Uncertainty Principle

Observation  Observations generally require energy interacting with matter. Light on a rulerLight on a ruler Radar on a carRadar on a car Echoes in a canyonEchoes in a canyon Touch on a surfaceTouch on a surface Voltmeter in a circuitVoltmeter in a circuit  In many cases this is scattering of EM waves.

 Direct contact creates an impulse. Change in momentum  EM waves have momentum as photons. Momentum transfer by reflection Planck’s law Impulse Moving charge reflected photon incident photon

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 only be measured in position to about one wavelength.  If momentum is transferred the target has a momentum uncertainty. Moving charge reflected photon incident photon

Uncertainty  The product of the uncertainties in position and momentum is a limit on measurement. Heisenberg Uncertainty PrincipleHeisenberg Uncertainty Principle  The relationship is based on the angular frequency. Shift by a factor of 2pShift by a factor of 2p Use constant h-bar h = h/2 Use constant h-bar h = h/2 

Stop Motion  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.

Confined Space  An atomic nucleus is m in diameter. Find the total energy in eV of an electron confined to that space.  Use hc = 1240 eV nm  x = nm  x = nm  Relativity may matter. mc 2 = MeVmc 2 = MeV  The uncertainty principle matches distance to momentum. Energy units here  Apply relativity to get total energy. Rest mass relatively small

Indeterminate  Newtonian physics is viewed as a deterministic system. Initial positions allow calculation of final statesInitial positions allow calculation of final states Knowledge of all past variables implies future knowledgeKnowledge of all past variables implies future knowledge  Quantum physics has an indeterminate element. Conjugate variables are of limited measurabilityConjugate variables are of limited measurability Impossible to have precise initial stateImpossible to have precise initial state Cannot know precise future statesCannot know precise future states next