WHAT WOULD EINSTEIN SAY?
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Gravity's Engines
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Editor's Note: This feature was originally published in our January 1992 issue. We are posting it because of recent discussions of the connections between chaos and quantum mechanics.
In 1917 Albert Einstein wrote a paper that was completely ignored for 40 years. In it he raised a question that physicists have only, recently begun asking themselves: What would classical chaos, which lurks everywhere in our world, do to quantum mechanics, the theory describing the atomic and subatomic worlds? The effects of classical chaos, of course, have long been observed-Kepler knew about the motion of the moon around the earth and Newton complained bitterly about the phenomenon. At the end of the 19th century the American astronomer William Hill demonstrated that the irregularity is the result entirely of the gravitational pull of the sun. So thereafter, the great French mathematician-astronomer-physicist Henri Poincaré surmised that the moon's motion is only mild case of a congenital disease affecting nearly everything. In the long run Poincaré realized, most dynamic systems show no discernible regularity or repetitive pattern. The behavior of even a simple system can depend so sensitively on its initial conditions that the final outcome is uncertain.
At about the time of Poincaré's seminal work on classical chaos, Max Planck started another revolution, which would lead to the modern theory of quantum mechanics. The simple systems that Newton had studied were investigated again, but this time on the atomic scale. The quantum analogue of the humble pendulum is the laser; the flying cannonballs of the atomic world consist of beams of protons or electrons, and the rotating wheel is the spinning electron (the basis of magnetic tapes). Even the solar system itself is mirrored in each of the atoms found in the periodic table of the elements.
Perhaps the single most outstanding feature of the quantum world is its smooth and wavelike nature. This feature leads to the question of how chaos makes itself felt when moving from the classical world to the quantum world. How can the extremely irregular character of classical chaos be reconciled with the smooth and wavelike nature of phenomena on the atomic scale? Does chaos exist in the quantum world'? Preliminary work seems to show that it does. Chaos is found in the distribution of energy levels of certain atomic systems; it even appears to sneak into the wave patterns associated with those levels. Chaos is also found when electrons scatter from small molecules. I must emphasize, however, that the term "quantum chaos" serves more to describe a conundrum than to define a well-posed problem.
Considering the following interpretation of the bigger picture may be helpful in coming to grips with quantum chaos. All our theoretical discussions of mechanics can be somewhat artificially divided into three compartments [see illustration] although nature recognizes none of these divisions.
Elementary classical mechanics falls in the first compartment. This box contains all the nice, clean systems exhibiting simple and regular behavior, and so I shall call it R, for regular. .Also contained in R is an elaborate mathematical tool called perturbation theory which is used to calculate the effects of small interactions and extraneous disturbances, such as the influence of the sun on the moon's motion around the earth. With the help of perturbation theory, a large part of physics is understood nowadays as making relatively mild modifications of regular systems. Reality though, is much more complicated; chaotic systems lie outside the range of perturbation theory and they constitute the second compartment.
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11 Comments
Add CommentI long for the good old days when intelligent people dominated the news. The only way to get attention these days is to forecast doom or blow yourself up!
Reply | Report Abuse | Link to thisAm I being thick? The text refers to a number of crucial figures, where are they?
Reply | Report Abuse | Link to thisTying this all to the zeta function seems to always be where such discussions of quantum (and other) chaos end. So many things seem to be built of characters which resemble the prime numbers - doesn't anyone notice the semantics of it all? When one asks the question " What exactly do I mean by prime and composite?" - one begins to realize that mathematics is "just another language".
Reply | Report Abuse | Link to thisWHERE ARE THE FIGURES???
Reply | Report Abuse | Link to thisSorry about the lack of figures, folks. We didn't have them handy and thought it more important to get the article out than to wait for the images.
Reply | Report Abuse | Link to thisThe article is excellent. However, the lack of figures illustrating/discussing the text makes it much less valuable than it should be. Surely SciAm should have been able to get hold of those figures by now? Please do publish them and let us know that you have done so. Thanks, -- GSC
Reply | Report Abuse | Link to thisIn arithmetic, operations are interchangeable if they are commutative. Nest non-commutative operations in program loops and results will be truncated with rounding errors, because decimal numbers are not reals. So such simple iterative loops cause results to go haywire within a few dozen repetitions. You can write computer programs to calculate as we do long-hand to great precision, but this increases execution times exponentially. No doubt to calculate quantum phases, computers are used, but how can we write programs which are not inherently chaotic, in view of the fact that we cannot know the position and velocity of a sub-atomic particle. Chaos theory applies to calculations as much as to physics. This article begs the question?
Reply | Report Abuse | Link to thisIt's excellent
Reply | Report Abuse | Link to thisThere are so many things to be understood from that text that I'm sure I don't understand the tenth of it.
Reply | Report Abuse | Link to thisBut quantum chaos seems to be a link between quamtum and classical mechanics. I am a determinist, I think that the probabilistic description of current quantum mechanics is just a statistical view of something that is in fact much more complex - a new mechanics to discover ? Anyway, I'm sure that quantum chaos has a role to play in all of this, I guess the future greatest progress in fundamental physics will have to do something with quantum chaos.
Consider the answer lays in the faqct that we need to look at the Universe at a much smaller scale.
Reply | Report Abuse | Link to thisWhat if the electron itself was not a fundamental particle but made up from 1.23 x 10 to the power of 20, such particles. Now everything makes a lot more sense it is not a probability density distribution -it is a cloud. Moreover, a cloud is almost exactly what you see when you look at the electron experimentally and mathematically.
You get quiter a lot of determinim back into your equations, but you haqve to remeber at that scale space-time is made nof the same harmonic quintessence. bottom mline is nyou will almost always get some chaos coming in - hence Heisenberg's uncertainty.
The bonus is that you can now deirive things like E=mc2 from first principles. See: The formulation od harmonic quintessence and a fundamental enenrgy equivalence equation. See Physics Essays 23: 311-319.
You can find the figures at http://www.dhushara.com/book/quantcos/qchao/quantc.htm I'm not sure why they haven't been included...?
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