Physics - a short introduction
New Directions in Quantum Physics - annoitated links
Some more links
The Emperor's New Mind (book review by Arvan Harvat, physicist)
More Book Reviews (by Arvan Harvat)
more material to be added...
The Copenhagen Interpretation
The Einstein-Podolsky-Rosen Paradox
The Aspect Experiment
Unlike other physical theories, quantum mechanics was not the the invention of one or two scientists. Those who took part in its discovery are collectively called the founding fathers. Planck, Einstein, Bohr, Heisenberg, Born, Jordan, Pauli, Fermi, Schrodinger, Dirac, de Broglie, Bose all made notable contributions. During the first part of the 20th century scientists were faced with a range of extraordinary physical phenomena showing the effects of quantum mechanics. They wondered whether the universe could really be as strange a place as their laboratory experiments appeared to show. Bit by bit they pieced together the results of experiments and found rules obeyed by matter. In 1936 Birkhoff and Von Neumann collected the rules together into the accepted axioms of quantum mechanics.
Birkhoff and Von Neumann showed that the axioms of quantum mechanics provide a consistent framework in which it is once again possible to predict the results of experiment, at least statistically. But, although these laws are mathematically consistent, most scientists agree that they are counter intuitive, and do not have any satisfactory known physical interpretation.
Almost every text book on quantum mechanics claims to adopt the 'orthodox' Copenhagen interpretation, developed largely in a series of papers and lectures by Niels Bohr and Werner Heisenberg, but it has never been entirely accepted. Its fundamental features are that a property does not exist unless it is measured, and that indeterminacy is a fundamental property of the universe. It side steps the issue of the collapse of the wave function by saying that it cannot be measured. The Copenhagen interpretation distinguishes between microscopic quantum systems, described by wave functions, and macroscopic measuring instruments, described by definite values. The quantum system triggers the measuring apparatus and, somewhere in the chain of events, the wave function collapses. It does not answer the question of how to interpret the wave function, but says it is actually wrong to try; the world cannot be understood and the sole function of physics is to make experimentally verifiable predictions.
It is easy to pick holes in the Copenhagen interpretation, and I do not believe that many first rank physicists find it convincing, though most try not to worry about it. First the distinction between microscopic and macroscopic systems is artificial. An objective description of nature should describe both systems as matter obeying the same laws of physics. Many physicists see the conflict between the probabilistic nature of microscopic physics and the determinist nature of macroscopic systems as the fundamental paradox of modern science. Second, by attributing the collapse of the wave function to measurement, or to observation, the Copenhagen interpretation becomes embroiled in philosophical knots. In quantum mechanics these problems have been nicely illustrated by the examples of Shrodinger's cat and Wigner's friend. Schrodinger and Wigner produced these examples to show that it has to be nonsense to attribute the collapse of the wave function to observation. The problem is that, until now, no one has come up with a better explanation. And yet, there is a huge body of experimental and mathematical evidence that the laws of quantum mechanics are obeyed, showing that quantum states have to be described by mixing the possible outcomes in a form of wave function, which only collapses into a definite outcome when the observation takes place.
Schrodinger put a cat in a box with a capsule of cyanide which would be triggered to break with a 50% chance by a quantum mechanical process, killing the cat. Oh, all right, he didn't actually do it, but he thought about it. A physicist looking at the box does not know whether the quantum process has broken the capsule or not, so he describes it with a quantum state, that is to say a wave function in which the process has part broken the cyanide capsule, and part not. If the wave function collapses when the observation takes place, then he should describe the cat with a quantum state as well, in which the cat is part alive and desperately trying to get out of the box before the cyanide gets him, and part dead and lying in a heap on the floor.
Although I have heard it said that the EPR paradox has been resolved by experiment in favour of quantum mechanics, and against Einstein, it is actually a far more serious a paradox than Schrodinger's cat. It cannot be regarded as solved, because it apparently demonstrates a very deep conflict between relativity and quantum mechanics.
