The Power of Inconsistency in Anti-Realist Realisms about Quantum Mechanics (Or: Lessons on How to Capture and Defeat Smoky Dragons)
TThe Power of Inconsistency inAnti-Realist Realismsabout Quantum Mechanics(Or: Lessons on How to Captureand Defeat Smoky Dragons)
Christian de Ronde ∗ Philosophy Institute Dr. A. Korn, Buenos Aires University - CONICETEngineering Institute - National University Arturo Jauretche, Argentina.Federal University of Santa Catarina, Brazil.Center Leo Apostel for Interdisciplinary Studies, Brussels Free University, Belgium.
Abstract
In this work we argue that the power and effectiveness of the Bohrian approach to quantum mechanicsis grounded on an inconsistent form of anti-realist realism which is responsible not only for the uncriticaltolerance —in physics— towards the “standard” account of the theory of quanta, but also —in philosophy—of the alarming reproduction of quantum narratives. Niels Bohr’s creative methodology can be exposedthrough the analysis of what John Archibald Wheeler called “the great smoky dragon”. We will discuss theexistence of such dragons within the “minimal interpretation” applied by physicists in the orthodox textbookformulation of quantum mechanics as well as within the many “supplementary interpretations” introduced byphilosophers —or philosophically inclined physicists— in order to solve the infamous measurement problem.After analyzing the role of smoky dragons within both contemporary physics and philosophy of physicswe will propose a general procedure grounded on a series of necessary theoretical conditions for producingadequate physical concepts that —hopefully— could be used as tools and weapons to capture and defeatthese beautiful and powerful creatures.
Key-words : Realism, empiricism, representation, observability.
Ts’ui Pe must have said once: I am withdrawing to write a book.And another time: I am withdrawing to construct a labyrinth.Every one imagined two works; to no one did it occurthat the book and the maze were one and the same thing.
Jorge Luis Borges.
Physics was born during the 6th Century B.C. in the Greek city of Miletos, on the coast of Asia Minor, where theIonians had established rich and prosperous colonies. Three men —Thales, Anaximander, and Anaximenes—appeared in quick succession claiming the existence of what they named physis —translated later on as ‘reality’.For the first time in the history of western thought physicists replaced mythical stories and narratives by rationalexplanation. As remarked by Jean-Pierre Vernant: ∗ This paper is dedicated to the memory of Diego Armando Maradona who taught me, when I was a very young child, that theimpossible can be achieved. a r X i v : . [ phy s i c s . h i s t - ph ] J a n Myths were accounts, not solutions to problems. They told of the sequence of actions by which the king orthe god imposed order, as these actions were mimed out in ritual. The problem found its solution without everhaving been posed. However, in Greece, where the new political forms had triumphed with the developmentof the city, only a few traces of the ancient rituals remained, and even their meaning had been lost. Thememory of the king as creator of order and maker of time had disappeared. The connection is no longerapparent between the mythical exploit of the sovereign, symbolized by his victory over the monster, andthe organization of cosmic phenomena. When the natural order and atmospheric phenomena (rains, winds,storms and thunderbolts) become independent from the functions of the king, they cease to be intelligiblein the language of myth in which they had been described hitherto. They are henceforth seen as questionsopen for discussion. These questions (the genesis of the cosimic order and the explanation for meteora ), intheir new form as problems, constitute the subject matter for the earliest philosophical thought. Thus thephilosopher takes over from the old king-magician, the master of time. He constructs a theory to explain thevery phenomena that in times past the king had brought about.” [50, p. 402]
The impact of this shift from myth to theory would reinforce the transformation of the structure of the Greeksociety and as a consequence, preachers, mediums and kings would be forced to share their power with the firstphysicists and philosophers. In this new democratic system known as science, all citizens would be entitled togain knowledge about reality: “[Before the Milesians,] [e]ducation was based not on reading written texts but on listening to poetic songstransmitted from generation to generation. [...] These songs contained everything a Greek had to know aboutman and his past —the exploits of heroes long past; about the gods, their families, and their genealogies,about the world, its form, and its origin. In this respect, the work of the Milesians is indeed a radicalinnovation. Neither singers nor poets nor storytellers, they express themselves in prose, in written textswhose aim is not to unravel a narrative thread in the long line of a tradition but to present an explanatorytheory concerning certain natural phenomena and the organization of the cosmos. In this shift from theoral to the written, from the poetic song to prose, from narration to explanation, the change of registercorresponds to an entirely new type of investigation —new both in terms of its object (nature, physis ) andin terms of the entirely positive form of thought manifested in it.” [50, p. 402]
Three fundamental presuppositions would guide this new form of thought and praxis. First, that physis isnot chaotic, that it possesses an internal order, what the Greeks called —after Heraclitus— a logos . Second,that physis is one, indivisible and inseparable. Like Heraclitus would express: “Listening not to me but to the logos it is wise to agree that all things are one” [f. 50 DK]. Third, that even though “ physis loves to hide” [f.123 DK] the logos of physis could be actually known through the development of theories , namely, through thecreation of unified, consistent and coherent schemes of thought that could explain phenomena. Already the firstphilosophers showed a clear recognition of the difficult problems involved within this scheme. To relate the logos of men to the logos of physis was obviously a difficult task, but through hard work and sensibility the lattercould be revealed in the former. Theories relate on the one hand to physis (the One), and on the other to themultiplicity of phenomena (the Many). And it is this kernel aspect which marks the characteristic feature ofscientific understanding itself. While ‘The One’ implies a unified theoretical standpoint of analysis grounded in physis , ‘The Many’ relates to the multiplicity of different phenomena and observations. In this way, theoriesbecame the bridge between a unified understanding of reality and the multiplicity of experience. As a youngWolfgang Pauli would explain to his friend Werner Heisenberg during a conversation in 1921: “knowledge cannot be gained by understanding an isolated phenomenon or a single group of phenomena, evenif one discovers some order in them. It comes from the recognition that a wealth of experiential facts areinterconnected and can therefore be reduced to a common principle. [...] ‘Understanding’ probably meansnothing more than having whatever ideas and concepts are needed to recognize that a great many differentphenomena are part of coherent whole. Our mind becomes less puzzled once we have recognized that aspecial, apparently confused situation is merely a special case of something wider, that as a result it can beformulated much more simply. The reduction of a colorful variety of phenomena to a general and simpleprinciple, or, as the Greeks would have put it, the reduction of the many to the one, is precisely what wemean by ‘understanding’. The ability to predict is often the consequence of understanding, of having theright concepts, but is not identical with ‘understanding’.” [34, p. 63] In this respect, it is important to recognize that physicists never claimed that theories “mirrored” reality. In fact, the idea thatreqlism implies a one-to-one correspondence relation between theory and reality-in-itself is an idea constructed by anti-realists inorder to diminish the possibilities of considering realism.
2f course, as we all know, very soon a strong opposition to these realist ideas also appeared in Athens, whichhad already become during the 5th. Century B.C., the rich and prosperous capital of Greek Empire. Sophists,as they would be called, would produce the first assault against the realist program arguing that there is nosuch thing as ‘a reality of things’, and even if such thing would exist, we would not be able to grasp it. Sophistsargued assuming a more skeptic down to earth position that we humans can only refer to our own perception. Itmakes no sense to talk about a reality independent of subjects because we individuals have only a relative accessto things, an access limited by our own personal experience. As Protagoras would argued: “Man is the measureof all things, of the things that are, that they are, of the things that are not, that they are not” [DK 80B1].From this sceptic standpoint, sophists criticized the physical idea of theoretical knowledge: realists —namely,physicists and philosophers— are too naïve, they do not recognize their own finitude and thus have ended upbelieving they can access the infinite, the real. The first battle of the war between realists and anti-realists hadbegun.As we know, it took the power of both Plato and Aristotle to overcome the sophist anti-realist riot. Throughthe creation of conceptual (or metaphysical) systems; they were both able to provide answers to the sophistsand take the realist program a step further. Metaphysics —regardless of the many different ways in which thisterm has been used— implied an essential shift in the representation of physis , going from ‘first elements’, onwhich pre-socratics had based their theories (e.g., fire, water, air, etc.), to an interrelated system of abstractconcepts and principles. Plato’s and Aristotle’s metaphysical systems were analyzed, discussed criticized anddeveloped for two millennia keeping realist ideas in the center of the stage of Western thought. But withthe rise of modernity in the 16th and 17th centuries things would begun to drastically change. The scientificrevolution that took place in modernity might be regarded not only as a culmination of the Greek scientificpath, but also as the beginning of its dissolution. On the one hand, the idea of the ‘One and the Many’was consistently articulated not only conceptually but also formally through the development of infinitesimalcalculus. Physicists had finally constructed the first closed, unified, consistent and coherent formal-conceptualrepresentation of physical reality, namely, classical mechanics. Through its development, physicists were capableof producing not only a conceptual qualitative understanding of phenomena but also the quantitative capacityto compute their accurate prediction. The understanding of the world and reality had been finally united withina space-time atomist representation of the physical world. The mathematical notion of invariance captured theessential idea of the Greeks, namely, the consistent unified understanding of a state of affairs given throughmultiple reference frame dependent representations. Essential to this development was the recognition by DavidHume that empirical observations were incapable to ground a secure path for scientific knowledge. The notion of causality was not something to be found within experience but instead a (metaphysical) concept that we humansimposed to phenomena as the result of mental habit and custom. In turn, it is this same finding which allowedthe development of the notion of objectivity by Immanuel Kant. Objectivity captured the essential mathematicalcontent of invariance but now in purely conceptual terms. And it is through the combination of both invarianceand objectivity that modern physics was able to succeed in producing what the Ancient Greeks had searchedfor, namely, a rigorous set of formal-conceptual conditions for producing a subject detached representation of areal state of affairs —conditions to which we will return in section 5. However, on the other hand, even thoughmodernity marks a period of essential accomplishments and advancements for the realist project, the 16th and17th centuries might be also considered as marking the beginning of the anti-realist era. The human perspectivewas —once again— beginning to be considered as the true fundament of knowledge. Both rationalism, with thecartesian cogito , and empiricism, with their direct reference to experience, would begin to philosophize placingthe subject at the center of their considerations. In doing so they were also introducing an essential separationwithin reality itself. As Heisenberg explains in
Physics and Philosophy : “The great development of natural science since the sixteenth and seventeenth centuries was preceded andaccompanied by a development of philosophical ideas which were closely connected with the fundamentalconcepts of science. It may therefore be instructive to comment on these ideas from the position that hasfinally been reached by modern science in our time. The first great philosopher of this new period of sciencewas René Descartes who lived in the first half of the seventeenth century. Those of his ideas that are mostimportant for the development of scientific thinking are contained in his Discourse on Method . On the basis ofdoubt and logical reasoning he tries to find a completely new and as he thinks solid ground for a philosophicalsystem. He does not accept revelation as such a basis nor does he want to accept uncritically what is perceivedby the senses. So he starts with his method of doubt. He casts his doubt upon that which our senses tell usabout the results of our reasoning and finally he arrives at his famous sentence: ‘cogito ergo sum.’
