bachelor thesis physics and astronomy

An Epistemological Approach toEinstein’s Thought Experiments

Author:M.R. Visser

Primary supervisor:Prof. dr. A.J. Kox

Secondary supervisor:Prof. dr. E.P. Verlinde

University of AmsterdamInstitute for Theoretical Physics

Science Park 9041090 GL, Amsterdam

The Netherlands

Abstract

In this bachelor thesis I will discuss four thought experiments of Einstein, concerningspecial relativity, general relativity and quantummechanics. My main concern is restrictedto the so-called epistemological problem. Einstein’s thought experiments are supposed togive us new knowledge of the natural world. But how is this possible when there isno new empirical input? I will discuss two main, recent responses in the philosophyof science: Norton’s argument view and Brown’s Platonism. I agree with Norton thatthought experiments are epistemically unremarkable. In my opinion, the epistemic sourceof thought experimental knowledge is twofold, just like that of ordinary knowledge. Onthe one hand, knowledge is based on sensory experience and, on the other hand, an act ofthe understanding is needed to produce knowledge. Thus, from an epistemological pointof view, thought experiments work the same as other scientific methods.

12 ECTS22 August 2011

5794722@student.uva.nl

Wie kommt aber ein ordentlich begabter Naturforscher uberhaupt dazu, sichum Erkenntnistheorie zu kummern? Gibt es nicht in seinem Fache wertvollereArbeit? So hore ich manche meiner Fachgenossen hierauf sagen, oder spure beinoch viel mehr, daß sie so fuhlen. Diese Gesinnung kann ich nicht teilen. Wennich an die tuchtigsten Studenten denke, die mir beim Lehren begegnet sind, d.h. an solche, die sich durch Selbstandigkeit des Urteils, nicht nur durch bloßeBehendigkeit auszeichneten, so konstatiere ich bei ihnen, daß sie sich lebhaft umErkenntnistheorie kummerten. Gerne begannen sie Diskussionen uber die Zieleund Methoden der Wissenschaften und zeigten durch Hartnackigkeit im Verfechtenihrer Ansichten unzweideutig, daß ihnen der Gegenstand wichtig erschien. Dies istfurwahr nicht zu verwundern.

— A. Einstein, ‘Ernst Mach’, Physikalische Zeitschrift 17 (1916)

Contents

Introduction 3

I Thought experiments in practice 5

1 Chasing the light 61.1 A childlike thought experiment . . . . . . . . . . . . . . . . . . . . . . . . . . 61.2 The search for an universal principle . . . . . . . . . . . . . . . . . . . . . . . 61.3 The paradox . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.4 Towards the special theory of relativity . . . . . . . . . . . . . . . . . . . . . 9

2 The moving magnet and conductor problem 112.1 Developing an ether free electrodynamics . . . . . . . . . . . . . . . . . . . . 112.2 “The difficulty to be overcome” . . . . . . . . . . . . . . . . . . . . . . . . . . 112.3 An apparent asymmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3 The equivalence principle 163.1 The generalized principle of relativity . . . . . . . . . . . . . . . . . . . . . . 163.2 The 1907 review paper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.3 Reversing the logic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.4 The elevator thought experiment . . . . . . . . . . . . . . . . . . . . . . . . . 203.5 “The happiest thought of my life” . . . . . . . . . . . . . . . . . . . . . . . . 21

4 The clock-in-the-box thought experiment 224.1 The great debate on the foundations of quantum mechanics . . . . . . . . . . 224.2 Einstein’s proposal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234.3 Bohr’s rejection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

II The epistemological problem 27

5 A classification of thought experiments 285.1 What do the four thought experiments of Einstein have in common? . . . . . 285.2 What is the main difference between the thought experiments? . . . . . . . . 28

6 Norton’s argument view 296.1 What are thought experiments? . . . . . . . . . . . . . . . . . . . . . . . . . . 296.2 Two epistemic resources of thought experiments . . . . . . . . . . . . . . . . . 306.3 A comparison with the actual practice . . . . . . . . . . . . . . . . . . . . . . 31

7 Brown’s Platonism 327.1 An a priori view of (some) thought experiments . . . . . . . . . . . . . . . . . 327.2 Intellectual perception . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337.3 Reviewing the epistemology of Platonic thought experiments . . . . . . . . . 35

Conclusion 36

2

Introduction

Thought experiments are experiments carried out only in the imagination. They provideus new understanding of the world, just by thinking. This is why thought experiments arephilosophically interesting in their own right. Thought experiments do not seem to fit in thestandard empirical view of acquiring knowledge. According to empiricists we can only learnabout the world via sensory experience. Physical experiments, for example, can provide usnew knowledge of reality because they involve interacting with reality. In contrast, thoughtexperiments seem problematic because the source of the knowledge which they produce isunclear. It seems one can start from a position of ignorance, sit and think, and gain newknowledge, despite the input of no new empirical data.1 But how can we learn about reality,just by thinking?2 My concern in this thesis is restricted to this one question, which, insecondary literature, is called the epistemological problem of thought experiments:3

The epistemological problem. Thought experiments are supposed to give us newknowledge of the natural world. How is this possible?

This problem is urgent, since most philosophers agree that thought experiments often produceaccurate knowledge. The prominent philosopher of science Thomas Kuhn has stressed this:“Thought experiments have more than once played a critically important role in the devel-opment of physical science. The historian, at least, must recognize them as an occasionallypotent tool for increasing man’s understanding of nature.”4

In this bachelor thesis, I will restrict myself to thought experiments in science, and es-pecially to thought experiments in Einstein’s work. Albert Einstein (1879-1955) was one ofthe greatest thought experimenters. His simple, but profound thought experiments had anenormous influence on physics. The well-known elevator thought experiment, for example,is an argument for the equivalence of an uniformly accelerating frame and a frame at restin a homogeneous gravitational field. It is this equivalence principle that led Einstein to ascientific breakthrough: the general theory of relativity.

In my search for a solution to the epistemological problem, I will try to do justice to thescientific practice. I realize the epistemological problem is a very challenging subject, whichcannot be fully grasped in such a short time. It is especially challenging since it is not anisolated topic, which only deals with thought experiments; it is related instead to the mainquestions of epistemology: what is knowledge? How do we acquire knowledge? How cancertain knowledge be justified? Therefore, for a fully satisfactory view, one should actuallytake the entire history of philosophy into account. That being said, by reading Bruno Latour,I became convinced that it is nevertheless possible to treat a big philosophical issue by lookingat what scientists do. Therefore, I will start with some examples of thought experiments andtry to discover a general pattern.

In Part I, I will address four of Einstein’s thought experiments: the thought experimentconcerning an observer who pursues light beam (chapter 1); the moving magnet and conductorthought experiment (chapter 2); the elevator thought experiment (chapter 3); and the clock-in-the-box thought experiment (chapter 4). They provide a variety of examples in the sensethat they describe different topics, ranging from quantum mechanics to relativity theory.

1Cooper (2005), p. 3282Brown (2010)3Norton (2004b), p. 11394Kuhn (1964), p. 240

3

After discussing these examples of thought experiments, I will focus on the epistemologicalproblem in Part II. There is a lively debate in the philosophy of science about the epistemo-logical problem and there is an array of different types of views. I will discuss two recentresponses: John Norton’s argument view (chapter 6) and James Brown’s Platonism (chapter7). These views should explain where the physical knowledge in Einstein’s thought experi-ments comes from. As it suits a down to earth philosopher of science, I will put this to apractical test. I will apply their solutions to the four discussed examples and compare themwith each other. Eventually, the scientific practice decides which view is the best answer tothe epistemological problem.

4

Part I

Thought experiments in practice

In part I, I will discuss four thought experiments in Einstein’s work. I will explore theirphysical relevance, by putting them in a context, and I will unfold the arguments hiddenin these thought experiments. One could dispute whether the four examples of thoughtexperiments really are thought experiments. This depends, of course, on the definition ofthought experiment to which one adheres. I will only examine thought experiments of Einsteinwhich are treated as such in secondary literature.

To start with, I will describe Einstein’s first thought experiment. At the age of sixteenhe imagined what would happen if we could pursue a beam of light (chapter 1). The secondthought experiment deals with an extraordinary coincidence in electrodynamics. A movingmagnet passing a stationary conductor turns out to produce the same electric current ascreated in a conductor, which moves relative to a magnet at rest. This insight eventually ledEinstein to the special theory of relativity (chapter 2). Thirdly, I will discuss the elevatorthought experiment and its result: the equivalence principle. This principle was the startingpoint for Einstein’s general theory of relativity (chapter 3). The last thought experiment ispart of the great debate between Einstein and Bohr on the foundations of quantum mechanics.Einstein introduced the clock-in-the-box thought experiment during the Solvay Conference of1930 as an argument against the uncertainty principle for energy and time. Niels Bohr, thefounding father of the Copenhagen interpretation of quantum mechanics, showed, however,that Einstein’s argument was flawed (chapter 4).

5

1 Chasing the light

1.1 A childlike thought experiment

At the age of sixteen, Einstein imagined what would happen if one follows a light beam withthe speed of light. He later recalled that this thought experiment already contained the germof the great discovery he made ten years later: special relativity.5 “This was the first childlikethought experiment related to the special theory of relativity.”6 Despite it being “kindlich”according to Einstein, the thought experiment is more difficult than it appears at first sight.Since there are only three short, unclear statements left – dating from twenty, forty and fiftyyears after the event – it is difficult to grasp what Einstein intended with his line of thought.It could be said there are as much interpretations as authors who wrote about it.