Einstein, Rosen and Podolsky imagined that a quantum mechanical process generates two particles flying in opposite directions with equal momenta. The momenta of the particles is not known, so the rules of quantum mechanics dictate that it is governed by a wave function. The two particles become separated and then an experiment is done to determine the momentum of one particle. According to conservation of momentum, the momentum of the other also becomes known at that precise point in time, so its state has been changed. Yet the separation between the particles implies that no influence can pass from one to the other. Einstein felt that "No reasonable definition of reality can permit this".
The reason the EPR paradox is so severe is that the predictions of quantum mechanics fly in flat contradiction to the laws of relativity, which are so solidly established and so successfully built into the deepest form of quantum mechanics, quantum electrodynamics. Nonetheless recent experiments based on Bell's inequality support these predictions.
Instantaneous action at a distance is prohibited by relativity because if anything were to travel faster than the speed of light, then it would also have to be able to travel backwards in time. If two physicists each measure the momentum of one of the particle, then the one who measures his particle first causes the other physicist's results to change. But relativity tells us that, according to a moving observer, it was the second physicist who affected the results of the first.
Einstein believed that some other process, such as a hidden variable, must dictate the experimental result. A hidden variable is an unknown quantity which is defined but which cannot be known, and which affects the results of the experiment without revealing its own value. Although David Bohm has produced a "hidden variables" theory based on a form of hidden variable, it is also non-relativistic, non-local, and can hardly be taken seriously as an interpretation of quantum mechanics.
For practical reasons, the EPR paradox cannot be tested in exactly the experiment suggested by Einstein, Podolsky and Rosen, but resolving it is of such importance that it has been developed, especially by John Bell, and tested experimentally a number of times, most significantly by Alain Aspect.
John Bell imagined that instead of measuring equal and opposite momenta, a process emits two particles with equal and opposite spin. Initially spin is not aligned, but it can be measured in each of the x, y and z directions. If the spin of a particle is measured, it aligns with the axis chosen for the measurement. This implies that the other particle must be aligned on the same axis, with opposite spin. Thus, the fact of a measurement of spin of one particle, will affect the results of a measurement spin of the other.
Bell established a mathematical inequality which showed a bit more than this. If each particle can be regarded as a system in its own right, Bell showed that the laws of quantum mechanics would be violated in experiments measuring the spin of each particle on different axes. Quantum mechanics predicts that the choice of the axis for the first measurement of spin will alter the results of measurement of spin of the second particle, in a manner which is not consistent with the notion that the two particles have separated and become independent.
The experiment had been carried out a number of times and it has been found that Bell's inequality is violated, and the predictions of quantum mechanics supported. It still left the possibility that the wave functions for both particles collapsed at the time of the decision of which axis to use, and that as this took place before the experiment, nothing need to travel faster than the speed of light.
Alain Aspect and his colleagues in Paris set up the experiment in such a way that the decision on which direction to measure spin was made by a pseudorandom generator, after the particles were emitted. They still found that Bell's inequality was violated and that the decision on which direction to measure spin of one particle changed the results of the measurement of the other, even though a message from the point where the decision was made to the second particle would have to travel faster than the speed of light.
The paradox only occurs when two particles are connected by a causal event; here they are emitted by a process which dictates that they have opposite spin. The measurement of the spin of A affects the measurement of the spin of B., even though a message from A to B would have to travel faster than light. A curious feature of the correlation is that no information travels from the results of one measurement to the other. You have to bring both sets of results together and compare the correlations between the results and the directions chosen to establish that Bell's inequality is violated. The question really is, if nothing travels faster than light, how can the correlation come about?
The issues involved in the paradoxes centre on the collapse of the wave function, and the statement that a property does not exist unless it is measured. This has been taken to imply that there is no physical reality, or that consciousness is responsible for the physical properties of matter, and even to suggest that electrons could not have existed before Thomson discovered them. Ultimately one might conclude that the world was flat until the discovery of America. The issue then would be whether it was Columbus who was responsible for the change, or whether it was the American Indians, or even whether they lived in thesame universe.
In the current state of philosophy of science, it seems that most philosophers maintain that it is not possible for science to deliver truth. I think they would say that the paradoxes do not need resolution because, as a matter of principle, the universe cannot be understood.
