Found Phys (2010) 40: 1171–1188DOI 10.1007/s10701-010-9449-8

Language and RealityPeter Mittelstaedt’s Contributions to the Philosophy of Physics

Brigitte Falkenburg

Received: 4 March 2010 / Accepted: 15 March 2010 / Published online: 19 May 2010© Springer Science+Business Media, LLC 2010

Abstract The article investigates the way in which Peter Mittelstaedt has been con-tributing to the philosophy of physics for half a century. It is shown that he pursues apath between rationalism and empiricism in the sense of Erhard Scheibe’s philosophyof the physicists. Starting from Kant’s a priori he gives a rational reconstruction of theconceptual revolutions of 20th century physics. The central topic of his philosophyof physics is the quest for semantic self-consistency, which for quantum mechanicsis a hard nut to crack.

Keywords A priori · Conceptual change · Object constitution · Quantum theory ·Relativity · Semantic self-consistency · Unsharp properties

1 The Philosophy of a Physicist

Erhard Scheibe’s last book Die Philosophie der Physiker (“The Philosophy of thePhysicists”) deals with the philosophical ideas of the founders of 20th centuryphysics. The cover shows Max Planck, Niels Bohr, Albert Einstein, Werner Heisen-berg, Erwin Schrödinger, Max Born, and Carl Friedrich von Weizsäcker. The bookis guided by a quotation attributed to the protestant theologian Adolf von Harnack,founder and first president of the Kaiser-Wilhelm-Gesellschaft in Berlin (the precur-sor of today’s Max-Planck-Gesellschaft) [1, p. 9]:

“It is complained that our generation has no philosophers. This is not correct:The philosophers are now sitting in the other faculty, their names are Planckand Einstein.”

In memory of Erhard Scheibe.

B. Falkenburg (�)Faculty 14, Philosophy, TU Dortmund, 44221 Dortmund, Germanye-mail: brigitte.falkenburg@tu-dortmund.de

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The statement stems from the 1920s. A generation later, in the 1950s, Erhard Scheibeand Peter Mittelstaedt both belonged to von Weizsäcker’s philosophical circle, at theMax Planck Institute of Physics in Göttingen. Peter was as a young nuclear physicistinterested in quantum logic, Erhard a young mathematician attracted by the founda-tions of quantum mechanics. In 1957, von Weizsäcker changed faculty following thecall to Ernst Cassirer’s former philosophy chair in Hamburg. Erhard Scheibe wentwith him as his philosophy assistant, starting his own career as an outstanding Ger-man philosopher of science.

Peter Mittelstaedt continued his physics career at CERN, in the Max Planck Insti-tute of Physics (then in Munich), as a physics Privatdozent, and finally, in 1965, asfull professor in the physics department of the University of Cologne. So, he becamea philosopher sitting in the other faculty, too. Starting from his Munich time, he hasbeen working for almost half a century on the philosophical question of what relativ-ity and quantum theory tell us about physical reality. His philosophical work on thefoundations of modern physics continues the history of the 20th century philosopher-physicists. It is condensed in the famous books Philosophische Probleme der moder-nen Physik [2] (Philosophical Problems of Modern Physics [11]), Sprache und Real-ität in der modernen Physik [3], Der Zeitbegriff in der Physik [4] and his recent TheLaws of Nature, written together with Paul Weingartner [5]. Currently he is workingon a new book with the title Physics Without Metaphysics?, that puts together hisinsights of the last decade. We are looking forward to seeing it published.

But his philosophical work was not restricted to the philosophy of physics. He hasalways been active in a broader field of interdisciplinary research. By investigatingthe language and the reality of physics, he also came to ask for the dialogue betweenscience and society. It is most fascinating to see how this wide-ranging work is linkedto his views about the semantics of physics. The leitmotif of his philosophy of physicsis the quest for semantic consistency. This quest is the thread that links all of hisphilosophical work. Let me pursue this thread beginning with his interdisciplinaryideas about the autonomy of physics as an exact science.

2 The Autonomy of Science

At the occasion of becoming the rector of the University of Cologne, in 1970, Pe-ter Mittelstaedt discussed the possible influences of politics on the development ofscientific research. His inaugural address contained nothing of today’s sporty plansof restructuring the universities according to economic needs. Quite on the contrary,it was a powerful defense of the autonomy of science. Its core was a challenginganalysis of the structure of physics, its empirical foundations, and the goal of self-consistency concerning the relations between theory and measurement. The crucialphilosophical point was that concerning these relations physical theories underlie astrong constraint. They are supposed to be semantically consistent with the way inwhich the measuring results supporting them are obtained. Based on the quest of thissemantic self-consistency, he concluded [6, p. 21]:

“Up to now, a direct influence of social structures or ideologies related to themon theory formation in physics has neither been stated nor is it to be expected.

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Due to the consistency of syntax and semantics of physical theories, there isno substantial plurality. The only possibility for such a plurality, that is, thefreedom of choice of the syntax, gives only rise to a pseudo-plurality [. . . ]. Anindirect influence of society on science by directed financial support is onlypossible at short sight. On the long run, any advantage of a specific field ofresearch will be balanced by the systematic connections between all scientificphenomena.”

Even then, these optimistic views about the long-term autonomy of scientific researchprovoked many objections. The discussions culminated in a conference on scienceand society which was published in a book series on democracy [7].

