Toy Models of Top Down Causation
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A New Kind of Science; Stephen Wolfram, Wolfram Media, Inc., 2002
A New Kind of Science; Stephen Wolfram, Wolfram Media, Inc., 2002. Almost twenty years ago, I heard Stephen Wolfram speak at a Gordon Confer- ence about cellular automata (CA) and how they can be used to model seashell patterns. He had recently made a splash with a number of important papers applying CA to a variety of physical and biological systems. His early work on CA focused on a classification of the behavior of simple one-dimensional sys- tems and he published some interesting papers suggesting that CA fall into four different classes. This was original work but from a mathematical point of view, hardly rigorous. What he was essentially claiming was that even if one adds more layers of complexity to the simple rules, one does not gain anything be- yond these four simples types of behavior (which I will describe below). After a two decade hiatus from science (during which he founded Wolfram Science, the makers of Mathematica), Wolfram has self-published his magnum opus A New Kind of Science which continues along those lines of thinking. The book itself is beautiful to look at with almost a thousand pictures, 850 pages of text and over 300 pages of detailed notes. Indeed, one might suggest that the main text is for the general public while the notes (which exceed the text in total words) are aimed at a more technical audience. The book has an associated web site complete with a glowing blurb from the publisher, quotes from the media and an interview with himself to answer questions about the book. -
The Problem of Distributed Consensus: a Survey Stephen Wolfram*
The Problem of Distributed Consensus: A Survey Stephen Wolfram* A survey is given of approaches to the problem of distributed consensus, focusing particularly on methods based on cellular automata and related systems. A variety of new results are given, as well as a history of the field and an extensive bibliography. Distributed consensus is of current relevance in a new generation of blockchain-related systems. In preparation for a conference entitled “Distributed Consensus with Cellular Automata and Related Systems” that we’re organizing with NKN (= “New Kind of Network”) I decided to explore the problem of distributed consensus using methods from A New Kind of Science (yes, NKN “rhymes” with NKS) as well as from the Wolfram Physics Project. A Simple Example Consider a collection of “nodes”, each one of two possible colors. We want to determine the majority or “consensus” color of the nodes, i.e. which color is the more common among the nodes. A version of this document with immediately executable code is available at writings.stephenwolfram.com/2021/05/the-problem-of-distributed-consensus Originally published May 17, 2021 *Email: [email protected] 2 | Stephen Wolfram One obvious method to find this “majority” color is just sequentially to visit each node, and tally up all the colors. But it’s potentially much more efficient if we can use a distributed algorithm, where we’re running computations in parallel across the various nodes. One possible algorithm works as follows. First connect each node to some number of neighbors. For now, we’ll just pick the neighbors according to the spatial layout of the nodes: The algorithm works in a sequence of steps, at each step updating the color of each node to be whatever the “majority color” of its neighbors is. -
The Case for Quantum Key Distribution
The Case for Quantum Key Distribution Douglas Stebila1, Michele Mosca2,3,4, and Norbert Lütkenhaus2,4,5 1 Information Security Institute, Queensland University of Technology, Brisbane, Australia 2 Institute for Quantum Computing, University of Waterloo 3 Dept. of Combinatorics & Optimization, University of Waterloo 4 Perimeter Institute for Theoretical Physics 5 Dept. of Physics & Astronomy, University of Waterloo Waterloo, Ontario, Canada Email: [email protected], [email protected], [email protected] December 2, 2009 Abstract Quantum key distribution (QKD) promises secure key agreement by using quantum mechanical systems. We argue that QKD will be an important part of future cryptographic infrastructures. It can provide long-term confidentiality for encrypted information without reliance on computational assumptions. Although QKD still requires authentication to prevent man-in-the-middle attacks, it can make use of either information-theoretically secure symmetric key authentication or computationally secure public key authentication: even when using public key authentication, we argue that QKD still offers stronger security than classical key agreement. 1 Introduction Since its discovery, the field of quantum cryptography — and in particular, quantum key distribution (QKD) — has garnered widespread technical and popular interest. The promise of “unconditional security” has brought public interest, but the often unbridled optimism expressed for this field has also spawned criticism and analysis [Sch03, PPS04, Sch07, Sch08]. QKD is a new tool in the cryptographer’s toolbox: it allows for secure key agreement over an untrusted channel where the output key is entirely independent from any input value, a task that is impossible using classical1 cryptography. QKD does not eliminate the need for other cryptographic primitives, such as authentication, but it can be used to build systems with new security properties. -
