arbitrarily small (not zero) by better experiment BUT… there is a theoretical limit on both simultaneously: Heisenberg Uncertainty Principle ΔX timesΔP is always more than h h = Planck constant (very small) • Smaller ΔX implies largerΔP ….and vice versa • Limit only noticeable at atomic sizes • Uncertainty Principle applies to everything, including us

  7. Revisit….Double slit photons: Quantum mechanics -> wave represents probability of particle detection -> measurement uncertainty Paradox ? Interference pattern result of two slits, but each particle must go through only one slit (surely?) QM : before detection, cannot say which slit particle went through (no definite path) Act of looking alters the wave.. If detect which slit each particle passes through -> no interference pattern

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