Throughout the years, Peter’s contributions to the dialogue between physics andsociety had a wide scope, embracing the relations of science to ethics, philosophy,and theology. In 1994, he organized a public discussion on Genetic Engineering in thehistorical town hall of Cologne [8]. He also participated in conferences on science andtheology. In a typical contribution, he gave a sharp analysis of the nature of physicalknowledge and its clear-cut separation from theological doctrines [9]. This clear-cut separation is just another mark of physics as an autonomous science. Accordingto the paper, the autonomy works in both directions. Physics neither is influencedby theological doctrines, nor does physical knowledge have any impact on what weknow about God.

These interdisciplinary activities have always been intimately connected to hisdeep insights into the structure of physics. The inaugural address of 1970 did not byaccident enter into a collection of philosophical papers titled Die Sprache der Physik(i.e., the language of physics) [10]. Like the other papers of the collection, it expressesthe quest for semantic consistency, the central theme of Peter’s philosophical work.Its argument reveals a strong belief that physics owes its autonomy to its rationallanguage. According to Peter Mittelstaedt, the semantic structure of physics is anoffspring of human rationality, and hence, a best guarantee of true knowledge.

Indeed, this view is grounded in the philosophical tradition of rationalism to whichthe 17th century founders of modern physics belonged. Galileo (if I may put him inthe tradition), Descartes, Newton and Leibniz had substantially different accounts ofthe foundations of physics and philosophical views. Nevertheless, they all the samewere convinced that the book of nature is written in the rational terms of mathemat-ics and logic, and that human reason is capable of understanding its true meaning.Independent of the respective religious background, their metaphysical beliefs cametogether with the crucial ideas of enlightenment, namely the trust in human rationalityand the autonomy of human thought.

3 The Philosophical Problems of Modern Physics

So much the worse, in quantum mechanics the semantic consistency of physics isat stake. The probabilistic interpretation of quantum mechanics and the nature ofquantum measurements give rise to intricate philosophical problems. Einstein’s dis-ease about indeterminism, Heisenberg’s uncertainty relations, the never-ending dis-cussions between Einstein and Bohr, von Neumann’s arbitrary projection postulate,

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Schrödinger’s cat, and all that showed that the relation between quantum theory andmeasurement is obscure.

In contradistinction to the philosophical writings of the big heroes of quantumphysics, Peter Mittelstaedt’s analysis of these problems is crystal clear. His famousbook Philosophische Probleme der modernen Physik [2] emerged from lectures givenat Munich in the early 1960s. The book was first published in 1964, one year beforehe became a full professor in Cologne. It had seven German editions and it wastranslated into English, Spanish and Romanian [11]. When I was studying physicsin Berlin in the 1970s, we were taught formal quantum mechanics without learninganything beyond the probabilistic interpretation. In order to understand more aboutthe kind of reality the theory dealt with, we read Peter’s book. Indeed, it became oneof the guiding lines for my own path from physics to philosophy.

The introduction explains the way in which relativity and quantum theory get intoconflict with traditional philosophical assumptions about the structure of the physicalworld. According to 20th century physics, at a large scale and at a small scale theworld is not like imagined for centuries. The observations of astronomy and the ex-periments of subatomic physics confirmed the most striking relativistic and quantumfeatures of the world [11, p. 2]:

“The involvement with philosophical problems of physics was concretely oc-casioned by certain assertions first made in physics [. . . ]. The issue was thatcertain structures, whose validity no one had questioned until then, were de-clared to be false. Euclidean geometry, the law of causality and logic were themost striking examples. From the physical point of view the justification forthese assertions were to be found in experience, the only legitimate source ofphysical knowledge.”

General Relativity describes the world in counter-intuitive terms of non-Euclideangeometry. Quantum mechanics is a probabilistic theory. Whereas classical physicstold deterministic causal stories about systems, quantum mechanics gives no accountof the cause of single events. Classical systems are supposed not to be disturbed bymeasurement, for the state of a quantum system measurement is crucial. The proba-bilistic interpretation splits the dynamics of a quantum system in two: the determin-istic evolution of Schrödinger’s wave function, and its indeterministic “reduction” bymeasurement. Quantum mechanics replaces the classical causal stories in an arbitraryway by von Neumann’s projection postulate. In addition, Heisenberg’s uncertaintyrelation is at odds with the classical logic of propositions about the spatio-temporalproperties of physical objects.

The striking a-causal features of quantum processes were noted from the very be-ginnings of quantum theory. Einstein questioned them from his very first paper on thelight quantum hypothesis and he could never accept them. Born, on the other hand,was open to rejecting determinism. His seminal paper on the probabilistic interpreta-tion of the wave function put the question of causality as follows [12, p. 54]:

“Here the whole problem of determinism comes up. From the standpoint of ourquantum mechanics there is no quantity which in any individual case causallyfixes the consequence of the collision; but also experimentally we have so farno reason to believe that there are some inner properties of the atom which

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condition a definite outcome for the collision. Ought we to hope later to dis-cover such properties [. . . ]? Or ought we to believe that the agreement of theoryand experience—as to the impossibility of prescribing conditions for a causalevolution—is a pre-established harmony founded on the nonexistence of suchconditions?”

