Open Questions: Quantum Theory

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See also: Quantum information and computing -- Quantum cosmology -- Quantum gravity -- Quantum field theory -- Quantum effects technology

Anyone who is not shocked by quantum theory has not understood it.

Niels Bohr

I can safely say that nobody understands quantum mechanics. ... Do not keep saying to yourself, if you can possibly avoid it, 'But how can it be like that?' because you will get 'down the drain', into a blind alley from which nobody has yet escaped. Nobody knows how it can be like that.

Richard Feynman



The Copenhagen interpretation

The "measurement problem"

Bohm's theory

Bell's theorem

Coherence and decoherence

Consistent histories

The "many worlds" interpretation

Quantum chaos

Recommended references: Web sites

Recommended references: Magazine/journal articles

Recommended references: Books


Quantum mechanics works. Nobody doubts that. Whenever we are able to derive predictions from the equations of quantum mechanics, they can be verified to the limits of experimental accuracy.

We just don't understand why quantum mechanics works.

Recommended references: Web sites

Site indexes

Open Directory Project: Quantum Mechanics
Categorized and annotated links. A version of this list is at Google, with entries sorted in "page rank" order.
The Net Advance of Physics: Quantum Mechanics
An index of tutorial and research articles located at the physics preprint archive.
Best of Physics Web: Atomic, Molecular and Quantum Physics
Directory of best feature articles, news stories, and external links on quantum physics at the Physics Web site.
Galaxy: Quantum Mechanics
Categorized site directory. Entries usually include descriptive annotations.

Sites with general resources

"Qwiki is a quantum physics wiki devoted to the collective creation of content that is technical and useful to practicing scientists. ... The site is nominally centered around quantum physics, but all scientists are invited to contribute, including -- but not limited to -- computer scientists, control theorists, electrical engineers, and mathematicians. More specifically, this site is designed for people who post content to the Arxiv and quant-ph."
New Scientist's Guide to the Quantum World
Good collection of news and tutorial articles on quantum physics and quantum computing.
Quantum Quotations
Stimulating quotations, mostly by physicists, on quantum mechanics. Collected by Jess Brewer.

Surveys, overviews, tutorials

Quantum mechanics
Article from Wikipedia. See also Interpretation of quantum mechanics, Bell's theorem, EPR paradox, Quantum entanglement, Mathematical formulation of quantum mechanics, Quantum chaos.
On the Interpretation and Philosophical Foundation of Quantum Mechanics
Very good essay by Anton Zeilinger on various interpretations of quantum mechanics.
The Copenhagen Interpretation of Quantum Mechanics
Good expository article by Ben Best. Contains a number of useful embedded external links.
Quantum theory poses reality's deepest mystery
Brief May 2008 comments by John Wheeler on quantum theory.
Quantum mysteries
A description of experiments that seem to demonstrate faster than light communication and other quantum strangeness, by John Gribbin.
Does God play dice?
December 2005 article from Physics World. "Four theorists - Gerard 't Hooft, Edward Witten, Fay Dowker and Paul Davies- outline their views on the current status of quantum theory and the way forward."
Probing the limits of the quantum world
March 2005 article from Physics World, by Markus Arndt, Klaus Hornberger, and Anton Zeilinger. "Molecules with over 100 atoms can be made to interfere, according to recent experiments that study the transition from the quantum to the classical world."
New life for Schrödinger's cat
August 2000 article from Physics World, by Tony Leggett. "The observation of quantum superpositions of distinct macroscopic states by groups at Stony Brook and Delft represents a milestone in experimental quantum physics. Both teams have reported spectroscopic evidence for currents of microamps flowing through a superconducting ring in opposite directions at the same time."
Schrodinger's cat comes into view
July 2000 new article from Physics World about the first demonstration of a macroscopic Schrodinger cat state.
Measuring decoherence in real time
January 2000 news article from Physics World about measurement of quantum decoherence in a mesoscopic system for the first time.
Quantum theory: weird and wonderful
December 1999 article from Physics World, by Tony Leggett. "Quantum mechanics is the most accurate theory we have to describe the world, but there is still much about it that we do not fully understand."
Wave-particle duality seen in carbon-60 molecules
October 1999 news article from Physics World about production of an interference pattern in a double-slit experiment involving carbon-60 molecules.
First for single-photon measurements
July 1999 news article from Physics Web about experimental techniques that allow repeated observation of a single photon without destroying it.
John Bell and the most profound discovery of science
December 1998 article from Physics World, by Andrew Whitaker. Some of the theory behind Bell's inequality is explained, along with biographical details on John Bell.
Intro to Quantum Mechanics
Single-page overview of quantum mechanics, by Todd Stedl.
Some Basic Ideas about Quantum Mechanics
Single page that introduces some of the ideas of quantum mechanics, by Stephen Jenkins.
Frequently Asked Questions: Quantum Mechanics
Technical answers to frequently asked questions, based on a list originally developed by Jim Carolan.
Physics Beyond the Limits of Uncertainty Relations
Excellent tutorial pages on "subquantum physics" by Michio Durdevich. There are additional, somewhat more technical papers on mathematical quantum theory at the author's home page.
Quantum Dèjá Vu
Brief October 1999 article from Scientific American, subtitled "In an exquisite 'quantum nondemolition' experiment, physicists see a single photon and then see it again."
Schroedinger's Cation
June 1996 Scientific American Explore article, subtitled "Physicists prove that an atom can be in two different places at once."
The Transactional Interpretation of Quantum Mechanics
Technical exposition, originally published in 1986, of a new alternative interpretation of quantum mechanics, by John G. Cramer.

