Chapter 2


The Collapse of The Wave Function



A pretty piece of juggling science does here. (Banesh Hoffmann)



For light phenomena, Thomas Young's double slit experiment has always been the hallmark of the wave-particle conflict. In this experiment, a ray of light is passed through two small openings onto a photographic plate. The ray, going through both openings at once, produces the familiar interference patterns on the plate. This means that two trains of waves are interfering with each other after passing through the slits. And this experiment works equally well with electrons and other particles. But what shocked everyone was the fact that when a single particle was projected towards the two slits in this way, it interfered with itself! That is, when a beam of particles passed through the two slits at the rate of one particle at a time, the interference pattern was still produced. How can a particle possibly interfere with itself?


The obvious answer is that it's not a particle at all.  It's a wave. But then what produces the individual scintillations on the photographic plate? The obvious answer is that it's not a wave at all. It's a particle.         


This is the “either-or” aspect of the wave-particle conflict. For if science is to properly define an object, the object itself cannot be ambiguous. And no experiment has been able to nullify one or the other.  This baffling enigma is the essence of what has been called, among other things, “the reality crisis” in physics.


The electron diffraction experiment alluded to earlier by Born, verified the existence of de Broglie's waves.  In these experiments Davisson and Germer reflected electrons from the surface of a piece of nickel.  The resulting patterns were not just the familiar patterns that depicted waves; they were the exact waves that de Broglie predicted.  This confirmed conclusively the wave theory of matter.            


But aside from the Davisson-Germer experiments in America (1925-1928), which draw most of the attention of historians, there were the electron diffraction experiments of G.P. Thomson in England.  He shared the 1937 Nobel Prize with Davisson for his efforts, yet, curiously, one rarely finds but meager mention of his observations.  It's curious because Thomson was philosophically astute for an experimenter – a rare breed in science – and wrote much about his exploits.


Thomson bombarded a sheet of gold foil one millionth of an inch thick with electrons (later, he used neutrons and protons with similar results). The metal was so thin that the thickness of only one atom was left. And since an atom is enormous compared to an electron, it should pass through the foil undisturbed and strike the awaiting photographic plate. But this was not the case. Thomson was astounded to find a series of concentric rings surrounding a central spot where the few undeflected rays landed.


After absorbing the initial shock of seeing these “diffraction halos”, Thomson noticed that these rings represented something that not only corresponded to de Broglie’s electron waves, but “in all probability these patterns were the electron.” He checked his computations, repeated the experiment and got the same results. The patterns revealed a puzzling disturbed area moving outward, but moving slower than the surrounding waves themselves. He was astonished because this implied that the electron may be spreading!  


The results of the experiments make it necessary to suppose that the waves extend over a considerable region… But if one regards the waves as in any sense forming part of the electron, this means that an electron is larger than an atom, and how then is it possible for many electrons to form part of a single atom.1


Of course, the obvious answer, that the atom spreads also, is the least acceptable one. It’s not even considered. But the important thing to remember here is that if the wave is real, then it definitely expands. Thomson goes on:


It seems as though the whole conception of size is a mistaken one...  It would seem as though for an electron the size was nothing but the region in which it exerted force, that this region has no very definite boundaries and may be larger or smaller according to circumstances.


It baffles me that these first-hand observations never seem to show up in the histories, textbooks or even in the modern expositions on the new physics.  I suppose it's because that it's unanimously assumed that they have no existential value because of the images they produce; images of atomic processes that are no longer allowed. Thomson continues:


The point which represents the energy of the electron is guided by the waves that surround it, and extend possibly to an indefinite distance in all directions...  The question of the physical nature of these waves is a very difficult one...  The waves, in fact must be regarded as perpetually running through the electron from behind so that the electron is always receiving a fresh supply [?].  But there is a kind of peculiarity in the waves which is associated with the electron and moves with it.  This peculiarity is called the "group".


The group Thomson refers to is a theme with many variations.  It is also called the “disturbed area”, “crowd waves”, and of course, the wave packet.  What's important here is that there are two different phenomena involving waves: the “pilot waves” coming “from behind” the electron, and these concentrated waves which seem to represent a constructed mass of the electron.  Schrödinger speaks of this phenomena in a similar manner:  “The single waves always rise alternately in front of, and behind the electron, so that they become intensified in the space between in such a way that a constantly created structure occurs which moves at precisely the same speed as that of the electron”2.  It seems almost as if the electron is being constructed from within itself! Thomson goes on:


For the electron waves the group velocity is equal to that of the electron...  For most purposes the group velocity is what matters; indeed, the wave velocity seems of the nature of a mathematical abstraction in that it is probably impossible to measure it directly.


And from another publication, Thomson tells us why, perhaps, these pilot waves cannot be measured or observed:  


Now the waves that accompany an electron definitely do not travel with the speed of light.  According to de Broglie's theory they travel much faster [?] and the slower the electron the faster the waves.3


What a coincidence; for light speed (c) is involved in determining the difference between energy and mass (e=mc2, or m=e/c2). Thomson concludes:


...roughly speaking the particles appear where the waves are strong.  But waves, as we have seen, do not go in straight lines...even when the waves are short.  Hence Galileo's idea of the particle acted on by no force which goes on forever in a straight line must be abandoned.  It is not that the particle would stop but that it would spread, for that is what waves do...  But how can a particle "spread"?


How a particle can spread is a question that is not given a whole lot of thought in physics.  Nor are many other questions that are raised within the domain of this new science.  Existential questions are usually brushed off as philosophical in essence, and, as one professor of physics quipped, “Your average quantum mechanic is about as philosophically minded as your average garage mechanic”4. Expediency is the name of the game. It's the only game in town, it appears.  For even Thomson succumbed to the popular view, the one all of us are asked to acknowledge: that the wave phenomena, in both of its forms, is “just” a mathematical device.  According to Robertson, who briefly describes this experiment in his book, New Gravity, he is “opting to subjective over-rule...  Thomson and all the physical science community are suffering from a psychological and extremely contagious mania definable as '3-d particle syndrome/pox'” (sic)5


Though it is overstated, his criticism has a strong element of truth. Except the “mania” he speaks of is the product of an entire culture, not just a select group.  Although it has never been seen or its existence positively confirmed, the hard, point-like particle or atom is taken as a matter-of-fact by almost everybody.


David Bohm is one of the few exceptions. He voiced his frustration on this very issue:  “The whole social structure of physics has the effect of confirming the particle hypothesis of matter.  As a consequence, other possibilities become more difficult to investigate”6.


One of the few critical evaluations of Thomson's work comes from J.W.N. Sullivan, “one of the world’s four or five most brilliant interpreters of physics” (Time Magazine).


In the system of waves constituting the electron there is a "disturbed area" which moves more slowly than the train of waves...  We see something similar in a storm at sea, where there are patches of intense disturbance moving comparatively slowly.  The advancing waves overtake and move through these patches.  These disturbed areas reveal the position of the electron.


Sullivan then makes a powerful and telling statement that illustrates both why the constructed mass or wave packet that moves “precisely” with the electron cannot in fact be the electron; and what the defenders of the faith fear the most, infinity:


But we cannot say that the disturbed area is the electron.  For any such area has a tendency to spread, and if the matter of our world consisted of a number of disturbed areas it would by now have spread indefinitely7. (emphasis added) 


This is an important comment because it says point-blank why the probability interpretation was so readily assimilated, proposed and accepted.  Likewise, it points out why a geometrical picture of atomic processes is so emphatically disallowed in the new “modern” quantum physical world.  And both of these subtleties can be illustrated with a single word: implication.  Sullivan continues:


Each electron, in fact, requires a three dimensional space to itself. This would seem to make it obvious that these waves are merely a mathematical device.  It is distinctly disconcerting, therefore, to find that experiment, as we have seen, confirms their existence.


This is amazing. Think about it. How can an object with mass and charge, that takes up a volume of space and whose existence is predicted by calculation and confirmed over and over by experiment, be “merely a mathematical device”?  Sullivan states that “It is the electron that is the key to the universe”, then, overwhelmed by the successes of the new Copenhagen epistemology with its “majority rule”, he slams the door in its face:


The apparent agreement between calculation and experiment seems to be in some sense illusory.  It is very difficult to avoid the conclusion that the experiments have not yet received their right interpretation.  And there, for the present, we must leave the matter.


Of course sixty-five years later, the matter, or more precisely, the illusory “agreement between calculation and experiment”, is still on hold.  The results of these experiments still lack an official graphic interpretation.  But according to the dogma, whatever it is that displays the spreading behavior just described by Thomson and Sullivan cannot be visualized or even imagined except through mathematics.  And the way this spreading behavior was obscured then and now is among the most absurd of all the absurdities that came out of the new physics: “the collapse of the wave function.” Nick Herbert:


This is the quantum law of motion:  Increase and multiply:  Starting from your inviolable realm, take all possible paths open to you.  The natural evolution of a quon's [a "quon" is any sub-atomic particle] proxy wave is to expand without limit.  However, in the measurement act a quon can't realize all its possibilities because only one measurement result actually happens.  Therefore, at some point between its creation in the quon gun and its registration as an experimental result, a quon must repudiate the universal law of motion, halt its unbridled natural expansion, and contract [!] into a single possibility corresponding to the single observed measurement result9.


Is this clever or what?  An unobserved electron is allowed to expand because, as one quantum law insists:  “No phenomenon is a real phenomenon until it is an observed phenomenon” (J. Wheeler).  Then the benign, unreal electron-wave is in a “superposition”, traveling in all directions at once until it's observed, whereupon it must collapse in size like a punctured balloon to within finite, observable and conceivable dimensions.  Or, as J. von Neumann put it, “and then a miracle occurs”.  The “miracle” is invoked, that is the collapse, to again avoid the implications. Fred Alan Wolfe says:


Because it is so tiny, it takes only one billionth part of a billionth part of a second for the atom to spread out into fuzziness [read uncertainty].  And it continues to spread out until you come along and observe it.  At that instant, depending on which experiment you perform, the atom is reduced to size.  Just think, without you all atoms would spread out into the universe at an alarming rate (emphasis added) 10.


J. von Neumann's fictional collapse was an extension of an idea by the English physicist, Paul Dirac—whose input was another timely coincidence enhancing both the ideas of Heisenberg and Born.  Dirac extended Heisenberg's concept of an electron being in all orbits at once to his law of superpostion, “one of the most fundamental and most drastic” laws of quantum mechanics (Dirac).  Basically, it means that two or more waves may be superimposed on each other, or that “their respective amplitudes summed in order to give a single wave in which the component waves interfere constructively or destructively depending on their phases.”11 Said another way, the electron could move in more than one direction at the same time (i.e., picture yourself walking upstairs and downstairs simultaneously). But when Dirac's idea met the psi-function, the spreading electron became “a combination state consisting of not just two but of an infinite number of pure motions all going on at once”.12 


But this mathematical phantom corresponded only to an unreal, or unobserved electron.  Once a measurement was taken, the electron was collapsed into a “pure state”; the very one that's observed!  With Diracs mathematical expertise he was able to work out a transformation between Heisenberg's matrices and Schrödinger's wave function Ψ, while incorporating Born's probability function Ψ2. Desperate situations call for desperate solutions.


But Schrödinger wasn't fooled for a moment:


We are faced here with the full force of the logical opposition between an


either-or (point mechanics)


and a


both-and (wave mechanics)


This wouldn't matter much, if the old [particle] system were to be dropped entirely and to be replaced by the new.  Unfortunately, this is not the case.  From the point of view of wave mechanics, the infinite array of possible point paths would be merely fictitious...13


Schrödinger, like Einstein and so many others, never accepted the new Copenhagen interpretation.  And, like Einstein, he maintained his position until his death in 1961.  But the method had enormous success.  And his altered wave function was to continue as the computational heart of this method.  The wave-packet, however, became a footnote to its history; the very first casualty in the new way to interpret nature.  And because philosophical reason became so perverted; and because understanding came to mean so little to this new science, Schrödinger left it with the comment, “I don't like it, and I'm sorry to think that I had anything to do with it”14.  Einstein rejected it in the same way and for the same reasons:  “The more successful it is the sillier it looks”.15