I cannotdoubt my existence since it follows from the fact that I am thinking. After establishing the existence of he I in this way he proceeds to prove the existence of God essentially on the lines of scholastic philosophy.Finally the existence of the world follows from the fact that God had given me a strong inclination to believein the existence of the world, and it is simply impossible that God should have deceived me. This basisof the philosophy of Descartes is radically different from that of the ancient Greek philosophers. Here thestarting point is not a fundamental principle or substance, but the attempt of a fundamental knowledge. AndDescartes realizes that what we know about our mind is more certain than what we know about the outerworld. But already his starting point with the ‘triangle’ God-World-I simplifies in a dangerous way the basisfor further reasoning. The division between matter and mind or between soul and body, which had startedin Plato’s philosophy, is now complete. God is separated both from the I and from the world. God in factis raised so high above the world and men that He finally appears in the philosophy of Descartes only as acommon point of reference that establishes the relation between the I and the world. While ancient Greekphilosophy had tried to find order in the infinite variety of things and events by looking for some fundamentalunifying principle, Descartes tries to establish the order through some fundamental division. But the threeparts which result from the division lose some of their essence when any one part is considered as separatedfrom the other two parts. If one uses the fundamental concepts of Descartes at all, it is essential that Godis in the world and in the I and it is also essential that the I cannot be really separated from the world. Ofcourse Descartes knew the undisputable necessity of the connection, but philosophy and natural science inthe following period developed on the basis of the polarity between the ‘res cogitans’ and the ‘res extensa,’ and natural science concentrated its interest on the ‘res extensa.’ The influence of the Cartesian division onhuman thought in the following centuries can hardly be overestimated, but it is just this division which wehave to criticize later from the development of physics in our time.” [33, pp. 41-42]
The main accomplishment of the so called Enlightenment period —which marks the starting point of theanti-realist approach to science [20]— is the separation of physis in three different regions that would becomecomplex in themselves and difficult to interrelate. It is this dissection that would allow in later times to destroycompletely the meaning and content of the notion of reality itself.
Divide et impera . This is the motto thatmight best characterize the anti-realist strategy against realism that begun in Modernity. Physics and philosophywere also beginning to be torn apart. While the first was reassigned the specific role of discussing about thematerial world, the latter had only to worry about matters of human nature. René Descartes would cut theGreek notion of reality —the One— into three separated “realities”: that of the I ( res cogitans ), that of theworld ( res extensa ) and that of God. Very soon the new architectonic designed by the physicist and philosopherImmanuel Kant would take the reality of the Cartesian God —which secured the certain relation between rescogitans and res extensa — further away from the reach of science, into an un-knowable noumenic dimension.In Kant’s co-relational metaphysics, reality was finally detached from scientific knowledge and replaced by thesubject’s capacity to account for objects of experience. The circular co-relation between subject and object hadlost its foundation. Realism had been deathly wounded. Kant argued that the sum of all objects, the empiricalworld, is a complex of appearances whose existence and connection occur only in our representations . Reality,renamed as a beast, das Ding an sich (the Thing-in-Itself), had survived but only as a monstrous paradoxicalcreature hiding beyond empirical sensibility, impossible to be known. As Kant would write in the
Prolegomenato Any Future Metaphysics : “And we indeed, rightly considering objects of sense as mere appearances, confessthereby that they are based upon a thing-in-itself , though we know not this thing as it is in itself, but only knowits appearances, viz., the way in which our senses are affected by this unknown something.” Kant had introducedthe un-knowable within his metaphysical system, limiting the scientific knowledge of physics to that of objectivereality —a reality restricted by his list of categories (grounded on Aristotelian metaphysics) and forms of intuition (Newtonian space and time) common to all human subjects. Thus, noumenic reality or reality-in-itself couldnot be considered anymore as the main goal of the scientific project. Friedrich Jacobi [1787: 223] famous remarkwould expose the problem in all its depth: “Without the presupposition [of the ‘thing in itself,’] I was unableto enter into [Kant’s] system, but with it I was unable to stay within it.” Furthermore, Arthur Schopenahuerwould make clear that the category of causality could not be applied within Kant’s system to noumenic reality and consequently, the disconnection from the categorical representation of objective phenomena was complete.Kant had introduced an essential separation between reality and representation . Reality had been cut intopieces and its essence finally captured and isolated. But it was still too soon for anti-realism to claim victory.Anti-realists would still have to wait two more centuries in order to rise as the supreme indisputable power ofWestern thought. It is in our postmodern age, during the 20th Century, that realism would be finally defeatedby anti-realism. And the main field of this final battle —between realists and anti-realists— would be no otherthan a new physical theory called quantum mechanics. 4
Anti-Realist Realism, Inconsistency and Quantum Mechanics
As described by Bas van Fraassen [49, p. 2]: “Kant exposed the illusions of Reason, the way in which reasonoverreaches itself in traditional metaphysics, and the limits of what can be achieved within the limits of reasonalone. But on one hand Kant’s arguments were not faultless, and on the other there was a positive part to Kant’sproject that, in his successors, engaged a new metaphysics. About a century later the widespread rebellionsagainst the Idealist tradition expressed the complaint that Reason had returned to its cherished Illusions, ifperhaps in different ways.” By the end of the 19th Century the Austrian physicist and philosopher Ernst Machwould produce a vigorous attack against the realist metaphysical presuppositions of classical mechanics. Througha return to empiricism, Mach developed a new positive scheme for physics which —grounding itself on empiricalobservability alone— would attempt to erase metaphysics from physics. The attack was focused in the Newtoniannotions of space, time —which acted as a priori concepts within the Kantian architectonic— and atom. TheAustrian physicist and philosopher was breaking the walls of the modern spatiotemporal atomist cage in whichphysics had been confined. But for him, the destruction of this prison implied the necessary demolition ofmetaphysics itself. The deconstruction of classical Newtonian mechanics and Kant’s metaphysical architectonicproduced a major crisis in the foundations of science during the 20th Century which Wolfgang Ernst Pauli —thegodson of Mach— would recognize in his own terms: “In many respects the present appears as a time of insecurity of the fundamentals, of shaky foundations.Even the development of the exact sciences has not entirely escaped this mood of insecurity, as appears,for instance, in the phrases ‘crisis in the foundations’ in mathematics, or ‘revolution in our picture of theuniverse’ in physics. Indeed many concepts apparently derived directly from intuitive forms borrowed fromsense-perceptions, formerly taken as matters of course or trivial or directly obvious, appear to the modernphysicist to be of limited applicability. The modern physicist regards with scepticism philosophical systemswhich, while imagining that they have definitively recognised the a priori conditions of human understandingitself, have in fact succeeded only in setting up the a priori conditions of the systems of mathematics andthe exact sciences of a particular epoch.” [43, p. 95]
Mach’s subversive deconstruction had broken physics from its space-time atomist chains. And it was certainlythis liberation which would become essential for the development of both Quantum Mechanics (QM) and rela-tivity theory. While Albert Einstein applied Mach’s positivist ideas in order to critically address the definitionof simultaneity in classical mechanics, both Max Planck and Werner Heisenberg were able to advance new non-classical mathematical postulates and formalisms which could explicitly escape —thanks to Mach’s work— themodern space-time representation of classical physics and in this way provide a quantitative operational accountof a new field of (quantum) phenomena. However, even though positivist ideas were becoming popular in Eu-rope —specially among physicists— Mach had lost a kernel battle against metaphysical atomism. Regardlessof their endorsement to Mach’s criticisms, physicists simply could not give up on the modern spatiotemporalrepresentation of reality. As a consequence, even the new theory of quanta which had been developed through aradical departure from classical ideas and presuppositions was anyhow pictured as related to a microscopic realmconstituted by elementary particles. The fact that Planck’s quantum postulate precluded a continuous descrip-tion did not seem to matter. The hope was that —sooner than later— this discreteness would be —somehow—explained in terms of the classical continuous representation. It is in this crossroad between quantum and classi-cal that Niels Bohr —maybe the most influential physicists of the 20the Century— would play an essential roleestablishing a new scheme for physics where both Mach’s positivist ideas and metaphysical space-time atomismwould co-exist. We