21. Identity Of Indiscernibles Essay by Allan Randall, relating Leibinz's criterion to Everett's possible worlds semantics of quantum mechanics. http://home.ican.net/~arandall/Indiscernibles/

http://home.ican.net/~arandall/Indiscernibles/ Quantum Superposition, Necessity and the Identity of Indiscernibles Allan F. Randall Toronto, Ontario, Canada arandall@ican.net http://home.ican.net/~arandall/ Abstract Those who interpret quantum mechanics literally are forced to follow some variant of Everett's relative state formulation (or "many worlds" interpretation). It is generally assumed that this is a rather bizarre result that many physicists (especially cosmologists) have been forced into because of the evidence. I look at the history of philosophy, however, reveals that rationalism has always flirted with this very idea, from Parmenides to Leibniz to modern times. I will survey some of the philosophical history, and show how the so-called paradox of quantum superposition can be considered a consequence of basic rationalist assumptions such as the principle of sufficient reason and the identity of indiscernibles. I. Introduction Most physicists see quantum weirdness as something we have to accept in spite of ourselves, because of the overwhelming empirical evidence in its favour. Richard Feynman argued that we must simply admit that Nature makes no sense - knuckle under and accept the evidence, no matter how weird it seems ( Feynman 1985 Yet several hundred years ago Gottfried Wilhelm Leibniz came remarkably close to formulating an early version of Quantum Theory, without the benefit of any of the empirical evidence that aids us today. His Principle of the Identity of Indiscernibles states that no two different objects can have the same description (

22. 2. Some Basic Ideas About Quantum Mechanics University of Exeter 2. Some Basic Ideas about quantum mechanics. Modernphysics is dominated by the concepts of quantum mechanics. http://newton.ex.ac.uk/people/jenkins/mbody/mbody2.html

2. Some Basic Ideas about Quantum Mechanics Modern physics is dominated by the concepts of Quantum Mechanics. This page aims to give a brief introduction to some of these ideas. Until the closing decades of the last century the physical world, as studied by experiment, could be explained according to the principles of classical (or Newtonian) mechanics: the physics of everyday life. By the turn of the century, however, the cracks were beginning to show and the disciplines of Relativity and Quantum Mechanics were developed to account for them. Relativity came first, and described the physics of very massive and very fast objects, then came Quantum Mechanics in the 1920's to describe the physics of very small objects. Neither of these theories provide an easy intuitive picture of the world, since they contradict the predictions of familiar Newtonian Mechanics in the regimes for which they were developed. Nevertheless, both schemes reproduce the Newtonian results when applied to the everyday world. In seeking to understand the physics of semiconductors at an atomic level we must start from a Quantum Mechanical viewpoint, since the entities with which we will be dealing (electrons, atoms, etc) are so very small....

23. Philosophical Foundations Of Physics Positivist view of Physics, which had influenced the Copenhagen Interpretation of the quantum mechanics (CI). http://www.marxists.org/reference/subject/philosophy/works/ge/carnap.htm

Rudolph Carnap (1966) Philosophical Foundations of Physics Chapter 23: Theories and Nonobservables Source Philosophical Foundations of Physics (1966) publ. Basic Books Inc. Chapters 23 to 26 reproduced here. ONE OF THE most important distinctions between two types of laws in science is the distinction between what may be called (there is no generally accepted terminology for them) empirical laws and theoretical laws. Empirical laws are laws that can be confirmed directly by empirical observations. The term "observable" is often used for any phenomenon that can be directly observed, so it can be said that empirical laws are laws about observable. A philosopher might object that the intensity of an electric current is not really observed. Only a pointer position was observed. An ammeter was attached to the circuit and it was noted that the pointer pointed to a mark labelled 5.3. Certainly the current's intensity was not observed. It was inferred from what was observed. The physicist would reply that this was true enough, but the inference was not very complicated. The procedure of measurement is so simple, so well established, that it could not be doubted that the ammeter would give an accurate measurement of current intensity. Therefore, it is included among what are called observables. Empirical laws, in my terminology, are laws containing terms either directly observable by the senses or measurable by relatively simple techniques. Sometimes such laws are called empirical generalisations, as a reminder that they have been obtained by generalising results found by observations and measurements. They include not only simple qualitative laws (such as, "All ravens are black") but also quantitative laws that arise from simple measurements. The laws relating pressure, volume, and temperature of gases are of this type. Ohm's law, connecting the electric potential difference, resistance, and intensity of current, is another familiar example. The scientist makes repeated measurements, finds certain regularities, and expresses them in a law. These are the empirical laws. As indicated in earlier chapters, they are used for explaining observed facts and for predicting future observable events.