Although the three accounts maybe sketchy and unclear, I will try to make sense of thethought experiment by putting Einstein’s accounts in their context. I will argue that thethought experiment leads to the compatibility of the two assumptions of special relativity:the constancy of the speed of light and the principle of relativity. To reach this conclusion,I will explore Einstein’s presentation of the thought experiment in his ‘AutobiographicalNotes’ from 1949 thoroughly. Since this is the best-known exposition and, presumably, theone Einstein drafted most cautiously, I will take this presentation as the canonical version ofthe thought experiment.7 I would like to emphasize, though, my interpretation is just that:an interpretation. I am aware of the fact that I try to reconstruct something in a rationalmanner which may not have started so rationally. In one of his accounts of the thoughtexperiment, Einstein admits this: “Discovery is not a work of logical thought, even if the finalproduct is bound in logical form.”8

1.2 The search for an universal principle

In his ‘Autobiographical Notes’ Einstein recalled that, at the beginning of the twentieth cen-tury, he was looking for an “universal formal principle” which could lead to true knowledge.9

Inspired by Planck’s postulate that electromagnetic energy can only be emitted and absorbedin ‘quanta’ of magnitude hν, Einstein searched for an adequate theory of matter, radiationand electricity. Neither classical mechanics nor Maxwell’s electrodynamics could fill this gap:they were in contradiction with Planck’s postulate. Despite Einstein’s successes in the earlydevelopments of quantum mechanics, especially his hypothesis that the energy of light quantawas quantized itself, he became despaired by “the possibility of discovering the true laws bymeans of constructive efforts based on known facts”.10 Therefore, he switched his attentionto finding first principles.

The field he would use as a model was thermodynamics, since it had a firm foundationupon which the rest was built. “The general principle was there given in the theorem: thelaws of nature are such that it is impossible to construct a perpetuum mobile (of the firstand second kind).”11 Was there another such universal principle upon which one could rely

5Einstein (1949), p. 536Einstein (1956), p. 107In this choice I follow Norton (2010), p. 38Einstein (1956), p. 109Einstein (1949), p. 53

10Idem11Idem

6

in the search for a new theory? In his official autobiography Einstein stated that the thoughtexperiment of frozen light, among other things, helped him finding this principle:12

“After ten years of reflection such a principle resulted from a paradox upon which I hadalready hit at the age of sixteen: If I pursue a beam of light with the velocity c (velocityof light in a vacuum), I should observe such a beam of light as a spatially oscillatoryelectromagnetic field at rest. However, there seems to be no such thing, whether onthe basis of experience or according to Maxwell’s equations. From the very beginning itappeared to me intuitively clear that, judged from the standpoint of such an observer,everything would have to happen according to the same laws as for an observer who,relative to the earth, was at rest. For how, otherwise, should the first observer know, i.e.,be able to determine, that he is in state of fast uniform motion?

One sees that in this paradox the germ of the special relativity theory is alreadycontained. Today everyone knows, of course that all attempts to clarify this paradoxsatisfactorily were condemned to failure as long as the axiom of the absolute character oftime, viz., of simultaneity, unrecognizedly was anchored in the unconscious. Clearly torecognize this axiom and its arbitrary character really implies already the solution of theproblem.”13[my italics, MRV]

How does this thought experiment work? It begins with the hypothetical situation of pursuinga light wave with the velocity of light c. A light wave is a sinusoidal oscillation of an electric andmagnetic field, whose waveform propagates at the speed of light. If one were to catch a lightwave and move with it, like a surfer catches a water wave, he would find a frozen light wave.14

The beam of light would then appear as a spatially oscillating static electromagnetic field andits wave properties would vanish. This time-independent wave field according to Einstein,however, does not exist, because it is never experienced and at variance with Maxwell’stheory.15

If the thought experiment were just a reductio ad absurdum argument, then its conclusionwould be that an observer can never reach the speed of light. The assumption (chasing after alight wave) leads to a contradiction (time-independent light wave), thus the assumption turnsout to be false, due to the modus tollens in classical logic. Although it is a true statementthat one cannot travel with the speed of light, because it would require an infinite energy, it isnot the point Einstein wanted to make. He stated clearly that an universal principle resultedfrom the paradox and that the problem can be solved by giving up the absolute character oftime.

1.3 The paradox

Before I will come to the point which Einstein wanted to make, I will quote another passage– often overlooked by other authors – where he defined the paradox contained in the thoughtexperiment:

“The above paradox may then be formulated as follows. According to the rules of con-nection, used in classical physics, of the spatial co-ordinates and of the time of events inthe transition from one inertial system to another the two assumptions of

(1) the constancy of the light velocity

12Einstein (1989), Vol. 2, xxi-xxii13Einstein (1949), p. 5314Norton (2010), p. 415I will leave aside whether these are convincing arguments.

7

(2) the independence of the laws (thus specially also of the law of the constancy of thelight velocity) of the choice of the inertial system (principle of special relativity)

are mutually incompatible (despite the fact that both taken separately are based onexperience).”16

According to Einstein, the paradox of the thought experiment consists of the incompatibilityof the two assumptions (1) and (2). But why is the principle of relativity incompatible withthe constancy of the velocity of light in classical physics? Einstein suggests it has somethingto do with “the rules of connection, used in classical physics, of the spatial co-ordinates andof the time of events in the transition from one inertial system”. These “rules of connection”,to which Einstein is referring, are the Galilean transformations, used in Newtonian physicsto transform coordinates of one inertial reference frame to another. I will show that theincompatibility in classical physical follows from the Galilean transformations.

First, it can be shown that these transformations entail that Newton’s laws of mechanics, ifvalid in one inertial system, must hold for all inertial systems. Thus, Galilean transformationsimply the classical principle of relativity.

Second, these transformations embody the intuitive notion of addition and subtraction ofvelocities, called ‘Galileo’s velocity addition rule’. A simple example can show how this ruleworks. Suppose a man walks 5 km/h down the corridor of a train going 60 km/h; his netspeed relative to the earth is intuitively 65 km/h. So the speed of A (man) with respect to C(earth) is equal to the speed of A relative to B (train) plus the speed of B relative to C:17

vAC = vAB + vBC . (1.1)

If A is a light beam coming from a flashlight on the train, then, according to Galileo, itsspeed relative to the ground would be greater than its speed with respect to the train. Inthis example, the speed of light is not constant. In general, Galileo’s velocity addition rule– and also his transformation laws and principle of relativity, for they are intertwined – is incontradiction with the assumption on the constancy of the velocity of light. Thus, in classicalphysics assumptions (1) and (2) are incompatible. If one assumption holds, the other doesnot.

But why are the two assumptions incompatible in this particular thought experiment?The answer to this question depends on the interpretation of the first assumption. Theassumption on the constancy of the light velocity can be expressed in two ways. In the firstpaper on special relativity Einstein defined this principle as follows: “Any ray of light movesin the ‘stationary’ system of co-ordinates with the determined velocity c, whether the raybe emitted by a stationary or by a moving body.”18 Later on, the assumption was put in adifferent way, namely that the speed of light is the same for all inertial observers. There aregood reasons to think that Einstein had the first expression in mind when he performed thisthought experiment. For one thing, in the 1905 paper, ten years later after the event, thelight velocity is consistently regarded as “independent of the state of motion of the emittingbody”.19 Therefore, I will also interpret the constancy of the light velocity in this way.

16Einstein (1949), pp. 55 and 5717Griffiths (1981), p. 48218Einstein (1905), p. 4119Idem, p. 38

8

Suppose an observer, who travels with the speed of light, creates a light beam with a flashlight.One would expect that the light beam travels with the speed of light. However, the observeris convinced that the beam does not propagate at all, but is at rest. Furthermore, if the speedof the observer would decrease, then the speed of the light beam with respect to the observerwould increase. In this slightly different version of the thought experiment, the results of themeasurements of the speed of light depend on the velocity of the emitting body. Therefore,the velocity of the light beam is not constant and the first assumption is not satisfied.

However, the second assumption (principle of relativity) holds always with respect toall inertial systems. This is reflected in Einstein’s statement: “From the very beginningit appeared to me intuitively clear that, judged from the standpoint of such an observer,everything would have to happen according to the same laws as for an observer who, relativeto the earth, was at rest.”20 Therefore, the assumptions (1) and (2) do not hold simultaneouslyin this hypothetical situation. The thought experiment is an example of the incompatibility ofthe constancy of the light velocity and the principle of relativity in classical electrodynamics.The incompatibility constitutes a paradox, because it is an apparent contradiction, as I willshow in the next section.

1.4 Towards the special theory of relativity

The ‘classical’ argument for the incompatibility of the constancy of the light velocity andthe principle of relativity is, of course, rejected by the special theory of relativity. In specialrelativity, the constancy of the light velocity and the principle of relativity are both regardedas universal postulates. What is more, the entire theory of special relativity can be derivedfrom these two assumptions. In the 1905 paper Einstein stated that the incompatibility ofthese two assumptions was only an apparent contradiction:

“We will raise this conjecture (the purport of which will hereafter be called ‘principleof relativity’) to the status of postulate, and also introduce another postulate, which isonly apparently irreconcilable with the former, namely, that light is always propagated inempty space with a definite velocity c which is independent of the state of motion of theemitting body. These two postulates suffice for the attainment of a simple and consistenttheory of the electrodynamics of moving bodies based on Maxwell’s theory for stationarybodies.”21 [my italics, MRV]

How did Einstein reconcile the two postulates? He recognized that the Galilean transforma-tions – from which the incompatibility resulted in classical physics – break down at speedsapproaching the speed of light. Therefore, he replaced them with another set of rules relatingtime and space coordinates between two coordinate systems: the Lorentz transformations.Furthermore, he replaced Galileo’s velocity addition rule with his own rule:22

vAC =vAB + vBC

1 + vABvBC/c2. (1.2)

The Lorentz transformations and Einstein’s velocity addition rule make the principle of rel-ativity and the principle of the constancy of the light velocity compatible. But, as a conse-quence, these rules also alter our notions of space and time radically. This is expressed in thefollowing quote from the ‘Autobiographical Notes’:

20Einstein (1949), p. 5321Einstein (1905), p. 3822Griffiths (1981), p. 482

9

“The insight which is fundamental for the special theory of relativity is this: The assump-tions (1) and (2) are compatible if relations of a new type (‘Lorentz-transformation’) arepostulated for the conversion of co-ordinates and the times of events. With the given phys-ical interpretation of co-ordinates and time, this is by no means merely a conventional step,but implies certain hypotheses concerning the actual behavior of moving measuring-rodsand clocks, which can be experimentally validated or disproved.