will call this inconsistent but highly effective approach created by Bohr: anti-realist realism.The first spectacular appearance within the physics community of Bohr dates back to 1913 with his proposalof a new model for the hydrogen atom —essentially an abstract set of rules capable of predicting spectral lines.Even though the model was essentially quantum, the proposal was framed as close as possible to the modernspace-time atomist representation of physical reality. The image created by Bohr was simple and comfortingto most physicists: electrons moved in quantized orbits around the nucleus just like planets orbited the sun.The microscopic realm was nothing but a simple reflection of our own planetary system. However, the price to It is interesting to note that concomitant with Mach’s deconstruction of the metaphysics of classical physics, Friedrich Nietzschewould also produce a major attack to metaphysics within philosophy. Mach’s positivist scheme for science can be resumed in four main principles. The first is the naive empiricist idea that observationis a self evident given of “common sense” experience. Second, that physics should be understood as an economy of such observations.Third, that metaphysics, understood mainly as narratives about the unobservable, should be completely erased from scientifictheories. And fourth, that physics does not talk about an “external reality” that would describe things beyond empirical observation. discrete quantum orbits within a continuous space simply did not make sense. Howcould continuous space be described in discrete terms? Why did electrons follow trajectories within confinedorbits but where unable to reach the outer regions of space? How could they actually disappear from a positionin space and reappear in another one without describing a trajectory? Where were electrons supposed to go inthe meantime of this apparently magical process? Furthermore, given that charged electrons were describingcircular orbits, why didn’t they irradiate, loose energy and collapse to the nucleus? None of these questions hadany answer. From a formal perspective the inconsistency was even more explicit. Planck’s discrete representationof energy implied, through the formula E = m v (where v = dxdt ), that space and time could not be representedin continuous terms. If energy was —according to Planck— fundamentally discrete ( ∆ E ) then velocity had tobe discrete as well, and consequently, also space and time ( v = ∆ x ∆ t ). Quantum discreteness was everywhere.Since the idea of a discrete space or time is in itself inconsistent, an oximoron , Planck’s quantum postulate implied the birth of a new physics detached from the continuous space-time representation imposed by modernscience. Unfortunately, this departure, in part due to Bohr’s influence, would be never fully accepted neitherby physicists nor philosophers. Against the radicalness of Planck’s postulate, Bohr would still apply classicalimages and pictures to his model gaining the sympathy of many conservative physicists who were not ready togive up on their “commonsensical” space-time atomist way of thinking. Bohr’s model did not actually provideany mathematical representation of any of these particles, but for him this was “just a way of talking”, a usefulfiction with no direct reference to an underlying reality. But that is what physicists wanted to hear, and that isexactly what Bohr was giving them. As Alisa Bokulich [7] has recently remarked: “As we know well today [...]Bohr orbits are fictions —according to modern quantum mechanics the electron in an atom does not follow adefinite classical trajectory in a stationary state and is instead better described as a cloud of probability densityaround the nucleus.” The strength and persistence of Bohr’s images is reflected in the fact that even though QMonly makes reference to probability transitions and says nothing about elementary particles this has not stopedcontemporary physicists and philosophers from —still today— referring to the existence of microscopic entities(e.g., see [56]).Apart from classical images, Bohr would also apply principles —in fact, ad hoc rules— which allowed himto justify why certain transitions between stationary states occurred and others did not. The correspondenceprinciple , as Bohr called it [4, p. 86], imposed an ambiguous relation between the quantum realm and classicalphysics which characterized “the asymptotic approach of the description of the classical physical theories in thelimit where the action involved is sufficiently large to permit the neglect of the individual quantum.” Onceagain, even though there was no theoretical account of this limit between quantum and classical the image waspowerful enough to serve its purpose. At the time, Arnold Sommerfeld [8] was not impressed by the proposalof the young Danish physicist: “Bohr has discovered in his principle of correspondence a magic wand (whichhe himself calls a formal principle), which allows us immediately to make use of the results of the classicalwave theory in the quantum theory.” Some years later his criticism would grow stronger: “The magic of thecorrespondence principle has proved itself generally through the selection rules of the quantum numbers, inthe series and band spectra? Nonetheless I cannot view it as ultimately satisfying on account of its mixing ofquantum-theoretical and classical viewpoints.” As remarked by Alisa and Peter Bokulich [8]: “Sommerfeld’scritical attitude toward the correspondence principle would prove influential on Wolfgang Pauli and WernerHeisenberg, both of whom were his doctoral students.” Pauli would write to Bohr in a letter dated December31st, 1924: “I personally do not believe, however, that the correspondence principle will lead to a foundationof the rule? For weak men, who need the crutch of the idea of unambiguously defined electron orbits andmechanical models, the rule can be grounded as follows: If more than one electron have the same quantumnumbers in strong fields, they would have the same orbits and would therefore collide.” Heisenberg, who wasat first clearly impressed by Bohr’s correspondence program, would also end up following in 1925 —thanks toPauli— exactly the opposite line of investigation. By detaching himself completely from the classical attempt todescribe the trajectory of electrons between atomic orbits and applying instead Mach’s observability principle We might recall that the essential step for the development of the classical space-time representation of Newtonian mechanicswas the creation of infinitesimal calculus which allowed for a rigorous mathematical definition of the continuum . It is interesting to note that, in consonance with Alisa Bokulich’s interpretation of Bohr’s approach, one might regard thecorrespondence principle as an attempt to produce a rational generalization of classical mechanics [6]. As Bohr [4, p. 87] himselfwould remark: “the aim of which [of the correspondence principle] was to let a statistical account of the individual quantum processesappear as a rational generalization of the deterministic description of classical physics.”
6o the intensive line-spectra observed in the lab, Heisenberg was finally able to construct a closed mathematicalformalism that he would call “quantum mechanics”. Unfortunately, Heisenberg’s unfinished theory would bevery soon replaced by Dirac’s axiomatic re-formulation in which Bohr’s correspondence principle as well as hisatomist narrative would be essentially restored as part of the new orthodoxy. Inconsistency of Quantum and Classical (Correspondence Principle):
Quantum mechanics makesreference to a microscopic realm constituted by irrepresentable quantum particles. There exist a limit betweenthis quantum microscopic realm and our classical macroscopic realm represented by classical physics.
At this point, some obvious questions might pop up to the attentive reader. First, how could it be possibleto make reference to a realm which cannot be represented? If it cannot be represented, how do we know thatthis realm talks about microscopic entities? And how can there exist a limit between a realm that cannot berepresented (i.e., the quantum) and one that is actually represented (i.e, the classical) in terms of bodies existingwithin space and time? There are no answers.An essential addition for the effectiveness of Bohr’s matrix is the creation of inconsistent dualities justifiedthrough the famous principle of complementarity . A principle shaped during his famous debates with AlbertEinstein during the 1920s where Bohr had already introduced a dualistic reference to ‘waves’ and ‘particles’ inorder to account for the famous double-slit experiment. Bohr would apply these two inconsistent representations to essentially the same experimental situation and argue that: “We must, in general, be prepared to accept thefact that a complete elucidation of one and the same object may require diverse points of view which defy a uniquedescription.” As explained by Jean-Yves Béziau [1]: “[Bohr] argues that there are no direct contradiction: froma certain point of view ‘K is a particle’, from another point of view ‘K is a wave’, but these two contradictoryproperties appear in different circumstances, different experiments. Someone may ask: what is the absolutereality of K, is K a particle or is K a wave? One maybe has to give away the notion of objective reality .” In turn,Bohr would also extend his notion of complementarity to quantum observables (e.g., position and momenta). This latter extension is explicit in Bohr’s reinterpretation of Heisenberg famous inequality as uncertainty relations —i.e., as a limit to the accuracy of quantum measurements [35]— as well as in his famous reply to the EPRpaper [2] —something that would end up being known in the contemporary literature as quantum contextuality.
Inconsistency of Classical Representations (Complementarity Principle):
Quantum objects requirecontradictory classical representations provided through the notions of ‘wave’ and ‘particle’. Complementaryquantum properties (e.g., position and momentum) as well as measurement outcomes also require complementaryexperimental arrangements which are necessary as a prerequisite for their consideration.