The quantum community split on this topic. Einstein and Schrödinger hoped for hid-den variables, whereas Bohr and Heisenberg believed that such conditions do notexist. When Heisenberg derived the uncertainty relation, he suggested [13, p. 73]:

“I believe that one can fruitfully formulate the origin of the classical ‘orbit’ inthis way: The ‘orbit’ comes into being only when we observe it.”

This statement sounds positivistic. Consequently, the members of the Vienna circleinterpreted Heisenberg’s and Bohr’s views in their empiricist terms. Since then, thephilosophical debate on the foundations of quantum mechanics has been dominatedby the options of either empiricism or metaphysical realism, respectively. It is strikingthat neither the views of the philosopher-physicists portrayed in Erhard Scheibe’sbook [1] nor the philosophical work of Peter Mittelstaedt fit into this scheme.

4 The Kantian Turn

It is well known that Bohr was unhappy about posing his Copenhagen interpretationtoo close to the views of Logical Positivism. Like the other founders of quantum the-ory, he was in search of an intermediate path in between rationalism and empiricism[1, 14]. Bohr’s writings are hard to read and in need of careful philosophical inter-pretation. The influence of his philosophical teacher Harald Høffding paved the waytowards his own specific path between empiricism and metaphysical realism, whichmay well be reconstructed in Kantian terms [15].

In the Critique of Pure Reason, Kant analyzed the “transcendental” conditions ofpossible experience, which are at the same time the preconditions of any experienceand the metaphysical presuppositions a priori of any objective knowledge, includingthat of physics. Kant thought that they are irrefutable. The crucial preconditions ofclassical physics are the ideas of absolute space and time and the principles of sub-stance and causality. As Kant showed in his Metaphysical Foundations of NaturalScience, they lay the grounds for classical mechanics. Exactly these ideas and princi-ples were rebutted by 20th century physics. Absolute space and time are given up inEinstein’s Special and General Relativity. The principles of substance and causalityare at odds with quantum mechanics. Bohr’s famous Como lecture suggests replacingthem by his principle of complementarity, which was far from being clear.

Peter Mittelstaedt’s views about the philosophical problems of physics, too, arecritical of any positivistic attitude. In contrast to Bohr’s implicit Kantianism, he madean explicit Kantian turn. Taking Kant’s preconditions of empirical knowledge and hismetaphysical foundations of classical physics seriously, he addressed the followingKantian question. How it is possible that any assertions based on physical experiencemay give rise to rejecting the basic structures of classical physics? [11, p. 2]

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“Against these assertions, but especially against their empirical basis, seri-ous philosophical objections can be raised. Every fixed methodological frame-work, by which a certain science is defined, uses certain categories, conceptsand schemata for ordering and interpreting phenomena. Already from theseschemata of ordering, by which perceptions are interpreted, it follows, in gen-eral without empirical cognition, that certain properties can be attributed a pri-ori to all objects of the science in question.”

According to the founders of Logical Positivism, the observations and experimentsof relativistic physics or quantum physics do not only rebut the classical theories ofspacetime, matter, and radiation. Rudolf Carnap and Hans Reichenbach believed thatthey also refute Kant’s theory of nature. Both philosophers of physics realized thatEinstein followed ideas of Ernst Mach when he developed Special and General Rel-ativity. Einstein’s early Machian views obviously gave rise to his famous operationalconcept of simultaneity. This success of operationalism made Carnap and Reichen-bach turn from Neokantians to followers of Mach. But when they developed theiranti-metaphysical, verificationist theory of meaning on the line of Mach’s episte-mological views, around 1930, Einstein was already convinced that these views areuntenable. The rise of quantum mechanics had cured him of empiricism.

In 1926, Einstein criticized Heisenberg’s matrix mechanics as a theory that is ex-pressed in operational terms of the observable light frequencies and intensities only.He objected to Heisenberg’s approach that the theory should determine what can beobserved, and not vice versa, [1, pp. 143, 168–169] and [16]. On the one hand, thisemphasis on the priority of theory is nothing but the axiomatic point of view asso-ciated with Einstein’s well-known quest of unification. On the other hand, it comesclose to Kantian or Neokantian views about the conceptual basis of physics, as Ein-stein himself pointed out much later, in 1949 [17].

Put in Peter’s terms about the semantic self-consistency of physics, Einstein ob-jected to Heisenberg’s quantum theory that is not semantically self-consistent. AsPeter’s work of decades made more and more explicit, this point has been the coreof all problems of quantum physics then and now. Noticing that physical experiencestrongly depends on conceptual schemes or structures a priori, he followed Einstein’scriticism of Heisenberg as well as Kant’s epistemology. According to Kant’s and Ein-stein’s views, such a priori structures are the very conditions of possible experience.Based on this insight, Peter put the intriguing question: Given that, how is it possiblethat these structures may be subject to revision? He insisted that the empiricist atti-tude does not help at all understanding any revolution in the conceptual foundationsof physics [11, p. 2–3]:

“Since the a priori validity of certain structures of experience can be thus clar-ified, preference to experimental results becomes meaningless whenever it isprecisely these structures that are to be examined.”

It should be noted that this was written at the time when Thomas S. Kuhn’s TheStructure of Scientific Revolution [18] started its marching through the history andphilosophy of science. The socio-cultural view of the formation of scientific theo-ries is completely foreign to Peter Mittelstaedt’s thought. The inaugural address of1970 explicitly rejects any long-term influences of society on the theories of physics.

