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QUANTUM MECHANICS Probability & Uncertainty 1.Probability 2.Uncertainty 3.Double-slit photons

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

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Quantum Mechanics Big Idea Solves wave-particle duality paradox Wave represents probability of particle detection at a particular place and time (Max Born) Wave = THEORY Particle = EXPERIMENT ( compare to dice) Quantum Waves: P = h 2 Wave Height h Intensity => Probability P Double Slits – Location of bright bands has high probability of photon hits

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U C N E R T A Y I N T 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 Probability : Cannot predict result of any one detection Detection : No objective reality before measurement

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

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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: ΔX times ΔP is always more than h h = Planck constant (very small) Smaller ΔX implies larger ΔP ….and vice versa Limit only noticeable at atomic sizes Uncertainty Principle applies to everything, including us Heisenberg Uncertainty Principle

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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) If detect which slit each particle passes through -> no interference pattern Act of looking alters the wave..

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