24. Time Development Of Quantum Mechanical Systems Welcome to the world of quantum mechanics! Change to Hungarian language http://newton.phy.bme.hu/education/schrd

Time development of quantum mechanical systems Welcome to the world of quantum mechanics! Change to Hungarian language This document presents the results of the solution of the time dependent Schrodinger equation for one-, two-, and three dimensional one particle systems. Simulation results for different V(r) potentials are displayed as images and animation. The program to calculate the images is also available. See also our mailing list devoted to physics education programs! Introduction Influence of the wave packet shape to its time development Two dimensional (2D) one particle simulations Three dimensional (3D) one particle simulations NEW! Download the programs Physics education programs mailing list (If you want to receive notifications about the new uploads to this server subscribe now!) Address: Institute of Physics Technical University of Budapest H-1111 Budafoki ut. 8. Budapest, Hungary Europe Tel: (+36-1)463-4107, Fax: 463-3999 Last updated: May 2, 2001 mark@sunserv.kfki.hu

25. Mark's Quantum Mechanics Applets A collection of sample Java applets which demonstrate various aspects of quantum mechanics, including Category Science Physics Education Java Applets......Mark's quantum mechanics Applets by Mark Sutherland This is a collectionof Java applets illustrating quantum mechanical processes. http://thorin.adnc.com/~topquark/quantum/quantumapplets.html

Mark's Quantum Mechanics Applets by Mark Sutherland This is a collection of Java applets illustrating quantum mechanical processes. The samples posted here are somewhat restricted in their functionality, but are still very useful for learning or teaching the concepts involved. Fully functional versions are available from the author. Hydrogen atom 2d slice Hydrogen atom in 3d Heisenberg's Uncertainty Principle Scattering from a 1-D square well ... The infinitely-deep square well

26. Homeopathy Is A Science Of Quantum Mechanics Authored by Ioannis Karpouzelis M.D. Includes a summary, how the remedies are prepared and in the patient. Details about a selfexperimentation and evidence of the action of the vibrating self-frequencies of the medicine. http://www.karpouzelis.sto.gr

27. Visual Quantum Mechanics The Visual quantum mechanics project is developing instructional materialsabout quantum physics for high school and college students. http://www.phys.ksu.edu/perg/vqm/

The Visual Quantum Mechanics project is developing instructional materials about quantum physics for high school and college students. Instructional units and/or courses are being created for high school and college non-science students, pre-medical and biology students, and science and engineering majors. Each set of the teaching-learning materials integrates interactive visualizations with inexpensive materials and written documents in an activity-based environment. The original Visual Quantum Mechanics project developed materials for high school students and for non-science college students. Teaching-learning materials for science and engineering students are now in development. Some tutorials for this audience are now available for testing. Instructional Units Tutorials Software Software ... On-line instruction Work in Progress Sampler Equipment Lists Interactive Engagements for use in an upper-level undergraduate quantum mechanics course are now in development. Some materials are available for testing. Using contemporary medical diagnosis tools as motivation the project is creating a course in modern physics for students interested in medicine and the biological sciences.

28. Avshalom Elitzur's Home Page Senior Lecturer, BarIlan University. Includes an autobiography, a curriculum vitae, and a list of publications in quantum mechanics, relativity, thermodynamics, evolutionary theory, philosophy of mind and psychoanalysis. http://www.weizmann.ac.il/chemphys/elitzur/

Physicist and philosopher Avshalom.Elitzur@weizmann.ac.il My unusual CV might justify adding a brief explanation. More Comments and suggestions to: Avshalom Elitzur Desinged by Anna Pomyalov Last modified: Sun Oct 8 14:31:49 IST 2000

29. Visual Quantum Mechanics Probability Illustrator. Energy Band Creator. Quantum Tunneling. Color Creator. HydrogenSpectroscopy. Java Color Creator. Quantum Motion. Making Waves. http://www.phys.ksu.edu/perg/vqm/software/

Spectroscopy Laboratory Suite Probability Illustrator Energy Band Creator Quantum Tunneling Spectroscopy Laboratory Suite Probability Illustrator Energy Band Creator Quantum Tunneling ... Making Waves

30. Quantum Mechanics History A history of quantum mechanics. Heisenberg wrote his first paper on quantummechanics in 1925 and 2 years later stated his uncertainty principle. http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/The_Quantum_age_begins.html

