Rethinking Thought Experiments

Rethinking Thought Experiments Alisa Bokulich

Boston University

An examination of two thought experiments in contemporary physics reveals that the same thought experiment can be reanalyzed from the perspectiv e of different and incompatible theories. This fact undermines those accounts of thought experiments that claim their justiŽcatory power comes from their ability to reveal the laws of nature. While thought experiments do play a genuine evaluative role in science, they do so by testing the nonempirical virtues of a theory, such as consistency and explanatory power. I conclude that, while their interpretation presupposes a whole set of background theories and putative laws, thought experiments nonetheless can evolve and be retooled for different theories and ends. 1. Introduction

A thought experiment can be understood as a hypothetical or counterfactua l scenario from which inferences are drawn.1 Historically, thought experiments have played a central role in the articulation and evaluation of scientiŽc theories. One of the earliest discussions of the use I would like to thank Harvey Brown for stimulating discussions about special relativity and ether theories. I am also grateful to Jim Cushing, Don Howard, and anonymous referees for helpful comments on an earlier draft of this paper. A portion of the research for this paper was made possible by the generous support of the National Science Foundation. 1. There is some controversy over how thought experiments should be deŽned. John Norton (1996) argues that thought experiments are essentially nothing but arguments from hypothetical states of affairs. The shortcomings of this approach have been adequately addressed by Michael Bishop (1999) and Tamar Szabó Gendler (1998) and will not be discussed here. Nancy Nersessian (1993), by contrast, has argued that thought experiments should be understood as narratives. My aim here is not to enter this debate concerning the deŽnition of thought experiments, but rather to clarify some misunderstandings about their function. Perspectives on Science 2001, vol. 9, no. 3 ©2002 by The Massachusetts Institute of Technology 285

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of thought experiments, or Gedankenexperimente, in physics is due to Ernst Mach (1897). In his book Knowledge and Error, he writes, “besides physical experiments there are others that are extensively used at a higher intellectual level, namely thought experiments. . . . Our ideas are more readily to hand than physical facts: thought experiments cost less, as it were. It is thus small wonder that thought experiment often precedes and prepares physical experiments” (Mach [1926] 1976, p. 136). For Mach, there is a continuum between thought experiments and ordinary experiments— both in the sense that they use a similar methodology2 and in the sense that many thought experiments Žnd a future realization in the laboratory.3 While a discussion of Mach’s views on the continuity between thought experiments and physical experiments is outside the scope of this paper, the challenge for any adequate account of thought experiments is to determine in which respects this continuity view can be maintained, and in which respects it breaks down. I argue below that, on one hand, there are certain respects in which thought experiments are more like ordinary experiments than has been previously admitted, while on the other hand, when it comes to the function of thought experiments, there is an important respect in which this continuity view breaks down. The assumption that thought experiments have the same function in the evaluation of theories as ordinary experiments do has led to difŽculties in several current accounts of thought experiments. In what follows, I examine two thought experiments in physics and show how, in both cases, the same thought experiment can be “rethought” from the perspective of different—and even incompatible—theories. While there are no necessary conditions for what is to count as “the same thought experiment,” one can argue for a lenient construal of the identity of two thought experiments by appealing to features such as a resemblance of the central narratives and a continuity through historical connection.4 While my discussion is focused speciŽcally on the role of thought experiments in contemporary physics, the conclusions drawn here do have implications for understandin g the function of thought experiments in science more generally. 2. Mach ([1926] 1976, p. 139). 3. A famous contemporary example of this is Alain Aspect et al.’s 1982 realization of the Einstein-Podolsky-Rosen thought experiment. The EPR thought experiment will be discussed in Section 4. 4. Sorenesen has similarly argued for a leniency in the standards for what is to count as an instance of the same thought experiment (Sorensen 1992a, p. 163). It should be noted that this is not a difŽculty unique to thought experiments; similar problems plague attempts to characterize what is to count as two instances of the same physical experiment.

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As I shall argue, the fact that the same thought experiment can be reanalyzed from the perspective of two incompatible theories has a number of important implications for understandin g the nature and function of thought experiments. First, just as Duhem showed in the case of ordinary physical experiments, the interpretation of a thought experiment presupposes a whole set of background theories and laws. For this reason, crucial experiments are no more possible in thought experiments than they are in physical experiments. Second, the ability to rethink a thought experiment from the perspective of two incompatible theories challenge s two recent accounts of how thought experiments function. More speciŽcally, both James Robert Brown (1991) and Roy Sorensen (1992b) argue that the knowledge we gain through some thought experiments is knowledge about the laws of nature, which can then be used in testing the empirical adequacy of our theories. The difŽculties in explaining where this knowledge comes from lead Brown, on the one hand, to give an a priori platonic account of our access to the laws of nature,5 while, on the other hand, they lead Sorensen to claim that our access to the laws of nature can be given a biological explanation in terms of natural selection.6 Both of these accounts share a misconception about the function of thought experiments in physics and fail to give an adequate account of the knowledge we gain from them. Third, the following analysis suggests an important respect in which the function of thought experiments differs from that of ordinary physical experiments: the evaluative function of thought experiments is not to test the empirical adequacy of our theories, but rather to test their nonempirical virtues—such as consistency and explanatory power. Finally, I shall argue that a more careful look at the history and development of two thought experiments in physics reveals that, contrary to Ian Hacking’s claim, thought experiments can have a life of their own (Hacking 1993, p. 307). 2. Duhem, Crucial Experiments, and Exp riences Fictives

Thought experiments are often presented in the form of reductio ad absurdum arguments. The strategy is to create a scenario in which the theory one is arguing against is shown to imply a contradiction or absurdity. A famous example of this is Galileo’s thought experiment on falling bodies used to undermine the Aristotelian theory of motion.7 On the Žrst day of 5. Brown (1991, p. 155). 6. Sorensen (1992b, p. 15). 7. Tamar Gendler (1998) has provided a detailed examination of this particular thought experiment and used it to argue against the view that thought experiments can be reduced to, or eliminated in favor of, pure arguments.

