understanding the uncertainty principle 26 th november 2012 will barnsley mike boardman nicolò...
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Understanding theUncertainty Principle
26th November 2012
Will BarnsleyMike BoardmanNicolò Forcellini
Azeem KhanLaith Meti
Paul SecularTom Varsavsky
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“ I think I can safely say that nobody understands quantum
mechanics ”
– Richard FeynmanThe Character of Physical Law (1965)
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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
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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.
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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
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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
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Heisenberg’s conclusions
• An electron has no position unless it is measured [1]
• An electron has no momentum unless it is measured [1]
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“Heisenberg’s microscope”thought experiment
Theoretically perfectmeasuring devices [2]
Gamma ray photon isscattered by electron [2]
Rejected by Bohr [1]
source: Radeksonic (Wikimedia Commons)
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Heisenberg’s measurement-disturbance relation
= 6.626 x 10-34 J s (Planck’s Constant)
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Measurement-disturbance
Generator of identical quantum systems
Position measurement followed by momentum
measurement
David Jennings (2012)
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Quantum uncertainty
Generator of identical quantum systems
Either position measured or momentumDavid Jennings (2012)
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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.
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Kennard’s uncertainty relation
= (reduced Planck constant)
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𝜎 𝑥
𝜎 𝑝
Reciprocal relationship
𝜎 𝑥𝜎𝑝 ≥ħ2
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The Uncertainty Principle
∆ 𝑥 ∆𝑝 h
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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.
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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]
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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)
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“ 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
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Conclusion
• “Information gain implies disturbance”– David Jennings (2012)
• Observables have an ‘inherent’ uncertainty, which is not due to measurement.
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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)