To sum up, the unity, consistency and coherency of theoretical representation, essential to the Greek scien-tific paradigm, developed also in modern times through the notions of invariance and objectivity , would becomecompletely subverted within Bohr’s matrix. The constitution of inconsistent dualities framed through ad hoc unjustified rules, principles and pseudo-explanations would allow Bohr to create a new foundation for physics,shaky and unstable, constantly moving back and forth between waves and particles, position and momenta,between causal mathematical representation and space-time events, between microscopic and macroscopic, sub-jective observations and objective interactions, between reality and fiction. David Deutsch has characterizedthis system simply as ‘bad philosophy’: “Let me define ‘bad philosophy’ as philosophy that is not merely false, but actively prevents the growthof other knowledge. In this case [i.e., QM], instrumentalism was acting to prevent the explanations inSchrödinger’s and Heisenberg’s theories from being improved or elaborated or unified. The physicist NielsBohr (another of the pioneers of quantum theory) then developed an ‘interpretation’ of the theory whichlater became known as the ‘Copenhagen interpretation’. It said that quantum theory, including the rule ofthumb, was a complete description of reality. Bohr excused the various contradictions and gaps by using acombination of instrumentalism and studied ambiguity. He denied the ‘possibility of speaking of phenomenaas existing objectively’ —but said that only the outcomes of observations should count as phenomena. He alsosaid that, although observation has no access to ‘the real essence of phenomena’, it does reveal relationshipsbetween them, and that, in addition, quantum theory blurs the distinction between observer and observed.As for what would happen if one observer performed a quantum-level observation on another, he avoided Something that has been exposed in contemporary quantum physics through the development of the principle of decoherencein 1970 by Dieter Zeh and popularized during the early 1980s by Wojciech Zurek. For a detailed discussion of the inconsistency present within the complementarity principle see [16]. For a detailed analysis of the complementarity principle see [38]. he issue. [...] For decades, various versions of all that were taught as fact —vagueness, anthropocentrism,instrumentalism and all— in university physics courses. Few physicists claimed to understand it. Nonedid, and so students’ questions were met with such nonsense as ‘If you think you’ve understood quantummechanics then you don’t.’ Inconsistency was defended as ‘complementarity’ or ‘duality’; parochialism washailed as philosophical sophistication. Thus the theory claimed to stand outside the jurisdiction of normal(i.e. all) modes of criticism —a hallmark of bad philosophy.” [23, p. 308-310] Maybe the most clear exposition of Bohr’s approach to QM can be found in a paper by John Archibald Wheeler,not only a prominent figure in the post-war physics commanded by the U.S. but also one of his closest studentsand followers. In 1983 Wheeler co-authored with one of his students, Warner Miller, a paper titled “Delayed-Choice Experiments and Bohr’s Elementary Quantum Phenomenon” where, together, they argued that the notionof elementary quantum phenomenon had to be regarded as the most important concept within the general schemeproposed by the Danish physicist. “What one word does most to capture the central new lesson of the quantum? ‘Uncertainty’, so it seemedat one time; then ‘indeterminism’; then ‘complementarity’; but Bohr’s final word ‘phenomenon’ —or, morespecifically, ‘elementary quantum phenomenon’— comes still closer to hitting the point. It is the fruit ofhis 28 year (1927-1955) dialog with Einstein, especially as that discussion came to a head in the idealizedexperiment of Einstein, Podolsky and Rosen. In today’s words, no elementary quantum phenomenon is aphenomenon until it is a registered (‘observed’ or ‘indelibly recorded’ phenomenon), ‘brought to a close’ byan ‘irreversible act of amplification’.” [41, p. 72]
Wheeler was right to point to the elementary phenomenon as one of the main elements within Bohr’s scheme.And even though at first sight this notion might have seemed as just a fancy way to talk about observations of‘clicks’ in detectors or ‘spots’ in photographic plates, Wheeler had recognized that there was something deeper,still unveiled. An elementary quantum phenomenon was in fact a monstrous creature: “The elementary quantum phenomenon is a great smoky dragon. The mouth of the dragon is sharp, where itbites the counter. The tail of the dragon is sharp, where the photon starts. But about what the dragon doesor looks like in between we have no right to speak, either in this or in any delayed-choice experiment. Weget a counter reading but we neither know nor have the right to say how it came. The elementary quantumphenomenon is the strangest thing in this strange world.” [41, p. 73]
Of course, a smoky dragon —contrary to Wheeler’s description— does not actually bite the counter, instead—as shown in figure 1— it produces fire in order to generate a ‘click’ in the detector. Regardless of this obviousinaccuracy, Wheeler’s dragon encapsulates perfectly well Bohr’s approach to QM. An inconsistent scheme ofthought which has the main purpose of justifying effectively operational models through fictional conceptswhich even though have no theoretical nor experimental support are —anyhow— capable of upholding the mostamazing illusions and narratives. A smoky dragon is a concept that cannot be (consistently) represented intheoretical terms, that has no experimental support but is anyhow regarded as part of an inconsistent realitythat becomes indistinguishable from fiction.
Smoky Dragon (Inconsistent Concept):
A smoky dragon is an irrepresentable meaningless concept whichprovides a pseudo-picture of a physical situation or process and, consequently, the illusion of understanding. Suchinconsistent concepts have no mathematical representation nor posses any operational testability procedure.Maybe the best example of a smoky dragon is Bohr’s famous quantum jump of electrons between quantizedorbits. For those acquainted with the theory, this notion generates a strange motion picture in our mindsallowing us to imagine a process that is not described by the mathematical formalism nor observed in the lab.Of course, hiding beneath these quantum jumps we find another smoky creature, namely, quantum particles themselves. Microscopic entities which must exist, since they are “small”, within space and time. However,it is also claimed that quantum objects cannot be actually represented and that their existence can be onlywitnessed through ‘clicks’ in detectors and ‘spots’ in photographic plates. Obviously, these two statements arecontradictory. If a quantum object is un-thinkable, irrepresentable, than it cannot be “small” nor can it inhabitspace and time —which are of course part of the modern metaphysical representation of classical physics. Since8igure 1:
Niels Bohr’s smoky dragon generating a ‘spot’ in a photographic plate. both quantum jumps and particles are part of the “standard” account of the theory of quanta, an obvious questionrises: How could such inconsistent fictional creatures been able to endure within a —supposedly— rational fieldlike physics? Essential to the survival of smoky dragons is Bohr’s outstanding use of misdirection. Managingaudience attention is the aim of all theater, and the foremost requirement of all magic acts. In theatrical magic,misdirection is a form of deception in which the performer draws audience attention to one thing to distract itfrom another. This is the key to understand the effectiveness of Bohr’s matrix. As we pointed out, in order tocomplete his trick Bohr did not only rely on the well known atomist images that physicists where expecting torecover, he would also tell everyone that the electrons orbiting the nucleus were capable of performing “quantumjumps” which allowed them to magically disappear from their orbits and immediately reappear in another one.The story was spectacular and physicists were immediately captured. How could this happen? What were thesefantastic “quantum jumps”? Are they actually real? How can particles disappear and reappear at will? Whereare these particles going in the meantime? The complete lack of answers did not matter. The trick had beenalready completed. The Danish conjurer had succeeded in drawing the focus of attention away from the criticalconsideration of atoms, electrons and protons —something that Mach had criticized just a few decades before—to the fictional existence of —unobserved and irrepresentable— quantum jumps. With great confidence a youngcharismatic Bohr would wispear to his audience: “It is weird because it is quantum!”The complete lack of justification within Bohr’s inconsistent scheme was clearly exposed during a meetingin 1926 that took place in Copenhagen where the Danish physicist had invited Erwin Schrödinger to discussabout the existence of ‘quantum jumps’. Under the attentive gaze of Heisenberg, Bohr’s young apprentice, theAustrian physicist would present several arguments exposing not only the lack of theoretical and experimentalsupport for the existence of quantum jumps but also the serious inconsistencies reached when introducing thisfantastic process within the theory. Schrödinger [34, p. 73] would then conclude that “the whole idea of quantumjumps is sheer fantasy.” However, with great mastery, without even confronting the strong arguments of hisenemy, making use of his powerful rhetorics Bohr would turn things completely upside-down in a single move: “What you say is absolutely correct. But it does not prove that there are no quantum jumps. It only provesthat we cannot imagine them, that the representational concepts with which we describe events in daily lifeand experiments in classical physics are inadequate when it comes to describing quantum jumps. Nor shouldwe be surprised to find it so, seeing that the processes involved are not the objects of direct experience.” [34,p. 74]
Reversing the burden of proof Bohr was asking Schroödinger either to grant him the existence of quantum jumps9r prove their non-existence. After his meeting, in a letter to Wilhelm Wien, Schroödinger would expose hissuspicions about Bohr’s rhetorics: “Bohr’s [...] approach to atomic problems [...] is really remarkable. He is completely convinced that anyunderstanding in the usual sense of the word is impossible. Therefore the conversation is almost immediatelydriven into philosophical questions, and soon you no longer know whether you really take the position he isattacking, or whether you really must attack the position he is defending.” [42, p. 228]