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Galileo’s Dialogues Concerning Two New Sciences, the character Salviati says, “But, even without further experiment, it is possible to prove clearly, by means of a short and conclusive argument, that a heavier body does not move more rapidly than a lighter one . . . as those mentioned by Aristotle” (Galilei [1638] 1991, p. 62). The thought experiment consists of tying a heavy cannon ball to a lighter musket ball and then comparing the speed of this composite system’s fall to that of a cannon ball falling alone. Salviati uses this thought experiment to argue that Aristotle’s theory implies a contradiction: on the one hand, this composite system must fall slower than a cannon ball (since the musket ball is retarding the composite system), while on the other hand, this composite system must fall faster (since the composite system is heavier than the cannon ball alone). Like Salviati, the proponent of a thought experiment often presents it as a crucial experiment, deciding unambiguously —and unavoidably —in favor of one theory and against another.8 Philosophers of science have long been wary of claims of crucial experiments. Pierre Duhem, who is well known for his critique of crucial experiments, writes, Those who assimilate experimental contradiction to reduction to absurdity imagine that in physics we may use a line of argument similar to the one Euclid employed so frequently in geometry. . . . Unlike the reduction to absurdity employed by geometers, experimental contradiction does not have the power to transform a physical hypothesis into an indisputabl e truth; in order to confer this power on it, it would be necessary to enumerate completely the various hypotheses which may cover a determinate group of phenomena; but the physicist is never sure that he has exhausted all the imaginable assumptions (Duhem [1914] 1954, pp. 188–190). Duhem’s critique of crucial experiments became the cornerstone of what would later, in retrospect, be called the Quine-Duhem thesis. Although there are stronger and weaker versions of this thesis, its basic claim is that experimental evidence alone cannot compel a scientist to accept or reject a theory. The reason that experimental evidence underdetermines theory 8. Gendler (1998), in her section “Four Ways Out,” argues that this thought experiment need not have been taken as decisive against the Aristotelian theory. She does not, however, connect this insight to Duhem’s work and his concerns about thought experiments. In the examples I discuss below, the challenge to “crucial thought experiments” does not simply come from the ability to modify a given theory in the face of disconŽrming evidence, but rather, from an underdetermination between two genuine rival theories.

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choice, according to Duhem, is that it is never an isolated hypothesis that faces an experiment, rather it is a whole group of interlocking hypotheses. A natural question, then, is whether these insights about crucial physical experiments apply to thought experiments as well. Duhem, like Mach, is among the earliest philosophers to discuss the methodological role that thought experiments play in physics. Unlike Mach, however, Duhem’s assessment of thought experiments is not favorable. Duhem refers to thought experiments as “Žctitious experiments” (expériences Žctives) and sees their use in physics as illegitimate . I would argue that Duhem’s distrust of thought experiments can be understood as connected to his critique of crucial experiments. For Duhem, “the interpretation of the slightest experiment in physics presupposes the use of a whole set of theories, and . . . the very description of this experiment requires a great many abstract symbolic expressions whose meaning and correspondence with the facts are indicated only by theories” (Duhem [1914] 1954, p. 204). Although he does not explicitly draw the connection between crucial experiments and thought experiments, it is arguably this holistic aspect to ordinary experiments that Duhem believed to be missing from thought experiments. This interpretation of Duhem gains support when one notes that his critique of thought experiments occurs in the middle of the chapter in which he argues that crucial experiments are not possible. It is also the case that in the paragraph which immediately precedes his discussion of thought experiments, Duhem reiterates the fundamental difference that he sees between the methods of physics and geometry. Apart from concerns about whether thought experiments exhibit holism, Duhem presents an even more difŽcult challenge to the legitimacy of the use of thought experiments in science. He writes, To invoke such a Žctitious experiment is to offer an experiment to be done for an experiment done; this is justifying a principle not by means of facts observed but by means of facts whose existence is predicted, and this prediction has no other foundation than the belief in the principle supported by the alleged experiment. Such a method of demonstration implicates him who trusts it in a vicious circle (Duhem [1914] 1954, p. 202). While Duhem is right to point out that thought experiments cannot provide any new empirical foundation for a theory or principle, he is wrong in concluding that they have no legitimate role to play in the evaluation and justiŽcation of scientiŽc theories. As the following two examples show, thought experiments do play a legitimate role in evaluating the nonempirical virtues of a theory.

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3. Th e Rocket s and Thread Thought Experiment: Einstein vs. Lorentz

The following thought experiment appeared in a 1959 American Journal of Physics article (Dewan and Beran 1959, pp. 517–518). Imagine two identically constructed rockets, B and C, both initially at rest in an inertial frame, S. The two rockets are arranged one behind the other, 100 meters apart in S and are connected by a thin piece of thread just long enough to connect the two rockets (as in Figure 1). Now imagine that both rockets Žre up their engines simultaneously in this frame and gently accelerate to relativistic velocities. Once they reach four-Žfths the speed of light relative to S, they simultaneously stop accelerating , and are now moving with a uniform velocity. According to an observer at rest in S, the two rockets have been moving in tandem and are still 100 meters apart. The question now is whether or not the thread will break. By carefully analyzing the situation in accordance with the special theory of relativity, it can be shown that, according to an observer in S, the thread must break because it is Lorentz-contracted (to a length of 60 meters) and so can no longer span the full 100 meters between the rockets. The mistaken belief that Lorentz contraction is simply an artifact of a mathematical transformation, and not a real effect, might lead one to worry that the thread breaking will lead to some inconsistency when we consider the same situation from the point of view of an observer on rocket A, at rest in the rockets’ Žnal inertial frame S moving with a uniform velocity of four-Žfths the speed of light relative to S. From the point of view of an observer on rocket A at rest in S , the initial separation of the rockets is only 60 meters. Rather than seeing the rockets Žre their engines simultaneously, however, the observer on rocket A will see rocket B accelerate and come to rest in S Žrst, followed by rocket C acceleratin g and coming to rest at a later time. Because the two rockets do not accelerat e and come to rest simultaneously according to an observer in S , the distance between these rockets has grown from 60 meters to 166.67 meters. In the S¢ rest frame the thread is, of course, 100 meters and so must break since it cannot stretch the 166.67 meters between the rockets. The intent of E. Dewan and M. Beran in Žrst introducing this thought experiment was to show that Lorentz contraction can cause measurable stresses on moving bodies.9 This conclusion is counterintuitiv e because, according to special relativity, Lorentz contraction is a frame-dependen t 9. There is an interesting pre-history to this thought experiment that involves an exchange between Paul Ehrenfest and Einstein on this question of whether Lorentz contraction can produce stress effects. See Document 44 in Stachel (1989). I thank Don Howard for bringing this reference to my attention.