I take an opposite view. In my Quantum Mechanics Primer I will show that these paradoxes are not evidence that the universe behaves in an incomprehensible manner, but are the inevitable, if unexpected, consequence of a true understanding of the nature of science and measurement.
According to the usual interpretation of quantum mechanics, the fundamental building blocks of matter are neither wave nor particle, but some inexplicable combination of wave and particle. Whenever we measure the position of a particle it appears as a hard point-like object with a precise position in space. But when left to its own devices, the evolution of the particle is described by the laws of wave mechanics. Quantum mechanics seems to contradict the idea that, prior to measurement, a particle is a point-like object with an unknown position, and appears to say that the particle is actually a wave spread over space.
A pair of quantum-entangled or conjugate particles are created. Polarization is typically assayed (the particles must possessorthogonal polarizations, but which is which?). It is the Bell Inequality applied to the Einstein-Podolsky-Rosen (EPR) paradox. If you measure one particle's polarization the other particle's polarization is fixed, yet neither particle has any polarization until you look (superposition of states). So you measure a sparse stream of entangled photons at widely separated points (your measurement interval being less than the distance divided by lightspeed) then get together and compare notes.
Many, many times, including one lovely test in Europe where a new fiberoptic cable was used before it was commissioned for a phone company to separate entangled photons by some 30 km before their wavefunction was collapsed by observation. Quantum mechanics won - instantaneous correlation when the datasets were later compared.
Quantum eraser experiments do a similar trick: the effect (classical or non-classical behavior at a double slit or equivalent) preceeds the cause (look or don't look behind the slit). Even more disturbing, you can look and get classical results, then lose the data and the pattern reverts to the usual double slit one. How do the particles know?
Absolutey not. It can be shown that no information is transferred, nor can it be.
No superluminal information can be transferred. There is no contradiction.
This is a very complex question. I can give you many layman's links, but, since I'm a bit disappointed in contemporary physics ( I'm a MSc in particle physics - also, have been working in chaos ( with meagre results ), and am now transferring again to particles, but also other Quantum Mechanics approaches ( Bohm's especially ). As for now, my position ( the result of works, meditation and I Ching ) is:
You got truly professional stuff at http://xxx.lanl.gov/ and good intro on http://math.ucr.edu/home/baez/physics/faq.html
http://www.weburbia.com/pg/theories.htm has ceased to deal with "esoteric" physics and is now just a dull timeline.
Other than that, you have useful linx like:
relatively bizarre http://members.cox.net/vtrifonov/
string linx http://www.superstringtheory.com/http://theory.caltech.edu/people/jhs/strings/index.htm http://www.physics.ucsb.edu/~jpierre/strings/
And the very useful Physics Encyclopaedia:http://members.tripod.com/~IgorIvanov/physics/
I'm planning to delve seriously in superstrings and Bohmian Quantum Mechanics in next 2-3 months. While my interest in superstrings is more of a "theoretical" nature ( no calculations, just an inquisitiveness in a paradigm - I'll flip through Greene's popular and Polchinsky's professional works ), I intend to analyze Bohmian paradigm more carefully ( along with other physics stuff like Ashtekar non-geometrical approach to cosmology). As for ordinary Quantum Mechanics - I don't think there is much to offer in this field - it's 20/30ies old stuff. Anyway, if you're interested in an easy-to-understand lectures, there is a link at http://ParticleAdventure.org/
|more Quantum Physics links and references|
CERN Home page - European laboratory for particle physics and birthplace of the Web
General Physics / Quantum physics links (themepage - by Zues Internet robot)
Topological Geometrodynamics (TGD), by Matti Pitkänen
Science - Stephen Paul King - papers and links
Our purpose is to explore alternative, unconventional models of reality in an effort to free ourselves of the current restrictive and inadequate Materialistic Dogma. We are currently looking into the Nature of Time and Mind from a computational and information/matter duality perspective and welcome any suggestion that, twisting the words of words of Dirac, "might be wrong."
more particle links
Emperor's New Mind : Concerning Computers, Minds, and the Laws of
by Roger Penrose - hardcover
Penrose's bestseller is by far the best exposition of...what ? Basically, all the stuff, ranging from AI and algorithms to classical and quantum mechanics, thermodynamics and basic tenets of Big Bang cosmology, is densely packed in 480+ pages and rushes vertiginously the the author's central interest- brain/mind problem and his particular answer to the "why consciousness" ancient question that has resurfaced after more than 70 years of post-Jamesian hibernation.