The Parallel Universes Interpretation of Cosmology
Cosmology, the Many Universes Interpretation of Quantum Mechanics and Immortality N H E PRINCE [email protected] July 1, 2016 Abstract Observational evidence suggests that the universe is infinite, geometrically flat, homogeneous and isotropic on large scales. Hence we should expect to find large numbers of identical copies of any object consistent with the laws of physics including conscious identities like people. Under suitable notions of continuity of identity, This would imply that immortality of these conscious identities is a consequence of functionalism. I argue that the same conclusion can be drawn using an Everett Deutsch interpretation of quantum mechanics. I also argue why this is the correct interpretation. Lewis’s “terrifying corollary” is reviewed and I discuss how Bostrom’s simulation argument, if correct, might mitigate our futures. 1 Introduction It has been referred to as “quantum physics dirty little secret” [1, p6] – perhaps because to publicise it might lead those people, who little understand it, to develop suicidal tendencies in the hope that they might get into a better universe – This is definitely not a good idea! We’ll look at this little secret in more detail later. But in order to do this we will need to develop some background. First it must be said that the word “worlds” is often used interchangeably for “universes” in the literature. It is not used to mean planets like our own parochial world. Also, the idea of an observation or experiment translates into ordinary language as “looking”, “listening”, “touching” etc. as well as for more technical approaches such as using Charge Coupled Devices to detect individual photons of light in astronomy or interferometry. -
A New Kind of Science: a 15-Year View
A New Kind of Science: A 15-Year View Stephen Wolfram Founder and CEO Wolfram Research, Inc. [email protected] Starting now, in celebration of its 15th anniversary, A New Kind of Science will be freely available in its entirety, with high-resolution images, on the web or for download. It’s now 15 years since I published my book A New Kind of Science — more than 25 since I started writing it, and more than 35 since I started working towards it. But with every passing year I feel I under- stand more about what the book is really about—and why it’s impor- tant. I wrote the book, as its title suggests, to contribute to the progress of science. But as the years have gone by, I’ve realized that the core of what’s in the book actually goes far beyond science—into many areas that will be increasingly important in defining our whole future. So, viewed from a distance of 15 years, what is the book really about? At its core, it’s about something profoundly abstract: the the- ory of all possible theories, or the universe of all possible universes. But for me one of the achievements of the book is the realization that one can explore such fundamental things concretely—by doing actual experiments in the computational universe of possible programs. And https://doi.org/10.25088/ComplexSystems.26.3.197 198 S. Wolfram in the end the book is full of what might at first seem like quite alien pictures made just by running very simple such programs. -
Consciousness and the Collapse of the Wave Function∗
Consciousness and the Collapse of the Wave Function∗ David J. Chalmers† and Kelvin J. McQueen‡ †New York University ‡Chapman University May 7, 2021 Abstract Does consciousness collapse the quantum wave function? This idea was taken seriously by John von Neumann and Eugene Wigner but is now widely dismissed. We develop the idea by combining a mathematical theory of consciousness (integrated information theory) with an account of quantum collapse dynamics (continuous spontaneous localization). Simple versions of the theory are falsified by the quantum Zeno effect, but more complex versions remain compatible with empirical evidence. In principle, versions of the theory can be tested by experiments with quantum com- puters. The upshot is not that consciousness-collapse interpretations are clearly correct, but that there is a research program here worth exploring. Keywords: wave function collapse, consciousness, integrated information theory, continuous spontaneous localization ∗Forthcoming in (S. Gao, ed.) Consciousness and Quantum Mechanics (Oxford University arXiv:2105.02314v1 [quant-ph] 5 May 2021 Press). Authors are listed in alphabetical order and contributed equally. We owe thanks to audiences starting in 2013 at Amsterdam, ANU, Cambridge, Chapman, CUNY, Geneva, G¨ottingen,Helsinki, Mississippi, Monash, NYU, Oslo, Oxford, Rio, Tucson, and Utrecht. These earlier presentations have occasionally been cited, so we have made some of them available at consc.net/qm. For feedback on earlier versions, thanks to Jim Holt, Adrian Kent, Kobi Kremnizer, Oystein Linnebo, and Trevor Teitel. We are grateful to Maaneli Derakhshani and Philip Pearle for their help with the mathematics of collapse models, and especially to Johannes Kleiner, who coauthored section 5 on quantum integrated information theory. -
Arxiv:1806.01736V3 [Quant-Ph] 17 Dec 2018 State Originally Received