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Figure 1. The initial situation before rockets B and C Žre, as viewed in the inertial frame S.

phenomenon, and hence, is not thought to lead to any observable effects, such as a thread breaking.10 Almost twenty years later, John S. Bell retooled this very thought experiment to show that the same conclusion could be reached by means of a very different sort of analysis. Rather than using the special theory of relativity to analyze this thought experiment, Bell uses Lorentz’s ether theory. Lorentz’s ether theory was, at least in 1905, an observationally equivalent rival theory to special relativity.11 According to Lorentz’s theory, all motion is relative to a stationary ether frame. The ether was thought to be the medium through which electromagneti c forces were propagated. Lorentz presents the following argument: We assume that molecular forces are also transmitted through the ether, like the electric and magnetic forces. . . . If they are so transmitted, the translation will very probably affect the action between two molecules or atoms in a manner resembling the attraction or repulsion between charged particles. Now, since the form and dimensions of a solid body are ultimately conditioned by the intensity of molecular actions, there cannot fail to be a change of dimensions as well (Lorentz [1895] 1952, p. 6). 10. The counterintuitiveness of this conclusion is evidenced by John Bell’s account of how the majority of physicists in the theory division at CERN, when presented with this thought experiment, initially gave the incorrect answer ([1976] 1993, p. 68). 11. Elie Zahar (1973) has argued that not only was Lorentz’s theory empirically adequate but it was also part of a non-ad hoc research program. Today it remains an open question whether or not it is possible to construct a Lorentzian ether theory that is in all respects empirically equivalent to special relativity.

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9 9

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Figure 2. A Minkowski space-time diagram of the relativistic account of the rockets and thread thought experiment.

From the molecular force hypothesis described above, Lorentz is able to derive the now well-known expression for Lorentz contraction, 1 - v 2 / c 2 , where v is the velocity of the object and c is the speed of light (Zahar 1973, pp. 114–115). Lorentz originally used the above argument as part of an explanation for how his ether theory could account for the results of the MichelsonMorley experiment (which many took to be a crucial experiment resulting in the refutation of the stationary ether theory). As Bell shows, however, the same argument can also be used to explain the results of the rockets and thread thought experiment. Bell models the atoms making up the thread in terms of nuclei with circular electron orbits. He then shows that as the nuclei begin to move relative to the stationary ether, the initially circular orbits will deform into ellipses, contracting in the direction of motion by the usual Lorentz factor (Bell [1976] 1993, p. 70). As the atoms and molecules contract, so too will the thread. If the thread is not strong enough to overcome the inertia of the rockets and draw them closer together as it contracts, then the thread will break. The rockets and thread thought experiment can be analyzed not only from the perspective of Einstein’s special theory of relativity, but also from the perspective of Lorentz’s ether theory. Although both theories agree on what happens (i.e., the thread breaks), they differ greatly when it comes to explaining how and why that event occurs. Bell draws two sorts of lessons from this thought experiment. The Žrst lesson is a pedagogica l one. In his discussion of why theoretical physicists often draw the wrong conclusion

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(that, according to special relativity, the thread will not break) he notes that those who are familiar with the work of Lorentz are more likely to see that the thread will indeed break in this thought experiment. The reason is that Lorentz’s ether theory, though by no means obvious, is more in accord with our classical views about space and time. In addition to noting the pedagogical advantage that teaching Lorentz’s theory might offer by being more in accord with our classical views, Bell also draws a stronger epistemological lesson from his Lorentzian analysis of this thought experiment. In his comparison of Lorentz’s approach to Einstein’s he writes, Lorentz, on the other hand, preferred the view that there is indeed a state of real rest, deŽned by the ‘aether’, even though the laws of physics conspire to prevent us identifying it experimentally. The facts of physics do not oblige us to accept one philosophy rather than the other. . . . [T]he laws of physics in any one reference frame account for all physical phenomena, including the observations of moving observers (Bell [1976] 1993, p. 77). Whether one could consistently develop a Lorentzian space time theory using a single preferred rest frame is an issue that is still debated, and not one that I wish to address here. Instead, the important conclusions to draw from Bell’s analysis are Žrst, that thought experiments are no more bound to any one particular theory than ordinary physical experiments are, and second, they can underdetermin e theory choice in the same way too. 4. Th e EPR Thought Experiment: Copenhag en vs. Bohm

The Einstein-Podolsky-Rosen (EPR) Gedankenexperiment is an example of a thought experiment that has evolved and been modiŽed over time. The original 1935 thought experiment can be described as follows. Consider two particles, 1 and 2, that interact and then become spatially separated. With the help of Schrödinger’s equation one can calculat e the state of the combined system (1 and 2) at some later time, which will be a superposition of various possible states for these two particles. If one decides to measure the position, for example, of particle 1, then the result of this measurement plus the information about the combined system allows one to determine a deŽnite value for the position of particle 2 (i.e., without having to make a measurement on that particle). EPR then invoke the following criterion: “If, without in any way disturbing a system, we can predict with certainty (i.e., with probability equal to unity) the value of a physical quantity, then there exists an element of physical reality corre-

