Understanding theUncertainty Principle

26th November 2012

Will BarnsleyMike BoardmanNicolò Forcellini

Azeem KhanLaith Meti

Paul SecularTom Varsavsky

“ I think I can safely say that nobody understands quantum

mechanics ”

– Richard FeynmanThe Character of Physical Law (1965)

The Uncertainty Principle

• There is an inherent uncertainty in position and momentum.

• This can be explained by the fact that measuring one must affect the other.

û

ü

Key concepts

3. These are not the same thing.

1. ‘Disturbance’ caused by measurements.

2. An ‘inherent uncertainty’ in quantum mechanics due to wave-particle duality.

German physicistand revolutionary

5th December, 1901 – 1st February, 1976(aged 74)

1932 Nobel Prize“for the creation of quantum mechanics”

Werner Karl Heisenberg

source: http://www.nobelprize.org/nobel_prizes/physics/laureates/1932/heisenberg.html

photo: Jochen Heisenberghttp://www.edge.org/3rd_culture/heisenberg07/heisenberg07_index.html

Cloud chamber experiment

Followed on from Einstein’s 1916 work on spontaneous emission [1]

Heisenberg observed that electrons had discontinuous tracks. He wanted to find out why… [1] photo: Dmitry Skobeltzyn (1927)

http://www.scienceclarified.com/Co-Di/Cosmic-Ray.html

Heisenberg’s conclusions

• An electron has no position unless it is measured [1]

• An electron has no momentum unless it is measured [1]

“Heisenberg’s microscope”thought experiment

Theoretically perfectmeasuring devices [2]

Gamma ray photon isscattered by electron [2]

Rejected by Bohr [1]

source: Radeksonic (Wikimedia Commons)

Heisenberg’s measurement-disturbance relation

= 6.626 x 10-34 J s (Planck’s Constant)

Measurement-disturbance

Generator of identical quantum systems

Position measurement followed by momentum

measurement

David Jennings (2012)

Quantum uncertainty

Generator of identical quantum systems

Either position measured or momentumDavid Jennings (2012)

Standard deviation as uncertainty

x pNo.

of m

easu

rem

ents

No.

of m

easu

rem

ents

The Uncertainty Principle says it is impossible to have two infinitely narrow peaks – even with perfect measuring devices.

Kennard’s uncertainty relation

= (reduced Planck constant)

𝜎 𝑥

𝜎 𝑝

Reciprocal relationship

𝜎 𝑥𝜎𝑝 ≥ħ2

The Uncertainty Principle

∆ 𝑥 ∆𝑝 h

Quantum uncertainty

Heisenberg explained the inherent uncertainty of quantum mechanics in terms of measurement-disturbance [2]

This is incorrect, yet many physicists and text books continue to confuse these two concepts.

Timeline1927 – Heisenberg publishes microscope thought experiment [2]

1927 – Kennard derives position-momentum uncertainty relation from the postulates of quantum mechanics [3]

1929 - 1930 – Robertson & Schrӧdinger generalise the relation to any two non-commuting observables [4][5]

2003 – Ozawa publishes a relation combining quantum uncertainty with the measurement-disturbance effect

2012 – Teams in Japan & Toronto verify Ozawa’s relation, and demonstrate a violation of Heisenberg’s measurement-disturbance formulation [6][7]

Masanao Ozawa

photo: http://mathsoc.jp/en/pamph/2009/spring_autumn_pr.html

“Universally valid reformulation of the Heisenberg uncertainty principle on noise and disturbance in measurement”Physical Review A 67 (2003)

“ The quantum world is still full of uncertainty, but at least our attempts to look at it don’t

have to add as much uncertainty as we used to

think! ”

– Lee Rozema (2012)http://media.utoronto.ca/media-releases/arts/university-of-toronto-scientists-cast-doubt-on-renowned-uncertainty-principle/

Experimental confirmation

Conclusion

• “Information gain implies disturbance”– David Jennings (2012)

• Observables have an ‘inherent’ uncertainty, which is not due to measurement.

References[1] Kumar, Quantum. Icon Books (2008)

[2] Heisenberg, The Actual Content of Quantum Theoretical Kinematics & Mechanics (1927)

[3] Furuta, One Thing Is Certain: Heisenberg's Uncertainty Principle Is Not Dead. Scientific American (2012)

[4] Robertson, The Uncertainty Principle. Physical Review 34 (1929)

[5] Schrӧdinger, About Heisenberg Uncertainty Relation (1930)

[6] Erhart, et al. Experimental demonstration of a universally valid error–disturbance uncertainty relation in spin measurements. Nature Physics 8 (2012)

[7] Rozema, et al. Violation of Heisenberg’s Measurement-Disturbance Relationship by Weak Measurements. Physical Review Letters 109 (2012)