It is common knowledge that the two theories of relativity
From the standpoint of a strict conventionalism
The conventionalist’s viewpoint neglects the fact that the concepts of space, time, and matter have their origin in prescientific structures of thinking and, no matter how advanced they may have become, derive part of their operational meaning from this origin.^{4} By contrast, the conventionalist viewpoint presupposes that they may be decoupled from their origin without losing meaning.
Conventionalist arguments also often brush over the question of the historical availability of the postulated alternative formulations. As a matter of fact it is usually not easy to come up with theoretical constructions that describe physical phenomena as either being tied up with the spacetime framework or as taking place within it. While it is difficult to prove the nonexistence of one of the conceivable alternative constructions, historically there is always only a limited but evolving repertoire of possibilities. And even where such alternative spacetime formulations of a specific physical theory are available, the novel spacetime structures involved will not in general be transferrable to phenomena outside of the domain of the theory. This would not be compatible with the expectation that all of physics takes place within one and the same arena of space and time.
Why do certain experiences have an effect on the structure of space and time rather than simply modifying the physics of things in space and time, while others do not? The above discussion shows that it is not possible to dismiss such questions on conventionalist grounds. From the perspective of an historical epistemology, we formulate three criteria that together constitute the necessary conditions for representations of physical experience to have an impact on the spacetime structure of physics.
These criteria may be illustrated by a simple example familiar from discussions of conventionalism
Experiences to which these criteria are applied have to be conceived of as always being ‘preprocessed’, i.e., processed prior to entering a new spacetime framework or other theoretical discourses. The essence of preprocessing is to assimilate any kind of input to preexisting internal or external knowledge representations. The question of whether experiences give rise to new spacetime structures thus translates into the question of whether such preexisting knowledge representations can be transformed or reinterpreted as such spacetime structures.
In the case of the expandable rods
A side remark may be in order. The above criteria may be applicable to conceptual developments more generally, even when less fundamental concepts are at stake than those of space and time. This is obvious for the criterion of constructibility. In more general cases the criterion of operationability may be reformulated in terms of the interpretability of novel constructs in terms of prior related concepts. The criterion of universality may be reformulated accordingly as a question of the domain of applicability of the new concept.
In the following section, we will briefly sketch aspects of the historical development of the relation between the concepts of space and time, up to classical physics, whose space concept is based on the exclusion of gravitation (section 7.2). We will then describe the impact of the growing corpus of experiential knowledge on optical and electromagnetic phenomena on the classical concepts of space and time (section 7.3). Next we discuss the reintroduction of gravitation into spacetimeconcepts, as it was brought about by general relativity (section 7.4). We will then discuss quantum theory as the case of a theory that had no comparable impact on the concepts of space and time (section 7.5). Finally, we shall come back to the questions raised at the beginning of this chapter concerning the experiences leading to new space and time concepts, and address them on the basis of the cases discussed.