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sponding to this physical quantity” (Einstein et al. [1935] 1983, p. 138). Thus, EPR conclude that particle 2 must really have a deŽnite position, since it is assumed that the decision to make a measurement of the position of particle 1 in no way could affect the state of particle 2 which is spatially separated from it (this is called the locality or separation principle12). The paradoxical aspect of this thought experiment arises when EPR point out that one could just as well have chosen to measure the momentum of particle 1. In this case, one could use the result of the momentum measurement on 1, plus the information about the state of the combined system, to determine a deŽnite value for the momentum of particle 2. From this EPR conclude that particle 2 must simultaneously have a deŽnite position and a deŽnite momentum (recall that by the locality assumption nothing we do to particle 1 can affect particle 2). The stated intention of EPR is to use this thought experiment to show that quantum mechanics is incomplete. If quantum mechanics is complete, then a particle cannot simultaneously have a deŽnite position and a deŽnite momentum; the accuracy to which complementary observables, such as position and momentum, can be deŽned is limited by Heisenberg’s uncertaint y principle. But, according to the EPR thought experiment, a particle can simultaneously have a deŽnite position and a deŽnite momentum. 13 Thus, they conclude, quantum mechanics is incomplete. With evidence from Einstein’s letters, Arthur Fine (1986) has shown that it was likely Podolsky who wrote up the EPR paper and that Einstein was unhappy with the way the paper came out, feeling that the essential point he wanted to make was obscured. Fine provides a convincing argument that Einstein saw this thought experiment, not as showing that quantum mechanics was incomplete, but rather as showing that one could not maintain both that quantum mechanics is complete and that states of spatially separated objects are independen t from each other.14 This illustrates the fact that even the coauthors of a thought experiment can dis12. Fine (1986, p. 36). 13. Speaking more precisely, it is possible to assign two different wavefunctions to the same reality and these wavefunctions can be eigenstates of noncommuting operators. According to the rules of the standard interpretation of quantum mechanics, if a system is in an eigenstate of some observable then that observable has a deŽnite value for that system. 14. Don Howard (1985) has argued for a similar interpretation of Einstein’s views on the EPR paper. Howard shows that in 1936 Einstein reformulated the EPR Gedankenexperiment in such a way to make the tension between completeness and the “separation principle” more explicit. SpeciŽcally, Einstein showed that the thought experiment does not depend crucially on the reality criterion or noncommuting operators, only on the fact that two different wavefunctions can be ascribed to the same reality. The relevant Einstein references can be found in Howard (1985).

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agree about what it is precisely that the thought experiment is supposed to show. In 1951, David Bohm retooled the EPR Gedankenexperiment into the form in which it is more generally known today. He writes, “we have modiŽed the experiment somewhat, but the form is conceptually equivalent to that suggested by them, and considerably easier to treat mathematically” (Bohm 1951, p. 614). Rather than considering position and momentum measurements, he considers spin measurements on two atoms that are the result of the disintegration of an initial spin-zero molecule. These atoms will thus have equal and opposite spin, irrespective of the direction along which the spin is measured (see Figure 3). Since the operators associated with spins in any two directions not on the same axis do not commute, we are presented with a situation similar to the original EPR Gedankenexperiment. The simpler conceptual and mathematical form of Bohm’s version of the thought experiment played a critical role in facilitatin g Bell’s construction of his famous inequality. Very briey, this inequalit y is derivable from (i.e., a logical consequence of) a condition that Bell called ‘locality,’ which is essentially equivalent to Einstein’s separation principle (Bell [1971] 1993, p. 36).15 This inequality, however, is incompatible with the predictions of quantum mechanics and with well-establishe d empirical data. The experimental violation of Bell’s inequality is typically taken to imply that Bell’s locality condition must be given up. Fine, however, makes the following point: Arguments by Bell and others suggest that separation alone may be incompatible with the quantum theory. . . . Should that be correct, then the dilemma of EPR could be resolved by abandoning separation. I do not believe that the Bell arguments are in fact strong enough to force the issue this way, but even if they are, the question of completenes s would remain. For it is possible that both separation and completeness turn out to be false (Fine 1986, pp. 38–39). The great value of the EPR Gedankenexperiment is that it reveals an inconsistency between a certain set of theoretical assumptions. It is by no means a crucial experiment, however, that forces the resolution of this contradiction one way or the other. 15. More information on Bell’s inequality can be found in the Cushing and McMullin (1989) anthology. Subsequent work has shown that what is here called locality is in fact the conjunction of two distinct conditions ( Jarrett 1984). Howard (1985) has argued that shortly after the 1935 EPR paper, Einstein himself became aware of essentially this distinction. Unfortunately, a discussion of these issues is outside the scope of this paper and I must refer the interested reader to the excellent collection of articles referenced above.

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Figure 3. Bohm’s version of the EPR Gedankenexperiment.

