What I will argue is that both the success and the frustrations of microphysics have common epistemological roots, which Thomistic philosophical considerations help to expose and illuminate.  While these considerations are not inherently theological, they have implications for theology just as they do for physics.  And it will turn out that the scope and limits of what we can know where the micro-world is concerned parallel the scope and limits of what Thomism says we can know by reason alone about the existence and nature of God.  In both cases, the human intellect can press well beyond what the senses alone could reveal, but only so far.  And in both cases, the intellect’s powers give out as it approaches one end or the other of the ontological spectrum – the divine essence being at the top of that spectrum, and what Thomists call prime matter at the bottom.

From atomos to strings

However suggestive, such speculations did not yield rigorously testable predictions.  But considerable progress was made after interest in atomism and related ideas was revived with the scientific revolution.  Studying the compression and expansion of gases, Robert Boyle (1627-1691) found that changes to the volume of a gas did not alter its mass.  This was hard to understand unless a gas is not a continuous thing but rather a collection of particles separated by empty space, with compression and expansion involving changes in the distances of the particles from one another.  Moreover, on the basis of this assumption, Boyle was able to formulate and support by experimental test his famous law describing the relationship between the volume of a gas and its pressure.

The kinetic theory of gases developed by Daniel Bernoulli (1700-1782) added further detail to the story.  Since a gas will spread evenly throughout a container it occupies, the particles that make it up must be in continual random motion.  For if they weren’t, they would collect in some part of the container rather than remaining evenly spread out.  The pressure of a gas could then be analyzed in terms of the collisions of particles against the inside surface of the container.  As the volume of the container increases or decreases, the distance the particles would have to travel to hit its inside surface will correspondingly increase or decrease, which leads to decreases or increases in pressure in conformity with Boyle’s law.  Temperature could also be explained in terms of the kinetic theory, which identifies it with the average kinetic energy of particles in motion.  James Clerk Maxwell (1831-1879) and Ludwig Boltzmann (1844-1906) would go on to formulate the theory with mathematical rigor.

Such mathematical and predictive precision made the reality of unobserved particles harder to deny, but what really settled the matter in the minds of scientists were developments in modern chemistry.  The law of the conservation of mass was established by Antoine Lavoisier (1743-1794), and this opened the way to determining the mass of each element in a compound.  By doing so, Joseph Proust (1754-1826) was able to show that the elements are always to be found in compounds in fixed proportions, a principle that would come to be known as Proust’s law.  Applying Proust’s law, John Dalton (1766-1844) argued that there must be some smallest unit of an element that cannot be broken down into parts that retain the properties of that element.  This he called an atom.  A molecule, the smallest unit of a compound, is thus made up of atoms.  Using Proust’s law, the relative masses of different elements, and thus of different atoms, could be deduced.  For example, from the proportion of hydrogen to oxygen in water, the oxygen atom could be shown to be sixteen times more massive than a hydrogen atom.  This in turn allows us to infer the relative masses of yet other atoms.  For example, since carbon dioxide also contains oxygen, knowing the mass of oxygen allows us to determine the mass of carbon.  From the relative atomic mass of the elements, Dmitri Mendeleev (1834-1907) was able to work out the periodic table, and successfully to predict new elements and their properties from the gaps in the table. 

Now, the chemist Amedeo Avogadro (1776-1856) had argued that equal volumes of gases contain equal volumes of molecules given that temperature and pressure are fixed.  This is so even if the volumes differ in mass.  The mathematical analysis of gases worked out by Maxwell and Boltzmann opened the way to determining exactly how many molecules are in a volume of gas.  This allowed, in turn, for inferences concerning the absolute mass of molecules and atoms, and about their sizes as well.  The predictive successes of a theory that revealed even the mass and size of atoms as well as the properties of the elements made the reality of the atom appear certain.

The electron was discovered by J. J. Thomson (1856-1940), who showed that cathode rays could be made to curve away from an electrically charged plate with a negative charge and toward one with a positive charge.  This showed them to behave like particles rather than waves, and particles of a negatively charged kind, specifically.  From the size of the charge of these particles, their mass was worked out, and this turned out to be smaller than that of the smallest atom.  Study of the photoelectric effect, in which light causes electrons to be emitted from a metal surface, showed that electrons are already present in the atoms from which they are ejected.  Further study showed that electrons had the same properties even when they came from the atoms of different kinds of metal.

Since atoms are electrically neutral, the presence in them of negatively charged electrons suggested that there must be some component with a positive charge to neutralize the negative charge.  Experiments by Ernest Rutherford (1871-1937) involved firing positively charged particles at thin gold leaf, behind which was a photographic plate.  The resulting patterns showed that most of the particles passed through as if nothing were there, while a few were significantly deflected.  This suggested that the atoms making up the gold leaf were mostly empty space, with a large positively charged mass at the center from which the deflected particles were repelled.  Rutherford concluded that the atom consists of a nucleus surrounded by a cloud of electrons.  Later experimentation revealed the existence of radiation that carried no electric charge.  This led to the discovery of the neutron by James Chadwick (1891-1974), and then in turn to the model of the atomic nucleus developed by Werner Heisenberg (1901-1976), according to which it comprises a tightly packed mass of positively charged protons and uncharged neutrons.