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According to the 1972 collection on the language of physics, the historical path oftheory formation in physics is contingent, winded, and far from being definite; butits final results are definitely fixed by the phenomena and the formal possibilities ofdescribing them in self-consistent terms [19]. In contradistinction to the followers ofKuhn, Peter asked for the rational basis of the conceptual revolutions of physics.

This rational basis is explained in Kantian terms. The formal possibilities of de-scribing the phenomena in self-consistent terms, and with them the conceptual foun-dations of physics, are fixed by the very preconditions of physical knowledge. Thelesson of 20th century physics is that these preconditions are not irrefutable. How-ever, only new insights into their structure may give rise to a revision of the concep-tual foundations of physics [11, p. 3]:

“On the basis of these considerations a change of those propositions that mustbe valid a priori for all experience is possible only if the conditions of thepossibility of cognition, and thus the methodological framework and with thatthe very concept of physics are changed.”

This Kantian diagnosis helps replacing the empiricist views, which the founders ofrelativity and quantum theory did not accept anyhow. It comes close to the quest fora “relative” a priori raised by Reichenbach in his early Neokantian days. The differ-ences between Peter’s approach and Reichenbach’s “relative apriori” cannot be dis-cussed here. Since there are striking similarities, it might be instructive to investigatefor what reasons Reichenbach abandoned his approach, in contradistinction to Peter.I suspect that Peter’s views are closer to Kant’s original ideas than the Neokantianviews floating around in the 1920s. His Kantian approach sheds new light on thephilosophical problems of 20th century physics [ibid.]:

“The question, how empirical results can at all influence the choice of the cat-egories with the aid of which these experiences come about, is the specificproblem that modern physics poses for a philosophical interpretation of its re-sults.”

The Kantian solution to this specifically Kantian problem is that Mach and his fol-lowers misunderstood the role of measurement in physics. One has to admit thatmeasurement plays a crucial role for scientific revolutions; in this point Peter’s viewscompletely agree with those of Carnap’s or Reichenbach’s after their empiricist turn.The point of departure is that the crucial role of measurement is not explained in em-piricist terms of sensory data and pointer positions, but rather in Kantian terms of theconditions of possible experience [ibid.]:

“This question can only be answered by an exact analysis of the conditionsunder which empirical-physical results are obtained: the laws that govern themeasuring process.”

At this point, the rationale behind Einstein’s objection against Heisenberg comes intoplay, that is, the quest for a self-consistent semantic structure of physics. According toall of Peter Mittelstaedt’s philosophical work, this quest is the core of modern physicsas a rational human enterprise. But unfortunately, this very quest is at odds withthe non-objectification theorem of the quantum mechanics of measurement. Before

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explaining non-objectification and the self-consistency problem associated with it,let me sketch Peter’s views about the radical revision of the foundations of physics insome more detail.

5 The Methodological Framework of Physics

Peter Mittelstaedt’s Kantian approach to understanding the scientific revolutions ofphysics circumnavigates the predominant views of 20th century philosophy of sci-ence. In contrast to the Scylla of empiricism, conceptual change is linked to the lawsthe measuring processes obey rather than to the measurement results. In contrast tothe Charybdis of post-Kuhnian irrationalism, the approach aims at a rational recon-struction of conceptual change.

Starting from Philosophische Probleme [2, 11] until Peter’s current work, thesereasons are spelled out in terms of the metaphysical presuppositions of classicalphysics, which are the preconditions of possible experience in Kant’s sense. But fromthe early work to the recent papers, there was an important shift of stress in definingthe problem of their revision. The early book [2, 11] focused on the way in whichfamiliar metaphysical presuppositions such as absolute space and time, substance,and causality got weakened in the transition from classical physics to relativity andquantum theory. A recent paper on The Intuitiveness and Truth of Modern Physics[20] stresses quite another point. The striking new insight is: Certain conceptual pre-suppositions of classical physics were an unnecessary metaphysical burden that hadto be thrown overboard anyhow. Hence, after studying the philosophical problemsof modern physics all of his academic life, Peter’s attention finally shifted from theconceptual problems of 20th century physics to the conceptual problems of classi-cal physics. That is to say, now he claims that the philosophical problems of modernphysics are posed by the very foundations of classical physics rather than the structureof 20th century physics.

It is instructive again to compare this shift with empiricism. Carnap’s and Reichen-bach’s turn from Neoantianism to empiricism is due to the belief that 20th centuryphysics refutes traditional metaphysics, that is to say, Kant’s a priori. With them, Pe-ter Mittelstaedt shares the belief that 20th century physics is a most effective critic oftraditional metaphysics. But his philosophical conclusion is completely different. Forhim, not Kant’s a priori as such is wrong. The failure lies only in the specific stock ofmetaphysics that entered both the framework of classical physics and Kant’s theoryof nature.

The methodological framework of classical physics is based on the metaphysicalconcepts of absolute space, absolute time, substance, and causality. These very con-cepts enter the conceptual foundations of classical physics as well as Kant’s theoryof nature. For classical mechanics and electrodynamics, they provide the conceptualframework of the respective dynamics. For Kant, they were a priori and irrefutable.20th century physics made them subject to the following revisions [2, 11]:

1. Newton introduced absolute space and time in order to describe the motions ofphysical objects. Absolute space is the ideal inertial frame. Absolute time is theideal of uniform change in absolute space that makes it possible to imagine an

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ideal clock. But according to Special Relativity, there is no absolute simultaneityand there are no such things as space and time as independent entities. There isonly Minkowski’s pseudo-Euclidean spacetime. According to General Relativity,spacetime is non-Euclidean, i.e., curved.