The universal principle of the special theory of relativity is contained in the postulate:The laws of physics are invariant with respect to the Lorentz-transformations (for thetransition from one inertial system to any other arbitrarily chosen system of inertia).This is a restricting principle for natural laws, comparable to the restricting principle ofthe non-existence of the perpetuum mobile which underlies thermodynamics.”23

In my view, this quotation should be related to the thought experiment. Other authors thinkthat the description of the thought experiment is restricted to the quote in section 1.2. But, inthat paragraph Einstein clearly states that an universal principle resulted from the thoughtexperiment. In my opinion, the thought experiment leads to the compatibility of the twopostulates of special relativity, which can be combined into one universal principle, namelythat “the laws of physics are invariant with respect to the Lorentz-transformations”24. HowEinstein reached this conclusion can only be guessed, since he did not explicitly explain this.There is indeed a big gap between the situation in which an observer chases after a beam oflight and the concept of Lorentz invariance. But, in the following paragraph I will attemptto explain how Einstein, in my view, set up the argument of the thought experiment in the‘Autobiographical Notes’.

To summarize, at the beginning of the twentieth century Einstein was looking for anuniversal principle that could lead him to assured results. This principle follows from athought experiment which he already performed at the age of sixteen. He imagined whatwould happen if one pursues a light beam with the speed of light. The ‘classical’ answerwas that he would observe such a beam of light as a spatially oscillatory electromagneticfield at rest. This implies that the velocity of the light beam is not independent of the stateof motion of the emitting body. The law of the constancy of the light velocity is, thus,not satisfied in this hypothetical situation, while the principle of relativity is, because ofits universality. However, this reasoning is flawed, since a time-independent wave field doesnot exist. Therefore, we are led to the idea that the contradiction between the principle ofthe constancy of the speed of light and the principle of relativity is only apparent. This iscompatible with special relativity. This theory solves the paradox of the incompatibility of thetwo principles by positing the Lorentz transformations. Furthermore, the principles can becombined into one universal principle, which forms the conclusion of this thought experiment:the laws of physics are invariant with respect to the Lorentz transformations.

23Einstein (1949), p. 5724Idem

10

2 The moving magnet and conductor problem

2.1 Developing an ether free electrodynamics

The second thought experiment originates from Einstein’s paper ‘On the Electrodynamicsof Moving Bodies’ (June 1905), in which he posits – what would later be called – the spe-cial theory of relativity. For some years before the publication of this paper, he had beentrying to develop an electrodynamics of moving bodies that did not invoke an ether frameof reference. After vain attempts to modify the Maxwell-Lorentz equations or replace themwith an emission theory of light, he found that the correct way to approach the problemwas to radically change basic kinematical concepts, like simultaneity.25,26 These new physicalinterpretations followed naturally from two first principles: the principles of relativity andthe principle of the constancy of the light velocity. Einstein’s approach of developing an etherfree electrodynamics compatible with the principle of relativity turned out to be very fertile.

To enforce this new approach Einstein started the paper with considering a magnet andconductor in relative motion. Although this elementary thought experiment can be explicatedin one paragraph – as Einstein did at the beginning of ‘On the Electrodynamics of MovingBodies’ – it leads to the astonishing result that “the phenomena of electrodynamics as wellas of mechanics possess no properties corresponding to the idea of absolute rest”. This ideainspired Einstein to raise the principle of relativity to the status of an universal postulate.In an unpublished manuscript dating from 1920 he wrote: “The phenomena of electromag-netic induction compelled me to postulate the principle of (special) relativity.”27 Hence, themoving magnet and conductor thought experiment was crucial for the development of specialrelativity. I will show that it is not only an argument for the principle of relativity, but alsoagainst the ether theory.

In this chapter, I will first put the thought experiment in its context by stating clearly theproblem (“Schwierigkeit”28) Einstein dealt with in his 1905 paper. Secondly, I will explainthe moving magnet and conductor thought experiment. Finally, I will consider how thisparticular line of reasoning leads to new knowledge.

2.2 “The difficulty to be overcome”

In his 1905 paper, as well as in his 1907 and 1909 reviews of the theory, Einstein describedthe theory of special relativity as arising from the apparent conflict between the principle ofrelativity and the Maxwell-Lorentz theory of electrodynamics. While the principle of relativityentails the physical equivalence of all inertial frames of reference, the Maxwell-Lorentz theoryimplies the existence of a privileged inertial frame. This so-called ‘luminiferous ether’ wasthought of as an all-pervading medium through which light waves propagate. At the timewhen Einstein worked on the electrodynamics of moving bodies, there were several optical

25Einstein (1989), Vol. 2, pp. xxii and 26426In a footnote of an unpublished manuscript, entitled ‘Fundamental Ideas and Methods of the Theory of

Relativity, Presented as it Developed’, Einstein wrote: “The difficulty to be overcome then lay in the constancyof the velocity of light in vacuum, which I first thought would have to be abandoned. Only after groping foryears did I realize that the difficulty lay in the arbitrariness of the fundamental concepts of kinematics”. Thisexpresses the fact that he first explored the possibility of an emission theory of light. After abandoning thisattempt, he realized that previously tacitly accepted kinematical assumptions about space and time should beoverthrown. (Einstein (1989), Vol. 2, pp. 263-5)

27as cited in Einstein (1989), Vol. 2, p. 26228Einstein (1907), Vol. 2, p. 434

11

experiments, such as the Michelson-Morley experiment, trying to confirm the existence of theether. If the ether does not move together with matter, it should be possible to detect motionrelative to the ether rest frame, according to the theory. However, all attempts to observethe velocity of the earth through the ether by electromagnetic experiments failed.29

Several physicists, apart from Einstein, confronted this contradiction between theory andexperiment. Lorentz, for example, asserted that relative motion of the earth through the etheris in principle undetectable. To explain the failure of the negative ether drift experimentsto first order in v

c , Lorentz introduced the concept ‘local time’, which he considered as amathematical trick. In addition, after a new null-result to second order in v

c , he proposed thehypothesis of length contraction in the direction of motion. In 1904 he generalized his theoryto all orders in v

c by introducing a set of transformations for the time and space coordinates(soon called the Lorentz transformations by Poincare) and for the electric and magnetic fieldcomponents.30 In our modern view these attempts may seem as a desperate way to patch upthe ether theory, but for Lorentz it was unthinkable to reject the ether.31

Einstein was the first who took the difficulties concerning the ether at face value. Heinterpreted the absence of experimental evidence for an ether drift as an empirical confirmationof the principle of relativity in electrodynamics and optics.32 While Lorentz tried to reconcilethe experiments with his ether theory, Einstein disposed of it as “superfluous”.33 Accordingto the deviser of special relativity, there is no absolute rest frame, because all laws of physics– including that of electrodynamics and optics – are the same in all inertial systems. This isexpressed in the second paragraph of ‘On the Electrodynamics of Moving Bodies’:

“Examples of this sort, together with the unsuccessful attempts to discover any motion ofthe earth relatively to the ‘light medium’, suggest that the phenomena of electrodynamicsas well as of mechanics possess no properties corresponding to the idea of absolute rest.They suggest rather that, as has already been shown to the first order of small quantities,the same laws of electrodynamics and optics will be valid for all frames of reference forwhich the equations of mechanics hold good. We will raise this conjecture (the purport ofwhich will hereafter be called the ‘Principle of Relativity’) to the status of a postulate, andalso introduce another postulate, which is only apparently irreconcilable with the former,namely, that light is always propagated in empty space with a definite velocity c which isindependent of the state of motion of the emitting body. These two postulates suffice forthe attainment of a simple and consistent theory of the electrodynamics of moving bodiesbased on Maxwell’s theory for stationary bodies. The introduction of a ‘luminiferousether’ will prove to be superfluous inasmuch as the view here to be developed will notrequire an ‘absolutely stationary space’ provided with special properties, nor assign avelocity-vector to a point of the empty space in which electromagnetic processes takeplace.”34

29Einstein (1989), Vol. 2, pp. 254-530Unfortunately, Lorentz’s expression for charge density and current were incorrect, so his theory did not

completely exclude the possibility of detecting the ether.31Einstein (1989), Vol. 2, pp. 255-732Idem33Lorentz (1916, p. 230) himself gives a very appropriate account of the difference between Einstein and him:

“His [Einstein, MRV] results concerning electromagnetic and optical phenomena (...) agree in the main withthose which we have obtained in the preceding pages, the chief difference being that Einstein simply postulates

what we have deduced, with some difficulty and not altogether satisfactorily, from the fundamental equationsof the electromagnetic field. By doing so, he may certainly take credit for making us see in the negative resultof experiments like those of Michelson, Rayleigh and Brace, not a fortuitous compensation of opposing effects,but the manifestation of a general and fundamental principle.” [my italics, MRV]

34Einstein (1905), pp. 37-8

12

Einstein had two main reasons for his conviction that the principle of relativity is universallyvalid and the concept of the ether should be abandoned. The first reason involves the “un-successful attempts to discover any motion of the earth relatively to the ‘light medium’” andthe second was the existence of certain “asymmetries which do not appear to be inherent inthe phenomena”.35 As an example of such an asymmetry, he considered a system consistingof a magnet and conductor. In 1952 Einstein reconstructed the birth of special relativityas follows: “My direct path to the special theory of relativity was mainly determined bythe conviction that the electromotive force induced in a conductor moving in a magneticfield is nothing other than an electric field. But the result of Fizeau’s experiment and thephenomenon of aberration also guided me.”36 Therefore, the moving magnet and conductorthought experiment, which I will discuss in section 2.3, was most important for the discoveryof the theory of special relativity.

The special theory of relativity is not only a new theory about inertial frames of reference,but it is at the same time a new interpretation of the theory of electrodynamics. At firstsight, Einstein’s special relativity completely contradicts Maxwell-Lorentz electrodynamics,since the ether concept is essential to the latter theory, whereas it is abandoned by theformer. Instead of revisiting the very foundations of electrodynamics, Einstein made themcompatible with the principle of (special) relativity. In his attempt to achieve this, he wasnot only confronted with the problem of the ether, but also with another problem.