In 1952 Bohm made a radical reversal, not only of his interpretation of the EPR thought experiment, but also of his entire interpretation of quantum mechanics. His new resolution of the EPR dilemma is to abandon both separation and completeness . In the paper in which Bohm develops the causal interpretation of quantum mechanics, he writes, In the usual interpretation of quantum theory, there is no . . . conceptual model showing in detail how the second particle, which is not in any way supposed to interact with the Žrst particle, is nevertheless able to obtain either an uncontrollabl e disturbance of its position or an uncontrollable disturbance of its momentum depending on what kind of measurement the observer decided to carry out on the Žrst particle. . . . In our suggested new interpretation of the quantum theory, however, we can describe this [EPR] experiment in terms of a . . . precisely deŽnable conceptual model (Bohm [1952] 1983, p. 389). Very briey described, Bohm’s causal interpretation begins with the standard Schrödinger equation and rewrites it in a form resembling a classical equation of motion (the Hamilton-Jacobi equation) containing the usual classical potential plus a new “quantum potential” term.16 This way of writing the fundamental equations of quantum mechanics suggests a new way of interpreting this formalism. While the standard interpretation of the formalism of quantum mechanics takes it to describe a fundamentall y indeterministic world, in which particles cannot have deŽnite trajectories, Bohm showed that one could also consistently interpret the formalism of quantum mechanics as describing a fundamentall y deterministic world where particles do always follow deŽnite trajectories. According to Bohm’s causal interpretation, the correlations in the EPR thought experiment can be explained in terms of a direct disturbance. On 16. For further information about Bohm’s causal interpretation see, for example, Cushing (1994).

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this causal view, the wavefunctio n is interpreted as a real Želd that encodes information about the entire two-particle and two-apparatus system. When the experimenter changes the settings on the apparatus to measure a certain observable of particle 1, this immediately produces a change in the overall wavefunctio n and alters the quantum potential. This change in the quantum potential can be said to generate a quantum force that acts instantaneously on the particles. Thus, the measurement made on particle 1 instantaneously disturbs particle 2 via this nonlocal quantum potential. 17 As in the rockets and thread thought experiment described in the last section, the EPR Gedankenexperiment can be reanalyzed from the perspective of different, and even incompatible , theories. While one might have thought that the EPR Gedankenexperiment could function as a crucial experiment to decide between standard quantum mechanics and hidden variable theories, it turns out to be explainabl e equally well by each of these rivals. The EPR Gedankenexperiment has been discussed in the literature on thought experiments before. Allen Janis, for example, has used the EPR Gedankenexperiment as an example of one of the ways in which thought experiments can fail. With regard to EPR, he writes, “the thought experiment failed to provide a clear basis for concluding that quantum mechanics is incomplete. Since this goal was the motivation for the thought experiment, however, the thought experiment failed”(Janis 1991, p. 116). The difŽculty with saying that thought experiments can fail in this way is that it makes sense only with respect to the intentions of the proponent of thought experiment. As we have seen, however, different people have put forward the EPR Gedankenexperiment with the intention of showing different things. For example, if Fine’s reading of Einstein is correct, then Janis should have concluded that the EPR did not fail—it succeeded in showing that one could not maintain both locality and completenes s (i.e., that one or the other, or both had to be given up). A more careful reading of the history of this thought experiment reveals that many discussions of the EPR Gedankenexperiment are oversimpliŽed and consequently have led to a mistaken understandin g of thought experiments. An important lesson to take away from this discussion is that to say that a thought experiment succeeds or fails makes sense only in reference to the intentions of the proponent of the thought experiment. As we have seen, however, there can be disagreement over what it is that a thought experiment shows. Moreover, we should not say that only 17. Because these nonlocal disturbances are uncontrollable and cannot be used to send a signal, there is arguably no conict with the Žrst principle of relativity.

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the intentions of the original author(s) of the thought experiment are to count; thought experiments can be rethought and retooled for new purposes. 5. Th ought Experiments and the La ws of Nature

In thinking through a thought experiment, it is difŽcult not to believe that one is learning something new. Kuhn, for example, asks “How, then, relying exclusively upon familiar data, can a thought experiment lead to new knowledge or to a new understandin g of nature?” (Kuhn [1964] 1977, p. 241). Two sorts of answers to this question have been given recently in the literature on thought experiments. Both Brown (1991) and Sorensen (1992b) argue that thought experiments function by revealing the laws of nature. While Brown argues that thought experiments give us a priori insights into the laws of nature, Sorensen argues that thought experiments harness physical intuitions shaped by laws through natural selection. Both accounts, however, misconceive the function of thought experiments and fail to give a satisfactory account of the knowledge that we gain from them. Brown argues for the existence of a special class of thought experiments which he calls “platonic.” He explains, A platonic thought experiment is a single thought experiment which destroys an old or existing theory and simultaneously generates a new one; it is a priori in that it is not based on new empirical evidence nor is it merely logically derived from old data; and it is an advance in that the resulting theory is better than the predecessor theory (Brown 1991, p. 77). The function of a platonic thought experiment is that of a crucial experiment, designed to decide unambiguously in favor of one theory and against another. I suspect that it was this sort of interpretation of thought experiments that led Duhem to be wary of them. Brown’s discussion of platonic thought experiments assumes that there is a direct path from such thought experiments to the relevant laws of nature. Although he sees these thought experiments functioning as crucial experiments revealing the laws of nature, he is not an empiricist. Rather, he argues that “[platonic] thought experiments give us (fallible ) a priori beliefs of how the physical world works. With the mind’s eye, we can see the laws of nature” (Brown 1991, p. 155). Brown looks for support for this view in the interpretatio n of laws as necessary relations among independently existing universals. The difŽculty, however, with deŽning laws of nature this way is that it divorces this notion from the sort of things that