Recommended references: Magazine/journal articles

Fungibility and the quantum multiverse
David Deutsch
Physics World, May 2011, pp. 34-38
Physicists have long debated whether the most fundamental phenomena of quantum physics is quantization, interference, or entanglement. But it may be something else entirely: fungibility.
A Quantum Threat to Special Relativity
David Z Albert; Rivka Galchen
Scientific American, February 2009
Chaos on the Quantum Scale
Mason A. Porter; Richard L. Liboff
American Scientist, November-December 2001, pp. 532-537
During the past century both quantum theory and chaos theory have emphasized the unpredictability of nature in many phenomena. Difficult as it may seem, techniques have been developed for modeling chaos on the quantum scale. Such models will be crucial for understanding and developing quantum scale technology.
[Abstract and references]
100 Years of Quantum Mysteries
Max Tegmark; John Archibald Wheeler
Scientific American, February 2001, pp. 68-75
In December 1900 Max Planck announced a formula describing blackbody radiation. The 100 years since then have seen the rapid development of quantum mechanics, but a number of "mysteries" and conceptual issues remain.
Consistent Histories and Quantum Measurements
Robert B. Griffiths, Roland Omnès
Physics Today, August 1999, pp. 26-31
The understanding of quantum mechanics in terms of measurements (the so-called Copenhangen interpretation) has proven problematical for various reasons -- for instance the notion that properties don't exist until measured and the paradox of Schrödinger's cat. New approaches such as "consistent histories" look promising.
Entanglement, Decoherence and the Quantum/Classical Boundary
Serge Haroche
Physics Today, July 1998, pp. 36-42
New experiments attempt to resolve the apparent paradox of "Schrödinger's cat" without harm to the feline.
Quantum Theory without Observers
Sheldon Goldstein
Physics Today, March 1998, pp. 42-46 and April 1998, pp. 38-42
Alternatives to Bohr's Copenhagen interpretation of quantum mechanics may ultimately provide a simpler, less paradoxical theory. The alternatives include "decoherent histories", "spontaneous localization", Bohm's deterministic theory, and Bell's strict non-locality results.
Bringing Schrödinger's Cat to Life
Philip Yam
Scientific American, June 1997, pp. 124-129
Recent experiments illuminate quantum theory at the border between the microscopic and macroscopic worlds.
Does Nature Violate Local Realism?
David Branning
American Scientist, March-April 1997, pp. 160-167
The standard interpretation of quantum mechanics is incompatible with the pre-quantum notion of "local realism". Experimental results continue to indicate that local realism is violated, but loopholes remain.
Review of Roland Omnès, The Interpretation of Quantum Mechanics
William Faris
Notices of the AMS, November 1996, pp. 1328-1339
The book under review is an attempt to survey different approaches to the interpretation of quantum mechanics. Omnès' own position is similar to the traditional Copenhagen interpretation, augmented by newer ideas such as decoherence and consistent histories. It is not clear, at least to the reviewer, that a satisfactory solution of the interpretation problem has yet been achieved.
[Article in PDF format]
The Duality in Matter and Light
Berthold-Georg Englert; Marlan O. Scully; Herbert Walther
Scientific American, December 1994, pp. 86-82
According to the complementarity principle of quantum mechanics, objects in the microworld can exhibit properties of both waves and particles. New experiments indicate this principle is even more fundamental than previously supposed.
Bohm's Alternative to Quantum Mechanics
David Z. Albert
Scientific American, May 1994, pp. 58-67
The quantum theory developed by David Bohm in the 1950s is an alternative to the Copenhagen interpretation. It is a fully worked out theory that is deterministic and denies the existence of superpositions, but it does possess the curious property of nonlocality.
Decoherence and the Transition from Quantum to Classical
Wojciech H. Zurek
Physics Today, October 1991, pp. 36-44
The concept of "decoherence" may help clarify our interpretation of quantum theory. It is applicable not only in defining the branches in the "many worlds" interpretation of quantum mechanics, but also in delineating the border between quantum and classical domains in Bohr's interpretation.
The Reality of the Quantum World
Abner Shimony
Scientific American, January 1988, pp. 46-53
A series of laboratory experiments have confirmed that the quantum world really is as strange as the theory suggests. For example, there are nonlocal effects in which widely separated entities can be "entangled" so that their behavior is correlated even though communication between the entities is impossible.