A history of Quantum Mechanics Mathematical Physics index History Topics Index It is hard to realise that the electron was discovered less than 100 years ago in 1897. That it was not expected is illustrated by a remark made by J J Thomson, the discoverer of the electron. He said I was told long afterwards by a distinguished physicist who had been present at my lecture that he thought I had been pulling their leg. The neutron was not discovered until 1932 so it is against this background that we trace the beginnings of quantum theory back to 1859. In 1859 Gustav Kirchhoff proved a theorem about blackbody radiation. A blackbody is an object that absorbs all the energy that falls upon it and, because it reflects no light, it would appear black to an observer. A blackbody is also a perfect emitter and Kirchhoff proved that the energy emitted E depends only on the temperature T and the frequency v of the emitted energy, i.e. E J T v He challenged physicists to find the function J In 1879 Josef Stefan proposed, on experimental grounds, that the total energy emitted by a hot body was proportional to the fourth power of the temperature. In the generality stated by Stefan this is false. The same conclusion was reached in 1884 by Ludwig

31. The Theory Of Positivist Mechanics - Abstract And Section 1: Introduction This theory proposed a framework by which the fundamental principles of quantum mechanics may be derived from classical (general relativistic) principles, thus providing a unification of GR and QM. http://www.geocities.com/straycat_md/TOPM.html

The Theory of Positivist Mechanics A Classical Solution to the Measurement Problem of Quantum Mechanics W. David Strayhorn, IV, Ph.D. (Cell Biology) Nashville, Tennessee For an online discussion of the ideas presented in this website, Click to check out my Yahoo! group: Yapquack , or yet another paradigm for quantum ducks, is an outgrowth of the ideas presented in TOPM and discussed in . Currently (as of July 2002) a collaborative effort between Ed Huff and David Strayhorn. Subscribe to QM_from_GR Powered by groups.yahoo.com Another excellent Yahoo! group for discussing and learning quantum mechanics is ; it is frequented by some very knowledgeable people. Leave your comments in my guestbook! Sign Guestbook View Guestbook Abstract and Section 1: Introduction Section 2: The Measurement Problem of QM Section 3: Non-Determinism in Classical Mechanics: the Classical Random-Effect Generator (C-REG) Section 4: Conceptual Solution to the Measurement Problem Section 5: Summary and Future Directions ... My homepage ABSTRACT Key Words: general relativity, quantum mechanics, quantum statistics, measurement problem, logical positivism, wormholes, scale relativity, stochastic quantum mechanics, non-determinism

32. Visual Quantum Mechanics - Sample Movies Home page of Visual quantum mechanics, You need QuickTimeto view these movies. Homepageof VQMthe book, About Visual quantum mechanics, About the author, http://www.kfunigraz.ac.at/imawww/vqm/pages/samples.html

You need QuickTimeto view these movies. Free motion: Direction of motion in 1D Superposition of Gaussian states in 2D Boundary conditions: Unit function in a Dirichlet box Double-slit experiment Harmonic oscillator: Squeezed state in 2D Constant shape of a shifted eigenstate Special systems: Free fall of a Gaussian Gaussian in a constant magnetic field Aharonov-Bohm effect Scattering: Potential step in momentum space Tunneling through a barrier Scattering at a cylindrical barrier Hydrogen atom: Superposition state: Oscillation Superposition state: Rotation Dirac equation: Zitterbewegung (free motion) Lorentz transformation Smooth potential well (positive energy) Smooth potential well (negative energy) ... Scattering at a very high step (Klein's paradox) These movies are examples from the CD packed with "Visual Quantum Mechanics" (Book One: TELOS/Springer 2000). For faster downloads the movies have been compressed which results in a loss of quality compared to the versions on the CD. The movies of the hydrogen atom and of the Dirac equation are samples from the second book which due to appear in 2002. The CDs packed with the two books contains more than 600 further movies illustrating various aspects of quantum mechanics. Most of the movies and visualizations were created with the help of

33. Quantum Mechanics Examples Some examples of quantum mechanics and the Mathematica code that generated them.Category Science Physics quantum mechanics Resources......5½ Examples in quantum mechanics. Nevertheless, quantum mechanics is usedon a daily basis by thousands of physicists, chemists and engineers. http://www.physics.csbsju.edu/QM/

HTTP 200 Document follows Date: Sun, 23 Mar 2003 05:31:57 GMT Server: NCSA/1.5.2 Last-modified: Thu, 22 Mar 2001 22:58:36 GMT Content-type: text/html Content-length: 18706 Index The new theories, if one looks apart from their mathematical setting, are built up from physical concepts which cannot be explained in terms of things previously known to the student, which cannot even be explained adequately in words at all. Like the fundamental concepts (e.g., proximity, identity) which every one must learn on his arrival into the world, the newer concepts of physics can be mastered only by long familiarity with their properties and uses. P.A.M. Dirac (1930) Preface The Principles of Quantum Mechanics We have always had a great deal of difficulty understanding the world view that quantum mechanics represents. At least I do, because I'm an old enough man that I haven't got to the point that this stuff is obvious to me. Okay, I still get nervous with it... You know how it is, every new idea, it takes a generation or two until it becomes obvious that there's no real problem... I cannot define the real problem, therefore I suspect there's no real problem, but I'm not sure there's no real problem. R. P. Feynman as quoted in