One of the most striking novel features of relativity
The specific characteristic of these models
In all theoretical traditions prior to relativity theory, however, space and time largely occur as separate concepts. This is all the more astonishing as the individual concepts of space and time vary significantly among different theoretical traditions. This separation is therefore probably inherited from intuitive thinking. In particular, the elementary identification of stable entities such as objects and places
This does not preclude, however, close connections between spatial and temporal aspects within thinking, in theoretical as well as in practical and specifically in metrological contexts. The way in which elementary spatial and temporal experiences are processed depends on the available means of representations, first and foremost language
As soon as spatial concepts and magnitudes are represented by the means of geometry, they could also be used for representing other magnitudes including (as is evident from the above) time. This possibility is for instance implicit in Euclid’s concept of magnitude
While motion is naturally described in terms of space and time, it is also intimately connected to the notion of causation. However, the borderline between a descriptive (spacetime) kinematics and an explanatory
Aristotelian space
Extensive exploration of this explanatory model – focused on planetary motion
The adaptation of the Aristotelian explanatory scheme to these challenges eventually led to the establishment of Newtonian mechanics
In Newtonian physics
What are the implications of Newtonian physics
Uniform motion in a straight line is distinguished in Newtonian physics
Since the notion of space of classical mechanics
Initially, the absence of internal motion in the ether
The MichelsonMorley experiment
When optics became part of Maxwell’s electrodynamic theory, realizing that light
With a further elaboration of electromagnetic theory it became possible to explain effects that had formerly been explained mechanically, such as ether
Lorentz
However, Lorentz could simplify the calculations when he observed symmetries between the equations for dielectric matter at rest in the ether
Taking account of the null results of the MichelsonMorley experiment
The last two paragraphs may appear unnecessarily technical in the context of an account of the emergence of the relativistic concepts of space and time, but they reveal an essential mechanism at work in this process. With his auxiliary time and his contraction hypothesis, Lorentz had effectively constructed a formal framework for new time and space variables. However, Lorentz’s techniques were neither derived nor presented in this manner, rather appearing as natural outgrowths of, or at least plausible assumptions within, a complex and phenomenologically rich dynamical theory, which in turn stabilized and at the same time constrained these innovations. Given the foreign character of these new spacetime variables, such a stabilization was indeed an important condition for integrating them into the larger body of physical knowledge that could not be achieved with equal ease by merely postulating them. Similarly, the constraints imposed by the underlying dynamical theory provided the new variables with a persuasive uniqueness not achievable by mere speculation.
This secured the constructibility of the new space and time variables. The price for this achievement was, however, that also the physical interpretation of the new variables was highly constrained by the framework in which they were embedded, concealing the possibility of implementing them as new concepts of space and time with their own operational meaning and a universal domain of reference.
Returning to the questions raised in the introduction, it may be asked what qualified the new space and time variables to serve as defining a new spacetime framework. Lorentz
From a broader perspective on the conceptual foundations of physics such a rethinking was natural and, more importantly, possible, because the constructibility of new space and time variables had already been established. The ultimate success of such rethinking depended, however, on further conditions. It had to be checked whether such newly constructed space and time concepts could be related to prior knowledge of space and time and whether they fulfilled the criterion of universality. From such a broader perspective, both Poincaré
While special relativity
As we have seen, in Newtonian physics
These alternatives had distinct implications for the understanding of space and time. It was, for instance proposed by Poincaré
In order to remain within this framework, furthergoing modifications of classical concepts such as that of mass were required, as was realized by Gunnar Nordström
The problematic criterion in this case turns out to be the constructibility. First, the realizability of reinterpreting measured differences as the geometrically relevant distances
With the attempts of Abraham
It was therefore plausible to turn this argument around and postulate the existence of a generalized gravitational field
The distinction between inertial
This means that one and the same mathematical structure, the metric
The question as to which experiences led to the establishment of new space and time concepts in general relativity
Remarkably, their sequence was different in the history of general relativity
Constructibility was afforded by the introduction of a new mathematical representation from differential geometry
The new spacetime concept brought about by general relativity
In quantum mechanics
It is therefore no surprise that in quantum field theory
Historically the field concept
Indeed, if only trajectories of particles are considered to be real, one may even speak of an identification of points in space. Had such a program been successful, it might have brought about new concepts of space and time. Whether the historical lack of success of this program reflects a principal obstacle or is merely a result of the limited means available, this example illustrates the crucial role of the actual constructibility of new concepts of space and time. In short, it turned out to be historically impossible to rebuild quantum physics as a more satisfying theory of matter and radiation by reformulating it within a new spacetime framework.
One might think of representing the history of physics as a sequence of ever more general concepts of space and time. It may, however, turn out to be misguided to expect that space and time will always maintain their fundamental status through all profound changes. Instead they may lose this status to other concepts which may lack the operational foundation in prior knowledge characteristic not only for space and time but also for other canonical fundamental concepts such as matter, motion, force, and causality. This process of marginalization of canonical fundamental concepts may again be illustrated by means of the history of quantum physics.
