Weekly Papers on Quantum Foundations (7)

Authors: David FauxMayank ShahChristopher Knapp

The classical “game of life” (GOL) due to Conway is a famous mathematical game constructed as a two-dimensional cellular automaton in which each cell is either alive or dead. A set of evolutionary rules determines whether a cell dies, survives or is born at each generation based on its local environment. The game of life is interesting because complexity emerges from simple rules and mimics real life in that a cell flourishes only if the environment is “just right” producing a breadth of life-like behavior including multi-cellular lifeforms. Results are presented from a quantum adaptation of the GOL which assigns a qubit to each cell which then evolves according to modified evolutionary rules. Computer simulation reveals remarkable evolutionary complexity that is distinct from the classical GOL and which mimics aspects of quantum biological processes and holds promise for the realistic simulation of species population dynamics. Liveness emerges as a probability density with universal statistical properties dependent solely on the evolutionary rules. New species of quantum lifeform are found. One quantum lifeform is shown to act as a seed to produce children, one or more classical and/or quantum lifeforms, classical oscillators, a liveness probability density or death with outcomes highly sensitive to the initial state. We observe the emergence of chaos and scaling phenomena making the quantum game of life an exciting prospect for further exploration as a model for life-like behaviors.

Authors: Luca CurcuraciStefano BacchiAngelo Bassi

In this work we study the unitary time-evolutions of quantum systems defined on infinite-dimensional separable time-dependent Hilbert spaces. Two possible cases are considered: a quantum system defined on a stochastic interval and another one defined on a Hilbert space with stochastic integration measure (stochastic time-dependent scalar product). The formulations of the two problems and a comparison with the general theory of open quantum systems are discussed. Possible physical applications of the situations considered are analyzed.

Authors: Arkady Bolotin

As per Einstein’s design, particles are introduced into the double-slit experiment through a small hole in a plate which can either move up and down (and its momentum can be measured) or be stopped (and its position can be measured). Suppose one measures the position of the plate and this act verifies the statement that the interference pattern is observed in the experiment. However, if it is possible to think about the outcome that one would have obtained if one had measured plate’s momentum instead of its position, then it is possible to consider, together with the aforesaid statement, another statement that each particle passes through either slit of the double-slit screen. Hence, the proposition affirming the wave-like behavior and the proposition affirming the particle-like behavior might be true together, which would imply that Bohr’s complementarity principle is incorrect. The analysis of Einstein’s design and ways to refute it based on an approach that uses exclusively assignments of the truth values to experimental propositions is presented in this paper.

Wallace, David (2019) Naturalness and Emergence. [Preprint]
Swanson, Noel (2018) Can Quantum Thermodynamics Save Time? [Preprint]

The fabric of space and time is widely believed by physicists to be emergent, stitched out of quantum threadsaccording to an unknown pattern. And for 22 years, they’ve had a toy model of how emergent space-time can work: a theoretical “universe in a bottle,” as its discoverer, Juan Maldacena, has described it.

The space-time filling the region inside the bottle — a continuum that bends and undulates, producing the force called gravity — exactly maps to a network of quantum particles living on the bottle’s rigid, gravity-free surface. The interior “universe” projects from the lower-dimensional boundary system like a hologram. Maldacena’s discovery of this hologram has given physicists a working example of a quantum theory of gravity.

But that doesn’t necessarily mean the toy universe shows how space-time and gravity emerge in our universe. The bottle’s interior is a dynamic, Escheresque place called anti–de Sitter (AdS) space that is negatively curved like a saddle. Different directions on the saddle curve in opposite ways, with one direction curving up and the other curving down. The curves tend toward vertical as you move away from the center, ultimately giving AdS space its outer boundary — a surface where quantum particles can interact to create the holographic universe inside. However, in reality, we inhabit a positively curved “de Sitter (dS) space,” which resembles the surface of a sphere that’s expanding without bounds.

Ever since 1997, when Maldacena discovered the AdS/CFT correspondence — a duality between AdS space and a “conformal field theory” describing quantum interactions on that space’s boundary — physicists have sought an analogous description of space-time regions like ours that aren’t bottled up. The only “boundary” of our universe is the infinite future. But the conceptual difficulty of projecting a hologram from quantum particles living in the infinite future has long stymied efforts to describe real space-time holographically.

