Quantum Mechanics Introduces a Conceptual Burr in the Saddle of Theoretical Physics

by Fernando Caracena ©2021 Fernando Caracena

I remember discussions with Bohr which went through many hours till very late at night and ended almost in despair; and when at the end of the discussion I went alone for a walk in the neighbouring park I repeated to myself again and again the question: Can nature possibly be so absurd as it seemed to us in these atomic experiments?

--Werner Heisenberg

Not only was one of the founders of quantum theory, Werner Heisenberg, distraught by the implications of quantum mechanics, but so were the rest of the founders, The big conceptual bump is very real and it continues to affect every gradate student in physics. As a PhD student I hit the same bump and got the same jolt. When we grad students would go out for beer and pizza early in the morning after tearing ourselves away from research this burr in the saddle was a hot topic of conversation.

Both Albert Einstein and Niels Bohr, the top physicists of those days, clashed at the big international physics conferences of the time. Physicists followed these debates hoping to finally see the removal of the conceptual burr from their saddle.

Schrödinger' s Equation

Meanwhile, Erwin Schrödinger had come up with a wave theory of quantum physics in the form of an equation that was not difficult to learn and allowed physicists to calculate the various predictions of quantum theory in a straight forward matter. It featured a complex wave function that was propagated deterministically, which was interpreted as a probability amplitude. Indirectly, the Schrödinger Equation made it possible for graduate students to do quantum mechanical calculations that bypassed the mysticism of quantum mechanics to give experimental testable result.

Schrödinger's theory was somewhat conceptually removed from the scenarios of what actually going on in the world of things that would be painted by classical physics; but, the numbers it gave for the final result of an experiments were right on, much better than what resulted from any classical theory. What Schrödinger's equation had done was that it had given physicists, including grad students, a clear way to calculate quantum theory results for any valid experimental. Pending some final philosophical settlement of the theory, physicists could get out of their mystified state and just shut up and calculate. The calculations themselves became the meat and potatoes of quantum based research. Physics graduate students could now solve involved quantum mechanical problems; chip away at a piece of physical reality; get their PHd early in their career; and move on to have an otherwise normal life.

I was dumped by several girl friends in graduate who got tired of waiting for me to finish up graduate school and move on to a "normal" life. I was actually doing these girls a favor. I saw how miserable were the wives of graduate students who were having a normal life involving children and husband, but they had to live a life of poverty. Their husbands were also only semi present in their world, often lost in thought or doing "don't-bother-me", rather involved calculations that required laser-focused concentration on into the early morning hours. Their wives would often find their husbands passed out on the couch behind a pile of scribbled-on papers on the coffee table.

After the ordeals of graduate school, the wives found that they and their husbands, once having occupied the same world, had now hopelessly drifted apart. The result was divorce. To be periodically dumped by a frustrated girlfriend seemed to be the most humane alternative. The former girlfriends easily found new boyfriends, and any wound to my emotions was quickly healed by doing quantum field theory calcualtions.

Given all the warts and wrinkles of graduate school, I would say that it was much more fun than is portrayed on the popular TV program, "Big Bang Theory".

So, What is the Burr in the Saddle?

In the formulation of quantum mechanics through the Schrödinger Equation there was a problem in interpreting the sudden shift from the probability density of locating an elementary particle, such as an electron, to its sudden manifestation in a point-like volume of a detector. This was called the collapse of the wave function. One could brush off such effects are artificial computational necessities, but that was not easy to do because there were also physical effects associated with the collapse.

Chemists, following the lead of physicist, puzzled at this quantum theory. For example, did it explain anything about the nature of the chemical bond and could you uses it to calculate binding energies of molecules? This question motivated research into the nature of the chemical bond, specifically could quantum theory shed any light on it (pun intended)? The answer to this was yes. Today, there are two theories that answer the question.

The reasoning the quantum theoretical modeling of bonding of atoms is based on the idea that an atomic electron in an orbit about its nucleus moves in a complex way, not from point A to point B within the atom, but that it is present in a spread out cloud as specified by the Schrödinger wave function. All its properties are spread out as specified by the probability density and you can calculate the effects of such clouds (called orbitals) by averaging various interactions over volumes of the orbitals.

When two atoms approach each other, there are perturbation effects on the orbital structures around the atoms. The bonding of two hydrogen atoms in which the orbital electrons are in their lowest energy states is the simplest instance to discuss. There are two separate nuclei involved, each surrounded an orbital electron. The atoms are neutral, but the distortion of the atomic orbitals causes the electronic clouds to bunch up or thin out in ways that cause the atoms to either attract or repel each other. As two hydrogen atoms approach each other, the two different configurations of orbital distortions are governed by the spin states of the orbital electrons. One state is associated with a lower energy level, and the other, with a higher energy level.

Feynman, the wizard of calculating quantum interactions, said that particles in quantum mechanical interactions sniffed out all the ways they could move. This idea is the basis of his famous Feynman Diagrams. Feynman, my favorite physicist, had such a clear thinking mind that he could explain quantum mechanics to kids.

When two hydrogen atoms approach each other with enough speed, the atomic orbitals distort two ways. The result is that they fall into a composite energy state that is lower than the energy state that they were in before. The antisymmetry of the spin and spatial distribution forces the electrons to have a total antisymmety in all their characteristics. In the case of two bonded hydrogen atoms, the spin of the two electrons become anti-aligned, or antisymmetric forcing the composite wave function of the two electrons to bunch up between the positive cores of the atom. the result is that this antisymmetry forces an arrangement of charges in the atom that you have a sandwich of charges that attract each other: like two positive slices of bread containing two slices of negtive meat between them.

Now here comes the rub. The distribution of negatively charged atomic orbitals combined is what bind the atoms together. the wave function for the two electron system describes the distribution of charge involved. If however, a very energetic photon (a cosmic ray) should happen to strike on of the orbital electrons, the wave function of the two electron orbitals would suddenly collapse to the size of the point of impact, which is small for very high energy transfers, and the hydrogen molecule would be converted into a hydrogen atom and a proton interacting with each other. The knocked out electron would be flung out at nearly the speed of light along with a spray of other particles that may have been generated by the conversion of the energy of the cosmic ray into various particle masses plus their kinetic energies. So the collapse of the wave function is not just a fictitious calculational event, but represents something real. It is a feature of quantum mechanics that Einstein called a "Spooky action at a distance." And it is the different ways that Relativity and Quantum Theory handle information in space and time that constitutes the burr in the saddle of theoretical physics.

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