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scientists typically refer to as laws of nature.18 While a full discussion of this notion of law is outside the scope of this paper, I want to argue that Brown’s account of laws fails to illuminat e our understanding of how thought experiments, like the EPR Gedankenexperiment, work. Brown views the EPR Gedankenexperiment as an example of platonic thought experiment that “destroyed the Copenhagen interpretation and established hidden variables” in its place (Brown 1991, p. 77). Brown, of course, notes that historically this was not the outcome of this thought experiment. Rather than seeing cases like this as posing a problem for his a priori platonic account, he appends the term “fallibilist ” to his position. To simply say that the EPR Gedankenexperiment was a failed case of seeing the laws of nature, still greatly misrepresents this thought experiment.19 Brown furthermore wants to claim that not only are these laws the cause of the knowledge we gain in the thought experiment, but that they are also somehow the cause of the correlations involved in the EPR Gedankenexperiment. Brown writes, Distant correlations are caused by the laws of nature. . . . A law of nature is an independentl y existing entity. . . . It is this very same entity, the abstract law, which plays a role in our knowledge of what is going on at the distant wing of an EPR-type experiment (Brown 1991, p. 152). Unfortunately, Brown does not go on to explain exactly what this particular law of nature is, nor what are the universals between which it is supposed to be a necessary relation. Further problems arise when one tries to make sense of what it might mean to attribute causal powers to a law. In the case of Bohm’s causal interpretatio n of the EPR Gedankenexperiment, for example, there is no need to postulate a law as the cause of these correlations, since the correlations are said to be caused by a real physical quantum potential, or force. In the case of the Copenhagen interpretation, the laws at work in this thought experiment are fundamentall y indeterministic , whereas in the case of the causal interpretation the laws at work in this same thought experiment are fundamentally deterministic. The fact that the same thought experiment can be rethought from the perspective of different and incompatible theories makes it less plausible that thought experiments work by allowing us to “see” the laws of nature. 18. Although David Armstrong, who is a proponent of this view of laws, admits this is the case, he does not view it as a shortcoming (Armstrong 1983, pp. 138–139). 19. I offer an alternative account of the knowledge we gain through thought experiments in Section 6.

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Sorensen offers an alternative account of the role that laws play in thought experiments. He writes, The laws of nature have led us to develop rough and ready intuitions of physical possibility which are then exploited by thought experimenter s to reveal some of the very laws responsible for those intuitions. The good news is that natural selection ensures a degree of reliability for the intuitions. The bad news is that the evolutionary account seems to limit the range of reliable thought experiment to highly practical and concrete contexts (Sorensen 1992b, p. 15). On this account, thought experiments are said to reveal the laws of nature by harnessing our physical, or modal, intuitions. In order to explain the source of these modal intuitions, and why they should generally give us reliable insight into the laws, Sorensen appeals to evolutionary theory. Although he admits that this “biological guarantee” does not logically entail reliable belief formation, he nonetheless thinks that it can explain our successes in using thought experiments (Sorensen 1992b, p. 35). A fundamental difŽculty for Sorensen’s account is to explain why one of the most successful areas in which thought experiments are used is theoretical physics. The description of the world given by contemporary physics is very far removed from our ordinary physical intuitions. In these contexts, it is particularly implausible that any appeal to the sort of physical intuitions that might have evolved evolutionarily would offer us any insight into how such thought experiments function. Although Sorensen admits that the pessimism his evolutionary account implies regarding the more theoretical and abstract thought experiments may not be entirely founded, he gives no clear explanation for how this fact is to be reconciled with his view. In my view, the reason that thought experiments can be successfully carried out in physics is that the formalism and mathematical structure of the theory play a central heuristic role in carrying our reasoning further than our common-sense physical intuitions could. This is precisely why we are able to evaluate thought experiments in theories like special relativity even though the relativistic account of distance and simultaneity is very far removed from our everyday understandin g of these concepts. It is simply a mistake to describe the sort of knowledge involved in these thought experiments as intuitions. Brown and Sorensen share a common misconceptio n that the immediate function of thought experiments is to reveal the laws of nature. It is because they see this as the function of thought experiments that they then must introduce an a priori or evolutionary account to explain how this might work. Thought experiments, however, are not “pre-theoretical ” entities that provide a pure empirical or a priori basis from which to dis-

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cover laws. In the spirit of Duhem we might put the point the following way: the interpretatio n of a thought experiment presupposes the use of a whole set of theories and (for thought experiments in physics) the very description of a thought experiment requires a great many abstract symbolic expressions whose meaning and correspondence with the facts are indicated only by theories.20 6. What Do Thought Experiments Teach Us?

If thought experiments do not work by allowing us to see the laws of nature, then the question of what it is that we are learning, when we perform a thought experiment, remains. The simple answer is that thought experiments work by drawing out the physical implications of our theories. In a thought experiment we begin with a theory or set of assumed laws and then use the thought experiment to uncover certain consequence s from these laws that might otherwise remain hidden. For example, in the rockets and thread thought experiment, one might understand the special theory of relativity, and know the laws that this theory postulates, but still not be aware that they imply the existence of relativistic stress effects. The thought experiment makes these consequence s explicit. While drawing out the implications of our theories is an important part of science, thought experiments are not limited to this function. Thought experiments do play a role in evaluating, accepting, and rejecting theories. It is a mistake, however, to see the role of thought experiments as testing the empirical adequacy of a theory. On this point, Duhem was right to charge those who attempt to do so with implicating themselves in a vicious circle. The key point to recognize, however, is that empirical adequacy is not the only criterion used in the evaluation of theories. In 1964 Kuhn provided the beginning of an answer to the question of how thought experiments teach us something new when he pointed out that thought experiments reveal contradictions between nature and the scientist’s conceptual apparatus. However, it is only after Kuhn’s 1973 article “Objectivity, Value Judgement, and Theory Choice” that a fuller Kuhnian explanatio n of the function of thought experiments in theory evaluation could be made clear.21 In this article, Kuhn points out that theory choice is not simply a matter of determining whether the theory is empirically adequate, but that it also depends crucially on other nonempirical criteria. These criteria can be described as internal consis20. Recall the quotation from Duhem (Duhem [1914] 1954, p. 204) given in Section 2 of the present work. 21. Kuhn himself did not, in later writings, return to the question of how thought experiments function.