There seemed to be a conflict between Einstein’s ideas on relative motion and a particularconsequence of electrodynamics: the independence of the light velocity of the velocity ofthe source. The velocity of light must be the same in all inertial frames, according to thecombination of the two postulates of special relativity, but not (necessarily) according toMaxwell-Lorentz theory. The old light principle implied – before the rise of the special theoryof relativity – that light propagates through a fixed medium, with respect to which its speedshould be measured. This seemingly contradiction between the principle of relativity and theprinciple of the light velocity can be solved – as we saw in chapter 1 – by revising kinematicalconcepts, such as time, and by replacing Galileo’s velocity addition rule with Einstein’s. “Herecognized that this conflict involves previously tacitly accepted kinematical assumptionsabout temporal and spatial intervals, leading him to examine the meaning of the concept ofthe simultaneity of distant events. He defined simultaneity physically, and constructed a newkinematical theory based on the relativity principle and the light principle, thus resolving theapparent conflict between them.”37

Thus, Einstein was confronted with two problems while developing his electrodynamicsof moving bodies. Both dealt with the (in)compatibility of Maxwell-Lorentz electrodynamicswith the principle of relativity. The first was the conflict between the absolute rest frameof the ether and the principle of relativity. He solved this by indicating the light ether as“superfluous”. The most important reason for Einstein to do this was given by the magnetand conductor thought experiment. Secondly, the relativity principle was in apparent con-tradiction with the principle of the constancy of the light velocity. By revisiting kinematicalconcepts Einstein removed this second conflict, and, moreover, he took the two principles asstarting point for his further theory.

35Einstein (1905), pp. 37-8 and Pais (1982), p. 14036as cited in Einstein (1989), Vol. 2, p. 26237Idem, p. 265

13

2.3 An apparent asymmetry

The thought experiment concerning a magnet and conductor in relative motion is describedas follows in Einstein’s paper on the electrodynamics of moving bodies:

“It is known that Maxwell’s electrodynamics – as usually understood at the present time –when applied to moving bodies, leads to asymmetries which do not appear to be inherentin the phenomena. Take, for example, the reciprocal electrodynamic action of a magnetand a conductor. The observable phenomenon here depends only on the relative motionof the conductor and the magnet, whereas the customary view draws a sharp distinctionbetween the two cases in which either the one or the other of these bodies is in motion.For if the magnet is in motion and the conductor at rest, there arises in the neighbourhoodof the magnet an electric field with a certain definite energy, producing a current at theplaces where parts of the conductor are situated. But if the magnet is stationary andthe conductor in motion, no electric field arises in the neighbourhood of the magnet.In the conductor, however, we find an electromotive force, to which in itself there is nocorresponding energy, but which gives rise – assuming equality of relative motion in thetwo cases discussed – to electric currents of the same path and intensity as those producedby the electric forces in the former case.”38

In the first case, the magnet is moving and the conductor is at (absolute) rest. As the magnetflies by, the magnetic field in the conductor will change and this induces an electric field,according to Faraday’s laws. The resulting electric field produces a current in the conductor.The second case involves an identical magnet and conductor which is also identical in set-up asto the relative positions and velocities of both. So the magnet is now at (absolute) rest and theconductor is moving. As the conductor passes by the magnetic field, a motional electromotiveforce is established. This emf is due to the Lorentz force on charges in the conductor.39 Theemf generates an electric current in the conductor of the same size as in the first case. “Thepresence of the induced electric field (...) clearly distinguishes the second case from the firstaccording to the theory. However, as far as the observables are concerned – that is, the mea-surable current in the conductor – the two cases are indistinguishable. Thus the observablesare sensitive only to relative velocities, whereas the theory is sensitive to absolute velocitiesas well.”40 This leads to the conclusion that electrodynamics should do without the idea ofan absolute state of rest and that the principle of relativity ought to apply to electrodynamics.

Finally, let us apply the main question of this thesis to the magnet and conductor thoughtexperiment. In his paper ‘Thought Experiments in Einstein’s Work’ Norton (1991, pp. 135-6)gives an appropriate reconstruction of the thought experiment. According to him, the argu-ment starts with the case of electromagnetic induction. In this case classical electrodynamicstells two states of affairs apart, because of the existence of an absolute state of rest. Observa-tionally, however, the two cases concerning the magnet and conductor in relative motion areindistinguishable.41 Classical electrodynamics, therefore, violates the ‘verifiability heuristic’for theory construction, which entails that states of affairs which are not observationally dis-tinct should not be distinguished by the theory. Thus, absolute velocities should be eliminatedfrom the theoretical account of electromagnetic induction. Up until this point, however, we

38Einstein (1905), p. 3739Griffiths (1981), pp. 478-940Norton (1991), p. 13641Note that due to this reference to an observation of reality, the magnet and conductor thought experiment

is not just a concoction of the mind, but really provides accurate knowledge of the physical world.

14

are not justified to remove the absolute state of rest from all electromagnetic phenomena. Aninductive step is necessary to go from this concrete example to a general principle. Nortoncontinues: “This example [of electromagnetic induction, MRV] is typical since (a) there areother examples of this type and (b) there is a history of unsuccessful attempts to detect thisstate of rest by optical experiments. Therefore absolute velocities should be eliminated fromelectrodynamics.”42 This justifies the raising of the conjecture, namely that the principle ofrelativity is universally valid, to the status of a postulate.

42Norton (1991), p. 136

15

3 The equivalence principle

3.1 The generalized principle of relativity

In the years following Einstein’s important paper on special relativity, published in September1905, he attempted to extend the principle of relativity to accelerated reference systems. Byasking for this extension, he actually came upon the inclusion of the laws of gravitation inthe theory of special relativity.43 The key to the extension lay in the unexplained empiricalcoincidence of the equality of inertial and gravitational mass. To interpret and exploit thiscoincidence Einstein introduced a new and powerful physical principle in 1907, which he latercalled the ‘principle of equivalence’. The equivalence principle was a guiding principle indeveloping general relativity. Although Einstein did not finish his general theory of relativityimmediately after his discovery of the equivalence principle, this discovery can be marked asa clear starting point. It took him more than eight years to finish his theory. After a longroad, marked by trials, errors and long pauses, in November 1915 the structure of generalrelativity as we know it lay before him.44

For my inquiry it is interesting to note how Einstein discovered the equivalence principlein the first place. There is a large amount of papers and books where he argues for theequivalence principle, but all of them entail, more or less, the structure of a thought experi-ment. The way in which this is most commonly expressed in textbooks who try to explain theprinciple, is the ‘elevator thought experiment’. The elevator argument is the third exampleof a thought experiment invented by Einstein and I will discuss it in this chapter. Becauseof its fundamental importance for the transition from special relativity to general relativity,it’s probably Einstein’s most important thought experiment. To put the elevator thoughtexperiment in a historical context, I will also explore some of Einstein’s other phrasings ofthe equivalence principle.

3.2 The 1907 review paper

The equivalence principle appeared for the first time – though not by name – in a review articleon special relativity in 1907, called ‘On the Relativity Principle and the Conclusions Drawnfrom It’. In section V of the article, entitled ‘Principle of Relativity and Gravitation’, he raisedthe question: “Is it conceivable that the principle of relativity also applies to systems thatare accelerated to each other?” He answered positively to this question, “which must occurto everyone who has followed the applications of the relativity principle”45. The argumentgoes as follows. Suppose a reference frame S1 is accelerated in the x direction with a constantacceleration g. A second frame S2 is at rest in a homogeneous gravitational field whichimparts to all objects an acceleration −g in the x direction. Observationally there is no

43From his early publications on the equivalence principle, especially his first article on this subject datingfrom 1907, it is clear that the question of the extension came to Einstein’s mind before that of the inclusion.But in later works he seems to contradict himself. In an unpublished document from 1920 he wrote (Pais(1982), p. 178): “When, in 1907, I was working on a comprehensive paper on the special theory of relativityfor the Jahrbuch der Radioaktivitat und Elektronik, I had also to attempt to modify the Newtonian theory ofgravitation in such a way that its laws would fit in the theory.” Moreover, in the ‘Autobiographical Notes’Einstein recalled (1949, p. 63): “That the special theory of relativity is only the first step of a necessarydevelopment became completely clear to me only in my efforts to represent gravitation in the framework ofthis theory.” See for further discussions Pais (1982), pp. 178-9 and Einstein (1989), Vol. 2, p. xxix.

44Pais (1982), pp. 177-183 and Norton (1985), p. 20345Einstein (1907), Vol. 2, p. 476

16

distinction in any respect between S1 and S2. All bodies are, to wit, equally acceleratedin the gravitational field. By generalizing this mechanical equality, Einstein postulated thecomplete physical equivalence of a gravitational field and the corresponding acceleration of thereference frame. This is the so-called ‘equivalence principle’.46

This assumption extends the principle of relativity to the case of uniformly acceleratedmotion of the reference frame. This means the laws of physics take the same form in a uni-formly accelerating coordinate system as in a system at rest with a homogeneous gravitationalfield. Although the equivalence principle does not follow necessarily from experience, it hasan important heuristic value – as Einstein called it – namely it permits the replacement of ahomogeneous gravitational field by a uniformly accelerated reference system.47

How does the argument lead to new knowledge? Before I can answer this question, I willdiscuss the assumptions on which the argument is based. In section IV of the review paperEinstein stated that the argument was founded on the assumption of the exact physical equiv-alence of gravitational and inertial mass.48 Also in later accounts he continued to emphasizethe importance of this equality for the equivalence principle. In The Evolution of Physics, forexample, Einstein stated that the principle “rests on one very important pillar: the equiva-lence of gravitational and inertial mass. Without this clew, unnoticed in classical mechanics,our present argument would fail completely.”49 The reason for this failure is that withoutthe equality, there would be an observational difference between S1 and S2. A body withinertial mass ma, but different gravitational mass mg, would have a constant acceleration grelatively to S1. The same body, however, would experience a different acceleration relativeto S2, namely a = mg

mag, according to Newton’s second law. Furthermore, in this hypothetical

situation different bodies would fall freely relative to S2 with different accelerations, sincethey would all have a different ratio of gravitational to inertial mass. An observer would thenbe able to distinguish S1 from S2 and this is in contradiction with the equivalence principle.

