Foundations o f Physics, Vol. 26. No. 4. 1996

Scientific Realism: A Challenge to Physicists ~ Fritz Rohrlich 2 Received September 26. 1995 I f a physicist claims to be a realist, he ar she must fitce at least the three problems outlined here: the carefid specification of the ealidi O, limits of every theo O, and model used, the coherence relationships that must hold between two theories of the same physical system but on different cognitil'e levels, and the ambiguit)' #1 the ontalogy of two different formulations oJ'emp#'ically equiralent theories.

1. S C I E N T I F I C

REALISM

As far as I know, most scientists claim to be realists. What they mean by this can perhaps best be expressed by Einstein's credo: The beliefin an external world independentof tile perceivingobject is the basis of all natural science,q~ But given this belief, there is a question that scientists pay little attention to but philosophers are very concerned about: Does science describe this external world the way it actually is? And if the description is only approximate, exactly how can this approximation be characterized? Among philosophers of science there are both realists and instrumentalists. Realists believe that scientific theories describe the world the way it actually is (at least approximately), and that the terms used in these theories r e f e r to actually existing objects and properties. Instrumentalists, on the contrary, consider scientific theories to be only tools or instruments for the purpose of relating empirical data (experimental or observational This paper is dedicated to Professor Max Jammer in honor of his eightieth birthday. I have learned a great deal from his many excellent papers and books in history and philosophy of physics. Thank you and congratulations! -' Department of Physics, Syracuse University,Syracuse, New York 13244-1130. 443 0015-9018/96/0400-0443509.50/0 ,I~ 1996 Plenum Publishing Corporation

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results); all that a scientific theory needs to satisfy is coherence and empirical adequacy. They give no credence to the ontology implied by theories. Thus, Niels Bohr sounds much more like an instrumentalist when he says: ... in o u r description of n a t u r e the p u r p o s e is not to disclose the real essence of the p h e n o m e n a but only to t r a c k d o w n , so far as it is possible, relations between the manifold aspects of o u r experienceJ 2~

Concerning "the real essence" instrumentalists remain noncommittal. In the following, I want to discuss three problems which bear on the question of scientific realism. These problems belong specifically to the field of physics so that physicists as realists should be very concerned about them. At the same time, physicists are also the most competent people to find answers for them. These answers will be decisive for maintaining a realist position. The three problems are: the problem of validity domain of a physical theory and of its models, the problem of levels, and the problem of uniqueness or what philosophers call "underdetermination." At the end, I shall summarize the challenge that these problems pose for anyone who wants to maintain a realist position.

2. THE PROBLEM OF VALIDITY DOMAIN Not very long ago, a well-known philosopher of science published a book with the challenging title "How the Laws of Physics Lie. ''~3~ She pointed out that if one asks whether a law of physics is true or false then one must admit that almost all of them are strictly false, i.e., "lie" because they are valid only under certain conditions that do not stricth, hold in the real world. One example will suffice: Kepler's laws are valid only under several assumptions including: there are only two objects in the system, the sun and one planet, and all other planets as well as all other matter (the moon and all interplanetary matter) are ignored. This is an assumption characterizing the model. The theory, Newtonian gravitation theory, of which this is a model, is characterized by the assumption that only low energies are involved (both kinetic and potential energies must be negligible compared to the rest energy of the planet). None of these assumptions are satisfied when the accuracy of observation is sufficiently high. Furthermore, even with low accuracy, the errors made due to these assumptions accumulate in time; over many centuries, for example, the perihelion motion of mercury will become measurable. In fact, when observations are extended over t'eo' long times, say millions of years, planetary motion deviates very widely from Kepler motion and the actual motion eventually becomes chaotic.

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What is called lbr is a very careful and complete statement of all the assumptions which underlie each law of physics. This is often not done, and the validity limits of a given model and even of a given theory are frequently violated even by prominent physicists. The history of physics is full of confusions resulting from such violations of the validity limits. An especially telling example of such a confusion is the following. Throughout most of this century, the classical electrodynamics of a point charge has been a bone of contention. Lorentz developed his theory of electrons in a famous article in 1892 and later published it in extended form in 1909. His basic equation is (ill units where c = 1) nl~ = F + (2e-'/3) i;

( 1)