Yet other particles were being discovered throughout the era in which these advances were being made.  For example, some cases of radioactive decay showed energy loss that could not be accounted for.  Given the law of conservation of energy, this energy could not simply have disappeared, so physicists such as Wolfgang Pauli (1900-1958) and Enrico Fermi (1901-1954) speculated that it was being carried away by particles which came to be called neutrinos.  The evidence indicated that these particles, if they existed, had very little if any mass and were not sensitive to nuclear or electromagnetic forces, all of which made them extremely difficult to detect.  Only experimental apparatus with shielding that could rule out an effect’s having been produced by any other particle could confirm their existence, and this was achieved in 1956.

So far I have been emphasizing the role theoretical considerations have played in discovering particles, but it is important to consider also the role of experimental apparatus like the kind just referred to.  Early twentieth-century devices included the Wilson cloud chamber, in which speeding particles can be made to leave behind small water droplets, yielding tracks from which inferences can be made about the nature of the particles.  With a Geiger-Müller counter, the presence of a radiating particle produces an electrical discharge that is converted to a clicking sound, and the number of clicks per second reflect the amount of radiation.   Later devices include bubble chambers, the use of which involves sending particles through pressurized superheated liquid, in which the particles leave tracks of bubbles that can be photographed and then analyzed.   Nuclear emulsions are photographic plates on which particle tracks are recorded.  Scintillators are devices which emit flashes of light when struck by particles.  In spark chambers, detected particles trigger an electrical pulse.  These gave rise to sophisticated devices in which the firings of individual counters are processed in order to produce an image that reconstructs the paths of the particles detected.

But by this means, various subatomic particles were discovered, such as mesons and hyperons.  In the early 1960s, Murray Gell-Mann (1929-2019) and George Zweig (1937- ) proposed that the protons and neutrons that comprise the atomic nucleus are themselves made up of more fundamental particles (called quarks) and their existence was confirmed experimentally in the following decades.  Gradually, physicists worked out what came to be known as the Standard Model, according to which the fundamental particles of which all other matter is composed comprise fermions on the one hand and bosons on the other.  Fermions include various types of quarks along with leptons, which comprise electrons and neutrinos as well as some other particles.  Bosons include, among other particles, photons and the famous Higgs boson.

The controversy today is over whether there are additional particles, or more fundamental entities out of which the particles now taken to be fundamental are composed, and if so how we could establish such conclusions.  Supersymmetry is an approach which proposes that there are a large number of additional particles that partner the particles of the standard model, plus a few more.  Its attraction derives from its mathematical elegance, the solution it provides to some technical problems in particle physics as it stands today, and in the fact that some of the particles it posits could plausibly be identified with dark matter (that is to say, the matter that is thought to make up the bulk of the universe but neither absorbs nor emits light).  The trouble is that so far the existence of none of these particles has been confirmed, and it is not clear what could confirm it given that existing methods have failed.

Retroduction and analogy

Now, you might suppose that this survey by itself already answers the question of why physics has learned as much as it has about the micro-world but has had trouble progressing further.  It might seem enough simply to say that it has established the reality of molecules, atoms, electrons, protons, neutrons, quarks, and so on by way of experimental testing and has been unable so far to establish the reality of supersymmetry particles or strings because of the lack of experimental evidence.  But that things are not that simple should be obvious enough when one recalls the traditional dispute between instrumentalists and scientific realists.  If instrumentalists are correct, even the reality of the particles modern physics does accept has not really been demonstrated by the experimental evidence.  That evidence shows only that our most successful theories are handy instruments for making predictions and developing technologies, but they may for all that merely be useful fictions.

Our overview of the history of microphysics vividly illustrates this.  As we have seen, theorists aim to explain observed phenomena such as: the divisibility and permeability of ordinary material objects; the pressure and temperature of gases; the proportions of the elements in a compound; the behavior of cathode rays and the photoelectric effect; the effects of firing particles at gold foil; unexplained energy loss in radioactive decay; tracks in cloud and bubble chambers and on emulsion plates; patterns of electrical pulses in particle detectors; and so on.  They construct theories that posit unobserved particles of various kinds, and show how the observed phenomena are made intelligible on the supposition that these unobserved particles are real and behave in the ways described by the theory.

