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UNCERTAINTY PRINCIPLE III: SINGLE SLIT EXPERIMENT by Robert Nemiroff Michigan Technological University Physics X: About This Course • Pronounced "Fiziks Ecks" • Reviews the coolest concepts in physics • Being taught for credit at Michigan Tech o o o o Michigan Tech course PH4999 Aimed at upper level physics majors Light on math, heavy on concepts Anyone anywhere is welcome • No textbook required o Wikipedia, web links, and lectures only QUANTUM MECHANICS: WHAT CHANCE H = 0? It might be cool if someone would estimate, given experimental uncertainty, the chance that h is actually zero. If true, then Δx Δp > 0 and the universe would be classical! I am sure this would be one of the smallest probabilities ever estimated --> 10-(VERY LARGE NUMBER). Still, it would be a small number with a very interesting interpretation. UNCERTAINTY PRINCIPLE: SINGLE SLIT EXPERIMENT • A series of photons go through a single slit o o o • the slit screen is otherwise opaque the imaging screen detects positions of photon impact all photons assumed prepared identically What happens depends on several variables o o o o o the wavelength of the photons: λ the width of the slit: D the distance to the imaging screen best single variable: λ / D the presence of observers (!?) UNCERTAINTY PRINCIPLE: SINGLE SLIT EXPERIMENT • Gamma rays through a wide slit o o small λ/D case classical result: o o photons like bowling balls - go straight single bright spot: slit projected onto the screen Diffraction unimportant UNCERTAINTY PRINCIPLE: SINGLE SLIT EXPERIMENT • Radio waves through a hairline slit o o large λ/D case classical result: o o no photons go through (tunneling not allowed) imaging screen totally dark Diffraction unimportant UNCERTAINTY PRINCIPLE: SINGLE SLIT EXPERIMENT • • Diffraction: photon wavelength same scale as slit opening o λ~D o o o things get messy and complex really strange things can happen fundamental physics shows itself! Diffraction o fundamentally a wave phenomenon UNCERTAINTY PRINCIPLE: SINGLE SLIT EXPERIMENT • Numerical approximation of diffraction pattern from a slit of width four wavelengths with an incident plane wave. The main central beam, nulls, and phase reversals are apparent. UNCERTAINTY PRINCIPLE: SINGLE SLIT EXPERIMENT • The imaging screen will show: o Null nodes where no photons will hit o screen dark at these locations hard to understand from classical particle perspective Photons can hit way off on the sides not very likely hard to understand from classical particle perspective UNCERTAINTY PRINCIPLE: SINGLE SLIT EXPERIMENT • Diffraction: λ ~ D o o • Near field: Fresnel diffraction Far field: Fraunhofer diffration The imaging screen will show: o Central peak incorporates projection of point source through slit Also called: Airy disk SINGLE SLIT EXPERIMENT: POPPER'S EXPERIMENT Sets of two photons are created that conserve momentum. Each is directed through single slits and impact an image screen. SINGLE SLIT EXPERIMENT: POPPER'S EXPERIMENT Slit screen B is now removed. Since photons move opposite of their counterparts, and the photons passing through slit A are confined, do the photons that hit the remaining image screen (behind B) spread out as if screen B was still there? 1. 2. Yes. No. SINGLE SLIT EXPERIMENT: POPPER'S EXPERIMENT 2. No. • Thought by Popper to test the Copenhagen interpretation uniquely, but all interpretations say this. • Although correlations can be found to exist between far removed particles, even seemingly faster than light (FTL), nothing that can allow communication -- like signaling -- can happen between far removed particles FTL.