Fortunately, however, differences between gravitational and inertial mass have never been– directly nor indirectly – observed. Einstein was definitely aware of this fact in 1907, be-cause he wrote in section IV of the review paper: “This proportionality between inertial andgravitational mass holds, however, without exception for all bodies with hitherto attained pre-cision, so we must assume the universality until proven otherwise” [my translation, MRV].50

Moreover, he definitely knew that the acceleration of different bodies in a gravitational fieldis independent of their mass. Thus, early on he was convinced of this experience based law(“Erfahrungsgesetz”).

In The Origins of the General Theory of Relativity Einstein stated, however, that at thattime he was not yet aware of the experiments of Lorand Eotvos.51 Eotvos researched the pro-portionality of inertial and gravitating masses with torsion pendulums. In 1889 he presentedhis result: the difference in the gravity of bodies should be less than 1/20,000,000.52,53

46Pais (1982), pp. 179-18047Einstein (1907), Vol. 2, p. 47648Idem, pp. 465-649Einstein (1938), p. 21750Einstein (1907), Vol. 2, p. 46551Einstein (1989), Vol. 2, p. 27452Eotvos (1890), pp. 65-8. The short presentation was held at the Hungarian Academy of Sciences in 1889,

but originally published in 1890 in the Mathematical and Natural Science Proceedings of Hungary.53Due to the development of technology, the equality has now been tested with even more accuracy, namely

10−13. (Hartle (2003), pp. 107-113)

17

Although Einstein was not aware of Eotvos results in 1907, later he emphasized the impor-tance of such an experiment. In a letter to Wilhelm Wien, dated 10th July 1912, he evenproposed an experiment by himself to verify the precise proportionality between inertial andgravitational mass.54 The experiment deals with alpha decay of uranium to lead. Einsteinpredicted a difference between the inertial and gravitational mass of lead – if inertial and grav-itational mass were not equal in principle – because the decay products would have gainedenergy at the expense of the inertial mass of lead, according to his famous equation E = mc2.He requested Wien to perform this experimentum crucis. The letter testifies that Einsteinwas not aware of the Eotvos experiment when he formulated the principle of equivalence,because his method was comparable to that of Eotvos. Moreover, it shows once again thathe was not a theoretical physicist living in an ivory tower, but also wanted to test his theoriesagainst reality.55

Thus I conclude that Einstein assumed, based on a strong conviction, that inertial and gravi-tational mass are equal under all circumstances. He knew from experience they were roughlyequal in certain situations, but suspected that the proportionality of inertial and gravitationalmass was exact for all bodies. By raising this conjecture to the status of a general principleor, what is more, a law of nature, Einstein made the first step towards the new knowledgecontained in the equivalence principle.

In this move of Einstein one could catch a glimpse of his idea that the equality of in-ertial and gravitational mass is no coincidence. At the beginning of the article ‘Outline ofa Generalized Theory of Relativity and of a Theory of Gravitation’ Einstein stated it veryclear: “The theory [of general relativity, MRV] expounded in what follows derives from theconviction that the proportionality between the inertial and the gravitational mass of bodiesis an exactly valid law of nature that must already find expression in the very foundationof theoretical physics.”56 Hence, he was looking for a fundamental principle from which theequality follows naturally. In the next section I will discuss Einstein’s explanation of theequality.

3.3 Reversing the logic

After the 1907 review paper, Einstein did not raise the question of the further extensionof the principle of relativity to nonuniform acceleration until 1911. In that year he hadbecome dissatisfied with his presentation of 1907 and, moreover, he realized that one of themost important consequences of the equivalence principle could be tested experimentally. Hepredicted that bending of light by the sun is detectable. This is already expressed in the titleof the 1911 paper: ‘On the Influence of Gravitation on the Propagation of Light’. I will comeback to the consequences of the equivalence principle in section 3.5.

In the 1911 paper Einstein started with the same reference frames S1 and S2 as in the 1907paper, but the argument for the equivalence principle is presented in a slightly different way.This new twist has profound consequences for his search for the theory of general relativity.The argument for the equivalence principle begins with the observation of the equivalenceof Newton’s mechanical laws in both frames. This will not have any deeper significance,however, unless the systems S1 and S2 are equivalent with respect to all physical processes,

54Einstein (1912), Vol. 5, p. 49755From Einstein’s first real scientific paper onwards this is a recurring theme in his work.56Einstein (1913), Vol. 4, p. 304

18

that is, unless the laws of nature with respect to S1 are in entire agreement with those withrespect to S2.

This assumption of the exact physical equivalence of S1 and S2 (‘the equivalence principle’)has two important theoretical consequences. Firstly, it makes it impossible to speak of anabsolute acceleration of the reference system, just as the relativity theory forbids us to speakof the absolute velocity of a system. Secondly, the equal fall of all bodies in a gravitational fieldbecomes self-evident. For if we assume that S1 and S2 are physically equivalent, that is, if weassume that we may just as well regard the system S1 as being in a space free from gravitationalfields and S2 as being uniformly accelerated, then we can transform properties of processes inS1 to corresponding processes in S2, and the other way around. For example, relatively to S1,all bodies sufficiently distant from other bodies move with the same acceleration, independentof their particular material composition. Then, due to the equivalence principle, all bodieswith respect to S2 are also equally and uniformly accelerated. The equal fall of all bodies ina gravitational field could, thus, be regarded as a consequence of the equivalence principle,rather than an unexplained law based on experience.57

The remarkable twist in this argument is that the equality of gravitational and inertialmass follows from the equivalence principle, rather than the other way around. Insteadof following the reasoning – equal fall of masses due to gravity ⇒ equivalence of uniformlyaccelerating frame and system with homogeneous gravitational field – he reversed the directionof the arrow of logic.58 This means that Einstein explained the equality of inertial andgravitational mass as an expression of a far more general principle. Thus, Einstein obtainednew knowledge by (1) generalizing observations to first principles, and (2) reversing the logicsuch that earlier observations are put in a new, wider perspective.

This reminds us of the way Einstein obtained new knowledge with the moving magnetand conductor thought experiment in chapter 2. I will show that the same two steps canbe recognized in the 1905 paper on special relativity. (1) In this paper he started withthe conjecture that phenomena concerning moving bodies in electrodynamics do not appearaccidentally. These phenomena led him to the idea that the same laws of electrodynamicsand optics are valid for all inertial frames of reference. Although this idea applies only to oneparticular field of physics, Einstein was convinced that it holds for all observable phenomena.Therefore, he raised his conjecture to the status of a general postulate. He assumed that thelaws of physics are the same for all inertial reference systems. This corresponds to raising theequivalence of a gravitational field and the corresponding accelerated frame to an universalprinciple. (2) Due to the positing of the principle of relativity, the reciprocal electrodynamicaction of a magnet and conductor could now be explained as a special case of it. Again,this corresponds to the explanation of the equality of gravitational and inertial mass as anexpression of the equivalence principle. Thus, the analogy with the moving magnet andconductor experiment is very appropriate. It seems that I have discerned a typical methodof Einstein which he used to discover new theories.

57Einstein (1911), pp. 99-10158Pais (1982), pp. 194-6

19

3.4 The elevator thought experiment

In contrast with the previously discussed presentations of the equivalence principle, whichcontained clear and simple arguments, is the following more elaborate and imaginary formu-lation of the principle: the elevator thought experiment.59 My description of this thoughtexperiment is based on two of Einstein’s books: Relativity: The Special and The GeneralTheory (1920) and The Evolution of Physics (1938).

Imagine an elevator in a region of free space, remote from gravitational source masses.A physicist inside the elevator is equipped with apparatus to perform physical experiments.Since gravity naturally does not exist for the observer, he floats around inside the room. Thereis a rope attached on top of the elevator, and suddenly a ‘being’ begins to pull at this with aconstant force. It is immaterial to us what kind of being this is and how it exerts a force. Theelevator, together with its contents, begin to move ‘upwards’ with a constant acceleration.Interested in what is happening, the man inside the box starts to perform experiments duringthis acceleration. He takes a handkerchief and a watch from his pocket and drops them atthe same time. What happens to these two bodies? More importantly, how do outside andinside observers interpret this experiment?

From the perspective of an outside observer, the elevator moves with a uniform accelera-tion, because a constant force is acting. If a body is left free, it soon collides with the floorof the elevator, since the floor moves towards the body. This happens exactly in the sameway for a watch and a handkerchief. But how does the observer inside the elevator regardthe process? He also convinces himself that the watch and handkerchief always fall towardsthe floor with the same acceleration. Whatever kind of body he may happen to use for thisexperiment, they all land on the floor at the same time. This equal fall of bodies remindshim – as befits a physicist – of free fall on Earth. Therefore, the inside observer comes tothe conclusion that gravity is forcing the watch and handkerchief to fall. He and the elevatorare in a gravitational field which is constant with regard to time. Maybe, he is puzzled fora moment as to why the elevator does not fall in the gravitational field. Then, however, hediscovers the rope on top of the elevator and concludes, consequently, that the elevator issuspended at rest in the gravitational field.

Then, Einstein asked: “Ought we to smile at the man [inside the elevator, MRV] and saythat he errs in his conclusion?”60 His answer: no. The inside observer’s mode of grasping thesituation neither violates reason nor known mechanical laws. The descriptions of the insideand outside observer are quite consistent, and there is no possibility of deciding which of themis right. This thought experiment shows that a consistent description of physical phenomenain two different frames of reference is possible, even if they are not moving relative to eachother with constant velocity. Einstein had thus good grounds for extending the principle ofrelativity to include system of reference which are accelerated with respect to each other, andas a result he had gained a powerful argument for a general postulate of relativity.61

59Another well-known presentation is to be found in Einstein’s paper ‘The Foundation of the General Theoryof Relativity’ (1916). In my view the small section in this paper on the equivalence principle is just a repetitionof earlier accounts, so I will not discuss it here.

