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The Andrew Wiles Building: a Short History Below: Charles L
Nick Woodhouse The Andrew Wiles Building: A short history Below: Charles L. Dodgson A short time in the life of the University (Lewis Carroll) aged 24 at his “The opening of this desk [Wakeling Collection] The earliest ‘mathematical institute’ in Oxford fantastic building is may have been the School of Geometry and Arithmetic in the main Quadrangle of the great news for Oxford’s Bodleian Library (completed in 1620). But it was clearly insufficient to provide space staff and students, who for everyone. In 1649, a giant of Oxford mathematics, John Wallis, was elected to the will soon be learning Savilian Chair of Geometry. As a married man, he could not hold a college fellowship and he together in a stunning had no college rooms. He had to work from rented lodgings in New College Lane. new space.” In the 19th century, lectures were mainly given in colleges, prompting Charles Dodgson Rt Hon David Willets MP (Lewis Carroll) to write a whimsical letter to Minister of State for Universities and Science the Senior Censor of Christ Church. After commenting on the unwholesome nature of lobster sauce and the accompanying nightmares it can produce, he remarked: ‘This naturally brings me on to the subject of Mathematics, and of the accommodation provided by the University for carrying on the calculations necessary in that important branch of science.’ He continued with a detailed set of specifications, not all of which have been met even now. There was no room for the “narrow strip of ground, railed off and carefully levelled, for investigating the properties of Asymptotes, and testing practically whether Parallel Lines meet or not: for this purpose it should reach, to use the expressive language of Euclid, ‘ever so far’”. -
Concerning Stephen Hawking's Claim That Philosophy Is Dead1
Filozofski vestnik | Volume XXXIII | Number 2 | 2012 | 11–22 Graham Harman* Concerning Stephen Hawking’s Claim that Philosophy is Dead1 The relations at present between philosophy and the sciences are not especially good. Let’s begin with Stephen Hawking’s famous words at the May 2011 Google Zeitgeist conference in England:1 […] almost all of us must sometimes wonder: Why are we here? Where do we come from? Traditionally, these are questions for philosophy, but philosophy is dead. Philosophers have not kept up with modern developments in science. Particularly physics. Scientists have become the bearers of the torch of discovery in our quest for knowledge.2 According to Hawking, philosophy is dead. Others are more generous and claim only that philosophy will be dead in the near future, and only partly dead. For example, brain researcher Wolf Singer tells us that he is interested in philoso- phy for two reasons: !rst because “progress in neurobiology will provide some answers to the classic questions in philosophy,” and second because “progress in the neurosciences raises a large number of new ethical problems, and these need to be addressed not only by neurobiologists but also by representatives of the humanities.”3 In other words, Singer is interested in philosophy as a poten- tial takeover target for the neurosciences, though he reassures us that philoso- phers should not fear this ambition, since Singer still needs ethics panels that will “also” include representatives of the humanities alongside neurobiologists. 11 Having escaped its medieval status as the handmaid of theology, philosophy will enter a new era as the ethical handmaid of the hard sciences. -
Multi-Dimensional Entanglement Transport Through Single-Mode Fibre
