4.10 THE BEING OF AN OBJECT OF EXPLANATION WHEN USED TO EXPLAIN AN ORDINARY MEASUREMENT

But if this threefold way is the manner of being of an object of explanation when observed through a predicated measurement, then we must ask concerning the manner of being of that selfsame object when merely used, unobserved, to explain some experience which we had quantified through an ordinary measurement. Preliminarily, it seems reasonable for us to assume that an object of explanation has the same manner of being whether observed or not, in which case we should take them to have the threefold manner of being described above even when they remained unobserved. Before making this preliminary assertion permanent, however, we must first understand the pervasive tendency of modern science to take the objects which explain its ordinary measurements as objects of experience, lest we miss some reason why the difference we identified between their manners of being does not carry over from predicated to ordinary measurements.

The reason for the community’s insistence that the constituents of matter are objects of experience resides, we suggest, in man’s natural tendency to associate reality to anything it can actually see, an inclination which modern science itself does nothing to discourage. According to the scientific project, the objects used to explain ordinary measurements are freely created by us for that express purpose and are subject to no additional requirements:

Physics constitutes a logical system of thought which cannot be distilled, as it were, from experience by an inductive method, but can only be arrived at by free invention. The justification of the system rests in the verification of the derived propositions by sense experience.
Albert Einstein, Physics and Reality (1936)

Evidently there is nothing in this process which informs us one way or another about the manner in which the explanatory objects involved are what they are. Consequently, we are free to ascribe to them any manner of being that we may wish. History shows that man has always instinctively tended to ascribe to them the manner of an object of experience because it is in man’s nature to assume that anything which was useful in explaining reality must itself be real. For instance, there is an overwhelming power of persuasion in seeing the trace associated with a particle passing through a Wilson chamber: how, one might ask, can an object of explanation, say an electron, not possess the reality of an object of experience if I can actually see it travel through the chamber like a golf ball would travel down the green? Needless to say, of course, what we actually observe are a succession of condensation centers, not the particle we have conceived in our mind in order to explain the succession. Therefore, to take the trace in the Wilson chamber as evidence of a particle is to confuse an explanation with the experience it explains. Nevertheless, because there is one, and only one, requirement for validating the explanation of an ordinary measurement, that is, our ability to verify propositions derived from it against sense experience, there is no bar to thinking that what we see there is in fact a real particle which has just passed by, and we therefore invariably do so.

On the conventional historic record, it appears that this ontological miss-assignment went largely unrecognized. As we indicated earlier in this chapter, however, the problem did in fact call attention to itself from the very beginning of the modern scientific project when the corpuscular theory of an ideal gas could not reproduce Boyle’s law. This failure to explain should have raised a question concerning the kind of object, other than an ordinary particle, that would have explained Boyle’s law, but it did not. As we recall, the argument used to avoid the question was, that because ordinary measurement of any property of a gas involved the contribution of large groups of molecules, the pressure measured by Boyle must have been the time average of the instantaneous pressures imparted by the gas molecules. However, since the derivation of that time average from the underlying dynamics would have been an impossibly tedious job, the dynamical average was replaced by a statistical one. And in fact, if one assumed that the probability distribution of molecule locations within the container was uniform, the familiar volume dependence law would have resulted immediately. This statistical argument appeared so plausible, and the explanatory success so comprehensive, that any attempt to suggest an alternative ontology for the constituents of matter would have been unjustified; thinking of a molecule as being everywhere at once when occupying the volume and as being localized in a point when hitting the walls would have provided the same result but would not have been any more acceptable then than it appears to be today.

There were, however, a few ordinary experiential situations which allowed of no such subterfuges; in those cases, the failure to explain resisted all attempts at circumvention and, therefore, to simply await an explanation from future theoretical development appeared to be preferable to considering alternative ontologies. The most preeminent of those cases is the temperature dependence of the specific heat of solids. The failure of the statistical theory to explain that temperature dependence remained a puzzle until 1907 when Einstein considered the implications of Planck’s theory for the corpuscular theory of solids. According to the empirical law established by Dulong and Petit in 1891, all simple solids have the same molecular specific heat at constant pressure. Indeed, at room temperature, they found the following values measured in joules/mole/degree:

Copper 24.5 Aluminum 24.4

Silver 25.5 White Tin 26.4

Lead 26.4 Sulfur 22.4

Zinc 25.4 Diamond 6.1

These ordinary measurements were conducted by setting up an experiential situation designed to quantify the familiar experience that warming up a solid increases its temperature. The corpuscular explanation of why the specific heat does not dependent upon the nature of the solid involved is then obtained by conceiving of the solid as a lattice of atoms, each of which are free to vibrate about their equilibrium positions in the lattice. Under this assumption, the mechanism by which heat affects the solid’s temperature is the increase in the vibrational energy of the lattice atoms which is produced by the addition of heat. The mathematical representation of this mechanism is obtained by applying classical mechanics to the system of atoms to determine its total energy. One finds that the total energy is the simple sum of 3N individual harmonic oscillators:

E = \sum_{i = 1}^{3 N} (\frac{p_{i}^{2}}{2 m} + \frac{1}{2} k_{i} q_{i}^{2})

Since, by the equipartition theorem, all the energies, both kinetic and potential, are equal to half $k T$ , we have:

E = 3 N 2 \frac{1}{2} k T = 3 N k T = 3 R T

which leads to the independence we sought to explain, as well as to the observed numerical value of 25 joule/mole/degree:

c_{V} = {(\frac{\partial E}{\partial T})}_{V} = 3 R

According to this explanation, extending the measurement to temperatures other than room should not change the resulting specific heats. That however does not turn out to be the case: the specific heat of solids decreases with temperature below the Einstein temperature which depends on the chemical nature of the solid, a fact we could have already noticed in the table above where the specific heat for diamond at room temperature is much lower than 25 joules/mole/degree. It is not possible within the explanatory structure described above to understand why the molecular specific heat of solids should fall at low temperature below the classical equipartition value of 3R, much less why it should do so in a substance specific way.

In his Annalen der Physik paper of 1907 Planck’s Theory of Radiation and the Theory of Specific Heat, Einstein reviewed Planck’s result for the average energy of his resonator and then raised the following question:

If it is true that the elementary oscillators that are used in the theory of energy transfer between radiation and matter cannot be interpreted in terms of the present molecular kinetic theory, must we then not also modify our theory for the other oscillators which are used in the molecular theory of heat? In my opinion there can be no doubt about the answer. If Planck’s theory of radiation really strikes the core of the matter, then it should be expected that in other areas of the theory of heat contradictions also exist between the present molecular kinetic theory and experience which can be resolved by the method just proposed.

Consequently, Einstein proceeded to employ for the energy of the harmonic oscillators making up the lattice the expression which Planck derived for the average energy of one of his oscillators. Assuming that all harmonic oscillators had the same frequency of oscillation, he found:

c_{V} = 3 R {(\frac{θ_{E}}{T})}^{2} \frac{e^{\frac{θ_{E}}{T}}}{{(e^{\frac{θ_{E}}{T}} - 1)}^{2}}

where the characteristic Einstein temperature:

θ_{E} = \frac{h ω}{2 π k}

depends upon the characteristic angular frequency $ω$ of the harmonic oscillators making up the solid under consideration. This expression for the specific heat falls to zero with the temperature T but approaches 3R at high temperatures.

The standard interpretation of Einstein’s paper is that it showed for the first time how quantum effects extended beyond the heat radiation experience where they were first introduced. For us however, the explanation put forth by Einstein makes an ontological rather than a purely epistemological point. Because the ordinary measurements conducted to determine the temperature dependence of the specific heat of solids could only be explained by an oscillator which had also explained the predicated measurements of Rubens and Kurlbaum, Einstein’s paper proves that the manner of being of an object which explains an ordinary measurement must be the same as the manner of being of an object which explains a predicated measurement. Hence, although we might have thought otherwise, the manner of being of an object of explanation is the same whether subjected to observation or merely used to explain.

We have now reached the end of our journey. Along the way we have traced the path from the pre-scientific to the scientific comportment of man towards things and focused upon the emergence of modern science. Our analysis of the transition to modern science revealed the ontological distinction between objects of experience and objects of explanation, a distinction which was entirely covered over by Descartes’ decision to split man from the things he observes. By avoiding that split, we managed to show that the manner of being of objects of explanation in general, and quantum objects in particular, differs from that of objects of experience and is intrinsically related to the act of observing them, despite Einstein’s firm rejection of that possibility.

Because modern science starts without recognizing any such distinction, the resulting theory is largely insensitive to ontology. While the scientific community no longer insists that atomic objects are quite like the objects we encounter in our daily experience, it has never seriously tried to determine the manner in which those objects are what they are; for all practical purposes, the objects of science are all objectively real with the distinction that some can and others cannot be directly encountered by man’s observing apparatus.

At the end of the journey we found that quantum objects have a threefold manner of being comprising referentiality, persistence through modification, and retention. In the next chapter we shall show that this threefold manner of being of a quantum object is at the root of all those strange features that characterize quantum mechanics. Far from being arbitrary ‘acts of desperation’ which we had to undertake in order to capture the results of experiments under the theory, these features are necessary consequences of the mismatch between the ontology of its objects and the language used by the theory to describe that ontology, a language which was designed to describe another ontology. The strangeness of quantum mechanics is a sign that the proper ontology of its objects is breaking through the improper ontological characterization the theory had assigned them.