60Einstein (1920), p. 8961Idem, pp. 87-92 and Einstein (1938), pp. 214-222

20

3.5 “The happiest thought of my life”

In retrospect, Einstein called the equivalence principle, in a paper which he wrote under theauthority of Nature but which was never published, “the happiest thought” of his life:

“Then there occurred to me the ‘glucklichste Gedanke meines Lebens’, the happiestthought of my life, in the following form. The gravitational field has only a relativeexistence in a way similar to the electric field generated by magnetoelectric induction.Because for an observer falling freely from the roof of a house there exists – at least in hisimmediate surroundings – no gravitational field. Indeed, if the observer drops some bodiesthen these remain relative to him in a state of rest or of uniform motion, independent oftheir particular chemical or physical nature (in this consideration the air resistance is, ofcourse, ignored). The observer therefore has the right to interpret his state as ‘at rest’.”62

A free-falling observer cannot, in principle, distinguish whether he is falling in a gravitationalfield or whether he is at rest in empty space far from any source of gravitation. The ob-server could think: “Let’s put it to a test. I will drop some bodies with different massesand observe how fast they will fall.” But all bodies will fall with the same acceleration (forthe sake of argument air resistance is ignored), according to Galileo’s observation. So thisparticular experiment is not helpful for the ‘weightless’ observer. Einstein claimed there isno experiment at all that can distinguish a free-falling system from a system at rest. Theobserver has the right to consider his state as one of rest and his environment as field-free rel-ative to gravitation. In effect, the gravitational field has vanished in the freely falling frame.63

Now that I have introduced some of Einstein’s phrasings of the equivalence principle, onecan ask for its (direct) consequences. Due to the principle, Einstein could draw conclusionsabout the effects of a homogeneous gravitational field on physical processes by analyzingcorresponding processes in a uniformly accelerated reference frame. Already in the 1907review paper, he foresaw four consequences of the equivalence principle: the gravitationalred shift; the invariance of Maxwell’s equations; bending of light; and gravitational energy= mc2. I will discuss the bending of light shortly, because this prediction was very importantfor further developments in general relativity and it made Einstein suddenly famous in 1919.With a simple extension of the elevator thought experiment one can show that light rays arebent by a gravitational field.

Suppose a light ray enters the elevator of section 3.4 horizontally through a side windowand reaches the opposite wall after a very short time. Since the elevator is acceleratingupward, the floor is rushing up to meet the light beam and the path of the beam appears toan inside observer to be bent downward. Due to the equivalence principle, one can replacethe accelerated elevator with an elevator at rest in a gravitational field. Since there is no wayto distinguish between these to cases, one must conclude that light will be bent downward inthe presence of a gravitational field.64,65

62as cited in Pais (1982), p. 17863Einstein (1920), pp. 87-9264Ryden (2003), pp. 27-30 and Einstein (1938), pp. 219-2265Unfortunately, the bending of light according to Einstein’s calculations from 1907 and 1911 based on the

equivalence principle, was two times smaller than the real effect. In 1915 he calculated the bending of lightagain with his new general theory of relativity. He realized that curved space provided the other half of theeffect.

21

4 The clock-in-the-box thought experiment

4.1 The great debate on the foundations of quantum mechanics

The last thought experiment I will discuss is an experiment on quantum mechanics. It iswidely known that Einstein – although he made important contributions to the old quantummechanics, especially by introducing the light quantum – was highly skeptical towards thetheory. While quantum mechanics was considered complete by most physicists in the 1930s,Einstein disagreed with this collective opinion throughout his life.

Einstein’s dissent towards quantum mechanics went through different stages. His first,and most famous, disapproval dates from December 1926, when in a letter to Max Born hewrote: “Quantum mechanics is certainly imposing. But an inner voice tells me that it is notyet the real thing. The theory says a lot, but does not really bring us any closer to the secretof the ‘old one’. I, at any rate, am convinced that He is not playing dice.”66 Here, Einsteinrejected Born’s statistical interpretation of the wave function. Born held that the materialworld consisted of particles which behaved purely random; yet Einstein believed that everyevent must have a cause, and constantly searched for a deeper explanation to bring order intothe chaotic subatomic world.

In the period of 1927-1931 Einstein was mainly concerned with proving the inconsistency ofthe so-called ‘Copenhagen interpretation’ of Niels Bohr and his followers. The debate betweenEinstein and Bohr was especially lively at the Solvay Conferences of 1927 (on electrons andphotons) and 1930 (on magnetism). All the pioneers of quantum mechanics were presentat the conferences and discussed the foundations of the theory. In the corridors Einsteinproposed some ingenious thought experiments, mainly against quantum indeterminism. Thethought experiment of this chapter was introduced by Einstein during the Solvay Conferenceof 1930. It was a profound attack on Heisenberg’s uncertainty principle for energy and time.Bohr reflected on Einstein’s arguments with great care and came up with a solution thatcleared the matter up in detail. The founder of the theory of relativity tried very hard, butnever succeeded in showing that quantum mechanics contained contradictions.

In 1931 Einstein surrendered, but not completely. In a nomination for a Nobel Prize toHeisenberg and Schrodinger he wrote: “I am convinced that this theory contains a part of theultimate truth.”67 He had accepted that quantum mechanics was a successful and consistenttheory. However, he was and forever remained deeply convinced that it was not the ‘whole’truth. In ‘On the Method of Theoretical Physics’ he said of the Schrodinger wave functions:“Those functions are only supposed to determine the mathematical probabilities to find suchstructures, if measurements are taken, at a particular spot or in a certain state of motion.This notion is logically unobjectionable and has important success to its credits. (...) I believein the possibility of a model of reality – that is to say, of a theory which represents thingsthemselves and not merely the probability of their occurrence.”68

From 1931 on, for Einstein the issue was no longer the consistency of quantum mechanicsbut rather its completeness.69 Together with Boris Podolsky and Nathan Rosen he publisheda paper in 1935, called ‘Can Quantum-Mechanical Description of Physical Reality Be Consid-ered Complete?’. With a subtle thought experiment the three physicists tried to demonstrate

66Born (1971), p. 9167as cited in Pais (1991), p. 42868Einstein (1954), pp. 275-669Pais (1982), p. 449

22

that quantum theory is inconsistent, i.e. that it does not fully capture physical reality. Theirpaper created a stir among other physicists and has played a major role in general philo-sophical discussions.70 Three months later Einsteins’ scientific opponent Bohr submitted hisreply to the EPR paper. His article was also called ‘Can Quantum-Mechanical Descriptionof Physical Reality Be Considered Complete?’ and his answer was an indubitably ‘Yes’. Hedid not believe that the EPR paper called for any change in the interpretation of quantummechanics. Most physicist nowadays agree with this opinion. The 1935 papers mark the endof the Bohr-Einstein debate insofar as it appeared in the scientific literature. It could bestated that no agreement was ever reached between these two great physicist.71

In this chapter I will analyse the clock-in-the-box thought experiment. I will first presentEinstein’s proposal at the Solvay conference of 1930 and then discuss Bohr’s response. Al-though there are no official records of the discussions between Bohr and Einstein during thisconference, I will try to reconstruct it by using Bohr’s essay ‘Discussion with Einstein onEpistemological Problems in Atomic Physics’ (1949). Finally, I will address the epistemo-logical problem. At first sight it seems that the problem is not applicable to this thoughtexperiment, since Einstein’s argument is invalid and does not lead to new knowledge. ButI will argue that the structure of Einstein’s line of thought and Bohr’s reply do suggest asolution to the epistemological problem.

4.2 Einstein’s proposal

The argument of Einstein’s clock-in-the-box thought experiment goes as follows. Considera box with a hole in its side, which can be open or closed by a shutter (see figure 1). Theshutter is controlled by a clockwork inside the box, so it can be opened at any chosen time.The box is filled with radiation. Now, the clockwork is set to open the shutter for a very shortperiod of time, during which one photon escapes through the hole. This implies that the timeof release of the photon is known with great accuracy. Moreover, it would also be possibleto measure the energy of the photon with any accuracy wanted, by weighing the whole boxbefore and after the event. Notice that the general relationship between energy and mass,E = mc2, must be used here. Thus, the thought experiment suggests that the photon’s energyand its time of passage can be found to arbitrary accuracy, in definite contradiction to theuncertainty relation between energy and time.72,73

The Belgian physicist Leon Rosenfeld – who was not invited to Solvay 1930 but hadtravelled to Brussels to meet Bohr – later recalled: “It was quite a shock for Bohr (...) hedid not see the solution at once. During the whole evening he was extremely unhappy, goingfrom one to the other and trying to persuade them that it couldn’t be true, that it wouldbe the end of physics if Einstein were right; but he couldn’t produce any refutation. I shallnever forget the vision of the two antagonists leaving the club [of the Fondation Universitaire]Einstein a tall majestic figure, walking quietly, with a somewhat ironical smile, and Bohrtrotting near him, very excited. (...) The next morning came Bohr’s triumph.”74

70Bohr (1949), p. 23271Pais (1991), pp. 429-3172Bohr (1949), pp. 225-673Pais (1991), p. 42774as cited in Pais (1982), pp. 446-7

23

Figure 1: A ‘pseudorealistic’ drawing of Einstein’s 1930s photon box by Bohr.

Figure 2: Bohr’s own version of the clock-in-the-box experiment.

24

4.3 Bohr’s rejection

In his search for a refutation of Einstein’s proposal, Bohr concentrated on the observationalsetup of the thought experiment. In his 1949 essay ‘Discussion with Einstein on Episte-mological Problems in Modern Physics’ he illustrated his arguments with the help of theexperimental arrangement as shown in figure 2. He believed that the solution lay withinthe details of the weighing process and the time measurement. According to him, these twoobservations were intrinsically connected.