34. PDEase2D 3.0 Main Page Solves partial differential equations numerically by finite element analysis for use in such problems as heat transfer, reaction diffusion, solid and fluid mechanics, electromagnetics, groundwater flow, and quantum mechanics. http://www.scientek.com/macsyma/pdmain.htm

Finite Elements with No Mesh, No Fuss PDEase2D gives you a new way to solve partial differential equations (PDEs) numerically by finite element analysis. Flexible PDEase solves a very wide range of nonlinear problems in heat transfer, solid mechanics, fluid mechanics, groundwater flow, electromagnetics, chemical reaction diffusion, and quantum mechanics. It simplifies finite element analysis with automatic gridding, automated error analysis, flexible solution methods, and a simple input language. PDEase2D solves static, dynamic, and eigenvalue problems in two space dimensions, including PDEs of mixed elliptic, parabolic and hyperbolic type. Friendly PDEase has remarkably simple input. You merely specify the PDEs and variables, define the terms and material properties that occur in the equations, and specify the boundary shapes and conditions. PDEase2D includes 140 sample problems in mechanical, electrical and mechanical engineering Automated PDEase defines its own element grid, performs error analyses, and refines the grid as needed until error criteria are met. It solves nonlinear equations by iterative methods, adaptively selects time step size in dynamic problems, and draws plots using the Macsyma Front End (its own plots and Macsyma graphics). While users can intervene in these decisions, the software takes great care to usually make good decisions without user guidance. For particularly complicated equations or for curvilinear coordinates, you can use Macsyma (a separate Macsyma Inc. product) to write the PDEs automatically and pass them to PDEase for numerical solution.

35. Index For The Quantum Mechanics Examples Index for 5½ Examples in quantum mechanics. Home Page Falling Motion in a LinearPotential One Dimensional classical motion PE, turning points, z(t), etc. http://www.physics.csbsju.edu/QM/Index.html

HTTP 200 Document follows Date: Sun, 23 Mar 2003 05:32:00 GMT Server: NCSA/1.5.2 Last-modified: Thu, 23 Mar 2000 23:16:53 GMT Content-type: text/html Content-length: 7075 Home Page Falling: Motion in a Linear Potential One Dimensional classical motion: PE, turning points, z(t) , etc. length and energy scales ... approximation methods: WKB, Rayleigh-Ritz (variational), perturbation theory Two Dimensional classical ballistic (projectile) motion separation of variables QM force-free motion: a moving lump of probability density visualizing the moving lump of probability density ... Problems Simple Harmonic Oscillator One Dimensional classical motion: PE, turning points, x(t) , etc. length and energy scales ... raising and lowering operators Two Dimensional xy 1D products, r : Laguerre polynomials degeneracy QM "motion": an orbiting wavefunction Three Dimensional xyz 1D products, r : Laguerre polynomials visualizing the wavefunctions in 3D WKB approximation in 3D Problems Hydrogen Atom classical motion: PE, turning points, Kepler's Laws, r(t) , etc. length and energy scales ... problems Square Wells One Dimensional classical motion: PE, turning points,

36. Quantum Mechanics, Chaos And The Bohm Theory A lengthy paper / ebook outlining the quantum mechanical equivalent of the classical chaotic kicked Category Science Physics quantum mechanics......quantum mechanics, Chaos and the Bohm Theory. Z. Malik Jon Spencer TueJan 16 135538 GMT 1996 Back to the Main quantum mechanics Page. http://www.phys.port.ac.uk/research/quantum/paper1/paper1.html

37. Quantum Mechanics History An overview of the development of quantum mechanics. http://history.math.csusb.edu/HistTopics/The_Quantum_age_begins.html