Multi-dimensional entanglement transport through single-mode fibre Jun Liu,1, ∗ Isaac Nape,2, ∗ Qianke Wang,1 Adam Vall´es,2 Jian Wang,1 and Andrew Forbes2 1Wuhan National Laboratory for Optoelectronics, School of Optical and Electronic Information, Huazhong University of Science and Technology, Wuhan 430074, Hubei, China. 2School of Physics, University of the Witwatersrand, Private Bag 3, Wits 2050, South Africa (Dated: April 8, 2019) The global quantum network requires the distribution of entangled states over long distances, with significant advances already demonstrated using entangled polarisation states, reaching approxi- mately 1200 km in free space and 100 km in optical fibre. Packing more information into each photon requires Hilbert spaces with higher dimensionality, for example, that of spatial modes of light. However spatial mode entanglement transport requires custom multimode fibre and is lim- ited by decoherence induced mode coupling. Here we transport multi-dimensional entangled states down conventional single-mode fibre (SMF). We achieve this by entangling the spin-orbit degrees of freedom of a bi-photon pair, passing the polarisation (spin) photon down the SMF while ac- cessing multi-dimensional orbital angular momentum (orbital) subspaces with the other. We show high fidelity hybrid entanglement preservation down 250 m of SMF across multiple 2 × 2 dimen- sions, demonstrating quantum key distribution protocols, quantum state tomographies and quantum erasers. This work offers an alternative approach to spatial mode entanglement transport that fa- cilitates deployment in legacy networks across conventional fibre. Entanglement is an intriguing aspect of quantum me- chanics with well-known quantum paradoxes such as those of Einstein-Podolsky-Rosen (EPR) [1], Hardy [2], and Leggett [3]. -
Everettian Probabilities, the Deutsch-Wallace Theorem and the Principal Principle
Everettian probabilities, the Deutsch-Wallace theorem and the Principal Principle Harvey R. Brown and Gal Ben Porath Chance, when strictly examined, is a mere negative word, and means not any real power which has anywhere a being in nature. David Hume (Hume, 2008) [The Deutsch-Wallace theorem] permits what philosophy would hitherto have regarded as a formal impossibility, akin to deriving an ought from an is, namely deriving a probability statement from a factual statement. This could be called deriving a tends to from a does. David Deutsch (Deutsch, 1999) [The Deutsch-Wallace theorem] is a landmark in decision theory. Nothing comparable has been achieved in any chance theory. [It] is little short of a philosophical sensation . it shows why credences should conform to [quantum chances]. Simon Saunders (Saunders, 'The Everett interpretation: probability' [unpublished manuscript]) Abstract This paper is concerned with the nature of probability in physics, and in quantum mechanics in particular. It starts with a brief discussion of the evolution of Itamar Pitowsky's thinking about probability in quantum theory from 1994 to 2008, and the role of Gleason's 1957 theorem in his derivation of the Born Rule. Pitowsky's defence of probability therein as a logic of partial belief leads us into a broader discussion of probability in physics, in which the existence of objective \chances" is questioned, and the status of David Lewis influential Principal Principle is critically examined. This is followed by a sketch of the work by David Deutsch and David Wallace which resulted in the Deutsch-Wallace (DW) theorem in Everettian quantum mechanics. -
Defining Physics at Imaginary Time: Reflection Positivity for Certain
Defining physics at imaginary time: reflection positivity for certain Riemannian manifolds A thesis presented by Christian Coolidge Anderson [email protected] (978) 204-7656 to the Department of Mathematics in partial fulfillment of the requirements for an honors degree. Advised by Professor Arthur Jaffe. Harvard University Cambridge, Massachusetts March 2013 Contents 1 Introduction 1 2 Axiomatic quantum field theory 2 3 Definition of reflection positivity 4 4 Reflection positivity on a Riemannian manifold M 7 4.1 Function space E over M ..................... 7 4.2 Reflection on M .......................... 10 4.3 Reflection positive inner product on E+ ⊂ E . 11 5 The Osterwalder-Schrader construction 12 5.1 Quantization of operators . 13 5.2 Examples of quantizable operators . 14 5.3 Quantization domains . 16 5.4 The Hamiltonian . 17 6 Reflection positivity on the level of group representations 17 6.1 Weakened quantization condition . 18 6.2 Symmetric local semigroups . 19 6.3 A unitary representation for Glor . 20 7 Construction of reflection positive measures 22 7.1 Nuclear spaces . 23 7.2 Construction of nuclear space over M . 24 7.3 Gaussian measures . 27 7.4 Construction of Gaussian measure . 28 7.5 OS axioms for the Gaussian measure . 30 8 Reflection positivity for the Laplacian covariance 31 9 Reflection positivity for the Dirac covariance 34 9.1 Introduction to the Dirac operator . 35 9.2 Proof of reflection positivity . 38 10 Conclusion 40 11 Appendix A: Cited theorems 40 12 Acknowledgments 41 1 Introduction Two concepts dominate contemporary physics: relativity and quantum me- chanics. They unite to describe the physics of interacting particles, which live in relativistic spacetime while exhibiting quantum behavior. -