This equation is not of second order as an equation of motion should be, and it also has, in addition to the many meaningful physical solutions, pathological ones. These are the "run-away" solutions and the preacceleration solutionsJ 4~ In 1938 Dirac derived a classical relativistic equation for a charged particle which is now often called the Lorentz-Dirac equation because the above Lorentz equation, (1), follows from it in the nonrelativistic limit. ~5~ He used the point limit of a finite-size particle and paid no attention to the fact that classical physics has a validity limit that is characterized by the Compton wavelength of the smallest-mass in the system. Below this size, quantum mechanics takes over. Therefore, the derivation cannot be expected to be valid for smaller distances than that and certainly not in the point limit. As one of the founders of quantum mechanics, it is somewhat surprising that Dirac was not aware of this and overstepped the classical limits entering the domain of quantum mechanics without any hesitation. No indication of such awareness can be found in the quoted paper. Since the Lorentz-Dirac equation has the above Lorentz equation as a nonrelativistic limit, it also has all the same kind of pathological solutions. In addition, during the derivation one encounters an electromagnetic mass which is infinite in the point limit and which Dirac "renormalized away." The derivation was therefore not mathematically clean. Despite that, it was difficult to understand why an equation derived from an otherwise as solid a foundation as the conservation laws would have pathological solutions. That problem resulted in an enormous amount of literature proposing remedies, since the fame of the authors gave the equation almost unquestioned credence. The fact that the point limit violated the domain of classical physics and that this is the reason for the pathologies did not enter into the discussions that lasted for most of this century. Today, we can demonstrate explicitly exactly how the overstepping

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of the validity limits of classical physics caused the problems. One can restrict oneself to the nonrelativistic case where all this can be made explicit much easier. Consider, therelbre, the classical nonrelativistic equation of motion of an extended charge (radius a and surface charge). Its equation of motion can easily be derivedJ 6~ It is nonlocal in time. In units in which the speed of light c = 1, this equation is me = F + m,.[v(t --2a) - v(t)]/2a

(2)

The electromagnetic mass m,. of the surface charge is 2e2/3a. Expanding this equation in time derivatives yields an infinite series whose first two nonvanishing terms are, respectively, the inertial term due to the electromagnetic mass, m,.t: (which is to be taken to the left side and "renormalized away"), and the last term of Eq. (1). In that approximation it therefore yields the Lorentz equation with a renormalized mass. In the limit as the radius a vanishes, that last term survives because it is independent of a while all the higher terms vanish. The mass m,. diverges. Thus, in that limit one obtains exactly the Lorentz equation (I), but this time with the renormalized mass containing an infinite contribution from the electromagnetic mass correction. This equation is now seen to be an equation for a point charge with all the pathologies of the relativistic equation. The finite size charge has an equation of motion which is a differential-difference equation. It corresponds to an infinite series in time derivatives. It has no pathological solutions lbr classical sizes a. This example demonstrates the importance of observing validity limits in actual calculations. But what matters for the question of realism is the fact that there are such limits for every theory and every model. Typically, all physical systems that are treated theoretically are necessarily isolated from their environment: ignoring the other planets in the Kepler problem, assuming boundary conditions for systems "in a box" or "in a heat bath of constant temperature," etc.. Such validity conditions strictly violate reality (they are counterfactual conditions). But since they are typically present in physical theory, one concludes that no single scientific theory or model can describe nature exactly. Science is a collection of approximations.

3. T H E P R O B L E M O F LEVELS

Our limited human cognitive abilities are severely challenged by the tremendous complexity of nature. So it is not surprising that our scientific activity leads to a natural separation into different cognitive levels. In the

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case of physics, well-known examples of such levels are the classical physics level, the quantum mechanics level, and the fundamental particles level. Levels differ in scales of size, energy, and/or other characteristics. ~v~A lower level may give the structure of objects on a higher level (for example, the molecular and atomic structure of macroscopic---classical--objects) or it may describe the same phenomenon on a different scale (for example, gravitation on the lower or deeper level is described by Einstein's gravitation theory and on the higher level by Newton's). New and deeper levels of theory are created in scientific revolutions. Historically, such a revolution may completely replace the old theory, may retain certain features of it, or may leave it almost entirely intact. As an example, consider our theories of the solar system. The Ptolemaic theory was completely replaced by the Copernican. Some important features of the Copernican theory were retained in Newton's gravitation theory. And Newton's theory was fully retained (but its validity limits redefined) when the deeper level of Einstein's theory became known. The scientific revolution currently in progress will redefine the validity limits of Einstein's theory and establish an even deeper level of theory: quantum gravity. There must of course be a relationship between the physical theories on different levels; nature shows no sharp boundaries between them (singularities such as phase transitions are typically not between levels but within a given cognitive level). And every physicist knows that, to continue the above example, Einstein's theory reduces to Newton's in a suitable limit) s~ This process of theoo, reduction is philosophically of crucial importance. Is it true that Einstein's gravitation theory implies Newton's so that Newton's theory is actually completely dispensible? This is where realists and instrumentalists differ widely. "Convergent realism" claims that there exists a fundamental theory (yet to be discovered) which constitutes the lowest level and from which all higher level theories follow. Reductionism claims that the later, deeper level theory is more fundamental and h,plies the higher level theory. And as progress continues, science converges to the lowest level theory, the final and ultimate theory from which all other theories follow, the "theory of everything. ''~9~ Today, only a minority still holds such a view. Theory reduction in the strict sense can hardly be defended any longer: even if it were possible to derive the mathematical structure of the higher level theory from the lower level one, the two theories differ in concepts that cannot be deduced one from the other. The concept of gravitational./brce is nowhere contained in Einstein's curved spacetime theory. The equations that emerge from the limiting procedure starting from Einstein's equations must be re#1terpreted in terms of force which is an entirely different concept. It is not sufficient to deduce the known equations of the higher level theory from those of the

