UNCERTAINTY PRINCIPLE III:

SINGLE SLIT EXPERIMENT

byRobert 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 PH4999o Aimed at upper level physics majorso Light on math, heavy on concepts o Anyone anywhere is welcome

• No textbook requiredo 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 the slit screen is otherwise opaqueo the imaging screen detects positions of photon impacto all photons assumed prepared identically

• What happens depends on several variableso the wavelength of the photons: λo the width of the slit: Do the distance to the imaging screeno best single variable: λ / Do the presence of observers (!?)

UNCERTAINTY PRINCIPLE:SINGLE SLIT EXPERIMENT

  • Gamma rays through a wide slit

o small λ/D caseo classical result:

photons like bowling balls - go straighto single bright spot: slit projected onto the screeno Diffraction unimportant

UNCERTAINTY PRINCIPLE:SINGLE SLIT EXPERIMENT

  • Radio waves through a hairline slit

o large λ/D caseo classical result: 

no photons go through (tunneling not allowed)o imaging screen totally darko Diffraction unimportant

UNCERTAINTY PRINCIPLE:SINGLE SLIT EXPERIMENT

• Diffraction: photon wavelength same scale as slit openingo λ ~ Do things get messy and complexo really strange things can happeno fundamental physics shows itself!

• Diffractiono 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

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

UNCERTAINTY PRINCIPLE:SINGLE SLIT EXPERIMENT

  • Diffraction: λ ~ D

o Near field: Fresnel diffractiono 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. Yes. 2. 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.