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Quantum Darwinism

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i ℏ d d t | Ψ ⟩ = H ^ | Ψ ⟩ {\displaystyle i\hbar {\frac {d}{dt}}|\Psi \rangle ={\hat {H}}|\Psi \rangle } Schrödinger equation
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Quantum Darwinism is a theory meant to explain the emergence of the classical world from the quantum world as due to a process of Darwinian natural selection induced by the environment interacting with the quantum system; where the many possible quantum states are selected against in favor of a stable pointer state. It was proposed in 2003 by Wojciech Zurek and a group of collaborators including Ollivier, Poulin, Paz and Blume-Kohout. The development of the theory is due to the integration of a number of Zurek's research topics pursued over the course of 25 years, including pointer states, einselection and decoherence.

A study in 2010 is claimed to provide preliminary supporting evidence of quantum Darwinism with scars of a quantum dot "becoming a family of mother-daughter states" indicating they could "stabilize into multiple pointer states"; additionally, a similar kind of scene has been suggested with perturbation-induced scarring in disordered quantum dots (see scars). However, the claimed evidence is also subject to the circularity criticism by Ruth Kastner (see Implications below). Basically, the de facto phenomenon of decoherence that underlies the claims of Quantum Darwinism may not really arise in a unitary-only dynamics. Thus, even if there is decoherence, this does not show that macroscopic pointer states naturally emerge without some form of collapse.

Implications

Along with Zurek's related theory of envariance (invariance due to quantum entanglement), quantum Darwinism seeks to explain how the classical world emerges from the quantum world and proposes to answer the quantum measurement problem, the main interpretational challenge for quantum theory. The measurement problem arises because the quantum state vector, the source of all knowledge concerning quantum systems, evolves according to the Schrödinger equation into a linear superposition of different states, predicting paradoxical situations such as "Schrödinger's cat"; situations never experienced in our classical world. Quantum theory has traditionally treated this problem as being resolved by a non-unitary transformation of the state vector at the time of measurement into a definite state. It provides an extremely accurate means of predicting the value of the definite state that will be measured in the form of a probability for each possible measurement value. The physical nature of the transition from the quantum superposition of states to the definite classical state measured is not explained by the traditional theory but is usually assumed as an axiom and was at the basis of the debate between Niels Bohr and Albert Einstein concerning the completeness of quantum theory.

Quantum Darwinism seeks to explain the transition of quantum systems from the vast potentiality of superposed states to the greatly reduced set of pointer states as a selection process, einselection, imposed on the quantum system through its continuous interactions with the environment. All quantum interactions, including measurements, but much more typically interactions with the environment such as with the sea of photons in which all quantum systems are immersed, lead to decoherence or the manifestation of the quantum system in a particular basis dictated by the nature of the interaction in which the quantum system is involved. In the case of interactions with its environment Zurek and his collaborators have shown that a preferred basis into which a quantum system will decohere is the pointer basis underlying predictable classical states. It is in this sense that the pointer states of classical reality are selected from quantum reality and exist in the macroscopic realm in a state able to undergo further evolution. However, the 'einselection' program depends on assuming a particular division of the universal quantum state into 'system' + 'environment', with the different degrees of freedom of the environment posited as having mutually random phases. This phase randomness does not arise from within the quantum state of the universe on its own, and Ruth Kastner has pointed out that this limits the explanatory power of the Quantum Darwinism program. Zurek replies to Kastner's criticism in Classical selection and quantum Darwinism.

As a quantum system's interactions with its environment results in the recording of many redundant copies of information regarding its pointer states, this information is available to numerous observers able to achieve consensual agreement concerning their information of the quantum state. This aspect of einselection, called by Zurek 'Environment as a Witness', results in the potential for objective knowledge.

Darwinian significance

Perhaps of equal significance to the light this theory shines on quantum explanations is its identification of a Darwinian process operating as the selective mechanism establishing our classical reality. As numerous researchers have made clear any system employing a Darwinian process will evolve. As argued by the thesis of Universal Darwinism, Darwinian processes are not confined to biology but are all following the simple Darwinian algorithm:

  1. Reproduction/Heredity; the ability to make copies and thereby produce descendants.
  2. Selection; A process that preferentially selects one trait over another trait, leading to one trait being more numerous after sufficient generations.
  3. Variation; differences in heritable traits that affect "Fitness" or the ability to survive and reproduce leading to differential survival.