But the history we surveyed also illustrates how crucial mathematical descriptions, specifically, have been to the development of modern microphysics from Boyle to string theory.  Here microphysics has simply applied to its own domain a more general mathematicizing tendency that has characterized modern physics from Galileo and Descartes onward.  Hanson has much of importance to say about how this mathematicization increasingly removed from modern physics’ conception of unobserved particles the attributes that characterize matter as we ordinarily experience it.  The Greek atomists had already taken the step of denying that basic particles have features like color or taste, though they did attribute to them shape, position, and motion.  When early modern scientists and philosophers revived the idea, they tightened it up into the now familiar distinction between primary and secondary qualities, with secondary qualities like color, taste, sound, and odor taken to resemble nothing in particles themselves.  The primary qualities that particles were said to possess were thought of as susceptible of a rigorous mathematical analysis. 

For example, electrons ‘veer away’ from negatively charged matter; they must therefore be like particles.  But electron beams diffract like beams of light, and therefore they must be like waves too.  The physicist fashions the electron concept so as to make possible inferences both to its particle and its wave behavior, and a conception so fashioned is unavoidably unpicturable… If microphysical explanation is even to begin, it must presuppose theoretical entities endowed with just such a delicate and non-classical cluster of properties…

Hesse distinguishes two main attitudes that have been taken by scientists and philosophers of science toward models and analogies.  The first, associated with Pierre Duhem and others, holds that while models and analogies might be useful in suggesting theories, what ultimately matters is the mathematical system the theorist arrives at.  The models and analogies that initiated theorizing drop away as inessential or even potentially misleading.  The second attitude, represented by the physicist N. R. Campbell, holds that models and analogies are necessary both in order to give an abstract mathematical theory genuine explanatory power, and to extend it to new phenomena. 

The triplex via and microphysics

To some extent the parallel will be obvious enough from what has been said so far.  Just as analogical language makes it possible for us to talk about God, so too does it make it possible for us to talk about unobservable particles.  Just as our knowledge of God begins with the via causalitatis, by which we reason to God as cause of the world, so too our knowledge of particles begins by positing them as the explanation of what we observe.  Just as, by the via negationis, we deny of God the limitations that characterize created things, so too do we deny of unobserved particles characteristics of ordinary material substances, such as color, odor, and determinate position or velocity. 

Now, as subsistent existence itself and supreme perfection, God is pure actuality.  That entails that there is no passive potency in him – no capacity whatsoever to change or be changed – but also that he is supreme in active potency, the capacity to bring other things into being and otherwise to affect them.  In Thomistic metaphysics, this puts him at the apex of the hierarchy of reality, at the other extreme end of which is prime matter, which is pure passive potency.  In my book Aristotle’s Revenge, I say the following about prime matter and its relationship to fundamental particles and observable physical substances:

Prime matter on its own is wholly indeterminate.  By itself it is not an actual particular physical thing of any kind, but rather the pure potentiality to be a particular physical thing of some kind.  If we think of matter on the analogy of the position of a needle on a dial and the values on the dial as representing the various specific kinds of material thing that might exist, prime matter is like a needle that is flitting wildly all across the face of the dial.  It has no intrinsic tendency to stop at any particular value, though potentially it could be made to stop at any of them…

You might say, then, that just as God is eminent in actuality or active potency, prime matter is eminent in potentiality or passive potency.  Just as angelic intellects, given their immateriality, are closer to the pure actuality and perfection of God than anything else in creation, so too fermions and bosons, given their indeterminacy, are closer to the pure potency of prime matter than anything else in creation.  Just as the attributes of material things preexist in God as their efficient cause, they preexist in fermions and bosons as their proximate material cause (prime matter being their ultimate material cause).  In theorizing about fundamental particles, physics deploys something analogous to the via eminentiae insofar as it deduces what the natures of these particles must be like in order for them to have the passive potency to constitute any and all of the ordinary material substances of our experience.  And just as the way of eminence orders the divine attributes, so too does its analogue order the properties attributed to particles.  As Hanson and Maritain emphasize, the mathematical description is paramount, because it is what does the real explanatory work.  Other descriptors, such as “particle” and “wave,” are interpreted in light of the mathematics, and any connotations of these terms that are inconsistent with the mathematics are negated.

Now, the higher we go in the hierarchy of being, the less firm is the intellect’s grasp of what it knows – not because angelic intellects and God are not intelligible in themselves, but rather because our intellects are naturally most at home in the realm of corporeal and extended things, and can only dimly grasp what is immaterial and metaphysically simpler or non-composite.  This is why Maritain says that we must make due with a “substitute” for the divine essence rather than a direct grasp of the divine essence itself.  But the intellect’s grasp of what it knows is also less firm the lower we go in the hierarchy of being, because here we get increasingly farther from ordinary corporeal and extended things and approach what is minimally intelligible in itself, namely prime matter.  Hence here too we must make due with what Maritain characterizes as mathematical “substitutes” for the essences of particles.