Mathematisches Forschungsinstitut Oberwolfach Reflection Positivity
Mathematisches Forschungsinstitut Oberwolfach Report No. 55/2017 DOI: 10.4171/OWR/2017/55 Reflection Positivity Organised by Arthur Jaffe, Harvard Karl-Hermann Neeb, Erlangen Gestur Olafsson, Baton Rouge Benjamin Schlein, Z¨urich 26 November – 2 December 2017 Abstract. The main theme of the workshop was reflection positivity and its occurences in various areas of mathematics and physics, such as Representa- tion Theory, Quantum Field Theory, Noncommutative Geometry, Dynamical Systems, Analysis and Statistical Mechanics. Accordingly, the program was intrinsically interdisciplinary and included talks covering different aspects of reflection positivity. Mathematics Subject Classification (2010): 17B10, 22E65, 22E70, 81T08. Introduction by the Organisers The workshop on Reflection Positivity was organized by Arthur Jaffe (Cambridge, MA), Karl-Hermann Neeb (Erlangen), Gestur Olafsson´ (Baton Rouge) and Ben- jamin Schlein (Z¨urich) during the week November 27 to December 1, 2017. The meeting was attended by 53 participants from all over the world. It was organized around 24 lectures each of 50 minutes duration representing major recent advances or introducing to a specific aspect or application of reflection positivity. The meeting was exciting and highly successful. The quality of the lectures was outstanding. The exceptional atmosphere of the Oberwolfach Institute provided the optimal environment for bringing people from different areas together and to create an atmosphere of scientific interaction and cross-fertilization. In particular, people from different subcommunities exchanged ideas and this lead to new col- laborations that will probably stimulate progress in unexpected directions. 3264 Oberwolfach Report 55/2017 Reflection positivity (RP) emerged in the early 1970s in the work of Osterwalder and Schrader as one of their axioms for constructive quantum field theory ensuring the equivalence of their euclidean setup with Wightman fields. -
Physics Nobel Prize 1975
Physics Nobel Prize 1975 Nobel prize winners, left to right, A. Bohr, B. Mottelson and J. Rainwater. 0. Kofoed-Hansen (Photos Keystone Press, Photopress) Before 1949 every physicist knew that mooted, it was a major breakthrough from 1943-45. From December 1943 the atomic nucleus does not rotate. in thinking about the nucleus and he was actually in the USA. Back in The reasoning behind this erroneous opened a whole new field of research Denmark after the war, he obtained belief came from the following argu• in nuclear physics. This work has for his Ph. D. in 1954 for work on rota• ments. A quantum-mechanical rotator years been guided by the inspiration tional states in atomic nuclei. His with the moment of inertia J can take of Bohr and Mottelson. thesis was thus based on the work for up various energy levels with rota• An entire industry of nuclear which he has now been recognized at tional energies equal to h2(l + 1)| research thus began with Rainwater's the very highest level. He is Professor /8TC2J, where h is Planck's constant brief contribution to Physical Review at the Niels Bohr Institute of the ^nd I is the spin. As an example, I may in 1950 entitled 'Nuclear energy level University of Copenhagen and a nave values 0, 2, 4, ... etc. If the argument for a spheroidal nuclear member of the CERN Scientific Policy nucleus is considered as a rigid body, model'. Today a fair-sized library is Committee. then the moment of inertia J is very needed in order to contain all the Ben Mottelson was born in the USA large and the rotational energies papers written on deformed nuclei and in 1926 and has, for many years, become correspondingly very small. -
Appendix E Nobel Prizes in Nuclear Science
