As a follow-up to my last two posts, I note that science can be considered as an onion with many different layers with different but corresponding interpretations of reality, and to reduce systemic isolation (& associated suffering) one needs to transcend the bubble (or onion layer) that one lives, in order to see reality from various/group points of view. In this regards correspondence (& duality) are not only related to the Holographic Principle, but to all of science as discussed in the linked Wikipedia article entitled: "Correspondence principle"https://en.wikipedia.org/wiki/Correspondence_principle
Extract: "In physics, the correspondence principle states that the behavior of systems described by the theory of quantum mechanics (or by the old quantum theory) reproduces classical physics in the limit of large quantum numbers. In other words, it says that for large orbits and for large energies, quantum calculations must agree with classical calculations
The principle was formulated by Niels Bohr in 1920, though he had previously made use of it as early as 1913 in developing his model of the atom.
The term is also used more generally, to represent the idea that a new theory should reproduce the results of older well-established theories (which become limiting cases) in those domains where the old theories work.
Classical quantities appear in quantum mechanics in the form of expected values of observables, and as such the Ehrenfest theorem (which predicts the time evolution of the expected values) lends support to the correspondence principle.
Related recent references on the topic of the importance of understanding correspondence (w.r.t. transcending the bubbles that we all live in), include the following:
Slava Emelyanov (2017), "Holography versus correspondence principle: Eternal Schwarzschild–anti–de Sitter geometry", Phys. Rev. D 95, 064044, DOI:https://doi.org/10.1103/PhysRevD.95.064044https://journals.aps.org/prd/abstract/10.1103/PhysRevD.95.064044
Abstract: "It is shown that the correspondence principle and the holographic principle are incompatible in the background of an eternal Schwarzschild–anti–de Sitter geometry. The argument is based on the observation that algebraic structures of local quantum field and conformal field theory (CFT) operators are not equivalent. This implies, in particular, that the bulk CFT must be singular near the black-hole horizon. A CFT Hilbert space representation is elaborated which may correspond to the AdS black hole in the dual theory."
Qian Wang and H. T. Quan (2017), "Understanding quantum work in a quantum many-body system", Phys. Rev. E 95, 032113; DOI:https://doi.org/10.1103/PhysRevE.95.032113https://journals.aps.org/pre/abstract/10.1103/PhysRevE.95.032113
Abstract: "Based on previous studies in a single-particle system in both the integrable [Jarzynski, Quan, and Rahav, Phys. Rev. X 5, 031038 (2015)] and the chaotic systems [Zhu, Gong, Wu, and Quan, Phys. Rev. E 93, 062108 (2016)], we study the correspondence principle between quantum and classical work distributions in a quantum many-body system. Even though the interaction and the indistinguishability of identical particles increase the complexity of the system, we find that for a quantum many-body system the quantum work distribution still converges to its classical counterpart in the semiclassical limit. Our results imply that there exists a correspondence principle between quantum and classical work distributions in an interacting quantum many-body system, especially in the large particle number limit, and further justify the definition of quantum work via two-point energy measurements in quantum many-body systems."
Hyunseok Jeong, Youngrong Lim, and M. S. Kim. "Coarsening Measurement References and the Quantum-to-Classical Transition." Physical Review Letters, DOI: 10.1103/PhysRevLett.112.010402 https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.010402
Abstract: "We investigate the role of inefficiency in quantum measurements in the quantum-to-classical transition, and consistently observe the quantum-to-classical transition by coarsening the references of the measurements (e.g., when and where to measure). Our result suggests that the definition of measurement precision in quantum theory should include the degree of the observer’s ability to precisely control the measurement references."
See also the linked article entitled: "Quantum-to-classical transition may be explained by fuzziness of measurement references"https://phys.org/news/2014-01-quantum-to-classical-transition-fuzziness.html
Extract: "The quantum and classical worlds are clearly very different, but how a physical system transitions between them is much less clear. The most well-known attempt to explain the quantum-to-classical transition is decoherence, which is the idea that interactions with the environment destroy quantum coherence, causing a quantum system to become classical.
But in more recent years, physicists have been investigating alternative explanations based on an observer's limited ability to control the precision of the measurements made on a system. The idea is that a system that appears to exhibit quantum behavior when observed with very precise measurements will appear to behave classically if the measurements are too coarse or fuzzy. In such a scenario, the coarsening of measurements forces the quantum-to-classical transition.
The problem is, fuzziness in measurements does not always result in the quantum-to-classical transition, and physicists aren't sure what exact conditions of the measurement process are necessary to definitively force the quantum-to-classical transition.
In a new study published in Physical Review Letters, physicists Hyunseok Jeong and Youngrong Lim at Seoul National University in Seoul, Korea, and M. S. Kim at Imperial College London in the UK, have proposed an explanation.
They explain that a complete measurement process is composed of two parts: one part is to set and control a measurement reference (such as timing or angle), and the other is the final detection. All of the previous studies have focused on coarsening the resolution of the final detection.
Here, the physicists looked at both parts of the measurement process and found that their coarsening leads to completely different outcomes. Their main result is that coarsening the measurement reference always forces the quantum-to-classical transition, while coarsening the final detection does not. This is because increasing the "macroscopicity" of the system, such as by increasing the number of photons in an entangled photon state, can make up for the coarseness of the final detection, but not for the coarseness of the measurement reference."
Madhav Krishnan V, Tanmoy Biswas, Sibasish Ghosh (2017), "Coarse-graining of measurement and quantum-to-classical transition in the bipartite scenario", arXiv:1703.00502v1https://arxiv.org/abs/1703.00502
Abstract: "The connection between coarse-graining of measurement and emergence of classicality has been investigated for some time, if not well understood. Recently in (PRL 112, 010402, (2014)) it was pointed out that coarse-graining measurements can lead to non-violation of Bell-type inequalities by a state which would violate it under sharp measurements. We study here the effects of coarse-grained measurements on bipartite cat states. We show that while it is true that coarse-graining does indeed lead to non-violation of a Bell-type inequality, this is not reflected at the state level. Under such measurements the post-measurement states can be non-classical (in the quantum optical sense) and in certain cases coarse-graning can lead to an increase in this non-classicality with respect to the coarse-graining parameter. While there is no universal way to quantify non-classicality, we do so using well understood notions in quantum optics such as the negativity of the Wigner function and the singular nature of the Gluaber-Sudharshan P distribution."
Boris Sokolov, Iiro Vilja, Sabrina Maniscalco (2017), "Quantum to classical transition induced by gravitational time dilation"; or arXiv:1702.02433v2https://arxiv.org/abs/1702.02433
Abstract: "We study the loss of quantumness caused by time dilation for a Schrodinger cat state, considering also the effect of a non-asymptotic observer. We give a holistic view of the quantum to classical transition by comparing the dynamics of several nonclassicality indicators, such as the Wigner function interference fringe, the negativity of the Wigner function, the nonclassical depth, the Vogel criterion and the Klyshko criterion. Our results show that only two of these indicators depend critically on the size of the cat, namely on how macroscopic the superposition is. Finally we compare the gravitation-induced decoherence times to the typical decoherence times due to classical noise originating from the unavoidable statistical fluctuations in the characteristic parameters of the system. We show that the experimental observation of decoherence due to time dilation imposes severe limitations on the allowed levels of classical noise in the experiments."
All of such references can be combined with information science to better understand what systemic challenges AI will be facing as it approaches the technological singularity circa 2045.
Edit: The attached image is related to the importance of free will in HIOTTOE.