Uncertainty Principle II: Circumventions

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Uncertainty Principle II: Circumventions. 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 Michigan Tech course PH4999

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Uncertainty Principle II:Circumventions

by

Robert Nemiroff

Michigan Technological University

• 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
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.

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?

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.

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)?

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.

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.

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.