Nuclear Science—A Guide to the Nuclear Science Wall Chart ©2018 Contemporary Physics Education Project (CPEP) Appendix E Nobel Prizes in Nuclear Science Many Nobel Prizes have been awarded for nuclear research and instrumentation. The field has spun off: particle physics, nuclear astrophysics, nuclear power reactors, nuclear medicine, and nuclear weapons. Understanding how the nucleus works and applying that knowledge to technology has been one of the most significant accomplishments of twentieth century scientific research. Each prize was awarded for physics unless otherwise noted. Name(s) Discovery Year Henri Becquerel, Pierre Discovered spontaneous radioactivity 1903 Curie, and Marie Curie Ernest Rutherford Work on the disintegration of the elements and 1908 chemistry of radioactive elements (chem) Marie Curie Discovery of radium and polonium 1911 (chem) Frederick Soddy Work on chemistry of radioactive substances 1921 including the origin and nature of radioactive (chem) isotopes Francis Aston Discovery of isotopes in many non-radioactive 1922 elements, also enunciated the whole-number rule of (chem) atomic masses Charles Wilson Development of the cloud chamber for detecting 1927 charged particles Harold Urey Discovery of heavy hydrogen (deuterium) 1934 (chem) Frederic Joliot and Synthesis of several new radioactive elements 1935 Irene Joliot-Curie (chem) James Chadwick Discovery of the neutron 1935 Carl David Anderson Discovery of the positron 1936 Enrico Fermi New radioactive elements produced by neutron 1938 irradiation Ernest Lawrence -
Physics 616 Quantum Field Theory I(3 Credits)
Physics 616 Quantum Field Theory I (3 credits) Fall 2011 Instructor: Prof. Michael Eides 279 Chem.-Phys. Bldg. Phone 257-3997 E-mail: [email protected] Office hours: Tuesday, 2:00-4:00 pm, or by appointment. Class meets Tuesday, Thursday, 9:30-10:45 am (CP 183). There will be no classes on Thursday, November 24 (Thanksgiving). Grading: I will give you home assignments approximately every 10 days. Your homework will be graded (40 points). Solutions to all problems will be placed in the library. I advice you to read my solutions with great care. If you have any questions about my solutions (as I expect you would), you are welcome in my office for discussion. I encourage you to discuss the homework together, and even to work on it together. However, you should write up your homework separately. Identical solutions would not earn any points. There will be no midterm exam. There will be a take-home final exam due Friday, December 12 (60 points). It could happen that I will change my mind and ask each of you to prepare a short talk (20-25 min) instead of the final exam. Student Evaluations: Course evaluations are an important (and mandatory!) component of our De- partment’s instructional program. The evaluation window for Fall 2011 will open on Wednesday, November 16, and close on Wednesday, Wednesday, December 7th. To access the system during this time, simply go to ”Courses” on the A&S Departmental Website page, and click on the link for Course Evaluations; then follow the instructions. -
Cavendish the Experimental Life
Cavendish The Experimental Life Revised Second Edition Max Planck Research Library for the History and Development of Knowledge Series Editors Ian T. Baldwin, Gerd Graßhoff, Jürgen Renn, Dagmar Schäfer, Robert Schlögl, Bernard F. Schutz Edition Open Access Development Team Lindy Divarci, Georg Pflanz, Klaus Thoden, Dirk Wintergrün. The Edition Open Access (EOA) platform was founded to bring together publi- cation initiatives seeking to disseminate the results of scholarly work in a format that combines traditional publications with the digital medium. It currently hosts the open-access publications of the “Max Planck Research Library for the History and Development of Knowledge” (MPRL) and “Edition Open Sources” (EOS). EOA is open to host other open access initiatives similar in conception and spirit, in accordance with the Berlin Declaration on Open Access to Knowledge in the sciences and humanities, which was launched by the Max Planck Society in 2003. By combining the advantages of traditional publications and the digital medium, the platform offers a new way of publishing research and of studying historical topics or current issues in relation to primary