Quantum Darwinism appears to conform to this algorithm and thus is aptly named:

  1. Numerous copies are made of pointer states
  2. Successive interactions between pointer states and their environment reveal them to evolve and those states to survive which conform to the predictions of classical physics within the macroscopic world. This happens in a continuous, predictable manner; that is descendants inherit many of their traits from ancestor states.
  3. The analogy to the Variation principle of "simple Darwinism" does not exist since the Pointer states do not mutate and the selection by the environment is among the pointer states preferred by the environment (e.g. location states).

From this view quantum Darwinism provides a Darwinian explanation at the basis of our reality, explaining the unfolding or evolution of our classical macroscopic world.

Notes

  1. Zurek, Wojciech Hubert (March 2009). "Quantum Darwinism". Nature Physics. 5 (3): 181–188. arXiv:0903.5082. Bibcode:2009NatPh...5..181Z. doi:10.1038/nphys1202. ISSN 1745-2481. S2CID 119205282.
  2. ^ Zurek, Wojciech Hubert (2003). "Decoherence, einselection, and the quantum origins of the classical" (PDF). Reviews of Modern Physics. 75 (3): 715–775. arXiv:quant-ph/0105127. Bibcode:2003RvMP...75..715Z. doi:10.1103/RevModPhys.75.715. S2CID 14759237. Archived from the original (PDF) on February 21, 2009. Retrieved 2008-08-05.
  3. Burke, A. M.; Akis, R.; Day, T. E.; Speyer, Gil; Ferry, D. K.; Bennett, B. R. (2010). "Periodic Scarred States in Open Quantum Dots as Evidence of Quantum Darwinism". Physical Review Letters. 104 (17): 176801. Bibcode:2010PhRvL.104q6801B. doi:10.1103/PhysRevLett.104.176801. PMID 20482124.
  4. Keski-Rahkonen, J.; Ruhanen, A.; Heller, E. J.; Räsänen, E. (2019-11-21). "Quantum Lissajous Scars". Physical Review Letters. 123 (21): 214101. arXiv:1911.09729. Bibcode:2019PhRvL.123u4101K. doi:10.1103/PhysRevLett.123.214101. PMID 31809168. S2CID 208248295.
  5. Luukko, Perttu J. J.; Drury, Byron; Klales, Anna; Kaplan, Lev; Heller, Eric J.; Räsänen, Esa (2016-11-28). "Strong quantum scarring by local impurities". Scientific Reports. 6 (1): 37656. arXiv:1511.04198. Bibcode:2016NatSR...637656L. doi:10.1038/srep37656. ISSN 2045-2322. PMC 5124902. PMID 27892510.
  6. Keski-Rahkonen, J.; Luukko, P. J. J.; Kaplan, L.; Heller, E. J.; Räsänen, E. (2017-09-20). "Controllable quantum scars in semiconductor quantum dots". Physical Review B. 96 (9): 094204. arXiv:1710.00585. Bibcode:2017PhRvB..96i4204K. doi:10.1103/PhysRevB.96.094204. S2CID 119083672.
  7. Keski-Rahkonen, J; Luukko, P J J; Åberg, S; Räsänen, E (2019-01-21). "Effects of scarring on quantum chaos in disordered quantum wells". Journal of Physics: Condensed Matter. 31 (10): 105301. arXiv:1806.02598. Bibcode:2019JPCM...31j5301K. doi:10.1088/1361-648x/aaf9fb. ISSN 0953-8984. PMID 30566927. S2CID 51693305.
  8. Keski-Rahkonen, Joonas (2020). Quantum Chaos in Disordered Two-Dimensional Nanostructures. Tampere University. ISBN 978-952-03-1699-0.
  9. Kastner, Ruth E. (2014). "'Einselection' of pointer observables: The new H-theorem?". Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics. 48: 56–58. arXiv:1406.4126. Bibcode:2014SHPMP..48...56K. doi:10.1016/j.shpsb.2014.06.004. S2CID 20719455.
  10. Zurek, Wojciech H. (2015). "Classical selection and quantum Darwinism". Physics Today. 68 (5): 56–58. Bibcode:2015PhT....68e...9Z. doi:10.1063/PT.3.2761.

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