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tency, external coherence with other theories, simplicity, and explanatory power. Philosophers such as Ernan McMullin (1988) and Paul Churchland (1985) have argued that these nonempirical criteria can be just as important as, and in some cases more important than, empirical criteria in evaluating a theory. This realization, that the testing and evaluating of theories involves not just empirical criteria, suggests a legitimate and substantial way in which thought experiments can be used in theory evaluation. In addition to bringing out the physical implications of our theories, a central function of thought experiments is to test and evaluate the internal consistency, external coherence, simplicity, and explanatory power of our theories. In special relativity, thought experiments are typically used to show that apparent contradictions in the theory can in fact be consistently accounted for. The special relativistic version of the rockets and thread thought experiment can be understood along similar lines. One might think that, because Lorentz contraction is a frame dependent phenomenon, an effect like the thread breaking would lead to an inconsistency when considered from another frame. If one could not account for the thread breaking from the perspective of the Žnal rest frame, then this would suggest an internal inconsistency in the theory. By carefully working through the thought experiment, however, one can show that there is no such inconsistency. The rethinking of the rockets and thread thought experiment from the perspective of Lorentz’s ether theory illustrates the great explanatory power that this theory has for accounting for the result. According to Bell, the ability of this theory to provide a concrete, visualizabl e model for the Lorentz contraction of the thread gives Lorentz’s theory an explanatory advantage over special relativity. In a similar way, the novel insights given by the EPR Gedankenexperiment can be seen in terms of its function in testing the nonempirical virtues of quantum theory. Quantum mechanics is one of the most empirically successful theories in history, and both the standard and causal interpretations share this empirical adequacy. The remarkable result of this 1935 thought experiment was to show that two fundamental assumptions of standard quantum theory, namely locality (the “separation” principle) and completeness , are inconsistent. When this thought experiment was analyzed in accordance with the causal interpretation, however, its purpose was both to demonstrate the explanatory power of this theory and to address concerns about its external coherence with relativity theory. Once we see that a central function of thought experiments is to test the nonempirical virtues of theories, it is not surprising that Bohm makes the fol-

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lowing point in the context of the causal interpretation’s account of the EPR Gedankenexperiment: The reason why no contradictions with relativity arise in our interpretation despite the instantaneous transmission of momentum between particles is that no signal can be carried in this way. For such a transmission of momentum could constitute a signal only if there were some practical means of determining precisely what the second particle would have done if the Žrst particle had not been observed; and as we have seen, this information cannot be obtained (Bohm [1952] 1983, p. 390).22 Bohm uses the causal interpretation’s description of the EPR Gedankenexperiment to argue that this interpretatio n involves no conict with the special theory of relativity. In other words, he is using this thought experiment to highlight the fact that his theory does indeed possess the nonempirical virtue of external coherence. While we are not learning anything new about the world through these thought experiments, they are teaching us something new about the degree of internal consistency, external coherence, simplicity, and explanatory power of our theories. In so doing, thought experiments are playing an important part in the evaluation of a scientiŽc theory even though physical experiments are still required to test its empirical adequacy. On this account of the function of thought experiments, there is no longer any need to explain the knowledge we acquire through thought experiments as an instance of fallibly seeing the laws of nature. 7. Why Thought Experiments Do Have a Life of Their Own

The function of thought experiments in science is to draw out the physical implications of our theories and to test their nonempirical virtues. In both these capacities, the description and interpretatio n of the thought experiment must begin by presupposing a set of background theories and laws. To say this, however, does not commit one to the view that thought experiments cannot be thought from the perspective of different theories. Against this view, Ian Hacking has argued that thought experiments do not have a life of their own. He explains what he means by ‘life of their own’ as follows, Over a decade ago I wrote that experiments have a life of their own. I intended partly to convey the fact that experiments are organic, 22. Whether this account of Bohm’s actually succeeds in establishing the external coherence of the causal interpretation with relativity is another matter, which will not be pursued here.

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develop, change, and yet retain a certain long-term development which makes us talk about repeating and replicating experiments. . . . I think of experiments as having a life: maturing, evolving, adapting, being not only recycled but also, quite literally being retooled. But thought experiments are rather Žxed, largely immutable. . . . what they think is what was once thought (Hacking 1993, p. 307). By ‘life of its own’ Hacking does not mean that the interpretation or description of an experiment can be made independentl y of all theories.23 Rather, he means that experiments have the ability to evolve and be adapted to different theories and ends. The closer analyses of the rockets and thread thought experiment in Section 2 and the EPR Gedankenexperiment in Section 3 reveal that, by the deŽnition given above, these thought experiments do indeed have a life of their own. The rockets and thread thought experiment, which was Žrst introduced by Dewan and Beran to show an overlooked consequence of the special theory of relativity, was readapted by Bell to show that the same result could be explained much more naturally in terms of Lorentz’s ether theory. Similarly, the 1935 EPR Gedankenexperiment evolved, at the hands of Bohm in 1951, into the simpler form it is usually known by today. In 1952, Bohm made an even more radical retooling of this thought experiment by reanalyzing it in terms of the causal interpretation of quantum mechanics. Far from being Žxed and immutable, what is being thought at each stage of these thought experiments is signiŽcantly different from what had been thought before. In the one case we saw how thoughts about the classical notions of distance and simultaneity breaking down gave way to thoughts about molecular forces transmitted by an ether. In the other case, thoughts about particles that do not possess well deŽned positions and momenta prior to measurement gave way to thoughts about particles that do always have well deŽned positions and momenta being guided by a quantum potential. In short, these examples show that thought experiments can have a life of their own. The impression that thought experiments do not have a life of their own can be understood as a result of the oversimpliŽed and ahistorical way that they are typically presented. Thought experiments are often used as pedagogica l and rhetorical devices. In these contexts, the complexities and 23. Hacking (1983) presents a much more comprehensive set of arguments for the independence of physical experiments from theory. Obviously not all of these points can be carried over to thought experiments. My point here is much more limited—namely, to show that this particular argument of Hacking’s for a fundamental difference between physical and thought experiments does not hold.