A purely formal marginalization of space already occurs in analytical mechanics
In quantum mechanics
But Hilbert space
We have started our chapter with two questions. First, which experiences led to the establishment of new space and time concepts in the history of modern physics? And second, why did these specific experiences have such consequences and why at a particular historical moment? In the previous sections we have tried to answer the first question by reviewing the historical development of space and time concepts from the perspective of the experiences that have given rise to them. Clearly, however, an equally important component of the development were the conceptual and formal tools allowing the formulation of these concepts. What shaped the dynamics of their development? Before we come to propose answers to the second question, we would therefore like to make a few remarks on the general dynamics of conceptual frameworks.
Concepts of space change only in the context of entire theories. These are not elements of an abstract set of theories but always develop historically out of preexisting knowledge systems. These systems comprise the available means for addressing the perceived problems and thereby define the space of possible solutions and further developments. The perceived problems possibly comprise new experiences, which have to be integrated with preprocessed experiences already incorporated in the knowledge system. The system character of knowledge has implications for the longterm development of the means of representation. These will only be elaborated and transmitted if they serve some function within a knowledge system, in particular as means for solving relevant problems. As a consequence, new means for articulating concepts of space and time will typically only emerge from the historical development of such larger systems, for instance comprehensive physical theories. Therefore, in addition to the three criteria mentioned in the introduction as conditions for the emergence of new concepts of space and time, i.e., constructibility, operationability, and universality, we actually have a fourth criterion, viability, requiring that a proposal for new space and time concepts is part of a theoretical framework that successfully addresses the relevant problems.
The criterion of constructibility is therefore not defined by the question of whether the necessary tools may have been in principle available to the historical actors, as if they were part of a universal tool box, but if the historical development of some available knowledge system could possibly have brought them about. Constructibility, in short, is defined by previous historical processes of construction and thus highly pathdependent. The historical sequence of the construction of knowledge systems involves an iterative procedure of representation and reflection. Representation is here understood in the broad sense of a set of external, i.e., material, representations of a knowledge system, such as its description in terms of language
Accordingly, means for solving problems within knowledge systems may be distinguished by their degree of reflexivity
The match between mathematical formalisms and the physical world has often been discussed as a puzzling fact, because of the difficulty to explain the adequacy of the mental constructions of mathematics for the description of physical experiences. However, when those mental constructions are understood as the result of long chains of sequences of reflections and representations, which at each stage involve specific experiences, the mathematical formalisms themselves turn out to be saturated with experience. This is, of course, not necessarily the same kind of experience that is to be captured by some physical theory. It thus may seem that, along this line of thinking, the puzzle can be reduced to the question of how to integrate different domains of experiences. This integration is, however, made even more difficult by the fact that the experiences underlying a given formalism are only implicitly represented by it, since the formalism is usually the result of a long chain of reflections and representations.
The codification of experience in terms of knowledge structures is indeed one of the reasons for the characteristic recursive blindness^{23} of abstract thinking with regard to its own experiential sources, a recursive blindness that also accounts for the seemingly a priori character associated with the concepts of space and time. Bringing together different domains of experience by matching physical experiences with mathematical formalisms, therefore, typically raises the question which aspects of a formalism represent experiences and which have to be considered either as merely formal aspects or as representing experiences in need of reinterpretation. For instance, in the case of the electrodynamics