Recommended references: Books

Tony Hey, Patrick Walters -- The New Quantum Universe
Cambridge University Press, 2003
This is very much a book for the general reader -- full of pictures, anecdotes, and pop culture. But it does cover most of the basics of quantum physics -- waves and particles, the double slit experiment, the uncertainty principle, Schrödinger's equation, the Pauli exclusion principle, the EPR paradox, and all that good stuff. There is also coverage of aspects of quantum technology, such as Bose-Einstein condensates, superconductivity, quantum information, and quantum computers. It also ventures into related areas of high-energy physics -- astrophysics, particle physics, and the standard model.
Amir D. Aczel -- Entanglement: The Unlikely Story of How Scientists, Mathematicians, and Philosophers Proved Einstein's Spookiest Theory
Four Walls Eight Windows, 2001
The subject is the so-called paradox of Einstein, Podolsky, and Rosen. The irony is that rather than discovering a logical inconsistency in quantum mechanics, Einstein and the others motivated the confirmation of aspects of quantum mechanics they regarded as absurd: entanglement and nonlocality. Aczel has written a pretty good account of the subject for a general audience, touching on Bell's theorem and the experiments of Alain Aspect and others which verified the genuinely "spooky" implications of quantum mechanics.
Daniel F. Styer -- The Strange World of Quantum Mechanics
Cambridge University Press, 2000
In a non-technical, mostly non-mathematical, yet generally precise manner this short book presents an introduction to quantum mechanics. Topics covereed include the Stern-Gerlach experiment, measurement, the Einstein-Podolsky-Rosen paradox, and quantum cryptography.
[Book home page]
Sam Treiman -- The Odd Quantum
Princeton University Press, 1999
If you're ready to try to understand what quantum mechanics is really about and aren't afraid of a little mathematics, this book is a must-read. As a mathematical theory, quantum mechanics is not at all mysterious, and this book will introduce you to that aspect. If what you want is the philosophy, it's not here -- there are numerous alternatives for that.
Roland Omnès -- Understanding Quantum Mechanics
Princeton University Press, 1999
This is one of the best books to appear which explains the philosophical foundations of quantum mechanics without demanding a detailed understanding of the mathematical theory. Omnès himself is responsible for some of the recent philosophical clarifications. Here, he starts from the starts from the standard Copenhagen interpretation, addresses the key "problem of measurement", and then goes into the consistent-histories interpretation. Quantum mechanics is still not an easy subject to understand, but this book is a big help.
Jeffrey Bub -- Interpreting the Quantum World
Cambridge University Press, 1997
The author's work, which requires some mathematical sophistication, is a modern study of the interpretation of quantum mechanics with a view to resolving the "measurement problem". Its concluding chapter on "the new orthodoxy" shows how ideas like, "decoherence", the "many worlds" interpretation, and "consistent histories" fit together in our current understanding of quantum mechanics.
David Deutsch -- The Fabric of Reality: The Science of Parallel Universes -- and its Implications
Penguin Books, 1997
One interpretation of quantum mechanics is called the "many worlds" theory. This interpretation helps illuminate a variety of notions such as virtual reality, quantum computation, and the possibility of time travel.
