Transcript Document

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
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Michigan Tech course PH4999
Aimed at upper level physics majors
Light on math, heavy on concepts
Anyone anywhere is welcome
• No textbook required
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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
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A series of photons go through a single slit
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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
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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
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Gamma rays through a wide slit
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small λ/D case
classical result:
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photons like bowling balls - go straight
single bright spot: slit projected onto the screen
Diffraction unimportant
UNCERTAINTY PRINCIPLE:
SINGLE SLIT EXPERIMENT
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Radio waves through a hairline slit
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large λ/D case
classical result:
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no photons go through (tunneling not allowed)
imaging screen totally dark
Diffraction unimportant
UNCERTAINTY PRINCIPLE:
SINGLE SLIT EXPERIMENT
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Diffraction: photon wavelength same scale as slit opening
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λ~D
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things get messy and complex
really strange things can happen
fundamental physics shows itself!
Diffraction
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fundamentally a wave phenomenon
UNCERTAINTY PRINCIPLE:
SINGLE SLIT EXPERIMENT
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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
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The imaging screen will show:
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Null nodes where no photons will hit
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screen dark at these locations
hard to understand from classical particle perspective
Photons can hit way off on the sides
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not very likely
hard to understand from classical particle perspective
UNCERTAINTY PRINCIPLE:
SINGLE SLIT EXPERIMENT
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Diffraction: λ ~ D
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Near field: Fresnel diffraction
Far field: Fraunhofer diffration
The imaging screen will show:
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Central peak
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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?
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Yes.
No.
SINGLE SLIT EXPERIMENT:
POPPER'S EXPERIMENT
2. No.
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Thought by Popper to test the Copenhagen interpretation uniquely,
but all interpretations say this.
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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.