On the strong side, Penrose has most lucidly expounded classical and quantum paradigmata ( plus thermodynamics and orthodox cosmology ). I think his finest writing is contained in these chapters/passages. Key quantum concepts have probably never been so thoroughly discussed and explicated as in chapter 6, "Quantum magic and quantum mystery". This could serve as a layman's quantum desert island solace, both serious and enchanting (use of math is minimalist). Chapters from 1-4 ( with the possible exception of chapter 3. ) are a dry read and not illuminating at all. Frankly, I'd say the entire AI, the Turing machine and computability "mythology" is just a scholiasts's fodder lacking the true cognitive strength.
So, where does Penrose stand?
Evidently, he is a "refined" physicalist/epiphenomenalist. I'd say his "consciousness" theory ( he's done not a few papers with Stuart Hameroff on Orch OR model ) is not a breakthrough at all. For more complex expositions of quantum physics, one should consult David Bohm's works ( apart from classical textbooks of Landau, Dirac or Sakurai ); for a more thought-provoking "brain" musings - Jean Pierre Changeux and his L'Homme Neuronal. For all the evident intent to "explain" the consciousness in terms of quantum mechanics, Penrose has achieved only one goal ( from his standpoint, probably a sideshow): a masterful presentation of modern physics by one of its preeminent virtuosi.
accessibility - Intermediate
quality - - his attempt is a failure, but daring nonetheless
Modern Quantum Mechanics by J. J. Sakurai
Rigorous and detailed treatment of Quantum Mechanics. What is lacking in
depth is more than amply made up by step-by-step derivation of math apparatus. A
slow-paced textbook good for slow-witted plodders (no offense). I've found it if
not illuminating, at least a useful reference.
accessibility - Advanced ( Intermediate University Textbook equivalent)
Principles of Quantum Mechanics by P. A. M. Dirac
Probably the single most important book on Quantum Mechanics. Although taught
in undergraduate courses (in Russia and elsewhere), too technical for a
beginner. Condensed, frequently taciturn, and packed with equations (this is
where the modern bra-ket approach got started). In my opinion: neither
aesthetically entharalling nor cognitively strong as the legend would have it.
But- that's just my opinion. I could be wrong.
accessibility - / Advanced (Intermediate to Advanced University Textbook equivalent)
Quantum Mechanics by L. D. Landau
Superb exposition. Detailed, all-encompassing and (surprise !)- deep.
Pedagogically seductive, intellectually satisfying, philosophically thought
provoking. A step-by-step sprawl, contains vast material not usually found in
other textbooks (or, if found, clumsily presented). Being a blend of intuition
and rigor, this is the book to learn Quantum Mechanics from and to revisit it
when in quantum dire strait.
accessibility - / Advanced (Intermediate to Advanced University Textbook equivalent)
Conceptual Developments of 20th Century Field Theories by Tian Yu Cao
Excellent (and virtually mathless, save for a few excurses) in-depth analysis
of the way our physical thinking evolved. It covers thoroughly all conceptual
signposts of the 20th century physics (stemming from distant past)- aether,
space, time, space-time, field, gravitation, inertia, quantum concepts like
quantization, anomalies and renormalizability. A gift of a bird's (better,
eagle's) view for an undergraduate student (that's what you don't understand
because you're busy solving the equations); a penetrating analysis for a patient
layman (who can grasp circa 70% of the book). Highly recommended.
accessibility - Intermediate (entry level textbook equivalent)
The Feynman Lectures on Physics : Commemorative Issue (3 Volume set) Richard Phillips Feynman, Matthew L. Sands, Robert B. Leighton
There is an anectode that Einstein, commenting on Frederick Engels's (cofounder of communism, along with Karl Marx) "Dialectics of Nature", humorously observed: " This is the way a physicist should not think". Well - Feynman's legendary lectures ooze the impression: this is the way a physicist should think. Great merits of the trilogy are: