Uncertainty Principle III: Single Slit Experiment

1. Uncertainty Principle III:Single Slit Experiment by Robert Nemiroff Michigan Technological University

2. Physics X: About This Course • Pronounced "Fiziks Ecks" • Reviews the coolest concepts in physics • Being taught for credit at Michigan Tech • Michigan Tech course PH4999 • Aimed at upper level physics majors • Light on math, heavy on concepts • Anyone anywhere is welcome • No textbook required • Wikipedia, web links, and lectures only

3. 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.

4. Uncertainty Principle:Single Slit Experiment • A series of photons go through a single slit  • 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 • 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 (!?)

5. Uncertainty Principle:Single Slit Experiment • Gamma rays through a wide slit • small λ/D case • classical result: • photons like bowling balls - go straight • single bright spot: slit projected onto the screen • Diffraction unimportant

6. Uncertainty Principle:Single Slit Experiment • Radio waves through a hairline slit • large λ/D case • classical result:  • no photons go through (tunneling not allowed) • imaging screen totally dark • Diffraction unimportant

7. Uncertainty Principle:Single Slit Experiment • Diffraction: photon wavelength same scale as slit opening • λ ~ D • things get messy and complex • really strange things can happen • fundamental physics shows itself! • Diffraction • fundamentally a wave phenomenon

8. 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.

9. Uncertainty Principle:Single Slit Experiment • The imaging screen will show: • Null nodes where no photons will hit • 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

10. Uncertainty Principle:Single Slit Experiment • Diffraction: λ ~ D • Near field: Fresnel diffraction • Far field: Fraunhofer diffration • The imaging screen will show: • Central peak • incorporates projection of point source through slit • Also called: Airy disk

11. 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.

12. 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? • Yes. • No. 

13. 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.