2. From Aristotle to Descartes or Locke, substance was considered to be an indepen-dent carrier of properties. Kant replaced this concept of traditional ontology bythe epistemic concept of something persistent in space in time. No matter if takenas an ontological or epistemic term, such a concept obviously underlies the con-stitution of persistent physical objects. In classical mechanics, these objects areconceived in terms of mass points and their trajectories in phase space, and theirphysical properties are completely determined by the equations of motion and theinitial conditions. But according to quantum mechanics (or any other quantum the-ory), subatomic particles do not carry all measurable properties. They only carrytwo kinds of “objective” properties: the conserved quantities such as mass andcharge that obey superselection rules, and the properties “objectified” by meansof a preparation procedure or a measurement.

3. For Kant, causality was a regulative principle. The principle claims that any law-like sequence of empirical events must be conceived in terms of cause and effect,and any empirical phenomenon must be considered to be caused by another phe-nomenon. Obviously, this is an indispensible heuristic principle of physics or ofany other science. The founders of classical mechanics, above all, Newton andLaplace, associated the law of gravitation and the motions of all bodies withcausality and determinism. In 20th century physics, causality and determinism arelimited. Special relativity restricts the causal connections to events inside the lightcone. Quantum mechanics restricts determinism to the evolution of Schrödinger’swave function, whereas the individual measurement outcomes are in general notdetermined.

In this way, the revisions of classical physics give rise to criticizing the traditionalconcepts. Special and general relativity reject Newton’s concepts of absolute spaceand time and the spatio-temporal framework of classical physics. Quantum mechan-ics rejects the classical concept of a physical object with well-defined spatio-temporalproperties and the underlying metaphysical concept of substance. Both relativity andquantum theory restrict the domain of the principle of causality. All of this criticismhas the following common features:

(I) The traditional metaphysical concepts and principles are no longer consideredto be universal.

(II) The corresponding physical concepts are restricted to certain domains.(III) These restrictions are justified by restricted conditions of possible experience.

Simultaneity and causality are restricted to the light cone; Euclidean spacetimeto small spacetime regions and local coordinates; definite physical properties to ob-servables immediately after measurements, if the corresponding quantum operatorsdo not commute; causality and deterministic evolution to the probability densitiesof quantum mechanics. The restricted conditions of possible experience are the re-spective measuring methods. Their limitations were not taken into account in thefoundations of classical physics.

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The domain of classical physics is defined by the condition that limited measuringmethods do not matter and therefore may be neglected. The relativistic domain is de-fined by the use of light signals for synchronizing clocks and measuring rods. Here,the finite value of the velocity of light matters, giving rise to the Lorentz transfor-mations. The quantum domain is defined by Heisenberg’s uncertainty relation whichexpresses the limitations of measuring the position and momentum of subatomic par-ticles simultaneously. Here, the non-zero value of Planck’s quantum of action matters,giving rise to the non-zero commutation relations of the position and momentum op-erators. Hence, the limitations of the measuring methods are due to the finite valuesof the constants of nature.

The above mentioned paper [20] concludes that the a priori of classical physics istoo strong. The philosophical lesson of 20th century physics is that must be weakenedin favor of the more general framework of relativity and quantum theory, respectively.Two recent papers show in more detail how these generalizations depend on the fi-nite values of the constants c and �, which the classical theories ignored by simplyassuming that c = ∞ and � = 0 [21, 22].

These insights obviously give rise to the quest for a general framework of physicsthat takes these limitations into account. This quest, however, raises substantial prob-lems. Up to the present day there is no fundamental theory of physics according towhich c �= ∞ and � �= 0, which in addition would embrace gravity. Today, manyphysicists hope for a quantum gravity at the Planck scale that explains the physicsat larger scales. According to Peter Mittelstaedt’s work on the language of physics[3, 10], such an all-embracing theory should satisfy the requirement of being seman-tically self-consistent. But such a theory is not in sight and the search for it is full ofintricate conceptual problems. The Planck length and Planck time are so small thatfor it no clear-cut experimental constraints are known. For the time being, there isno hope to resolve the associated conceptual problems in terms of any conditions ofpossible experience. Some philosopher-physicists argue that the most successful re-spective research program, the superstring approach, turned physics into metaphysics[23, 24].

What is worse, the ways in which causality is restricted in special relativity hereand quantum theory there are helplessly different. It is far from obvious how theymight be reconciled. Special and general relativity are deterministic theories. Theymake it possible to describe individual processes and their continuous trajectoriesin spacetime. Quantum mechanics (or any other quantum theory) does not, at leastwithout constituting quantum objects in terms of “unsharp” properties [25, 26]. Viceversa, quantum mechanics predicts non-local correlations over space-like distances,whereas special relativity precludes any causal interactions-at-a-distance.