In the last year, though, three physicists have made progress toward a hologram of de Sitter space. Like the AdS/CFT correspondence, theirs is also a toy model, but some of the principles of its construction may extend to more realistic space-time holograms. There is “tantalizing evidence,” said Xi Dong of the University of California, Santa Barbara, who led the research, that the new model is a piece of “a unified framework for quantum gravity in de Sitter .”

Dong and co-authors Eva Silverstein of Stanford University and Gonzalo Torroba of the Bariloche Atomic Center in Argentina constructed a hologram of dS space by taking two AdS universes, cutting them, warping them and gluing their boundaries together.

The cutting is needed to deal with a problematic infinity: the fact that the boundary of AdS space is infinitely far away from its center. (Picture a ray of light traveling an infinite distance up the saddle’s curve to reach the edge.) Dong and co-authors rendered AdS space finite by chopping off the space-time region at a large radius. This created what’s known as a “Randall-Sundrum throat,” after the physicists Lisa Randall and Raman Sundrum, who devised the trick. This space is still approximated by a CFT that lives on its boundary, but the boundary is now a finite distance away.

Next, Dong and co-authors added ingredients from string theory to two of these theoretical Randall-Sundrum throats to energize them and give them positive curvature. This procedure, called “uplifting,” turned the two saddle-shaped AdS spaces into bowl-shaped dS spaces. The physicists could then do the obvious thing: “glue” the two bowls together along their rims. The CFTs describing both hemispheres become coupled with each other, forming a single quantum system that is holographically dual to the entire spherical de Sitter space.

“The resulting space-time has no boundary, but by construction it is dual to two CFTs,” Dong said. Because the equator of the de Sitter space, where the two CFTs live, is itself a de Sitter space, the construction is called the “dS/dS correspondence.”

Silverstein proposed this basic idea with three co-authors back in 2004, but new theoretical tools have enabled her, Dong and Torroba to study the dS/dS hologram in greater detail and show that it passes important consistency checks. In a paper published last summer, they calculated that the entanglement entropy — a measure of how much information is stored in the coupled CFTs living on the equator — matches the known entropy formula for the corresponding spherical region of de Sitter space.

They and other researchers are further exploring the de Sitter hologram using tools from computer science. As I described in a recent Quanta article, physicists have discovered in the last few years that the AdS/CFT correspondence works exactly like a “quantum error-correcting code” — a scheme for securely encoding information in a jittery quantum system, be it a quantum computer or a CFT. Quantum error correction may be how the emergent fabric of space-time achieves its robustness, despite being woven out of fragile quantum particles.

Dong, who was part of the team that discovered the connection between AdS/CFT and quantum error correction, said, “I believe that de Sitter holography also works as a quantum error-correcting code, and I would very much like to understand how.” There’s little hope of experimental evidence verifying that this new perspective on de Sitter space-time is correct, but according to Dong, “you instinctively know you are on the right track if the pieces start to fit together.”

Patrick Hayden, a theoretical physicist and computer scientist at Stanford who studies the AdS/CFT correspondence and its relationship to quantum error correction, said he and other experts are mulling over Dong, Silverstein and Torroba’s dS/dS model. He said it’s too soon to tell whether insights about how space-time is woven and how quantum gravity works in AdS space will carry over to a de Sitter model. “But there’s a path — something to be done,” Hayden said. “You can formulate concrete mathematical questions. I think a lot is going to happen in the next few years.”

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Authors: Aida AhmadzadeganFatemeh LaleganiRobert B. Mann

We present a new method by which, in principle, it is possible to “see in absolute darkness”, i.e., without exchanging any real quanta through quantum fields. This is possible because objects modify the mode structure of the vacuum in their vicinity. The new method probes the mode structure of the vacuum through the Unruh effect, i.e., by recording the excitation rates of quantum systems that are accelerated.

Authors: Adrian Kent (Centre for Quantum Information and Foundations, DAMTP, University of Cambridge and Perimeter Institute for Theoretical Physics)

Several versions of quantum theory assume some form of localized collapse. If measurement outcomes are indeed defined by localized collapses, then a loophole-free demonstration of Bell non-locality needs to ensure space-like separated collapses associated with the measurements of the entangled systems. This collapse locality loophole remains largely untested, with one significant exception probing Diosi’s and Penrose’s gravitationally induced collapse hypotheses. I describe here techniques that allow much stronger experimental tests. These apply to all the well known types of collapse postulate, including gravitationally induced collapse, spontaneous localization models and Wigner’s consciousness-induced collapse.

