U NCERTAINTY P RINCIPLE III: S INGLE S LIT E XPERIMENT 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 Michigan Tech course PH4999 o Aimed at upper level physics majors o Light on math, heavy on concepts o Anyone anywhere is welcome No textbook required o Wikipedia, web links, and lectures only

Q UANTUM M ECHANICS : W HAT 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.

U NCERTAINTY P RINCIPLE : S INGLE S LIT E XPERIMENT A series of photons go through a single slit o the slit screen is otherwise opaque o the imaging screen detects positions of photon impact o all photons assumed prepared identically What happens depends on several variables o the wavelength of the photons: λ o the width of the slit: D o the distance to the imaging screen o best single variable: λ / D o the presence of observers (!?)

U NCERTAINTY P RINCIPLE : S INGLE S LIT E XPERIMENT Gamma rays through a wide slit o small λ /D case o classical result:  photons like bowling balls - go straight o single bright spot: slit projected onto the screen o Diffraction unimportant

U NCERTAINTY P RINCIPLE : S INGLE S LIT E XPERIMENT Radio waves through a hairline slit o large λ /D case o classical result:  no photons go through (tunneling not allowed) o imaging screen totally dark o Diffraction unimportant

U NCERTAINTY P RINCIPLE : S INGLE S LIT E XPERIMENT Diffraction: photon wavelength same scale as slit opening Diffraction o λ ~ D o things get messy and complex o really strange things can happen o fundamental physics shows itself! Diffraction o fundamentally a wave phenomenon

U NCERTAINTY P RINCIPLE : S INGLE S LIT E XPERIMENT 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.

U NCERTAINTY P RINCIPLE : S INGLE S LIT E XPERIMENT The imaging screen will show: o Null nodes where no photons will hit  screen dark at these locations  hard to understand from classical particle perspective o Photons can hit way off on the sides  not very likely  hard to understand from classical particle perspective

U NCERTAINTY P RINCIPLE : S INGLE S LIT E XPERIMENT Diffraction: λ ~ D o Near field: Fresnel diffraction o Far field: Fraunhofer diffration The imaging screen will show: o Central peak  incorporates projection of point source through slit  Also called: Airy disk

S INGLE S LIT E XPERIMENT : P OPPER ' S E XPERIMENT P OPPER ' S E XPERIMENT Sets of two photons are created that conserve momentum. Each is directed through single slits and impact an image screen.

S INGLE S LIT E XPERIMENT : P OPPER ' S E XPERIMENT P OPPER ' S E XPERIMENT 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. Yes. 2. No.

S INGLE S LIT E XPERIMENT : P OPPER ' S E XPERIMENT P OPPER ' S E XPERIMENT 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.