Uncertainty Principle II: Circumventions

1. Uncertainty Principle II:Circumventions 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 (ΔE t > 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 Principle:Energy versus Time ΔE Δt > h / 4 π Not exactly like "regular" uncertainty principle: time is not like position.  Δt really refers to the measured lifetime of a given state with energy E known to accuracy ΔE. Effective definition: A state that exists for only a time Δt cannot have an energy better defined than ΔE.

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