To sum up, it is not the case that the factor that systematically varies in the historical development of physical theories is primarily the ever larger extent of experience described by them, while the availability of adequate mathematical formalisms enters as a contingent factor or one that is governed by an entirely different logic. Rather, the development of formalisms itself involves the processing of experiences and is often closely related to the development of physical theories in the sense of our fourth criterion of viability. Therefore, from a larger perspective, there is a coevolution of physical theories and the formalisms they employ to cover the experiences they strive to explain: while they may belong to separate intellectual or disciplinary traditions
This coevolution also accounts for the global dominance, despite the persistent emergence of locally viable alternative solutions, of a single stream of development in the sense of ‘the winner takes all’. As in evolutionary theory, optimization is a local phenomenon always working with the available means, rather than within an abstract set of theories. In this process of optimization, any established solution (e.g. Newtonian classical mechanics
It is this local dynamics that accounts for an overall development that, at the level of a history of ideas decoupled from their embodiment in the material means and concrete experiences, may seem to display a rather astonishing movement back and forth among fundamental notions of space. In particular, there is, as we have seen, the dissociation of space from gravity in Newtonian physics
This we can see more clearly, when we take into account that there is another fundamental reason for the streamlining of global developments, in addition to the winnertakesall logic described above explaining the extrusion of alternatives. Alternatives themselves typically only emerge in the process of exploring the available means (e.g. as special relativity
From this perspective, let us therefore once more review our account of the historical evolution of the concepts of space and time in physics with particular attention to the viability of alternative trajectories. For a long time, gravitation
Historically, alternatives to the geocentric world view were formulated in ancient Greece
On the other hand, the connectivity of the system developed over the centuries and the large amount of knowledge incorporated gave the addition of new insights a potentially large impact on the system as a whole. Thus, when astronomical developments eventually favored a view in which the Earth was no longer at the center of the universe, not only could the question arise whether the fall of bodies was just an Earthbound phenomenon and not a manifestation of natural motion in a cosmological context
From terrestrial physics, and the analysis of projectile motion
Why did the new concept of gravitation
All such attempts fall short, however, of constructing dynamical field equations
Abraham, Max (1912a). Der freie Fall. Physikalische Zeitschrift 13:310–311.
– (1912b). Zur Theorie der Gravitation. Physikalische Zeitschrift 13:1–4.
BenMenahem, Yemima (2006). Conventionalism. Cambridge: Cambridge University Press.
Damerow, Peter (1994). Vorüberlegungen zu einer historischen Epistemologie der Zahlbegriffsentwicklung. In: Der Prozeß der Geistesgeschichte. Studien zur ontogenetischen und historischen Entwicklung des Geistes. Ed. by Günter Dux and Ulrich Wenzel. Frankfurt a.M.: Suhrkamp, 248–322.
Earman, John (1989). World Enough and SpaceTime: Absolute versus relational theories of space and time. Cambridge, MA: MIT Press.
Ehlers, Jürgen (1973). The Nature and Structure of Spacetime. In: The Physicist’s Conception of Nature. Ed. by Jagdish Mehra. Dordrecht: Reidel.
Einstein, Albert (1921). Geometrie und Erfahrung. Berlin: Springer.
– (2001). The Collected Papers of Albert Einstein, Vol. 7. English translation of selected texts. Princeton: Princeton University Press.
Feynman, Richard Phillips, Robert B. Leighton, and Matthew L. Sands (1989). The Feynman lectures on physics, Vol. 2. Redwood City: AddisonWesley.
Jammer, Max (1954). Concepts of Space: The History of Theories of Space in Physics. Cambridge, MA: Harvard University Press.
Janssen, Michel and John Stachel (2004). The Optics and Electrodynamics of Moving Bodies. Preprint 265, Max Planck Institute for the History of Science, Berlin.
Laue, Max von (1917). Die Nordströmsche Gravitationstheorie. Jahrbuch der Radioaktivität und Elektronik 14:263–313.
Lorentz, Hendrik Antoon (1892). La théorie électromagnétique de Maxwell et son application aux corps mouvants. Archives néerlandaises des sciences exactes et naturelles 25:363–552.
– (1895). Versuch einer Theorie der electrischen und optischen Erscheinungen in bewegten Körpern. Leiden: Brill.
Minkowski, Hermann (1908). Die Grundgleichungen für die elektromagnetischen Vorgänge in bewegten Körpern. Nachrichten der Königlichen Gesellschaft der Wissenschaften zu Göttingen:53–111.
Misner, Charles W., Kip S. Thorne, and John A. Wheeler (1973). Gravitation. New York: Freeman.
Nordström, Gunnar (1912). Relativitätsprinzip und Gravitation. Physikalische Zeitschrift 13:1126–1129.
