Download Uncertainty Principle

Uncertainty Principle
Observation
 Observations generally
require energy interacting
with matter.
•
•
•
•
•
Light on a ruler
Radar on a car
Echoes in a canyon
Touch on a surface
Voltmeter in a circuit
 In many cases this is
scattering of EM waves.
Impulse
p  Ft
 Direct contact creates an
impulse.
• Change in momentum
 EM waves have momentum as
photons.
p 
h

reflected photon
incident photon
Moving charge
• Momentum transfer by
reflection
• Planck’s law
Atomic Scale
 At the atomic scale the
momentum of a photon may be
comparable to the momentum
of a particle.
 The photon as a wave can
p 
only be measured in position
to about one wavelength.
h

reflected photon
 If momentum is transferred the
target has a momentum
uncertainty.
x  
incident photon
Moving charge
Uncertainty
 The product of the uncertainties in position and
momentum is a limit on measurement.
• Heisenberg Uncertainty Principle
 The relationship is based on the angular frequency.
• Shift by a factor of 2p
• Use constant h-bar h = h/2p

 x p 
2
Stop Motion

p 
2 x

x 
2 p
 The uncertainty principle says
that if the position is perfectly
known the momentum is
unknown.
 If the momentum is perfectly
known then the position is
unknown.
 The two variables are
interrelated.
• Conjugate variables
Harold Edgerton (1964)
Freezing Time
 The energy of a wave is
related to its frequency.
 Energy and frequency
complement like momentum
and wavelength.
 The uncertainty principle
applies to energy and time as
well.
E  hf
E
 p  h
f
E t 

2
Confined Space
 An atomic nucleus is 10-14 m in
diameter. Find the total energy
in eV of an electron confined to
that space.
 Use hc = 1240 eV nm
c  197 eV nm
•
x =
 The uncertainty principle
matches distance to
momentum.
• Energy units here
c
pc 
 9.85 MeV
2x
 Apply relativity to get total
10-5
nm
energy.
• Rest mass relatively small
 Relativity may matter.
• mc2 = 0.511 MeV
E  (mc2 ) 2  ( pc) 2  9.86 MeV
Indeterminate
 Newtonian physics is viewed as a deterministic system.
• Initial positions allow calculation of final states
• Knowledge of all past variables implies future knowledge
 Quantum physics has an indeterminate element.
• Conjugate variables are of limited measurability
• Impossible to have precise initial state
• Cannot know precise future states
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