First, let us examine the weighing process thoroughly. In Bohr’s drawing, the box issuspended in a spring-balance and is furnished with a pointer.75 The initial weighing is nowperformed by reading the position of the pointer on the scale attached to the balance frame.After the photon is released, the box is lifted upwards by the spring. This loss of weight canbe compensated by a load underneath the box that returns the pointer to its initial positionwith an accuracy ∆q.76 The imprecision ∆q in the displacement of the box produces anuncertainty ∆m in the measurement of the mass. Moreover, according to the energy-massrelation, the displacement ∆q causes also an uncertainty ∆E in the determination of the(photon) energy.

Second, Bohr pointed out that the weight measurement disturbed other observations,especially that of time. He proceeded with: “The essential point is now that any determinationof this position with a given accuracy ∆q will involve a minimum latitude ∆p in the controlof the momentum of the box connected with ∆q by the relation [∆q∆p ≈ h, MRV].”77 Anaccurate measurement of the position of the pointer would lead to an inherent uncertaintyin the momentum of the box, since to read the scale would require it be illuminated.78 Theinaccuracy in the momentum must of course be smaller than the total impulse, which can begiven by the gravitational field to a body with a mass ∆m:

∆p ≈ h

∆q< tg∆m, (4.1)

where t is the time taken to readjust the pointer and g is the gravitational acceleration. “Thegreater the accuracy of the reading q of the pointer, the longer must, consequently, be thebalancing interval t, if a given accuracy ∆m of the weighing of the box with its content shallbe obtained.”79 This is actually where Bohr’s argument comes down to: a more accuratereading of the pointer, and thus a better measurement of the photon energy, generates a lessprecise determination of time, and vice versa.

To derive the indeterminacy relation between energy and time exactly, Bohr invoked thegravitational redshift formula.80 He had found that the weight measurement could move thebox a little, as well as the clock inside it. So, because of the displacement of the box, theclock was positioned slightly different in the gravitational field. The redshift formula nowpredicts that the rate of a clock depends in a specific way on its position in a gravitationalfield. “A clock, when displaced in the direction of the gravitational force by an amount of

75Bohr (1949), p. 22676Pais (1982), p. 44777Bohr (1949), p. 22678Kumar (2008), p. 28579Bohr (1949), p. 22680Note that the redshift formula is based on the special relativistic time dilation and on the equivalence

of inertial and gravitational mass. Bohr was well aware of this fact and emphasized it in his article. (Bohr(1949), p. 226 and Pais (1982), p. 448)

25

∆q, will change its rate in such a way that its reading in the course of a time interval t willdiffer by an amount ∆t given by the relation:”81

∆t

t=

g∆q

c2. (4.2)

Finally, by combining equations (4.1), (4.2) and the energy-mass relation E = mc2, oneobtains the indeterminacy principle between energy and time:

∆E∆t > h. (4.3)

To sum up, the act of measuring the pointer against the scale altered the position of the boxin the gravitational field. So, the greater the accuracy in measuring the photon energy, thegreater the uncertainty in the displacement of the box. This imprecision of position wouldgenerate an uncertainty in the rate of the clock due to gravitational time dilation, making itimpossible to measure the exact moment that the photon escaped from the box. Through thischain of uncertainties, Bohr showed that the accuracy with which the energy of the photonis measured, restricts the precision with which its time of escape can be determined.82

Einstein’s clock-in-the-box thought experiment was particularly directed against the energy-time uncertainty relation, but Bohr also took it as an attack in general on his complementarityprinciple. This is why he was so concerned about it and why he was eager to find a solu-tion. The complementarity principle implies it is impossible to distinguish “the behaviourof atomic objects and the interaction with the measuring instruments which serve to definethe conditions under which the phenomena appear”.83 Einstein argued, however, that theenergy and time – a complementary pair – could both be determined with arbitrary accuracywithout any disturbance of the measuring instruments. Bohr, on the other hand, pointedout that the very arrangement that enables the determination of the photon energy will leadto an uncontrolled exchange of momentum with the box, which comprises the accuracy ofthe time control. So, Bohr rejected Einstein’s proposal successfully and thereby saved hiscomplementarity principle.

Following Norton (1991, pp. 139-42), I will now reconstruct the clock-in-the-box thoughtexperiment as an explicit argument. Einstein’s proposal consists of two steps. Firstly, hedeveloped an experiment that can measure simultaneously the exact energy of the photonand time at which it had it. Secondly, this implied that quantum mechanics is not a completetheory for individual processes. Bohr’s reply began with the insight that in the experimen-tal arrangement of figure 2 one can determine either the energy or the time of the photonaccurately, leaving the other uncontrollably altered. Yet, this is not enough to reject theproposal, since there could be another observational setup compatible with Einstein’s de-scription. Therefore, Bohr implicitly made an inductive step. He assumed that there is noexperiment at all which can determine energy and time of a photon more accurate thanHeisenberg predicted. Hence, Einstein had no experimental support any more to maintainthat the Copenhagen interpretation is incomplete. Thus, we can conclude once again thatthe thought experiment is characterized by an inductive step and an appeal to observations.

81Bohr (1949), p. 22782Kumar (1949), pp. 286-783Bohr (1949), p. 210

26

Part II

The epistemological problem

In part I, I have researched four thought experiment invented by Einstein. This was doneto find a solution to the epistemological problem. For each thought experiment I gave apreliminary exposition of how that particular argument led to new knowledge. However, Inever completely and satisfactory solved the problem for thought experiments in general.So, where does the knowledge of thought experiments about the physical world come from?In part II, I will try to answer this question for thought experiments in physics by usingsecondary literature. There is a hot debate going on in the philosophy of science about thisepistemological topic. Unfortunately, I cannot give a full overview of all existing accounts.Therefore I will describe the views of two main, recent contributors.

In chapters 6 and 7, I will discuss how John Norton and James Brown, respectively, treatthe epistemological problem. I will also state their accounts of what a thought experiment is,since the definition already contains a glimpse of the answer to the epistemological question.Finally, as it suits a down to earth philosopher of science, I will apply their solutions toEinstein’s thought experiments and consider whether they make any sense according to theactual practice.

Before I will turn to the main question of this thesis, I think it is important to comparethe previously discussed thought experiments with regard to the epistemological problem.In chapter 5, I would like to set forth the similarities and differences between these thoughtexperiments more clearly.

27

5 A classification of thought experiments

In this chapter I will answer two questions which will help me solve the epistemic problem:

5.1 What do the four thought experiments of Einstein have in common?

Firstly, it is important to note they could all be reconstructed as arguments. Although thoughtexperiments are mostly “disguised in some vivid picturesque or narrative form”, they couldalways be revealed as clear arguments without the particulars invoked in the original presen-tation.84 Secondly, every thought experiment is based on earlier made observations and/or onphysical theories which are corroborated by experience.85 All discussed thought experimentsare directly or indirectly related to reality, in contradiction to what thought experiments seemto be at first sight. Thirdly, in the case of the last three thought experiments, reconstructingthem in explicit argument clearly revealed an inductive step. That was precisely the stepwere new knowledge was produced. To conclude, the thought experiments are quite similarin the way the epistemological problem is solved.

5.2 What is the main difference between the thought experiments?

There are many different kinds of thought experiments described in secondary literature. Forexample, a few classifications are: science versus philosophy, normative versus factual, andconstructive versus destructive.86 However, in my personal opinion, the most appropriate cri-terium of classification is whether thought experiments can be performed as real experiments.When this is the case, the supposed gap between thought experiments and the real world isdissolved and the epistemological question does not pose a problem any more. Therefore, Iwill put the four thought experiments on a scale ranging from imaginary to already performed.

First, chasing after a beam of light is, of course, the most imaginary thought experiment,since no mass can reach the speed of light. Secondly, the elevator thought experiment was alsoquite imaginary in the time Einstein lived. It does indeed have some far-fetched elements,for example the being which pulls the elevator. However, because of new developments inspace travel, a simplified version can be performed. Nowadays, we can send a box intofree space and drop one in a gravitational field. Moreover, many modern experiments havetested the equivalence principle with great accuracy. Thirdly, the clock-in-the-box thoughtexperiment was probably already performable in the 1930s. In fact, Bohr designed a detailedexperimental arrangement to carry it out. Einstein, however, did not devise the thoughtexperiment to actually perform it, but to make a stand against quantum mechanics. Finally,the least imaginary thought experiment is that concerning the magnet and conductor inrelative motion. It was already performed by Faraday decades before Einstein shed his lighton it. Thus, the correct order of Einstein’s thought experiments from imaginary to alreadyperformed is: light beam – elevator – photon box – magnet and conductor.

84Norton (2004b), p. 113985In his first thought experiment Einstein argues that a spatially oscillatory electromagnetic field at rest

does not exist “whether on the basis of experience or according to Maxwell’s equations” (Einstein (1949), p.53). The moving magnet and conductor problem actually describes two real experiments and it refers to “theunsuccessful attempts to discover any motion of the earth relatively to the ‘light medium’” (Einstein (1905),p. 37). The elevator thought experiment is founded on the physical equivalence between gravitational andinertial mass. The clock-in-the-box thought experiment made use of the uncertainty principle between positionand momentum, the energy-mass relation and the gravitational redshift formula.

