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Transcript of Understanding the Uncertainty Principle 26 th November 2012 Will Barnsley Mike Boardman Nicolò...
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)