There Is No Quantum Theory!
Date: Tuesday, April 26, 2005 @ 22:09:31 UTC
Topic: Science


In the yahoo HSG group John E. Barchak writes: Many people suffer from the illusion that somehow the energy levels of hydrogen magically pop out of Schroedinger's equation and that quantum theory actually predicts those levels. Actually, there is no Quantum Theory. What is called a "theory" is really an empirical structure that could be replaced by a set of empirical curve fitting algorithms and empirical hamiltonians. It makes no predictions at all. All of the information contained in Schroedinger's equation was put there by Schroedinger and Hermann Weyl.

Much of the information for hydrogen was empirical from the Lymann, Balmer, Paschen, Brackett, and Pfund spectrum series. DeBroglie provided the motivation for Schroedinger's equation (DeBroglie felt that matter could be modeled as waves), but he had no direct involvement in the development of the wave equation. It was Hermann Weyl who assisted Schroedinger in the development of the wave equation so that the stable states of the hydrogen atom could be derived from it. Schroedinger's equation was designed to give the "right" answers. It is entirely empirical.

The following passage is from page 28 of "The Infamous Boundary" by David Wick (Copernicus 1996):

"Weyl was expert in many topics in mathematical physics, including the non-Euclidian geometry exploited by Einstein a decade before to construct a new theory of gravity. (In Space, Time, Matter (1918), the book young Heisenberg claimed to have read, Weyl had advanced his own version of relativity, including an attempt to unify gravity with electromagnetism that had drawn criticism from Einstein.) Most importantly from Schrodinger's point of view, Weyl knew the theory of "proper vibrations" in continuous media. This well developed mathematical discipline treated standing waves in a variety of situations, including water in a lake, air in an organ pipe, and strings on a guitar. Schrodinger hoped it would apply to the atom as well. With Weyl's help, he succeeded in deriving Bohr's stable states of the hydrogen atom, without any recourse to the classical picture of the electron as a point particle."

It was Born who put the point particle back in (but in a stochastic manner). Schrodinger regretted the reintroduction of the point particle until his last days.

The following is an excerpt from Ed Jaynes "Scattering of Light by Free Electrons as a Test of Quantum Theory": "Is Quantum Theory a System of Epicycles? Today, Quantum Mechanics (QM) and Quantum Electrodynamics (QED) have great pragmatic success -- small wonder, since they were created, like epicycles, by empirical trial-and-error guided by just that requirement. For example, when we advanced from the hydrogen atom to the helium atom, no theoretical principle told us whether we should represent the two electrons by two wave functions in ordinary 3-d space, or one wave function in a 6-d configuration space; only trial- and-error showed which choice leads to the right answers.

Then to account for the effects now called 'electron spin', no theoretical principle told Goudsmit and Uhlenbeck how this should be incorporated into the mathematics. The expedient that finally gave the right answers depended on Pauli's knowing about the two-valued representations of the rotation group, discovered by Cartan in 1913.

In advancing to QED, no theoretical principle told Dirac that electromagnetic field modes should be quantized like material harmonic oscillators; and for reasons to be explained here by Asim Barut, we think that it is still an open question whether the right choice was made. It leads to many right answers but also some horrendously wrong ones that theorists simply ignore; but it is now known that virtually all the right answers could have been found without, while some some of the wrong ones were *caused by*, field quantization.

Because of their empirical origins, QM and QED are not physical theories at all. In contrast, Newtonian celestial mechanics, Relativity, and Mendelian genetics are physical theories, because their mathematics was developed by reasoning out the consequences of clearly stated physical principles which constrained the possibilities. To this day we have no constraining principle from which one can deduce the mathematics of QM and QED; in every new situation we must appeal once again to empirical evidence to tell us how we must choose our mathematics in order to get the right answers.

In other words, the mathematical system of present quantum theory is, like that of epicycles, unconstrained by any physical principles. Those who have not perceived this have pointed to its empirical success to justify a claim that all that all phenomena must be described in terms of Hilbert spaces, energy levels, etc. This claim (and the gratuitous addition that it must be interpreted physically in a particular manner) have captured the minds of physicists for over sixty years. And for those same sixty years, all efforts to get at the nonlinear 'chromosomes and DNA' underlying that linear mathematics have been deprecated and opposed by those practical men who, being concerned only with phenomenology, find in the present formalism all they need.

But is not this system of mathematics also flexible enough to accomodate any phenomenology, whatever it might be? Others have raised this question seriously in connection with the BCS theory of superconductivity. We have all been taught that it is a marvelous success of quantum theory, accounting for persistant currents, Meissner effect, isotope effect, Josephson effect, etc. Yet on examination one realizes that the model Hamiltonian is phenomenological, chosen not from first principles but by trial-and- error so as to agree with just those experiments.

Then in what sense can one claim that the BCS theory gives a *physical explanation* of superconductivity? Surely, if the Meissner effect did not exist, a different phenomenological model would have been invented, that does not predict it; one could have claimed just as great a success for quantum theory whatever the phenomenology to be explained.

This situation is not limited to superconductivity; in magnetic resonance, whatever the observed spectrum, one has been able to invent a phenomenological spin-Hamiltonian that "accounts" for it. In high-energy physics one observes a few facts and considers it a big advance - and great new triumph for quantum theory - when it is always possible to invent a model conforming to QM that "accounts" for them. The 'technology' of QM, like that of epicycles, has run far ahead of real understanding.

This is the grounds for our suggestion (Jaynes, 1989) that present QM is only an empty mathematical shell in which a future physical theory may, perhaps, be built. But however that may be, the point we want to stress is that the success - however great - of an empirically developed set of rules gives us no reason to believe in any particular physical interpretation of them. No physical principles went into them.

Contrast this with the logical status of a real physical theory; the success of Newtonian celestial mechanics does give us a valid reason for believing in the restricting inverse-square law, from which it was deduced; the success of relativity theory gives us an excellent reason for believing in the principle of relativity, from which it was deduced. Theories need not refer specifically to physics: the success of economic predictions made from the restricting law of supply and demand gives us a valid reason for believing in that law."

Jaynes, E. T. (1989), "Clearing up Mysteries: The Original Goal", in
*Maximum Entropy and Bayesian Methods*, J. Skilling, Editor, Kluwer Academic Publishers, Dordrecht, Holland, pp. 1-27.

"Scattering of Light by Free Electrons as a Test of Quantum Theory" is found at: http://bayes.wustl.edu/etj/articles/scattering.by.free.pdf

All the best
John B.





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