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lower level one: one must also introduce the concepts peculiar to that higher level theory that are not contained in the lower level one. Comparing the concepts of two theories on different levels soon shows some of these concepts to be completely unrelated (like spacetime curvature and force): theories on different levels are conceptually im'ommensurable. The absurdity of full reductionism is beautifully demonstrated by an example given by Fr6hlichJ lt~ Consider a cup without a handle made of some homogeneous material. If it is embedded in a region of a fixed constant temperature it should be in thermodynamic equilibrium. But in that case, it must have the shape of a sphere! Obviously, very small microphysical differences account for large macrophysical differences. A deduction of the shape of the cup fi'om microphysics then requires to take such small deviations fi'om equilibrium into account when solving the simultaneous Schr6dinger equations of some 1024 molecules m mutual interaction! But that is exactly what would be necessary if one were to claim that macroscopic theory is dispensable and is replaceable by microscopic theory. Reductionism can thus be maintained only partially) ~ The conceptual jump from one level to another remains even in cases when a mathematical relationship between higher and lower levels can be established. The degree to which a reductionist relation between theories exists varies greatly. The Einstein to Newton theory of gravity is among the strongest cases of reduction. Much weaker cases exist in the less mathematical sciences such as biology. But a certain minimal degree of reduction may even be necessary to ensure the coherence that different descriptions of the same world demand. In the next Section, another argument in favor of some reduction will be presented. The usefulness and indeed the need of the higher levels despite the lower ones is clearly present. The different levels are only in a certain sense a hierarchy; in another sense, they conq~lement one another. We could not function if we had to express our everyday objects in terms of quantum mechanics! And everyone knows that we use Newtonian gravitation theory rather than general relativity (which is more accurate) in serving the needs of space exploration. The scientific theories on different cognitive levels thus have a certain autonomy not only in usefulness but also in terms of our cognitive needs. A complete description of nature is not just "better served" by having the various levels complement one another, but these other levels are in fact necessarl'.

4. U N I Q U E N E S S Philosophers of science speak of "underdetermination." They mean by this that the empirical evidence does not determine the scientific theory

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uniquely. And it is indeed possible that there exist two (or more) different theories which account equally well for all the empirical data (experiments as well as observations ), and which at the same time imply very different (and mutually contradictory) ontologies. Consider a few examples. Quantum mechanics exists in two very different formulations, the conventional "Copenhagen" or Bohr formulation and the (usually ignored) Bohm formulation? ~2~The latter is so constructed that all prediction of the Bohr theory also are predictions of the Bohm theory. There is no empirical evidence that can distinguish between the two theories. Yet, they imply completely different ontologiesJ ~3~ General relativity is usually expressed in terms of a Riemannian curved spacetime and perfect rulers and clocks. But an equivalent formulation exists in terms of a flat spacetime and "rubber geomtry," i.e. the assumption that rulers and clocks are distorted from place to place. These imply different ontologies but are empirically indistinguishable)~4, Quantum field theory can be formulated in terms of an operator formulation on Hilbert space (the axiomatic formulation) ~5~ or in terms of functional integralsJ jr'~ These formulations seem to command quite different ontologies. What is one to make of such ambiguities of ontology? The instrumentalists have no problem: these theories are different mathematical "instruments" for relating the empirical evidence and no deeper significance is to be attached to the ontologies. They are not claimed to describe the world "the way it really is." One simply picks one of the alternative descriptions essentially by convention which is apparently determined by historical social factors. Does the answer to this lack of uniqueness lie in the interpretation we provide? Is it that we don't really know which terms of a theory really r~:/er to "what is out there'"? Are we too naive in the ontological interpretation of our theories? If that is the case, the truth may lie somewhere between the realist and the instrumentalist view. Alternatively, one may simply adopt the instrumentalist view capitulating to the nonuniqueness problem. But for the realist this is a serious problem. The following is suggested as a possible solution for the realist. It might be the case that the further development of an ambiguous (underdetermined) theory will lead to a preference of one alternative over another on the basis of conceptual coherence in the reductive relationship between the higher level ambiguous theory and the new lower level one. Thus, quantum gravity theory may lead to a preference of curved over flat spacetime. Similarly, the various formulations of relativistic quantum field theory may eventually lead to a preference of the Bohr over the Bohm formulation of nonrelativistic quantum mechanics.