Authors: Marijn WaaijerJan van Neerven

We present an analysis of the Frauchiger–Renner Gedankenexperiment from the point of view of the relational interpretation of quantum mechanics. Our analysis indicates that the paradox obtained by Frauchiger and Renner arises from a combination of allowing self-measurement and reasoning about other agent’s knowledge in the past without validation by surviving records. A by-product of our analysis is an interaction-free detection scheme for the existence of records from the past.

Authors: Enrico Celeghini

The Paradigms introduced in philosophy of science one century ago are shown to be quite more satisfactory of that introduced by Galileo. This is particularly evident in the physics based on Hilbert Spaces and related mathematical structures that we apply in this paper to Quantum Mechanics and to Theory of Images. An exhaustive discussion, that include the algebraic analysis of the operators acting on them, exhibits that the Hilbert Spaces — that have fixed dimension — must be generalized to the Rigged Hilbert Spaces that contains right inside spaces with continuous and discrete dimensions. This is the property of Rigged Hilbert Spaces that allows a consistent formal description of the physics we are considering. Theory of Quantum Mechanics and of Images are similar and the fundamental difference between them come from the definition of measure that is outside the theory of the spaces: while in Quantum Mechanics the measure is a probabilistic action, in Images it is a classical functional.

KEYWORDS: Optics, Quantum Mechanics, Rigged Hilbert Spaces, Lie Algebras

Authors: Andrei Khrennikov

By filtering out the philosophic component we can be said that the EPR-paper was directed against the straightforward interpretation of the Heisenberg’s uncertainty principle or more generally the Bohr’s complementarity principle. The latter expresses contextuality of quantum measurements: dependence of measurement’s output on the complete experimental arrangement. However, Bell restructured the EPR-argument against complementarity to justify nonlocal theories with hidden variables of the Bohmian mechanics’ type. Then this Bell’s kind of nonlocality – {\it subquantum nonlocality} – was lifted to the level of quantum theory – up to the terminology {\it “quantum nonlocality”}. The aim of this short note is to explain that Bell’s test is simply a special {\it test of local incompatibility of quantum observables}, similar to interference experiments, e.g., the two-slit experiment.

Publication date: Available online 14 February 2019

Source: Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics

Author(s): David Wallace

Abstract

I present in detail the case for regarding black hole thermodynamics as having a statistical-mechanical explanation in exact parallel with the statistical-mechanical explanation believed to underlie the thermodynamics of other systems. (Here I presume that black holes are indeed thermodynamic systems in the fullest sense; I review the evidence for that conclusion in the prequel to this paper.) I focus on three lines of argument: (i) zero-loop and one-loop calculations in quantum general relativity understood as a quantum field theory, using the path-integral formalism; (ii) calculations in string theory of the leading-order terms, higher-derivative corrections, and quantum corrections, in the black hole entropy formula for extremal and near-extremal black holes; (iii) recovery of the qualitative and (in some cases) quantitative structure of black hole statistical mechanics via the AdS/CFT correspondence. In each case I briefly review the content of, and arguments for, the form of quantum gravity being used (effective field theory; string theory; AdS/CFT) at a (relatively) introductory level: the paper is aimed at readers with some familiarity with thermodynamics, quantum mechanics and general relativity but does not presume advanced knowledge of quantum gravity. My conclusion is that the evidence for black hole statistical mechanics is as solid as we could reasonably expect it to be in the absence of a directly-empirically-verified theory of quantum gravity.

Authors: Chandramouli ChowdhurySusmita DasSurojit DaluiBibhas Ranjan Majhi

We re-advocated the conjecture of indistinguishability between the quantum fluctuation observed from a Rindler frame and a real thermal bath, for the case of a free massless scalar field. To clarify the robustness and how far such is admissible, in this paper, we investigate the issue from two different non-inertial observers’ perspective. A detailed analysis is being done to find the observable quantities as measured by two non-inertial observers (one is Rindler and another is uniformly rotating) on the real thermal bath and Rindler frame in Minkowski spacetime. More precisely, we compare Thermal-Rindler with Rindler-Rindler and Thermal-rotating with Rindler-rotating situations. In the first model it is observed that although some of the observables are equivalent, all the components of renormalised stress-tensor are not the same. In the later model, we again find that this equivalence is not totally guaranteed. Therefore we argue that the indistinguishability between the real thermal bath and the Rindler frame may not be totally true.

Oldofredi, Andrea (2019) Some remarks on the mentalistic reformulation of the measurement problem. A reply to S. Gao. [Preprint]

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