Unconstrained Summoning for relativistic quantum information processing Adrian Kent Centre for Quantum Information and Foundations, DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA, U.K. and Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, ON N2L 2Y5, Canada. (Dated: December 18, 2018) We define a summoning task to require propagating an unknown quantum state to a point in space-time belonging to a set determined by classical inputs at points in space-time. We consider the classical analogue, in which a known classical state must be returned at precisely one allowed point. We show that, when the inputs are unconstrained, any summoning task that is possible in the classical case is also possible in the quantum case. INTRODUCTION In the not necessarily distant future, many or most significant economic decisions may depend on algorithms that process information arriving around the world as efficiently and quickly as possible, given light speed signalling constraints. Such algorithms will need to decide not only whether to make a trade, but also when and where. Quantum money enables efficient transactions, by allowing a delocalized quantum money token effectively to be “summoned” to a given space-time point as a result of information distributed through space-time. There are also alternative technological solutions [1] in the form of token schemes that do not require long term quantum state storage and in some embodiments are based entirely on classical communication. This paper defines types of summoning task that naturally arise in relativistic economies, and shows that for an important and natural class of these tasks the two technologies have the same functionality. -
Testing Causal Quantum Theory
Testing Causal Quantum Theory Adrian Kent∗ Centre for Quantum Information and Foundations, DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA, United Kingdom and Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, ON N2L 2Y5, Canada. Causal quantum theory assumes that measurements or collapses are well-defined physical pro- cesses, localised in space-time, and never give perfectly reliable outcomes and that the outcome of one measurement only influences the outcomes of others within its future light cone. Although the theory has unusual properties, it is not immediately evident that it is inconsistent with experiment to date. I discuss its implications and experimental tests. INTRODUCTION There are fairly compelling theoretical and experimental reasons [1{17] to believe that nature violates local causality and that local hidden variable theories are incorrect. However, while loopholes remain, the case is not quite conclusive. In particular, the collapse locality loophole [18] remains largely untested. Moreover, causal quantum theory [18] is a theoretically interesting example of a local hidden variable theory that remains consistent with Bell experiments to date by exploiting this loophole. Causal quantum theory assumes that measurements or collapses are well-defined physical processes, localised in space-time, and never give perfectly reliable outcomes. Unlike standard quantum theory, it also assumes that mea- surement outcomes respect a strong form of Minkowski or Einstein causality, in that the outcome of one measurement only affects the probability distributions for the outcomes of other measurements within its future light cone. This gives it very peculiar properties, which evoke the suspicion that it must already be excluded by experiments other than Bell experiments and/or cosmological observations. -
Or, How to Share a Quantum Secret in Spacetime
Localizing and excluding quantum informa- tion; or, how to share a quantum secret in spacetime Patrick Hayden1 and Alex May2 1Stanford University 2The University of British Columbia October 15, 2019 When can quantum information be localized to each of a collection of spacetime regions, while also excluded from another collection of regions? We answer this question by defining and analyzing the localize-exclude task, in which a quantum system must be localized to a collection of authorized regions while also being excluded from a set of unauthorized regions. This task is a spacetime analogue of quantum secret sharing, with authorized and unauthorized regions replacing authorized and unauthorized sets of parties. Our analysis yields the first quantum secret sharing scheme for arbitrary ac- cess structures for which the number of qubits required scales polynomially with the number of authorized sets. We also study a second related task called state-assembly, in which shares of a quantum system are requested at sets of spacetime points. We fully characterize the conditions under which both the localize-exclude and state-assembly tasks can be achieved, and give explicit protocols. Finally, we propose a cryptographic application of these tasks which we call party-independent transfer. Patrick Hayden: [email protected] arXiv:1806.04154v4 [quant-ph] 14 Oct 2019 Alex May: [email protected] Accepted in Quantum 2019-07-02, click title to verify 1 Contents 1 Introduction2 2 Localizing and excluding quantum information4 2.1 Localizing quantum information to many regions . 4 2.2 Localizing and excluding quantum information . 10 3 State-assembly 19 3.1 State-assembly with authorized regions . -
Depictions of Quantum Reality in Kent's Interpretation of Quantum