In modern times philosophers engaged in a process of dissection of the Greek notion of physis (section 1).As a culmination of this process, reality was effectively separated in three distinct realms: subjective reality,objective reality and reality-in-itself. Kant had limited physics to the circular interrelation between subjectiveand objective realities; distancing this co-relational form of knowledge from reality-in-itself which —according tohim— would then remain unreachable, unknowable, unthinkable. Reality had been torn apart and detached fromphysics. Three centuries later, in post-modern times, Bohr was ready to generate a new system, more complex,stable and powerful than its predecessor. It is the introduction of fictional reality as a constitutive elementof physical representation itself that would allow to replace the need of mathematical invariance, conceptualobjectivity and operational testability —to which we shall return in section 5— by narratives and interpretationswith no connection whatsoever to any theoretical formalism nor experimental evidence. The Bohrian matrixcould be pictured as a highly effective Möbius strip machine generating motion through the constant creationof dualistic poles applied within a never-ending line of reasoning. Going back and forth between contradictorystatements and principles, Bohr was able to create a never-ending progression of rhetorical self-justification.Scrambling epistemology (i.e., gnoseology) with ontology he would argue that the fictional consideration of aquantum object imposed a limit to representation [5, v. 2, p. 62]: “In quantum mechanics, we are not dealingwith an arbitrary renunciation of a more detailed analysis of atomic phenomena, but with a recognition that suchan analysis is in principle excluded.” It was the quantum of action which —according to the Danish physicist—was to be blamed for this impossibility [3, p. 79]: “not being any longer in a position to speak of the autonomousbehavior of a physical [quantum] object, due to the unavoidable interaction between the [quantum] object and the[classical] measuring instrument.” However, proposed by Max Planck in 1900, the discrete quantum theoreticalrepresentation of energy, ∆ E = h.n , was not only imposing a limit to the possibilities of representation, it wasalso —according to Bohr— describing something truly real, something going on in each and every interactionbetween a quantum particle and a classical apparatus. As he would explain in his famous reply to EPR [2, p.701]: “The impossibility of a closer analysis of the reactions between the [quantum] particle and the [classical]measuring instrument is indeed no peculiarity of the experimental procedure described, but is rather an essentialproperty of any arrangement suited to the study of the phenomena of the type concerned, where we have todo with a feature of [quantum] individuality completely foreign to classical physics.” Thus, (quantum) physicscould not represent objective reality as described by quantum objects due to the (real) interaction betweenthe (fictional) quantum object and the (real) classical measuring device. But turning things upside-down,once again, this epistemological limit had to be understood —according to Bohr— not as a technical limit ofour instruments or our human capabilities but rather as an ontological feature of reality-in-itself, namely, itsown irrepresentability! This typical scrambling of gnoseological and ontological claims, of realist and fictionalstatements, is part of Bohr’s incredibly effective pendular rhetorics. The Borian Möbius strip of reasoning is anamazing device, a never ending process which forces us to remain in constant motion always between two poles:between waves and particles, between the objective interaction of systems and subjective observations, betweenmicroscopic and macroscopic, between theory and measurement, between ontology and epistemology, betweenreality and fiction... Bohr’s pendular rhetorics about microscopic particles, classical apparatuses and measurement outcomes remainsthe discursive basis of what is known today in physics as “Standard QM” (SQM), a general set of (inconsistent)rules framed under the Dirac-von Neumann axiomatic formulation sometimes referred to as “the Copenhagen This sort of proof is known in jurisprudence as the probatio diabolica [the diabolical proof], namely, the legal requirement toachieve an impossible proof. Such Devil’s Proof is the logical dilemma that while evidence will prove the existence of something,the lack of evidence fails to disprove it. Regardless of the many difficultieswithin the field, there are two main points of profound consensus between physicists about the standard accountof the theory of quanta which expose the penetration of Bohr’s anti-realist realism. The first point of absoluteconsensus is the unquestionable fact that SQM makes reference to a microscopic realm constituted by elementaryparticles [56]. As explained by the Richard Feynman [28, Chap. 37]: “Quantum Mechanics is the descriptionof the behavior of matter and light in all its details and, in particular, of the happenings on an atomic scale.”However, strange as it might seem, there is another point of generalized agreement between contemporaryphysicists when questions begin to pop up, namely, that “nobody understands QM” —a phrase also madepopular by Feynman [29, p. 129]. These statements are clearly contradictory. If we do not know what QM istalking about then we cannot know that it talks about atoms. Period. As a result, still today Bohrian rhetoricsare commonly applied by physicists who do not even recognize the inconsistent jumps they perform when goingfrom metaphysical claims such as “QM is a theory that talks about microscopic particles” to purely instrumentalones such as [31, p. 70]: “[...] quantum theory does not describe physical reality. What it does is provide analgorithm for computing probabilities for the macroscopic events (‘detector clicks’) that are the consequencesof experimental interventions.” A common way out of this conundrum is to argue that quantum particles are“fundamental”. But as recognized by Xiao-Gang Wen [56], a theoretical physicist at the Massachusetts Institute ofTechnology: “We say [electrons, photons, quarks] are ‘fundamental’. But that’s just a [way to say] to students,‘Don’t ask! I don’t know the answer. It’s fundamental; don’t ask anymore’.” The attempt to answer thesequestions has been indeed banished from theoretical physics and replaced under the jurisdiction of philosophywhere —to our complete surprise— we can also find the profound influence of Bohr’s anti-realist realism. Infact, the creation of philosophy of QM can be easily related to the creation of a smoky dragon analogous to theone created by Bohr in 1913.The story begins in the year 1930 when a young English engineer and mathematician called Paul Dirac—following Bohr’s teachings— would give to birth a dragon so powerful it could turn an abstract mathematicalformula into a real empirical observation —or in more technical terms, a quantum superposition into a singlemeasurement outcome. This would become to be known between physicists as the “collapse” of the quantumwave function —also called projection postulate or measurement axiom . The introduction of this fantastic processwhich would soon become an essential cornerstone of the standard understanding of the theory was presentedwithin the first chapters of The Principles of Quantum Mechanics . In a typical Bohrian fashion, making referenceto the polarization measurement of photons, Dirac would describe the real effect of observations: “When we make the photon meet a tourmaline crystal, we are subjecting it to an observation. We are observ-ing wether it is polarized parallel or perpendicular to the optic axis. The effect of making this observation isto force the photon entirely into the state of parallel or entirely into the state of perpendicular polarization.It has to make a sudden jump from being partly in each of these two states to being entirely in one or theother of them. Which of the two states it will jump cannot be predicted, but is governed only by probabilitylaws.” [24, p. 9]
Dirac argued explicitly that “science is concerned only with observable things” [24], however, he was less explicitabout the fact that observations —according to him— had to be necessarily restricted to a binary representation.In this respect, the introduction of the collapse had the sole purpose to do away with quantum superpositionsand in this way restore his presupposed narrow understanding of (binary) observability. Quite ironically, thisrestriction was doing away with the positivist observational rule which had allowed Heisenberg to come up withQM in the first place just five years before —in a nutshell, forget about fictional orbits and classical trajectories,forget about particles and consider instead what is actually observed in the lab, namely, a list of intensive valuesthat can be represented by matrices. Dirac’s formulation reinforced by the influential mathematician John vonNeumann with his 1932
Mathematical Foundations of Quantum Mechanics [52] would become orthodoxy and thenewborn jumping dragon would be soon ready to give birth to another monster baptized as “the measurementproblem of QM”. The fact that this process created a serious inconsistency within the mathematical formalism,that it had never ever been observed nor measured within the lab, or that it was not even necessary from anoperational perspective —for Heisenberg’s matrix mechanics already provided a consistent operational accountof experiments [18]— did not seem to matter to most instrumentalist physicists. However, a few of them —withclear philosophical inclinations— would not let go and begin to desperately try to come up with stories that As the U.S. physicist John Clauser [13, p. 70] would stress: “given Bohr’s strong leadership, the net legacy of their argumentsis that the overwhelming majority of the physics community accepted Bohr’s ‘Copenhagen’ interpretation as gospel, and totallyrejected Einstein’s viewpoint.” Sean Carroll [12] has recently unveiled the mystery of what actuallyhappens to those students that simply won’t shut up: “Many people are bothered when they are students andthey first hear [about SQM]. And when they ask questions they are told to shut up. And if they keep asking theyare asked to leave the field of physics.” It is in this context that the debates about the measurement problem thatbegun very slowly during the 1950s might have seemed like an oasis for the young rebels still wondering aboutreality. Today, things do not seem to have changed a lot. As Maudlin [45, p. 52] —a former physics studentexpelled from the field— explains: “The most pressing problem today is the same as ever it was: to clearlyarticulate the exact physical content of all proposed ‘interpretations’ of the quantum formalism is commonlycalled the measurement problem, although, as Philip Pearle has rightly noted, it is rather a ‘reality problem’.”But is the measurement problem a secure refugee for true realists or is it in fact a trap carefully designed byanti-realists themselves in order to avoid the construction of a meaningful theoretical reference to reality?The anti-realist collapse introduced by Dirac in 1930 had soon become not only a cornerstones of SQM, butalso a great exemplification of the way in which empirical science could always impose the reference to actualobservations. During the following decades as the influence of Bohr and positivism would grow stronger physicswould be reframed in an instrumentalist fashion. As Karl Popper [44] would describe during the 1960s: “Todaythe view of physical science founded by Osiander, Cardinal Bellarmino, and Bishop Berkeley, has won the battlewithout another shot being fired. Without any further debate over the philosophical issue, without producingany new argument, the instrumentalist view (as I shall call it) has become an accepted dogma. It may well nowbe called the ‘official view’ of physical theory since it is accepted by most of our leading theorists of physics(although neither by Einstein nor by Schrödinger). And it has become part of the current teaching of physics.”Popper argued that this result had been a direct consequence not only of the successful technical applicationsobtained in the U.S., “some of them with a big bang”, but also of Bohr’s complementarity approach. In thecontext of the U.S. post-war anti-realist program of science questions about reality and foundations had no place,but the unease and pressure of those who still wanted to actually understand the theory could be felt in theclassrooms. Trying to deal with this conflictive situation, during the 1970s, a new field of research was specificallycreated in order to contain the few subversive students and even fewer Professors that were still willing to makequestions. Young realist physicists who wanted to destroy their academic careers were given the opportunityto have a new job as philosophers of physics. As such, they were given a very specific task to accomplish: try As Clauser [13, pp. 72-73] recalls from his student days in the 1960s: “Any physicist who openly criticized or even seriouslyquestioned these foundations (or predictions) was immediately branded as a ‘quack’. Quacks naturally found it difficult to finddecent jobs within the profession. [...] Religious zeal among physicists prompted an associated powerful proselytism of students. Aspart of the ‘common wisdom’ taught in typical undergraduate and graduate physics curricula, students were told simply that Bohrwas right and Einstein was wrong. [...] Any student who questioned the theory’s foundations [i.e., SQM], or, God forbid, consideredstudying the associated problems as a legitimate pursuit in physics was sternly advised that he would ruin his career by doing so. Iwas given this advice as a student on many occasions by many famous physicists on my faculty at Columbia and Dick Holt’s facultyat Harvard gave him similar advice.” For very similar remarks by David Albert and Lee Smolin see [20]. Karl Popper [44] saw the future with hope: “I trust that physicists will soon come to realize that the principle of complementarityis ad hoc , and (what is more important) that its only function is to avoid criticism and to prevent the discussion of physicalinterpretations; though criticism and discussion are urgently needed for reforming any theory. They will then no longer believe thatinstrumentalism is forced upon them by the structure of contemporary physical theory.”