– (1913a). Träge und schwere Masse in der Relativitätsmechanik. Annalen der Physik 40:856–878.
– (1913b). Zur Theorie der Gravitation vom Standpunkt des Relativitätsprinzips. Annalen der Physik 42:533–554.
Norton, John D. (1989). What Was Einstein's Principle of Equivalence? In: Einstein and the History of General Relativity. Ed. by Don Howard and John Stachel. Boston: Birkhäuser, 5–47.
– (1992). Einstein, Nordström and the Early Demise of Scalar, Lorentz Covariant Theories of Gravitation. Archive for History of Exact Sciences 45:17–94.
– (2007). Einstein, Nordström and the Early Demise of Scalar, Lorentz Covariant Theories of Gravitation. In: Gravitation in the Twilight of Classical Physics: Between Mechanics, Field Theory, and Astronomy. Ed. by Jürgen Renn and Matthias Schemmel. Dordrecht: Springer, 413–487.
Pauli, Wolfgang (1979). Scientific Correspondence with Bohr, Einstein, Heisenberg a.o., Vol. 1: 19191929. Ed. by Armin Hermann, Karl von Meyenn, and Victor Frederick Weisskopf. New York: Springer.
Pfister, Herbert (2004). Newton’s First Law Revisited. Foundations of Physics Letters 17(1):49–64.
Piaget, Jean (1959). The Construction of Reality in the Child. 5th print. The Basic Classics in Psychology. New York: Basic Books.
Poincaré, Henri (1906). Sur la dynamique de l'électron. Rendiconti del Circolo Matematico di Palermo 21:129–175.
– (1952). Science and Hypothesis. New York: Dover.
Renn, Jürgen, ed. (2007a). The Genesis of General Relativity. 4 Vols. Boston Studies in the Philosophy of Science 250. Dordrecht: Springer.
Renn, Jürgen (2007b). The Summit Almost Scaled: Max Abraham as a Pioneer of a Relativistic Theory of Gravitation. In: Gravitation in the Twilight of Classical Physics: Between Mechanics, Field Theory, and Astronomy. Ed. by Jürgen Renn and Matthias Schemmel. Dordrecht: Springer, 305–330.
Renn, Jürgen and Malcolm Hyman (2012). Survey: The Globalization of Modern Science. In: The Globalization of Knowledge in History. Ed. by Jürgen Renn. Berlin: Edition Open Access, 491–526.
Renn, Jürgen and Matthias Schemmel (2012). Theories of Gravitation in the Twilight of Classical Physics. In: Einstein and the Changing Worldviews of Physics. Ed. by Christoph Lehner, Jürgen Renn, and Matthias Schemmel. Einstein Studies 12. Boston: Birkhäuser.
Schemmel, Matthias (2014). Medieval Representations of Change and Their Early Modern Application. Foundations of Science 19:11–34.
– (2016). Historical Epsitemology of Space: From Primate Cognition to Spacetime Physics. Cham: Springer.
[1]
“Alles Wesentliche was ich im Laufe eines langen Lebens erstrebt habe, gruppiert sich um die Frage[:] Was kann für die Physik methodisch geschlossen werden aus der Thatsache eines universellen Gesetzes der Lichtausbreitung und aus der Gleichheit der trägen und schweren Masse?” This is Albert Einstein’s response to an inquiry of the Technische Rundschau, Bern, 31 January 1955; Albert Einstein Archives 1–199. We are grateful to Diana Buchwald, editor in chief of the Collected Papers of Albert Einstein, for pointing our attention to this quotation and for providing the translation.