Depictions of Quantum Reality in Kent's Interpretation of Quantum Theory Brendan Marsh∗ Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA, U.K. At present, quantum theory leaves unsettled which quantities ontologically, physically exist in a quantum system. Do observables such as energy and position have meaningful values only at the precise moment of measurement, as in the Copenhagen interpretation? Or is position always definite and guided by the wave function, as in de Broglie-Bohm pilot wave theory? In the language of Bell, what are the \beables" of quantum theory and what values may they take in space and time? This is the quantum reality problem. A definitive answer requires not just describing which physical quantities exist in a quantum system, but describing what configurations of those quantities in space and time are allowed, and with what probability those configurations occur. Adrian Kent sets out a new vision of quantum theory along these lines. His interpretation supplements quantum theory to infer the value of physical quantities in spacetime from the asymptotic late-time behavior of the quantum system. In doing so, a Lorentz-covariant and single-world solution to the quantum reality problem is achieved. In this paper, the framework of Kent's interpretation is presented from the ground up. After a broad overview, a derivation of the generalized Aharonov-Bergmann- Lebowitz (ABL) rule is provided before applying Kent's interpretation to toy model systems, in both relativistic and non-relativistic settings. By adding figures and discussion, a broad introduction is provided to Kent's proposed interpretation of quantum theory. -
Mistrustful Quantum Cryptography
Mistrustful Quantum Cryptography Adrian Kent Centre for Quantum Computation DAMTP, University of Cambridge Two lectures for MIT Independent Activities Period. 2pm on 28.01.03 and 29.01.0; Sponsored by the CMI Beyond key distribution: mistrustful cryptography • Life requires controlled information exchange between not necessarily trusting parties. (Some cynics might say life is controlled information exchange between not necessarily trusting parties.) • For example: trustable electoral systems that allow secret ballot, secure auctions, tax collection that preserves privacy, remote authentication to a computer, decisions on joint corporate (or other) ventures, job interviews, “helping the police with their enquiries”, … • Cryptography can help, at least with some of these, by regulating the information flow – instead of trusting the other party, you need only trust the cryptosystem, which if well designed is provably secure modulo reasonable assumptions. Mistrustful cryptography: often referred to as “Post Cold War” cryptography • Cold War cryptography: your aim is to communicate with your agents behind enemy lines. • You (let’s hope) trust your agents, or at any rate trust them enough to want the message to get to them: the worry is about enemy eavesdroppers. • Whereas in the post Cold War world… Mistrustful cryptography and physics • Classical cryptographers have identified key “primitives” – elementary tasks that can be used as building blocks for many mistrustful cryptographic purposes (and are often very useful in their own right). • Given the example of key distribution, where quantum information allows classically unattainable security, we naturally want to understand which mistrustful tasks quantum information can be useful for. We don’t! (Mostly. Yet.) • More generally, we want to know what physics can do for cryptography. -
View Curriculum Vitae
PETER J. LEWIS Curriculum Vitae July 19, 2019 Department of Philosophy, Dartmouth College 6035 Thornton Hall, 19 College St Hanover, NH 03755 Tel: 603-646-2308 Email: [email protected] Web page: https://sites.google.com/site/peterlewisphilosophy/ EDUCATION: Ph.D. in philosophy, University of California, Irvine, March 1996. M.A. in philosophy, University of California, Irvine, June 1992. B.A. in physics, Brasenose College, Oxford, June 1988. EMPLOYMENT: Professor, Dartmouth College, July 2017 to present. Associate Professor, University of Miami, August 2007 to July 2017 Assistant Professor, University of Miami, August 2001 to August 2007. Visiting Lecturer, University of Miami, August 2000 to August 2001. Visiting Lecturer and Honorary Visiting Assistant Professor, University of Hong Kong, December 1998 to August 2000. Assistant Professor, Texas Tech University, September 1998 to August 2000. Visiting Assistant Professor, Texas Tech University, May 1997 to May 1998. Visiting Instructor, Texas Tech University, September 1995 to May 1997. Teaching Associate/Assistant, University of California, Irvine, September 1990 to June 1995. AREAS OF SPECIALIZATION: Philosophy of Physics, Philosophy of Science. AREAS OF COMPETENCE: Epistemology, Metaphysics. BOOKS: Quantum Ontology: A Guide to the Metaphysics of Quantum Mechanics. Oxford University Press (2016). REFEREED ARTICLES: (with Don Fallis), “Accuracy, conditionalization, and probabilism”, forthcoming in Synthese, doi: 10.1007/s11229-019-02298-3. “Against ‘experience’”, forthcoming in S. Gao (ed.), Quantum Mechanics and Consciousness. Oxford University Press. “Bohmian philosophy of mind?” forthcoming in J. Acacio de Barros and C. Montemayor (eds.), Quanta and Mind: Essays on the Connection between Quantum Mechanics and Consciousness. Springer. “Quantum Mechanics and its (Dis)Contents”, forthcoming in J.