The phenomena have been “marginalized,” then, insofar as the connection between observational evidence and theoretical entities has become increasingly distant.  Dawid notes other ways in which the phenomena have been marginalized.  The layers of theory that come between experimental evidence and the particles judged to have been detected by way of it have increased in number.  The conceptualization of particles has gotten further away from modeling them on matter of the kind we know from perceptual experience.  And whereas, in the early history of particle physics, experiment came first and theorizing about its results followed, in later history theory would come first and experiment was devoted to testing its predictions.  Now theorizing has reached the point at which it relies largely on non-empirical considerations, with results that currently cannot be tested experimentally.

Dawid himself defends this development as a legitimate and needed transformation of the methods of physics.  But physicists like Hossenfelder, Penrose, Smolin, and Woit regard it as instead a departure from sound scientific method, at least insofar as string theorists maintain their position with a confidence that has no basis in actual empirical evidence.  It seems to me that Thomists, given their general epistemology and the philosophy of science that thinkers like Maritain have developed on its basis, are bound to agree with these skeptics.  Unless and until the claims of string theory and the like can be tested experimentally, they cannot count as knowledge and we have no basis for affirming the reality of the entities they posit.  Insofar as such theories are driven by abstract mathematical considerations rather than experiment, they have the flavor of rationalist metaphysics.  For the Thomist, the existence and nature of God cannot be arrived at a priori, after the fashion of the ontological argument and perfect being theology.  We must instead reason a posteriori from the empirical world to God as its cause.  Similarly, the existence and nature of material particles can be known only a posteriori rather than a priori.  Moreover, just as a posteriori reasoning about the divine nature must at some point hit a ceiling beyond which it cannot ascend, so too is a posteriori reasoning about the microstructure of matter bound to hit a floor below which it cannot dig further.  While it would be rash peremptorily to rule out the possibility that string theorists might yet find a way to test their theory experimentally, it could turn out the theory is to physics what Leibniz’s theory of monads and rationalist theology are to metaphysics.

Beauty and scientific method

One problem, the critics point out, is that such judgements are subjective.  As Woit notes, though some physicists judge string theory to be elegant and beautiful, others take it to be ugly and complicated.  Another problem, as Hossenfelder, Penrose, and Smolin point out, is the history of physics shows that physical theories judged to be beautiful have sometimes turned out to be wrong.  Moreover, as Penrose adds, there are theories in mathematics that are very beautiful but have no apparent relevance for physics in the first place.

Why has beauty turned out to be such an unreliable guide, and why do physicists nevertheless persist in being guided by it?  I believe Thomism sheds light on these questions as well.  Beauty is traditionally taken to be among the transcendentals, alongside being, one, true, good, thing, and other.  These concepts are “transcendental” in that they transcend all categories and apply to all reality.  That is to say, any reality of any kind has being, is one, is true, is good, is beautiful, and so on.  In this connection, the transcendentals are also said to be convertible in the sense that being, unity, truth, goodness, beauty and the rest are one and the same thing looked at from different points of view.

At the same time, Thomists would emphasize that what is fundamental in the ordo essendi or order of being is not fundamental in the ordo cognoscendi or order of discovery.  For example, God is the most fundamental reality, and is supreme in being, unity, beauty, and so on.  All the same, and contrary to what a rationalist like Descartes supposes, his existence and nature are not among the fundamental pieces of knowledge.  Rather, we have to reason to God’s existence and nature from what we know about metaphysically far less fundamental features of reality, such as the fact that the things we experience undergo change and are contingent.  There are no shortcuts whereby we might deduce God’s existence and nature from the idea of God as the highest reality, after the fashion of the ontological argument.

Similarly, fundamental features of nature such as its basic material constituents and the laws that govern them will no doubt turn out to be beautiful.  But we cannot reliably deduce their existence and nature from considerations of beauty, unity, and the like alone, any more than we could reliably deduce God’s existence or much about his nature from the idea of him as supreme in being, unity, beauty or the like.  We have to rely instead on reasoning of the kind I have been describing, which relies on analogy and parallels to the triplex via.  Hossenfelder’s book is titled Lost in Math: How Beauty Leads Physics Astray, and what I have been arguing is that her diagnosis is one that dovetails with a Thomist epistemology and philosophy of science.  The emphasis that string theorists and other contemporary physicists put on the beauty of mathematical constructs lacking experimental foundation has led the field to create castles in the air, in a manner that parallels the way in which early modern rationalism led metaphysics into the same fate. 

The remedy is to reject the advice of Dawid and others to abandon modern physics’ traditional insistence on experimental verification.  But this will entail rejecting also the hubris of supposing that physics will inevitably hit upon some final “theory of everything.”  As when we approach the divine apex of the hierarchy of reality, so too when we approach the basement, our vision is likely to become less clear rather than more.

End notes