Admittedly, there is a relativistic quantum field theory with c �= ∞ and � �= 0.Indeed the theory is empirically most successful and for its quantum correlations anon-signalling-theorem has been proven. Unfortunately, the proof presupposes theassumption of micro-causality which is the very condition of Einstein’s causality, ap-plied to the observables of the corresponding quantum algebra. Hence, to a certaindegree the non-signalling-proof is circular, as Peter noted [27]. In addition, quantumfield theory is full of conceptual problems such as the non-convergence of its pertur-bation expansion. No theoretician believes that quantum field theory is fundamental.

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It has the features of an effective theory that only holds at a certain energy scale. Notby accident, in a far-reaching formal analogy the apparatus of quantum field theoryapplies to the many-particle systems of condensed matter physics [28, pp. 239–241].

6 The Constitution of Quantum Objects

As mentioned above, the traditional metaphysical concept of substance came in twoversions. For Aristotle, Descartes, or Locke, a substance is an independent carrierof properties, a concrete entity that is spatio-temporally individuated. For them, sub-stances are the furniture of the world; their respective concepts of substance are cru-cial terms of their ontology. For Kant, “substance” is only the epistemic concept ofsomething persistent in space and time. In whatever version (ontological or epistemic)the concept underlies the way in which persistent physical objects are conceived. Toput it in Kantian terms, the concept of substance is crucial for the constitution ofphysical objects.

Only in classical physics the constitution of objects is no problem. The equationsof motion and the initial conditions of mechanics or electrodynamics completely de-termine the properties of classical particles or fields. In quantum mechanics theydo not. For quantum particles, only the “objective” properties are well-determined.There are two types of objective properties: the properties such as mass and chargefor which superselection rules hold (they correspond to the observables that commutewith all other observables); and the properties “objectified” by means of a preparationprocedure or measurement. Heisenberg’s uncertainty relation expresses that in con-tradistinction to classical objects, subatomic particles do not carry a definite amountof all measurable properties, but only of some of them. According to quantum me-chanics, there can be either a sharp momentum value p or a sharp position q but therecan not be both simultaneously. According to the POV measures approach, which ismore appropriate to express the claim of Heisenberg’s uncertainty relation, in generalneither of both quantities have an approximately sharp value and the sharper one ofthem, the unsharper the other one. In the Como lecture [29] and later, Bohr claimedthat therefore there are no quantum objects but only complementary quantum phe-nomena. The uncertainty relation �q�p ∼ � is at odds with the requirement thatboth position q and momentum p may be attributed simultaneously to a subatomicparticle. Therefore, Bohr emphasizes that the definition of a quantum object is at oddswith the conditions of possible experience. (In quantum field theory the situation issimilar. In particular, it is impossible to attribute sharp values of the phase and theamplitude simultaneously to a field mode.)

Peter Mittelstaedt always insisted that this is not the whole story. In PhilosophischeProbleme der modernen Physik, he criticized Heisenberg’s “semi-classical deriva-tion” of the uncertainty relation [2, pp. 101–104], [11, p. 92]. Heisenberg had ex-plained the relation �q�p ∼ � by in terms of a collision that disturbs the momen-tum of a particle by measuring its position, or vice versa [13]. Bohr’s concept ofcomplementarity [29] and his discussions with Einstein [30] rely on these semi-classical considerations, according to which the measurement disturbs the path ofan individual particle. This semi-classical view is an important heuristic tool up to

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the present day. But it gives rise to conceptual confusion, too. Based on this semi-classical heuristics, in recent quantum optics even the silly question arose what ismore fundamental, Heisenberg’s uncertainty relation or Bohr’s concept of comple-mentarity [28, pp. 296–301].

In order to replace the semi-classical heuristics by a rigorous quantum formula-tion, Peter and his collaborators worked in two different directions. First, they de-veloped the quantum theory of measurement [31]. Then, they made the meaning ofHeisenberg’s uncertainty relation precise in terms of positive operator valued (POV)measures [32].

The quantum theory of measurement describes what happens according to quan-tum mechanics in Hilbert space if a single quantum system is coupled to a measuringdevice. To be more precise, it describes what does not happen. There is no “objectifi-cation”. In general, the coupling never gives rise to a definite measurement outcome,neither now nor a hundred million years from now. The system and the measuringdevice remain entangled forever, resulting in a quantum superposition of the possiblemeasurement outcomes results rather than any definite result. Only John von Neu-mann’s projection postulate [33] forces the “reduction” of a superposition

∑ci |�i〉

of possible final states |�i〉 to one-and-only-one actual outcome |�k〉. The quantumtheory of measurement proves that the coupled system does not give rise to objectifi-cation [34].

However, the formal apparatus of POV measures makes it possible to attribute “un-sharp” probabilistic properties to individual quantum objects [26]. These “unsharp”properties have the physical meaning of probability measures, in accordance with theprecise (i.e., probabilistic) meaning of Heisenberg’s uncertainty relation.

Based on these formal tools, Peter Mittelstaedt was finally able to tackle the mostchallenging problem of 20th century physics, the notion of a quantum object. Bohrhad claimed that Heisenberg’s uncertainty relation precludes the definition of theconcept of a quantum object, since the definition of such an object is at odds withthe possibilities of measuring its properties. Peter does not agree. Over the years, hegathered four convincing philosophical arguments that show how the constitution ofquantum objects is possible, in view of the non-objectification problem.

