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
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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
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.