A history of Quantum Mechanics Mathematical Physics index History Topics Index It is hard to realise that the electron was discovered less than 100 years ago in 1897. That it was not expected is illustrated by a remark made by J J Thomson, the discoverer of the electron. He said I was told long afterwards by a distinguished physicist who had been present at my lecture that he thought I had been pulling their leg. The neutron was not discovered until 1932 so it is against this background that we trace the beginnings of quantum theory back to 1859. In 1859 Gustav Kirchhoff proved a theorem about blackbody radiation. A blackbody is an object that absorbs all the energy that falls upon it and, because it reflects no light, it would appear black to an observer. A blackbody is also a perfect emitter and Kirchhoff proved that the energy emitted E depends only on the temperature T and the frequency v of the emitted energy, i.e. E J T v He challenged physicists to find the function J In 1879 Josef Stefan proposed, on experimental grounds, that the total energy emitted by a hot body was proportional to the fourth power of the temperature. In the generality stated by Stefan this is false. The same conclusion was reached in 1884 by Ludwig

38. Bohm, Bell, And Boom! Quantum Mechanics And The End Of Modern Dualism From History and Philosophy of Science, Fall, 1997. By Dr. Ess. http://www.drury.edu/faculty/ess/philsci/bell.html

Notes on David Peat, Einstein's Moon: Bell's Theorem and the Curious Quest for Quantum Reality History and Philosophy of Science - Fall, 1997 - Dr. Ess Outline: "Bohm, Bell - and Boom! The End of Modern Dualism" The End of Cartesian Dualism: Physics (re)discovers Philosophy over against Cartesian and especially 19th ct. positivist dualisms which separate physics and philosophy - the emergence of quantum mechanics forces physicists to be become philosophers again. Indeed, the logic of complementarity which q.m. requires ripples into a larger (re)turn to complementary relationships between physics, philosophy, and religion. (In other terms: Cartesian dualism defines both 19th ct. positivism and fundamentalism as "mirror images" of one another: each agree that only one mode of knowing can be true - and the alternative mode(s) must be false: Positivism Fundamentalism ("calculative") reason (= natural science) "religion" "religion" reason/science The end of Cartesian dualism thus undermines the dualistic epistemologies of both positivism and fundamentalism.)

39. Development Of Quantum Mechanics The Development of quantum mechanics. Click here to go to the UPSCALE homepage. Click Comparing the Two Forms of quantum mechanics. Despite http://www.upscale.utoronto.ca/GeneralInterest/Harrison/DevelQM/DevelQM.html

The Development of Quantum Mechanics Click here to go to the UPSCALE home page. Click here to go to the Physics Virtual Bookshelf home page. Click here to go to the JPU200Y home page. Author This document was written in March 2000 by David M. Harrison, Department of Physics, University of Toronto, mailto:harrison@physics.utoronto.ca. . This is version 1.3, date (m/d/y) 03/06/02. This material may be distributed only subject to the terms and conditions set forth in the Open Content License, v1.0 or later (the latest version is presently available at http://opencontent.org/opl.shtml Introduction The Conceptual Development of Quantum Mechanics (McGraw-Hill 1966). Here we briefly outline some of the key features of these developments. Some of the material is well-known, but other parts of what follows are not. The level is consistent with an upper-year liberal arts course in modern physics without mathematics that is given at the University of Toronto. Heisenberg's Matrix Mechanics Heisenberg's starting point was the Bohr model of the atom. This model had been extended by Sommerfeld, and by the Summer of 1925 many physicists had learned through trial and error how to navigate through some of the morass of atomic physics. This circumstance, however, is far short from having a good

40. PhysicsWeb - A Quantum Leap For Cosmology A theory that unites quantum mechanics and general relativity claims that there was no first moment in time, but it still agrees with the predictions of classical cosmology. http://physicsweb.org/article/world/14/11/3

Advanced site search physics world January February March April May June July August September October November December Latest issue Subscribe to Physics World Media Information ... Editorial Staff quick search Search Physics World Previous Physics World November 2001 Next A quantum leap for cosmology Physics in Action: November 2001 A theory that unites quantum mechanics and general relativity claims that there was no first moment in time, but it still agrees with the predictions of classical cosmology. It's in the stars One of the most challenging problems in modern physics is the application of quantum theory to the universe as a whole. Progress in this area has been plagued by two types of problem: conceptual and technical. The conceptual problems arise from the old difficulties of interpreting quantum theory. The standard interpretations require that the measuring instruments and observers are outside the quantum system described by the wavefunction. In the late 1950s, however, Hugh Everett proposed an interpretation of quantum theory that might apply to systems that include the observers and measuring instruments, but the adequacy of such interpretations has remained controversial to this day. The technical problems are no less severe or fundamental. Ever since the pioneering work of Bryce DeWitt, Charles Misner and others in the 1960s, quantum cosmology has basically been studied by applying quantum theory to simple models of the universe. These models typically assume that the universe is completely homogeneous. As a result they only have a few degrees of freedom - the radius of the universe and the value of one or more matter fields. One then makes a quantum-cosmological model by quantizing these simple descriptions of the universe.

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