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historical evolution of the thought experiment are omitted. It would be a mistake, however, to conclude that rhetoric and pedagogy are their only function; thought experiments have a more substantial role to play in scientiŽc practice. They are important, not only for drawing out the physical implications of our theories, but also for testing their internal consistency, external coherence, simplicity, and explanatory power. In this way, thought experiments, just like ordinary physical experiments, can teach us something new. References

Aspect, A., J. Dalibard, and G. Roger. 1982. “Experimental Tests of Bell’s Inequality Using Time-Varying Analyzers.” Physical Review Letters 49: 1804–1807. Armstrong, D. 1983. What is a Law of Nature? Cambridge: Cambridge University Press. Bell, J.S. [1971] 1993. “Introduction to the Hidden-Variabl e Question.” Pp. 29–39 in Speakable and Unspeakable in Quantum Mechanics. Cambridge: Cambridge University Press. ———. [1976] 1993. “How to Teach Special Relativity.” Pp. 67–80 in Speakable and Unspeakable in Quantum Mechanics. Cambridge: Cambridge University Press. Bishop, M. 1999. “Why Thought Experiments Are Not Arguments.” Philosophy of Science 66(4): 534–541. Bohm, D. 1951. Quantum Theory. Englewood Cliffs, NJ: Prentice Hall. Republished by Dover Publications, New York in 1989. ———. [1952] 1983. “A Suggested Interpretation of the Quantum Theory in Terms of “Hidden Variables, I and II.” Pp. 369–402 in Quantum Theory and Measurement. Edited by J. Wheeler and W. Zurek. Princeton: Princeton UP. Brown, J.R. 1991. The Laboratory of the Mind: Thought Experiments in the Natural Sciences. London: Routledge. Churchland, P. 1985. “The Ontological Status of Observables: In Praise of the Superempirical Virtues.” Pp. 35–47 in Images of Science. Edited by P. Churchland and A. Hooker. Chicago: University of Chicago Press. Cushing, J. 1994. Quantum Mechanics: Historical Contingency and the Copenhagen Hegemony. Chicago: University of Chicago Press. Cushing, J. and E. McMullin. 1989. Philosophical Consequences of Quantum Theory: Reections on Bell’s Theorem. Notre Dame: University of Notre Dame Press. Dewan, E. and M. Beran. 1959. “Note on Stress Effects Due to Relativistic Contraction.” American Journal of Physics 27: 517–518.

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Duhem, P. [1914] 1954. The Aim and Structure of Physical Theory. Princeton: Princeton University Press. Einstein, A., B. Podolsky, and N. Rosen. [1935] 1983. “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?” Pp. 138–141 in Quantum Theory and Measurement. Edited by J. Wheeler and W. Zurek. Princeton: Princeton University Press. Fine, A. 1986. The Shaky Game: Einstein Realism and the Quantum Theory. Chicago: University of Chicago Press. Galilei, G. [1638] 1991. Dialogues Concerning Two New Sciences. Buffalo: Prometheus Books. Gendler, T. 1998. “Galileo and the Indispensabilit y of ScientiŽc Thought Experiment.” British Journal for the Philosophy of Science 49: 397–424. Hacking, I. 1983. Representing and Intervening: Introductory Topics in the Philosophy of Natural Science. Cambridge: Cambridge University Press. ———. 1993. “Do Thought Experiments Have a Life of Their Own? Comments on James Brown, Nancy Nersessian and David Gooding.” Pp. 302–308 in PSA 1992. Volume 2. Edited by D. Hull, M. Forbes, and K. Okruhlik. East Lansing: Philosophy of Science Association. Howard, D. 1985. “Einstein on Locality and Separability.” Studies in the History and Philosophy of Science 16(3): 171–201. Janis, A. 1991. “Can Thought Experiments Fail?” Pp. 113–118 in Thought Experiments in Science and Philosophy. Edited by T. Horowitz and G. Massey. Savage, MD: Rowan & LittleŽeld Publishers, Inc. Jarrett, J. 1984. “On the Physical SigniŽcance of the Locality Conditions in the Bell Arguments.” Noûs 18: 569–589. Kuhn, T. [1964] 1977. “A Function for Thought Experiments.” Pp. 240–265 in The Essential Tension. Chicago: University of Chicago Press. ———. [1973] 1977. “Objectivity, Value Judgement, and Theory Choice.” Pp. 320–339 in The Essential Tension. Chicago: University of Chicago Press. Lorentz, H. [1895] 1952. “Michelson’s Interference Experiment.” Pp. 1–7 in The Principle of Relativity: A Collection of Original Papers on the Special and General Theory of Relativity. Translated by W. Perret and G. Jeffrery. New York: Dover. Mach, E. 1897. “Über Gedankenexperimente. ” Zeitschrift für den Physikalischen und Chemischen Unterricht 10: 1–5. ———. [1926] 1976. Knowledge and Error: Sketches on the Psychology of Enquiry. Dordrecht: D. Reidel Publishing Company. McMullin, E. 1988. “Values in Science.” Pp. 349–373 in Introductory Readings in the Philosophy of Science. Edited by E. Klemke, R. Hollinger, and A. Kline. Buffalo: Prometheus Books.

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Nersessian, N. 1993. “In the Theoretician’s Laboratory: Thought Experimenting as Mental Modeling.” Pp. 291–301 in PSA 1992. Volume 2. Edited by D. Hull, M. Forbes, and K. Okruhlik. East Lansing: Philosophy of Science Association. Norton, J. 1996. “Are Thought Experiments Just What You Thought?” Canadian Journal of Philosophy 26(3):333–366. Sorensen, R. 1992a. Thought Experiments. Oxford: Oxford University Press. ———. 1992b. “Thought Experiments and the Epistemology of Laws.” Canadian Journal of Philosophy 22(1):15–44. Stachel, J. 1989. The Collected Papers of Albert Einstein. Volume 2. Princeton: Princeton University Press. Zahar, E. 1973. “Why Did Einstein’s Programme Supersede Lorentz’s?(I).” British Journal for the Philosophy of Science 24: 95–123.