(i) Even though quantum physics lacks the strong self-consistency of classicalphysics, it is self-consistent in a weaker sense. As shown in Sprache und Re-alität [10], its formal structure establishes links between language and reality,which can be made precise in terms of quantum logic. In accordance with theselinks, the “object semantics” of classical physics is replaced by “process seman-tics”. Classical physical objects are conceived to be the carriers of all measur-able properties. Quantum objects are only the carriers of objectified properties.But some quantum properties, namely quantities such as mass or charge whichare subject to superselection rules, are objective in all quantum states. Theyare conserved in all quantum processes (to be more precise, in all processes ofnon-relativistic quantum mechanics). Their conservation laws make it possibleto conceive of a quantum object as the carriers of the physical properties con-served in a quantum process.

(ii) This idea gives rise to object constitution in terms of symmetries. Following Kant[35] and von Weizsäcker [36], the concept of substance may be associated with

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conserved physical magnitudes such as mass, momentum, or energy. Accordingto the Noether theorem of physics, conservation laws are associated with thesymmetries or invariances of physics. According to a well-known paper of Eu-gene P. Wigner’s [37], the elementary states of a quantum theory correspond tothe irreducible representations of symmetry groups, and the latter are classifiedin terms of conserved quantities (such as mass, spin, and parity). In this way, onearrives at explaining the constitution of physical objects in terms of invariances[38, 39]. So, quantum objects are finally constituted in terms of the symmetryproperties of classes of objects, which are the carriers of conserved quantities.This weaker version of object constitution generalizes the way in which Kantconceived of objective reality in terms of substance and causality. It nicely cor-responds to the practice of current particle physics.

(iii) Concerning the semantic self-consistency of quantum mechanics, the quantumtheory of measurement gives rise to a further important results [33, 40, 41].Probability-free quantum mechanics makes it possible to derive the Born-vonNeumann probabilistic interpretation as follows. The quantum theory of mea-surement is applied to many uncoupled individual systems. Each of them con-sists of a single coupled system, i.e., quantum system plus measurement device.All these systems are equal and prepared in the same quantum state. Then, in thelimit of infinitely many such systems the quantum theory of measurement pre-dicts that the distribution of the different possible measurement outcomes overthe individual systems is equal to the frequencies of the probabilistic interpreta-tion. Hence, at the probabilistic level quantum mechanics is semantically self-consistent. The non-objectification problem remains. At the level of individualmeasurement outcomes quantum mechanics is not self-consistent. These resultsperfectly agree with the claims of decoherence [42]. The decoherence approachpredicts that at the probabilistic level the quantum superpositions dissipate intothe environment. But it does not explain why an individual measurement hasany definite outcome.

(iv) The individual quantum objects may finally be constituted in terms of unsharpproperties. The unsharp properties of a quantum object are defined in terms ofPOV measures. They express the probabilities of the conjoint values of the mag-nitudes for which a (generalized) Heisenberg uncertainty relation holds. Thebenefit is that in this way (and only in this way) individual quantum objectscan be defined. The cost is that many of their properties are not actual but justpossible. Unsharp properties are probability measures, that is, probabilistic mag-nitudes, which are attributed to individual objects. This does not mean that thequantum objects are not substantial. Due to the persistent quantum propertiesmass and charge (i), for which conservation laws and symmetries (ii) hold, theyare. But they are chameleon-like. The chameleon has no definite color. Theyhave no definite kinematic properties. In particular, they are not local. To put itin other words, they are non-local carriers of unsharp kinematic and sharp dy-namic properties. Their mass and charge is sharp. Their position, momentum,angular momentum components and so on are unsharp.

Putting all these arguments together, quantum objects are defined (or constituted) asfollows.

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(i) They are the carriers of dynamic quantum properties for which superselectionrules hold and which are conserved in quantum processes.

(ii) They are constituted in terms of symmetries, as proposed by the well-knowndefinition of elementary particles in terms of the irreducible representations ofsymmetry groups.

(iii) Their description is semantically self-consistent at the probabilistic level, but notat the level of individual measurement results. Hence, they only are constitutedin terms of classes of objects, in accordance with (ii).

(iv) Finally, individual quantum objects are constituted in terms of unsharp prop-erties. Their dynamic properties are sharp, but their kinematic properties areunsharp.

What remains is the question of whether these chameleon-like unsharp quantumobjects are the furniture of the world. One might suspect that this question is nolonger Kantian. It rather seems to belong to the rationalist tradition of metaphysicalrealism. True Kantianism bans such ontological questions, restricting our a prioriknowledge of the world to epistemic claims. To be more precise: According to Kant,only empirical substances and their causes belong to the furniture of the world, assubject to objective knowledge. Hence, the crucial question is in which sense unsharpobjects may be ranked among the causes of empirical substances.

7 Unsharp Reality?

So far, we did end up with two worlds. Up here at the top is the classical worldwith its object semantics. Down there at the bottom is the quantum world with itsprocess semantics. The classical world corresponds perfectly to the claims of tradi-tional metaphysics minus the traditional views about space and time. The quantumworld is at odds with the traditional concepts of substance and causality; but it maybe is explained in weaker terms of sharp dynamic properties such as mass and charge,and unsharp kinematic properties such as position and momentum. How are these twoworlds connected? To what extent are they compatible? What is the furniture of theworld? Is there any unique furniture of the world, after all? Or are we committed to apluralistic ontology, according to which the borderline between the classical and thequantum world is fuzzy and far from being clear?

