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.