[2]
Thus, Max Born speculated in 1919 “that the way out of all quantum difficulties has to be sought starting from fundamental considerations: one must not transfer the concepts of space and time as a fourdimensional continuum from the macroscopic world of experience to the atomistic world, the latter obviously demands another kind of manifold of numbers as an adequate image.” (Max Born to Wolfgang Pauli, 23 December 1919; the German original has: “daß der Ausweg von allen Quantenschwierigkeiten von ganz prinzipiellen Punkten aus gesucht werden muß: man darf die Begriffe des Raumes und der Zeit als eines 4dimensionalen Kontinuums nicht von der makroskopischen Erfahrungswelt auf die atomistische Welt übertragen, diese verlangt offenbar eine andere Art von Zahlenmannigfaltigkeit als adäquates Bild.” Pauli 1979, 10).
[3]
For a detailed account on conventionalism, and its geometrical version in particular, see BenMenahem 2006.
[4]
This also appears to be the point of Einstein’s insistence on the importance of rods and clocks as “independent concepts” (Einstein 2001, 213) in relativity theory; see Einstein 1921.
[5]
See Poincaré 1952, 65–68; see also Feynman et.al. 1989, 42/1–42/5.
[6]
See, e.g., the discussion in Piaget 1959.
[7]
See Schemmel 2016; see also Chapter 1.
[8]
Schemmel 2014.
[9]
See Pfister 2004 for a particularly lucid exposition of this formulation of Newton’s first law, including definitions of ‘free particle’ and ‘straight line’.
[10]
See Pfister 2004, 56–58. Historically, the idea of space having a Euclidean measure and time flowing uniformly, which Newton explicitly adhered to, predated the formulation of the law of inertia. Note, however, that this does not imply the existence of a spacetime metric, which does indeed not exist for Newtonian spacetime. (Ehlers 1973 and later Earman 1989 designate a spacetime with Euclidean spacemeasure and a timemeasure by the term ‘Leibnizian’ spacetime.)
[11]
This section is partly based on a close rereading of Janssen and Stachel 2004 and personal discussion with Michel Janssen.
[12]
Lorentz 1892.
[13]
Lorentz 1895.
[14]
Lorentz 1895.
[15]
Poincaré 1906 and the Appendix of Minkowski 1908. English translations and discussions of both texts are found in Renn 2007a, Vol. 3.
[16]
Abraham 1912b; Abraham 1912a. English translations of these texts and further references are found in Renn 2007a, Vol. 3; see, in particular, the discussion in Renn 2007b. See also Renn and Schemmel 2012.
[17]
Nordström 1912; Nordström 1913a; Nordström 1913b. English translations of these texts are found in Renn 2007a, Vol. 3. For a discussion of Nordström’s theories see, in particular, Norton 1992 (reprinted as Norton 2007).
[18]
As late as 1917, Max von Laue used the conceptual unfamiliarity of general relativity to argue for Nordström’s theory and its specialrelativistic framework (Laue 1917).
[19]
See, e.g., Norton 1989.
[20]
Albert Einstein in his foreword to Jammer 1954, xiv.
[21]
Loss of projectibility is also given in statistical mechanics, of course, but does not imply a change in ontology and only reflects our state of knowledge.
[22]
See Damerow 1994, 268–270 and Schemmel 2016, 47–50.
[23]
Renn and Hyman 2012, 493.
[24]
For an introduction to that formulation, see Misner et.al. 1973, 289–303.
Table of Contents
1 Towards a Historical Epistemology of Space: An Introduction
Matthias Schemmel
2 Spatial Concepts in NonLiterate Societies: Language and Practice in Eipo and Dene Chipewyan
Martin Thiering, Wulf Schiefenhövel
3 The Impact of Notation Systems: From the Practical Knowledge of Surveyors to Babylonian Geometry
Peter Damerow
4 Theoretical Reflections on Elementary Actions and Instrumental Practices: The Example of the Mohist Canon
William G. Boltz, Matthias Schemmel
5 Cosmology and Epistemology: A Comparison between Aristotle’s and Ptolemy’s Approaches to Geocentrism
Pietro Daniel Omodeo, Irina Tupikova
6 Space and Matter in Early Modern Science: The Impenetrability of Matter
Peter Damerow
7 Experience and Representation in Modern Physics: The Reshaping of Space
Alexander Blum, Jürgen Renn, Matthias Schemmel
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