On the lines of Bohr’s thought, I would rank the existence of the classical worldamong the preconditions of doing quantum physics, thus tending to the second op-tion [28]. Voting for pluralism is pragmatic. It simply avoids asking for the emergenceof the classical world. For all practical purposes, the features of both worlds are com-patible. At the probabilistic level, the classical theories derive from the correspondingquantum theories under well-defined conditions. At the level of individual objects andprocesses, it is sufficient to assume that quantum theory has local universality, i.e., itis universally valid for all subatomic processes everywhere within the classical world.We are not committed to think that quantum theory has global universality; i.e., thatit is valid for the whole world or the universe, too; or that it is meaningful to talk ofquantum cosmology.

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This kind of pluralism is comfortable. But it gives up the traditional trust in hu-man rationality, that is, the hope that we are capable of decoding the book of naturein consistent terms, or of expressing the unity of nature in a unified theory of physics.However, this pragmatic attitude of mine is in addition supported by a Kantian sus-picion. There may be limitations of human knowledge, which may give rise to some-thing like cosmological antinomies when we attempt to complete our knowledge ofthe physical world [43]. According to Kant, only top-down knowledge of the world isobjective, whereas I bottom-up reconstructions of the world exceed the limitations ofpossible objective knowledge. I suspect that the lack of semantic self-consistency inthe quantum domain may be due to this kind of problem. But this suspicion is vagueand can hardly be proven.

Peter Mittelstaedt, in contrast, defends the view that quantum theory is fundamen-tal. For him, unsharp quantum objects are the furniture of the world. According to hisquantum fundamentalism, the appearance of a classical world derives from the quan-tum world. The theories of classical physics only hold in a restricted domain and theyare only approximately valid. Quantum theory is universally valid in a strong sense.In addition to local universality it has global universality, i.e., it applies to the wholeworld or the universe, too. Peter’s kind of quantum fundamentalism is not committedto the many-world interpretation. According to his belief in the global universalityof quantum objects, the quantum world consists of individual objects with unsharpproperties. In the following point his unsharp quantum ontology is close to the deco-herence approach. The world that emerges from quantum theory is not the classicalworld but just the appearance of a classical world. It is not made up of actual things,facts, and events. It rather is a giant superposition of possible things, facts, and events.What appears to be a classical world is in reality a giant quantum interference. Peter’sunsharp quantum world is best demonstrated by René Magritte’s picture The BlankCheck (Fig. 1).

Peter has shown this picture in several talks and he once communicated to me [44]:

“The picture [. . . ] shows a macroscopic quantum interference, of which I stilldo not know how it may be avoided.”

So far, the concept of unsharp quantum objects seems to re-establish full semanticself-consistency for the quantum domain. But three big question marks remain.

First, in the unsharp quantum world there are no actual facts and events at allbut only possibilities. Thus, there are no objective empirical events left to which theunsharp quantum objects may be related as their causes. This means that the Kantianapproach is abandoned to a certain degree, with a tendency towards the tradition ofrationalism. The “unsharp” metaphysical reality is far beyond empirical reality inKant’s sense.

Second, without objective events, there are no relative frequencies and no prob-abilistic ensemble. Hence, the event structure of the quantum probabilities remainsunexplained. Quantum theory again turns out to be at odds with its own empiricalbasis. Due to the missing objectification, the semantic self-inconsistency reappears atthis point.

Third, quantum mechanics is not the fundamental theory. Neither is quantum fieldtheory. Furthermore, in quantum field theory the objectification problem is much

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Fig. 1 René Magritte: The Blank Check (Le Blanc-Seign). © René Magritte, the Blanc Check, 1965,c/o Pictoright Amsterdam 2010

worse. The dynamic properties of individual elementary particles such as mass andcharge are no longer subject to superselection rules. After all, just the energy of areal (i.e., non-virtual) quantum process remains as a true candidate for the furnitureof the world. But how the macroscopic carriers of quantum processes are consti-tuted remains unexplained. Surely they consist of atoms, and atoms surely are boundsystems of electrons, protons, and neutrons. The protons and neutrons in the atomicnucleus are made up of quarks and gluons. According to the standard model of parti-cle physics, the quarks indeed only exist in superpositions of their mass states. So far,the ontology of unsharp quantum objects seems to be absolutely correct. But there isno clear quantum explanation of compound systems of quarks and gluons in boundstates. (There is no quantum field theory of bound states.) How do the quarks andgluons manage to make up the proton and the neutron? How do they manage to makeup the atom, together with the electrons? And how do the atoms manage to make upmacroscopic solids? (Philip W. Anderson emphasized in one of his books that we donot know why there are solids.)

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Are these unsharp quantum objects really the furniture of the macroscopic world,as claimed by Peter’s fundamentalist bottom-up approach? Or do their compoundsystems only exist within the classical world, in accordance with Bohr’s pluralistictop-down approach? Both views have their advantages and their disadvantages. Thereis no easy solution. A century after the rise of quantum theory, probably we still are asdistant from understanding the nature of the quantum as Kant was from understandingthe nature of spacetime. Along the thorny path between rationalism and empiricismtowards a better understanding, Peter Mittelstaedt substantially brought forward thephilosophy of the physicists, in defense of rationality and in Kantian terms.

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