12o solve the measurement problem through the introduction of a narrative —what philosophers would call intechnical jargon an interpretation of the theory— that would somehow picture what was really going on whenmeasurements were actually performed. Or in other words, provide an answer to the measurement problem.Ever since, many physicists transformed into philosophers of physics —I am myself one of them— helped also byphilosophers, logicians and mathematicians have been creating stories to calm their own metaphysical anxieties.As Hervé Zwirn [57, p. 639] described: “Faced to what seems a real inconsistency inside the quantum formalism,physicists have proposed many solutions largely depending on their initial philosophical inclination.” However,there was a barrier left behind by anti-realists. Anyone —physicist, philosopher, logician or mathematician—attempting to add an interpretation to SQM would be faced with a serious obstacle, namely, there was noplace whatsoever for any of these narratives within the anti-realist account of (empirical) theories. And with no objective link between theory and interpretation these metaphysical narratives would always remain in a fictionallimbo floating free from physics (see for a detailed discussion [54, 55] and references therein). As John Horgandescribed, when attending in 1992 a symposium at Columbia University in which philosophers and physicistsattempted to discuss the meaning of quantum mechanics: “The symposium demonstrated that more than 60 years after quantum mechanics was invented, its meaningremained, to put it politely, elusive. In the lectures, one could hear echoes of Wheeler’s it from bit approach,and Bohm’s pilot-wave hypothesis, and the many-worlds model favored by Steven Weinberg and others. Butfor the most part each speaker seemed to have arrived at a private understanding of quantum mechanics,couched in idiosyncratic language; no one seemed to understand, let alone agree with, anyone else. [...][W]hen I revealed my impression of confusion and dissonance to one of the attendees, he reassured me thatmy perception was accurate. “It’s a mess,” he said of the conference (and, by implication, the whole businessof interpreting quantum mechanics). The problem, he noted, arose because, for the most part, the differentinterpretations of quantum mechanics cannot be empirically distinguished from one another; philosophersand physicists favor one interpretation over another for aesthetic and philosophical —that is, subjective—reasons.” [36, p. 88]
The truth is that most physicists trained today in an instrumentalist fashion do not even know that such a“realist debate” about QM even exists. They simply don’t care. And there is a very good reason for thecomplete lack of interest, namely, this “realist debate” is not regarded as a scientific one. Science today isorthodoxly understood in empirical terms which, following Bas van Fraassen [48, pp. 202-203], can be resumedin the following: “an empiricist account of science is to depict it as involving a search for truth only about theempirical world, about what is actual and observable”, more specifically, “science aims to give us theories whichare empirically adequate: an acceptance of a theory involves as belief only that it is empirically adequate.” Thisis why Roberto Torretti [46, p. 367] seems correct to point out that interpretations of QM should be consideredas “meta-physical ventures [...] for they view the meaning and scope of QM from standpoints outside empiricalscience.” Taking this point into consideration Arthur Fine [30, p. 149] gives us the following very reasonableadvise: “Try to take science on its own terms, and try not to read things into science. If one adopts thisattitude, then the global interpretations, the ‘isms’ of scientific philosophies, appear as idle overlays to science:not necessary, not warranted and, in the end, probably not even intelligible.” However, regardless of the sarcasticreference made by many anti-realists to interpretations, as we have argued in [19], their introduction has playedan essential role for the perpetuation of their own program. In fact, the creation of narratives has created theperfect smoky shield for hiding the many dragons flying freely within the so called “minimal interpretation” ofQM. But even more importantly, the introduction of interpretations has also allowed anti-realists to control andrestrict the activities of realists in term of a praxis placed outside the limits of empirical science itself. Buteven this seems to have run out of control. The complete lack of experimental or theoretical constraints inorder to come up with crazy stories —tolerated in some cases and embraced in others— has turned philosophyof QM into breeding field of smoky dragons. As David Mermin [40, p. 8] declared: “[Q]uantum theory is themost useful and powerful theory physicists have ever devised. Yet today, nearly 90 years after its formulation,disagreement about the meaning of the theory is stronger than ever. New interpretations appear every day.None ever disappear.” In the last decades, the situation is becoming to be recognized as untenable and Adán Let us remark that not even “non-collapse” interpretations (e.g., many worlds and modal) reject the projection postulate [18]. As Maximilian Schlosshauer [45, p. 59] remarks: “It is no secret that a shut-up-and-calculate mentality pervades classroomseverywhere. How many physics students will ever hear their professor mention that there’s such a queer thing as different interpreta-tions of the very theory they’re learning about? I have no representative data to answer this question, but I suspect the percentageof such students would hardly exceed the single-digit range.”
Adán Cabello’s realist map of interpretational madness in quantum theory in [10].
Cabello —a prominent physicist in the field of quantum information— has even characterized it as “a map ofmadness” [10]. How did we get to this point?Even though the boom of interpretations can be placed —with the rise of philosophy of QM— during the1980s and 1990s, the introduction of these narratives goes back to the late 1950s with Heisenbergs’, Margenau’sand Popper’s hylemorphic interpretations in terms of potentialities, latencies and dispositions (see [19]). Allthese narratives are good examples of this second layer of smoky dragons which, as Mauro Dorato [25, p. 4] hasrecognized, have failed to provide a consistent representation of what the theory is talking about: “In a word,the use of the language of ‘dispositions’ [and also ‘potentialities’ and ‘latencies’] does not by itself point to aclear ontology underlying the observable phenomena, but, especially when the disposition is irreducible, refersto the predictive regularity that phenomena manifest. Consequently, attributing physical systems irreducibledispositions, even if one were realist about them, may just result in more or less covert instrumentalism.” Exactlythe same happens with the notion of ‘world’ or ‘branching’ introduced by Bryce DeWitt during the 1960s inwhat has become today’s popular many worlds interpretation of QM —a metaphysical account of Hugh Everett’srelative state formulation. There is no theoretical account of what a ‘world’ is according to the theory nor anyway to test experimentally their actual existence, and the same counts for the ‘branching process’ [18]. Ina typical Bohrian fashion, the contemporary justification for the complete lack of theoretical representation orexperimental support for these narratives is grounded on the simple fact that “QM is weird”. As Sean Carroll [11]explains: “As you learn more and more about the world, as you do more science, as you uncover more and morefacts, observations become more precise, you go into realms that you hadn’t yet seen —distant stars and galaxiesand the subatomic world. Would you expect —that as your learn all these new things— your best descriptionof the world would become more intuitive and everyday or more and more weird and surprising? It will becomemore and more weird and surprising because we are looking at things that we are not trained to experience.”Unrelated to the theory they attempt to refer to the introduction of these new interpretations can be regardedas an effective misdirection which has allowed the standard account of the theory to remain safe from criticalattacks. Addressing the role of interpretations, Bas van Fraassen —one of the most prominent contemporaryanti-realists— explains that, regardless of the fact that any fictional story responding to the question ‘what isthe world like according to the theory?’ could —in principle— be true , the interpretation does not need to beactually true in order for the theory to be good [48, p. 10]. In fact —according to anti-realists— we will neverknow for real if any of these fictions describes reality-in-itself. Thus, it might seem far more reasonable andconvenient to remain simply “agnostic” —as van Fraassen himself has called his skeptic standpoint. After all,empirical science is only meant to describe actual observations. Period. Realists are then easily portrayed byanti-realists either as “naive” or “fanatic” believers in interpretations they cannot justify nor relate to the theory.They are essentially correct.To sum up, the second layer of smoke created by the addition of interpretations plays a major role withinthe anti-realist understanding of QM hiding and protecting from critical through the first layer of fictionsalready introduced within the supposedly un-interpreted standard account of the theory —which refers to atoms,electrons, jumps, measuring devices, etc. While interpretations shift the focus of attention to a supposedly“realist debate” about potentialities, propensities, worlds, histories, modalities, etc., the orthodox “recipe” andits microscopic-instrumentalist narrative remains shield from criticism. Physicists can then continue to use their“recipe”, while philosophers are creating new dragons. Cabello [10], who has characterized this situation as “odd As Alan Musgrave [14, pp. 1209-1210] remarks: “As usually understood, the realism-antirealism issue centers precisely on thequestion of truth. Positivists deny the existence of ‘theoretical entities’ of science, and think that any theory which asserts theexistence of such entities is false . Instrumentalists think that scientific theories are tools or rules which are neither true nor false .Empistemological antirealists like van Fraassen or Laudan concede that theories have truth-values, even that some of them might betrue, but insist that no theory should be accepted as true .” It is only what anti-realists have termed “scientific realists” who arguethat interpretations are true.