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The history of science is not without precedence of ontological puzzles that were resolved by a later development. Newtonian gravitation theory implied instant propagation of gravitational action, a kind of"action-at-adistance." While Newton himself was well aware of it, he was unable to resolve that difficulty. But later developments, general relativity, led to a finite speed of propagation of gravitational interaction which is infinite only in the Newtonian limit.

5. THE CHALLENGE TO PHYSICISTS The three problems presented in the previous sections present a challenge to physicists who hold (or would prefer to hold) a realist point of view. Unfortunately, too many of them pay no attention to these problems. They are pursuing their research work using "whatever works" to achieve their goal; they are pragmatists and behave like instrumentalists while claiming to be realists. But those who wish to have a coherent belief system and claim to be realists must face the above difficulties. First, accepting that scientific theory can only give an approximate description of nature, the realist physicist must spell out exactly what this approximation consists of. Under what conditions and up to what accuracy of measurement does a theory or a model give reliable results? Specification of these validity limits is not a difficult problem but is often ignored. Second, the existence of cognitive levels requires the realist to establish a certain minimal coherence between them. In the absence of the possibility of a full reduction, the degree to which theories on different levels can be related is a difficult task that demands attention. Just think of the inadequacy of the Ehrenfest theorems for relating quantum mechanics to classical mechanics. Yet, this problem has still not been solved. (A full solution would also solve the measurement problem which deals with the interaction between a classical and a quantum system). In general, too little attention is being paid to the relationship between theories on the same subject but on different levels. At the same time there is a lot of good physics involved in studying such "coherence relations. ''c~7~ I know of no clean derivation of relativistic classical electrodynamics (both the Maxwell equations and the relativistic particle equations of motion) from quantum electrodynamics. The deduction of thermodynamics from statistical mechanics is largely restricted to relatively simple systems in equilibrium. The limiting relations for more complex nonequilibrium situations are rarely discussed. Third, the resolution of the lack of uniqueness of some of our most basic theories and the implicit existence of incompatible ontologies becomes a necessity. Most physicists are barely aware of this problem

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because they are so completely used to one of the two alternatives (for example, Bohr rather than Bohm quantum mechanics) that they simply ignore the other logical alternative. Unfortunately, claiming that the other alternative "can't be right" is not a very strong argument against it. This third problem is the most difficult one to solve. I am posing it to the realist physicist for selfish reasons: I would love to know the answer. REFERENCES 1. A. Einstein, The Worm As I See It (Covici Friede, New York, 1934), p. 60. 2. N. Bohr, Atomic Theory and the Description of Nature (Cambridge University Press, Cambridge, 1934), p. 118. 3. N. Cartwright, How the Laws of Physics Lie (Oxford University Press, Oxford, 1985). 4. For references and details of this and the following issue see my book Classical Charged Particles (Addison-Wesley, Redwood City, 1965 and 1990). 5. P. A. M. Dirac, Proc. R. Soc. London A 167, 148 (1938). 6. E. Moniz and D. Sharp, Phys. Rer. D 15, 2850 (1977). 7. M. Dresden, "Reflections on "fundamentality and complexity," Physieal Reality and Mathematical Description, C. Enz and J. Mehra, eds. (Reidel, Dordrecht, 1974). 8. F. Rohrlich, Found. Phys. 19, 1151 (1989). 9. S. Weinberg, Dreams of a Final Theory (Pantheon Books, New York, 1992). 10. H. Fr6hlich, "The Connection between Macro-and Microphysics," Rev. Nuot,o Cimento 3, 490 ( 1973 ). 11. Perceptive physicists have recognized this fact a long time ago; see P. W. Anderson, "More is different," Science 177, 393-396 (1972). 12. Max Jammer, The Philosophy of Quantum Mechanics (Wiley, New York, 1974). 13. For a recent detailed study see J. C. Cushing, Quantum Mechanics: Historical Conth~genc.v and the Copenhagen Hegemony (University of Chicago Press, Chicago, 1994). 14. K. S. Thorne, Black Holes and Time Warps (Norton, New York, 1994). 15. R. F. Streater and A. S. Wightman, PCT, Spin and Statistics and All That (Benjamin/ Cummings, Reading, 1964). 16. J. Glimm and A. Jaffe, Quantum Physics 2nd edn. (Springer New York, 1987). 17. F. Rohrlich, Found. Phys. 20, 1399 (1990).

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