materials that are otherwise not easily available. The volumes are available both as printed books and as online open access publications. They are directed at scholars and students of various disciplines, and at a broader public interested in how science shapes our world. Cavendish The Experimental Life Revised Second Edition Christa Jungnickel and Russell McCormmach Studies 7 Studies 7 Communicated by Jed Z. Buchwald Editorial Team: Lindy Divarci, Georg Pflanz, Bendix Düker, Caroline Frank, Beatrice Hermann, Beatrice Hilke Image Processing: Digitization Group of the Max Planck Institute for the History of Science Cover Image: Chemical Laboratory. -
Quantum Theory Needs No 'Interpretation'
Quantum Theory Needs No ‘Interpretation’ But ‘Theoretical Formal-Conceptual Unity’ (Or: Escaping Adán Cabello’s “Map of Madness” With the Help of David Deutsch’s Explanations) Christian de Ronde∗ Philosophy Institute Dr. A. Korn, Buenos Aires University - CONICET Engineering Institute - National University Arturo Jauretche, Argentina Federal University of Santa Catarina, Brazil. Center Leo Apostel fot Interdisciplinary Studies, Brussels Free University, Belgium Abstract In the year 2000, in a paper titled Quantum Theory Needs No ‘Interpretation’, Chris Fuchs and Asher Peres presented a series of instrumentalist arguments against the role played by ‘interpretations’ in QM. Since then —quite regardless of the publication of this paper— the number of interpretations has experienced a continuous growth constituting what Adán Cabello has characterized as a “map of madness”. In this work, we discuss the reasons behind this dangerous fragmentation in understanding and provide new arguments against the need of interpretations in QM which —opposite to those of Fuchs and Peres— are derived from a representational realist understanding of theories —grounded in the writings of Einstein, Heisenberg and Pauli. Furthermore, we will argue that there are reasons to believe that the creation of ‘interpretations’ for the theory of quanta has functioned as a trap designed by anti-realists in order to imprison realists in a labyrinth with no exit. Taking as a standpoint the critical analysis by David Deutsch to the anti-realist understanding of physics, we attempt to address the references and roles played by ‘theory’ and ‘observation’. In this respect, we will argue that the key to escape the anti-realist trap of interpretation is to recognize that —as Einstein told Heisenberg almost one century ago— it is only the theory which can tell you what can be observed. -
The Beginning of Infinity: Explanations That Transform the World Pdf, Epub, Ebook
THE BEGINNING OF INFINITY: EXPLANATIONS THAT TRANSFORM THE WORLD PDF, EPUB, EBOOK David Deutsch | 487 pages | 29 May 2012 | Penguin Putnam Inc | 9780143121350 | English | New York, NY, United States The Beginning of Infinity: Explanations That Transform the World PDF Book Every argument includes premises in support of a conclusion, but the premises themselves are left unargued. Nov 12, Gary rated it it was amazing Shelves: science. In other words we must have some form of evidence, and it must be coherent with our other beliefs. Nov 12, Gary rated it it was amazing Shelves: science. I can't say why exactly. It seems more to the point to think of it as something emotive — as the expression of a mood. This will lead to the development of explanatory theories variation , which can then be criticized and tested selection. Accuracy and precision are important standards in our evaluation of explanations; standards that are absent in bad explanations. Every argument includes premises in support of a conclusion, but the premises themselves are left unargued. Deutsch starts with explanations being the basis for knowledge, and builds up basic, hard-to-argue-with principles into convincing monoliths that smash some conventional interpretations of knowledge, science and philosophy to tiny pieces. His reliance on Popper is problematic. I will be re-reading them again until it really sinks in. Evolution, in contrast, represents a good explanation because it not only fits the evidence but the details are hard to vary. Barefoot Season Susan Mallery. But the "Occam's Razor" described by the author is not the one practiced in reality.