It is essential to acknowledge that —even from a realist perspective— through its criticisms, anti-realism hasalways played an essential role for the development of science. Without sophistry, it would have been impossiblefor Plato and Aristotle to create metaphysics and without Mach’s criticism to Newton’s and Kant’s metaphysicalpresuppositions it would have been impossible to develop QM and relativity theory. Undoubtedly, it is thebalance between realism and anti-realism which has been kernel for the critical advancement of science in thehistory of Western thought. Unfortunately for all of us during the last century this balance has been brokenand the distinction between realism and anti-realism erased. Anti-realists have been finally able to conquer bothphysics and philosophy producing the most outstanding re-foundation of the meaning of science itself. In thiscontext, the main triumph of anti-realism has been to trap realists in a fictional world which they themselveshave been compelled to build up. Realists slaves have become so comfortable they would certainly refuse —ifgiven the opportunity— to escape their prison. Could we say that realism is actually dead? Is there any hopeleft for the reconstruction of the realist program beyond fictions, interpretations and narratives? Or in otherwords, would it be possible for realists to capture and defeat smoky dragons?Smoky dragons are powerful illusions capable of creating the fantasy of an ungrounded reference with no(realist) theoretical nor experimental support. QM illustrates perfectly well the extreme dangers created by anextremist anti-realist account of science supplemented by a fake fictional realism. The annihilation of conceptualcritical thought produced by smoky dragons has created a desert in which realists wonder with no compass,preaching and fighting between each other for imaginary stories that no one really cares about. The power ofthese creatures comes from the darkness of un-scientific mythical thought exposing the return to a dark pre-scientific rationality (section 1). However, our optimistic claim is that realists already possess the tools andweapons to fight and defeat smoky dragons. Realists simply need to remember the basic ideas that support theirflag, namely, that theoretical representations are not interpretations and physical concepts are not just wordsin a story. According to realism, a physical theory is a unified formal-conceptual representation of a state ofaffairs which relates to experience coherently and consistently in a qualitative and quantitative fashion. In thisrespect, it is essential to note that, while physical representations are both dependent on (conceptual) subjectivepreconditions and (formal) reference frames, realism seeks their unity in order to make reference to the same (real) state of affairs through objectivity and invariance. What Einstein called repeatedly a subject detached account of physical reality.
Definition 5.1 Realism:
The presupposition that physis (or reality) is knowable through the creation oftheories, namely, unified, consistent and coherent formal-conceptual invariant-objective representations whichprovide an account of a state of affairs and experience detached from both particular subjects and referenceframes. Definition 5.2 Anti-Realism:
The claim that realists are wrong and that even if physis (or reality) wouldactually exist, due to our human limitations it would anyhow remain always un-reachable, un-knowable.
What is essential to realize is that the mathematical formalism and the conceptual system that conforma theory are constrained by a specific set of necessary conditions within the realist program. It is these sameconditions, essential for the creation of adequate physical concepts, that could be used today as powerful weaponsagainst smoky dragons. Let us address some of these realist conditions in some detail.Operational-invariance and phenomenological-objectivity provide a rigorous foundation in order for a theoryto refer to a state of affairs that can be considered as real; i.e., a representation completely detached from theperspectival perception of subjects or the choice of any particular frame of reference.
Operational-Invariance points to the fact that a mathematical representation must be able to provide a consistent scheme for the It should be remarked , once again, that realism does not refer to “stuff”, it refers to reality. Knowing reality does not implythe idea that representation should describe reality-as-it-is ; i.e., the idea there should exist a correspondence relation between therepresentation of a theory and reality. This claim is actually made by many anti-realists (e.g., van Fraassen) in order to create theweakest possible form of realism and a “straw realist” easy to attack and defeat. the same rabbit.
Definition 5.3 Operational Invariance:
A physical concept must be able to provide a consistent unifiedaccount of its operational testability considered with respect to different frames of reference (or bases).
This condition is fulfilled in classical mechanics via the Galielan transformations and in relativity theory viathe Lorentz transformations. On the contrary, in QM the orthodox interpretation of probability in terms ofbinary measurement outcomes together with the non-invariant definition of quantum state has destroyed theoperational invariance present within Heisenberg’s original matrix formulation (see for a detailed analysis anddiscussion [21, 22]). This mathematical condition can be translated in conceptual terms as a phenomenological-objective condition which imposes the need to discuss about the same object of experience independently of theparticular viewpoint taken by an agent. Observers from different perspectives should be able to agree aboutwhat they observe. Thus, unlike in the case of the famous story by Jorge Luis Borges,
Funes the Memorius [9],a ‘dog observed form a profile’ should be considered as the same ‘dog observed from the front’ (see [17]).
Definition 5.4 Phenomenological Objectivity:
A physical concept must be able to bring into unity themultiplicity of physical phenomena observed from different perspectives.
Classical mechanics and electromagnetism are good examples of how both the formal and the conceptual partsof a theory can be brought into unity in order to consistently and coherently imagine the evolution of a realstate of affairs. In these particular cases, the physical concepts that provide a consistent account of what isgoing on are particles and electromagnetic waves . On the very contrary, the notion of object discussed by Bohrin QM plays exactly the opposite role. Instead of providing a unified account of phenomena, it is defined as thatwhich differs from itself in every observation. Going back to George Berkeley’s dictum, esse est percipi , Bohr’sprinciple of complementarity has allowed to bypass objectivity and invariance generating instead an inconsistentnarrative which makes reference to the act of perception of either waves or particles, position or momenta. Bohr’sempiricist standpoint, in line with positivism, contrasts radically with Einstein’s theoretical realism accordingto which it is only the theory which decides what can be observed: “I dislike the basic positivistic attitude, which from my point of view is untenable, and which seems to me tocome to the same thing as Berkeley’s principle, esse est percipi. ‘Being’ is always something which is mentallyconstructed by us, that is, something which we freely posit (in the logical sense). The justification of suchconstructs does not lie in their derivation from what is given by the senses. Such a type of derivation (inthe sense of logical deducibility) is nowhere to be had, not even in the domain of pre-scientific thinking. Thejustification of the constructs, which represent ‘reality’ for us, lies alone in their quality of making intelligiblewhat is sensorily given.” [27, p. 669]
As famously remarked by Einstein when addressing the concept of simultaneity within classical mechanics, aphysical concept requires not only a clear mathematical and conceptual definition, it must also possess operationalcontent: “The concept does not exist for the physicist until he has the possibility of discovering whether or not it isfulfilled in an actual case. We thus require a definition of simultaneity such that this definition supplies uswith the method by means of which, in the present case, he can decide by experiment whether or not boththe lightning strokes occurred simultaneously. As long as this requirement is not satisfied, I allow myself tobe deceived as a physicist (and of course the same applies if I am not a physicist), when I imagine that I amable to attach a meaning to the statement of simultaneity. (I would ask the reader not to proceed fartheruntil he is fully convinced on this point.)” [26, p. 26]
Thus, the development of an adequate physical concept —within the realist program— involves also the provisionof a consistent link to its experimental testing.
Definition 5.5 Conceptual Operationality:
A physical concept must provide a consistent link to its op-erational testability. different ’,it becomes then impossible to keep track of anything. Things which are observed only once are impossible toinvestigate from a scientific standpoint. This is a problem which is well known since Heraclitus’ theory ofbecoming and was referred to by the Greeks as ‘the problem of movement’. In short, what can be regarded as an identity within difference ? Clearly, if there is no repeatability, the reference of different experiences is precludedright from the start and just like in
Funes the Memorious , the necessary link between the observation of a ‘thedog at three-fourteen’ and ‘the dog at three fifteen’ is nowhere to be found. A meaningful physical concept mustbe capable of providing the conditions of its testing in different instants of time.
Definition 5.6 Operational Repeatability:
A physical concept must be able to bring into unity the mul-tiplicity of physical phenomena observed in different subsequent tests.
An object must be capable of bringing into unity a multiplicity of different observations. An object whichcan only relate itself to a single measurement outcome is not an object, it is just an ‘event’ which lacks theconditions required by a realist physical representation. Physics does not talk about observations or events, ittalks in terms of physical formal-conceptual invariant-objective representations. In standard QM, the notion of‘quantum particle’ does not fulfill operational repeatability , for —according to the orthodox narrative— particlesare destroyed with every measurement that is actually performed (see for a detailed discussion [18]). Quantumparticles are explicitly defined as non-repeatable existents, they are just ‘clicks’ in detectors and ‘spots’ inphotographic plates. Such spatiotemporal events or measurement outcomes are essentially irrepeatable. Everymeasurement creates always a new ‘click’, a new ‘spot’, different to the ones preceding it, different to the ones tocome. Of course, this goes against the very basic goal of science which in the words of Pauli refers to the attemptto account for the unity of different phenomena through concepts: “ ‘Understanding’ probably means nothingmore than having whatever ideas and concepts are needed to recognize that a great many different phenomenaare part of coherent whole.”It is quite clear that the standard “recipe” of QM fails to fulfill any of these basic conditions required for arealist understanding of the theory. Thus, instead of fictional narratives which have no link whatsoever withexperience or the mathematical formalism, it is these general set of conditions which should guide realists intheir future production of a unified, consistent and coherent representation for the theory of quanta. In thisrespect, the unquestionable fact that QM is “weird” should not be understood as necessarily imposing a limitto physical representation itself, but rather as exposing the limit of the very specific representation provided byclassical physics. The Bohrian claim that experience can be only described in terms of classical concepts standsat the center of this widespread confusion. If we accept, as any realist should, that experience is derived fromthe theory —and is not the “self evident” unproblematic given which ground science—, then we will be necessaryconfronted not to the irrepresentability of the theory of quanta but with the need to develop a new adequateconceptual scheme that matches all the conditions we have discussed above.17
Conclusion
In this article we have argued that interpretations and narratives attempting to justify an anti-realist fictionalcollapse of the quantum wave function —introduced in order to make reference to single measurement outcomeswithout any experimental or theoretical support— are clearly non-starters for a realist account of QM. Fictionshave nothing to do with realism. Instead, the realist program should focus itself in the attempt to producean invariant-objective representation of a real state of affairs. Something that can only be done by followingthe general theoretical conditions we have discussed in the previous section. From a realist standpoint, wemust recognize that smoky dragons are nothin but contemporary myths which embrace contextuality insteadof objectivity, preferred bases instead of operational-invariance, measurement-collapses and outcomes instead ofoperational repeatability. The lesson coming from this analysis is quite straightforward. It is only by stayingclose to the basic ideas of realism, refusing to enter the anti-realist labyrinth of interpretations and narratives,that we can hope to capture and defeat these fantastic creatures. The fight against them has just begun.