David Lindley -- Where Does the Weirdness Go?
Basic Books, 1996
Non-mathematical survey of the phemomena on which quantum theory is based, and the "measurement problem" in particular. Attempts to demystify some of the seeming paradoxiality of the theory.
Victor J. Stenger -- The Unconscious Quantum: Metaphysics in Modern Physics and Cosmology
Prometheus Books, 1995
Stenger performs a welcome and most useful service by explaining quantum theory and at the same time debunking popular attemps to turn the science into a kind of mysticism. Important topics such as the EPR experiment, Bell's theorem, hiddeen variables, and nonlocality are thoroughly covered.
David Wick -- The Infamous Boundary: Seven Decades of Heresy in Quantum Physics
Birkhäuser Boston, 1995
A non-mathematical history of the experiments and interpretations of quantum mechanics. The stress is on the controversies themselves rather than on a definitive resolution of the issues.
Euan Squires -- The Mystery of the Quantum World
Institute of Physics Publishing, 1994
Squires offers a fairly concise but sophisticated introduction to the various interpreations of quantum mechanics and the philosophy of the theory. Topics include measurement, "external reality", the possible relevance of consciousness, the "many worlds" interpretation, hidden variables, non-locality, the EPR thought experiment, "pilot waves" and Bohm's interpretation, and Bell's theorem. Attempts to interject theological considerations into the discussion constitute a minor blemish.
David Z. Albert -- Quantum Mechanics and Experience
Harvard University Press, 1992
An introduction to the foundations of quantum mechanics with relatively mild mathematical prerequisites. Includes an extensive account of Bohm's quantum theory, as developed by John Bell.
Jim Baggott -- The Meaning of Quantum Theory
Oxford University Press, 1992
Survey of the fundamentals of quantum mechanics, different interpretations of the theory, the EPR experiment, Bell's theorem.
F. David Peat -- Einstein's Moon: Bell's Theorem and the Curious Quest for Quantum Reality
Contemporary Books, 1990
Introduction to interpretations of quantum mechanics. Focuses on the Einstein-Podolsky-Rosen "paradox" and how Bell's theorem has helped resolve it.
James T. Cushing, Ernan McMullin (eds.) -- Philosophical Consequences of Quantum Theory: Reflections on Bell's Theorem
University of Notre Dame Press, 1989
Collection of theoretical and philosophical essays on the meaning and interpretation of Bell's theorem.
J. S. Bell -- Speakable and Unspeakable in Quantum Mechanics
Cambridge University Press, 1987
A collection of papers on quantum philosophy, by the discoverer of Bell's Theorem. Covers many topics and uses real mathematics.
P. C. W. Davies, J. R. Brown (eds.) -- The Ghost in the Atom
Cambridge University Press, 1986
An overview of the philosophy of quantum mechanics, with interviews of leading experts in quantum physics.
Alastair Rae -- Quantum Physics: Illusion or Reality?
Cambridge University Press, 1986
Introduction to the conceptual issues of quantum mechanics. Covers such topics as the possibility of hidden variables, the Copenhagen interpretation, and the many worlds interpretation.
Nick Herbert -- Quantum Reality: Beyond the New Physics
Anchor Books, 1985
A breezy but thorough popularization of quantum theory, reality, and non-locality. Despite its age, it remains in print on account of the quality of the treatment of most of the key topics up to and including Bell's theorem.


Copyright © 2002 by Charles Daney, All Rights Reserved