Uncertainty Principle II: Circumventions - PowerPoint PPT Presentation

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Uncertainty Principle II: Circumventions

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UNCERTAINTY PRINCIPLE II: CIRCUMVENTIONS by Robert Nemiroff Michigan Technological University Physics X: About This Course Pronounced – PowerPoint PPT presentation

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Title: Uncertainty Principle II: Circumventions


1
Uncertainty Principle IICircumventions
  • 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
Uncertainty Principle Heisenberg's Microscope
  • A particle (blue) sits at the focus
  • of a microscope.
  • Shooting long wavelength photons 
  • at it will determine the particle's
  • position only crudely but the 
  • low recoil will create only a small 
  • uncertainty in its momentum.
  • This is a simple example of a direct 
  • measurement that cannot break
  • the uncertainty principle.

4
Uncertainty Principle Einstein's Slit
  • A photon goes through a slit in a wall.
  • Einstein By measuring both the 
  • resulting momentum of the photon
  • AND the wall, one might determine 
  • the photon's momentum arbitrarily well, 
  • violating the uncertainty principle.
  • Does this work?

5
Uncertainty Principle Einstein's Slit
  • Bohr No -- there will be uncertainty also 
  • in the wall's measured position.  
  • When everything is accounted for,
  • the uncertainty principle sill holds.

6
Uncertainty Principle Einstein's Box
  • Einstein A box filled with photons 
  • has a shutter that opens at a very 
  • precise time.  A photon leaves. 
  • The box is then re-weighed to find
  • out the photon's precise energy.
  • Doesn't this violate the energy-time
  • uncertainty principle (?E t gt h)?

7
Uncertainty Principle Einstein's Box
  • Bohr No.  When the photon leaves, 
  • the reduced gravity does make the box 
  • sag.  However, the uncertainty of the clock 
  • position in the gravity field includes
  • GR gravitational slowing, so that an 
  • uncertainty in the position of clock leads
  • to an uncertainty of the slowing of the 
  • clock which leads in an uncertainty in time.
  • The uncertainty principle holds.

8
The "Other" Uncertainty PrincipleEnergy versus
Time
  • ?E ?t gt h / 4 p
  • Not exactly like "regular" uncertainty principle
    time is not like position.  ?t really refers to
    the measured lifetime of a given state with
    energy E known to accuracy ?E.
  • Effective definition A state that exists for
    only a time ?t cannot have an energy better
    defined than ?E.

9
The "Other" Uncertainty PrincipleEnergy versus
Time
  • Can conservation of Energy be violated for short
    times ?t?  No -- but which energy state a
    particle is in can remain unknown.  
  •  
  • More on this when virtual particles are explored.
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