Acknowledgements
I want to thank Matias Graffigna for discussions on subjects related to this paper. This work was partially sup-ported by the following grants: Project PIO CONICET-UNAJ (15520150100008CO) “Quantum Superpositionsin Quantum Information Processing”, UNAJ INVESTIGA 80020170100058UJ.
References [1] Béziau, J.-Y., 2014, “Paraconsistent logic and contradictory viewpoint”,
Revista Brasileira de Filosofia ,241.[2] Bohr, N., 1935, “Can Quantum Mechanical Description of Physical Reality be Considered Complete?”,
Physical Review , , 696-702.[3] Bohr, N., 1937, “Causality and complementarity” In The Philosophical Writings of Niels Bohr, Volume4: Causality and Complementarity, Supplementary Papers , 1994, pp. 83-91, Ox Bow Press, Woodbridge.[4] Bohr, N., 1963,
Atomic Physics and Human Knowledge , John Wiley & Sons, New York.[5] Bohr, N., 1987,
The Philosophical Writings of Niels Bohr , 3 Volumes, Ox Bow Press, Woodbridge.[6] Bokulich, A., 2005, “Niels Bohr’s Generalization of Classical Mechanics”,
Foundations of Physics , ,347-371.[7] Bokulich, A., 2011, “How scientific models can explain”, Synthese , 33-45.[8] Bokulich, A. & Bokulich, P., 2020, “Bohr’s Correspondence Principle”,
The Stan-ford Encyclopedia of Philosophy (Fall 2020 Edition) , E.N. Zalta (ed.), forthcoming.https://plato.stanford.edu/archives/fall2020/entries/bohr-correspondence/.[9] Borges, J.L., 1989,
Obras completas: Tomo I , María Kodama y Emecé (Eds.), Barcelona. Translated byJames Irby from
Labyrinths , 1962.[10] Cabello, A., 2017, “Interpretations of quantum theory: A map of madness”, in
What is Quantum Infor-mation? , pp. 138-143, O. Lombardi, S. Fortin, F. Holik and C. López (eds.), Cambridge University Press,Cambridge.[11] Carroll, S., 2013, “Jim Holt and Sean Carroll: Why Does the World Exist?”, Min: 11.00,https://vimeo.com/68101888[12] Carroll, S., 2020, “A Brief History of Quantum Mechanics - with Sean Carroll”,
The Royal Institution
Quantum (Un)speakables: From Bellto Quantum Information , Bell, J., Bertlmann, R., and Zeilinger, A. (Eds.), Springer.1814] Curd, M. & Cover, J. A., 1998,
Philosophy of Science. The central issues , Norton and Company (Eds.),Cambridge University Press, Cambridge.[15] Dawid, R., 2013,
String Theory and the Scientific Method , Cambridge University Press, Cambridge.[16] da Costa, N.C.A. & Krause, D., 2006, “The Logic of Complementarity”, In
The Age of Alternative Logics:Assessing Philosophy of Logic and Mathematics Today , J. van bent hem, G. Heinzmann, M. Rebuschiand H. Vesser (Eds.), 103-120, Springer.[17] de Ronde, C., 2020, “The (Quantum) Measurement Problem in Classical Mechanics”, in
Probing theMeaning of Quantum Mechanics , D. Aerts, J. Arenhart, C. de Ronde, G. Sergioli (Eds.), World Scientific,Singapore, in press. (quant-ph:2001.00241).[18] de Ronde, C., 2020, “Measuring Quantum Superpositions (Or, “It is only the theory which decides whatcan be observed.”)”, preprint. (quant-ph:2007.01146).[19] de Ronde, C., 2020, “Quantum Theory Needs No ‘Interpretation’ But ‘Theoretical Formal-ConceptualUnity’ (Or: Escaping Adán Cabello’s “Map of Madness” With the Help of David Deutsch’s Explanations)”,preprint. (quant-ph:2008.00321)[20] de Ronde, C., 2020, “Understanding Quantum Mechanics (Beyond Metaphysical Dogmatism and NaiveEmpiricism)”, preprint. (quant-ph:2009.00487)[21] de Ronde, C. & Massri, C., 2017, “Kochen-Specker Theorem, Physical Invariance and Quantum Individ-uality”,
Cadernos da Filosofia da Ciencia , , 107-130.[22] de Ronde, C. & Massri, C., 2020, “Against the Tyranny of Pure States in Quantum Theory”,
Foundationsof Science , forthcoming.[23] Deutsch, D., 2004,
The Beginning of Infinity. Explanations that Transform the World , Viking, Ontario.[24] Dirac, P.A.M., 1974,
The Principles of Quantum Mechanics , 4th Edition, Oxford University Press, Lon-don.[25] Dorato, M., 2006, “Properties and Dispositions: Some Metaphysical Remarks on Quantum Ontology”,
Proceedings of the AIP , , 139-157.[26] Einstein, A., 1920, Relativity. The Special and General Theory , Henry Holt & Company, New York.[27] Einstein, A., 1949, “Remarks concerning the essays brought together in this co-operative volume”, in
Albert Einstein. Philosopher-Scientist , P.A. Schlipp (Eds.), pp. 665-689, MJF Books, New York.[28] Feynman, R.P., Leighton, R.B. & Sands, M., 1963,
Lectures on Physics, Volume 1 , McGraw Hill, NewYork.[29] Feynman, R.P., 1967,
The Character of Physical Law , Massachusetts Institute of Technology Press,Massachusetts.[30] Fine, A., 1986,
The Shaky Game , University of Chicago Press, Chicago.[31] Fuchs, C.A. & Peres A., 2000, “Quantum theory needs no ‘interpretation” ’,
Physics Today , 70-71.[32] Freire Jr., O., 2015, The Quantum Dissidents. Rebuilding the Foundations of Quantum Mechanics (1950-1990) , Springer, Berlin.[33] Heisenberg, W., 1958,
Physics and Philosophy , World perspectives, George Allen and Unwin Ltd., London.[34] Heisenberg, W., 1971,
Physics and Beyond , Harper & Row, New York.[35] Hilgevoord, J. & Uffink, J., 2001, “The Uncertainty Principle",
The Stanford Encyclopedia of Philoso-phy (Winter 2001 Edition) , E. N. Zalta (Ed.), http://plato.stanford.edu/archives/win2001/entries/qt-uncertainty/. 1936] Horgan, J., 2015,
The End of Science , Basic Books, New York.[37] Kaiser, D., 2011,
How the Hippies Saved Physics: Science, Counterculture, and the Quantum Revival , W.W. Norton.[38] Lahti, P., 1980, “Uncertainty and Complementarity in Axiomatic Quantum Mechanics",
InternationalJournal of Theoretical Physics , , 789-842.[39] Maudlin, T., 2019, Philosophy of Physics. Quantum Theory , Princeton University Press, Princeton.[40] Mermin, D., 2012, “Quantum Mechanics: Fixing the Shifty Split”,
Physics Today , 65, 8-10.[41] Miller, W.A. & Wheeler, J.A., 1983, “Delayed-Choice Experiments and Bohr’s Elementary QuantumPhenomenon”, in
Proceedings of the International Symposium in Foundations of Quantum Mechanics ,pp. 140-152, Tokyo.[42] Moore, W., 1989,
Schr¨0dinger , Cambridge University Press, New York.[43] Pauli, W., 1994,
Writings on Physics and Philosophy , Enz, C. and von Meyenn, K. (Eds.), Springer,Berlin.[44] Popper, K.R., 1963,
Conjectures and Refutations: The Growth of Scientific Knowledge , Routledge, Lon-don.[45] Schlosshauer, M. (Ed.), 2011,
Elegance and Enigma. The Quantum Interviews , Springer-Verlag, Berlin.[46] Torretti, R., 1999,
The Philosophy of Physics , Cambridge University Press, Cambridge.[47] ’T Hooft, G., 2001, “Can There Be Physics without Experiments? Challenges and Pitfalls.”
InternationalJournal of Modern Physics A , , 2895-2908.[48] Van Fraassen, B.C., 1980, The Scientific Image , Clarendon, Oxford.[49] Van Fraassen, B. C., 2002,
The Empirical Stance , Yale University Press, New Haven.[50] Vernant, J.-P., 2006,
Myth and Thought among the Greeks , Mariner books, New York.[51] Vickers, P., 2008, “Bohr’s Theory of the Atom: Content, Closure and Consistency.”, preprint. (philsci-archive.pitt.edu/4005).[52] Von Neumann, J., 1955,
Mathematical Foundations of Quantum Mechanics.
Discussions on physics, metaphysics and metametaphysics: Interpretingquantum mechanics , PhD dissertation, Universidad Federal de Santa Catarina.[55] Wohnrath Arroyo, R. & Arenhart, J., 2020, “Floating free from Physics: The Metaphysics of QuantumMechanics”, in
Probing the Meaning of Quantum Mechanics , D. Aerts, J. Arenhart, C. de Ronde, G.Sergioli (Eds.), World Scientific, Singapore, in press. (quant-ph:2009.00487).[56] Wolchover, N., 2020, “What is a Particle”,
Quanta Magazine
Foundations ofPhysics ,46