86Brown (2010)

28

6 Norton’s argument view

6.1 What are thought experiments?

Norton defines thought experiments in his paper ‘Thought Experiments in Einstein’s Work’(1991) as follows:

“Thought experiments are arguments which:

(i) posit hypothetical or counterfactual states of affairs, and

(ii) invoke particulars irrelevant to the generality of the conclusion.”87

The above definition provides necessary (but not sufficient) conditions for something to bea thought experiment. First of all, it must be an argument. This is the core thesis ofNorton’s account of thought experiments. It is based on the assumption that pure thoughtcannot produce knowledge on its own. All knowledge about the physical world is derived fromexperience, according to the empiricist doctrine which Norton supports. The knowledge whichis produced by thought experiments, however, does not rest upon new experience, but on whatwe already know.88 That being so, the function of pure thought and of thought experimentsis to “transform existing knowledge”.89 The only way this transformation can be effected isthrough argumentation. Thus, the success of the thought experiment is determined by thevalidity of the argument. “A good thought experiment is a good argument; a bad thoughtexperiment is a bad argument.”90

The core thesis is actually more demanding than just saying that thought experimentscan always be reconstructed as arguments (context of justification). Norton emphasizes thatthe actual conduct of a thought experiment consists of the execution of an argument (contextof discovery). A thought experiment is just an argument. He defends this statement byurging that the epistemic reach of a thought experiment coincides exactly with that of anargument.91 Then, he asks rhetorically: “How are we to explain this coincidence if not bythe simple assumption that thought experimenting merely is disguised argumentation?”92

Second, the argument should posit hypothetical or counterfactual states of affairs to be athought experiment. This condition (i) gives thought experiments their thought-like character.For if they did not posit such imaginary state of affairs they would be the description ofa physical experiment. As a consequence, this necessary condition distinguishes thoughtexperiments from physical experiments.93

Third, the argument should contain elements inessential to the conclusion. This condition(ii) gives thought experiments their experimental-like character. In the elevator thoughtexperiment, for example, Einstein asks us to imagine a physicist inside an elevator observinga watch which he drops. Since these particulars are not important for the point whichEinstein wanted to make, they could also be eliminated. Thus, the conclusion of any thoughtexperiment can also be reached by an argument which does not contain these particulars.Norton calls this claim: the ‘elimination thesis’.94

87Norton (1991), p. 12988Norton (1996), p. 35489Norton (2004c), p. 4990Norton (1991), p. 13191Norton (2004b), pp. 1142-392Norton (2004c), p. 5193Norton (1991), p. 13094Idem, pp. 130-1

29

6.2 Two epistemic resources of thought experiments

In this section I will describe Norton’s answer to the epistemological problem. He is verymuch concerned with this problem and has published many papers restricted to this onetopic. In ‘Why Thought Experiments Do Not Transcend Empiricism’ he explicitly formulatesthe problem: “Thought experiments are supposed to give us knowledge of the natural world.From where does the knowledge come from?”95

The solution he gives is actually already contained in his characterization of what thoughtexperiments are. The definition of section 6.1 entails that thought experiments are disguisedarguments in a vivid pictorial or narrative form. Norton explains: “If thought experimentsare capable of producing knowledge, it is only because they are disguised, picturesque ar-guments.”96 This statement is, of course, worked out more by Norton, and, as I will showbelow, he distinguishes two reasons why thought experiment are capable of producing newknowledge.

First, every argument is based implicitly or explicitly on premises. The presumptions ofthought experiments are not based on new experimental data, since otherwise condition (i)would not be satisfied, i.e. the argument would not involve an imaginary situation. However,a thought experiment draws upon what we already know of the world, either explicitly ortacitly. Thus, experience based knowledge enters thought experiments as assumptions. Thisis the first epistemic resource which guarantees that thought experiments are related to theworld.

Second, each argument leads to a conclusion via inferences of a recognized sort, for exampleinduction or deduction. In a similar way, thought experiments also draw inferences fromtheir assumptions. “Thought experiments are devices that reorganize or generalize theseassumptions to yield the outcome of the thought experiment. (...) Insofar as the device merelyreogranizes, it is a deductive argument; insofar as it generalizes in the broadest sense, it is aninductive argument.”97 Thus, according to Norton, thought experiments transform what wealready know about the physical world by (disguised) deductive or inductive argumentation.These transformations form the second epistemic resource of thought experiment and theypreserve the truth or probability of the assumptions.

This completes Norton’s answer to where the knowledge of thought experiments comesfrom. First, thought experiments can only teach us about the world, as empiricists claim,by drawing on our experience of it. Second, they are capable of producing knowledge byreorganizing or generalizing the experience based assumptions. “Insofar as they can tell usabout our world, they do so using our standard epistemic resources: ordinary experiences andthe inferences we draw from them.”98

Norton emphasizes there is nothing special about these epistemic resources. Althoughthought experiments seem to be extraordinary in the sense that they generate their resultswith such dramatic ease; according to Norton, they are epistemically unremarkable, becausethey can do nothing more than argumentation.99 Thought experiments do not perform epis-temic miracles.

95Norton (2004c), p. 4496Idem, p. 4997Norton (1996), p. 33598Idem, p. 33499Idem, pp. 365-6

30

6.3 A comparison with the actual practice

I will now compare Norton’s account of how thought experiments work with my findingsabout the four thought experiments of Einstein. First, I would like to say that the fourexamples could indeed be reconstructed as arguments. I showed this explicitly at the endsof chapters 1 to 4. Norton himself has also offered many other examples of typical thoughtexperiments in various papers (1991, 1996, 2004c) and was capable of presenting them clearlyas arguments. So, there is every appearance that Norton is correct about this point. As to thediscussion whether thought experiment can only be represented as arguments or whether theyare arguments themselves, I do not think this is important to the epistemological problem.In my opinion, a reconstruction on its own is enough to prove that a thought experiment isrelated to reality.

Second, I want to discuss the clock-in-the-box thought experiment shortly, because theargument view explains it very well. This thought experiment is a special one, since it does notproduce new knowledge. Einstein was unsuccessful in showing the incompleteness of quantummechanics (see chapter 4). By identifying thought experiments with arguments, Norton cameto a new way of explaining why such thought experiments can err. “They can fail to in justthe same way that arguments can fail; that is, either may proceed from false premises oremploy fallacious reasoning.”100 In this case, the clock-in-the-box thought experiment failsbecause it employs a fallacious reasoning. Einstein forgot to take gravitational time dilationinto account. Therefore, the energy and time of a photon cannot be measured simultaneouslywith great precision.

Third, I would like to note that all four thought experiments indeed started from earliermade observations (see section 5.1). For Norton this is a confirmation of his empiricism,i.e. the doctrine that all knowledge is derived from sensory experience. I agree that all(empirical) knowledge must, mediate or immediate, ultimately be related to information fromthe senses. But I would like to emphasize this is only one way of looking at knowledge. Besidesinformation from the senses, understanding is also necessary for acquiring knowledge. Namely,an observation without an act of the understanding cannot yield knowledge. In support, Iwill quote a famous statement of Kant: “Thoughts without content are empty, intuitionswithout concepts are blind. It is thus just as necessary to make mind’s concepts sensible (i.e.,to add an object to them in intuition) as it is to make its intuitions understandable (i.e., tobring them under concepts).”101 Next, I will show Norton does not neglect the capacity ofthe understanding completely.

Fourth, I can confirm the other epistemic resource which Norton indicates: deductive andinductive inferences. According to my reconstruction, the last three thought experimentsof Einstein contain an inductive step. This is precisely where new knowledge is produced.Thus, the capacity which makes inferences (understanding) is as important for cognition asthe capacity through which objects are given to us (sensibility). While Norton does notput emphasis on the understanding as a capacity which is necessary for performing thoughtexperiments – because he is an empiricist – he does note the importance of argumentation.

To sum up, Einstein’s four thought experiments display all the main characteristics of Nor-ton’s account. Although Norton does not emphasize the two epistemic resources (experienceand understanding) equally in his articles, they actually solve the epistemological problementirely.

100Norton (2004c), p. 49101CPR, A 51/B 75

31

7 Brown’s Platonism

7.1 An a priori view of (some) thought experiments

A direct opponent of Norton’s argument view is James Brown. Since 1991 there has been anongoing debate between the two philosophers about thought experiments. In a way, Brown’saccount contrasts sharply with that of Norton. “The views of Brown and Norton representthe extremes of Platonic rationalism and classic empiricism, respectively.”102 I will first statesome general features which Brown attributes to thought experiments:

“It’s difficult to say precisely what thought experiments are. Luckily, its also unimportant.We know them when we see them, and thats enough to make discussion possible. Afew features are obvious. Thought experiments are carried out in the mind and involvesomething akin to experience; that is, we typically see something happening in a thoughtexperiment. Often there is more than mere observation. As in a real experiment, theremight be calculating, some application of theory, guesswork, and conjecture. The best wayto get a grip on what thought experiments are is to simply look at lots of examples.”103

This shows that, Brown does not give such a precise definition as Norton does. He calls hisapproach: “definition by example”.104 He takes it for granted that thought experiments havea legitimate use in physics and is rather interested in how thought experiments work.105 Inorder to provide some sort of pattern in the diverse collection of examples, he constructs asimple taxonomy of thought experiments.

The first class of thought experiments, which he distinguishes, only destroys (or at leastpresents serious problems for) an existing theory. They are called destructive and, typically,entail some sort of reductio ad absurdum of a theory.106 According to Brown, chasing a lightbeam and the clock-in-the-box are examples of destructive thought experiments.

The second class of thought experiments is called constructive. Instead of playing a refut-ing role, these thought experiments provide supporting evidence for a theory.107 Constructivethought experiments also admit a further division, but it will not be discussed here, since itdoes not add anything to Brown’s central epistemic claim. The moving magnet and conductorand Einstein’s elevator could be labeled as ‘constructive’, since they establish the special andgeneral theory of relativity, respectively.

Thirdly, there is a small number of thought experiments which are simultaneously de-structive and constructive. Brown calls them Platonic – in section 7.2 I will explain why –and pays special attention to them. Actually, his main epistemological claim pertains onlyto this special class of thought experiments.108 He finds them “quite remarkable”109, sincethey can destroy the old theory and create a new one in a single blow. In addition, Brownargues, the new knowledge which is produced by Platonic thought experiments is ‘indepen-dent of sensory experience’, i.e. a priori. This does not mean, however, that the results of

102Moue (2006), p. 69103Brown (2004), p. 1126104Brown (1986), p. 4105Idem106Brown (1991), p. 123107Idem108Norton (1996), pp. 337-8109Brown (1986), p. 9

32

these thought experiments are necessarily true.110 Brown often emphasizes that all thoughtexperiments are fallible.111 Thus Brown’s central epistemological thesis is:

“A thought experiment which is both destructive and conclusive [a special type of con-structive thought experiment, MRV] provides the ground for an a priori transition fromone theory to its successor.”112

In many occasions, Brown argues for this claim. In the next section, I will specify a fewreasons for the a priori character of Platonic thought experiments and, more importantly,I will discuss how these reasons solve the epistemological problem. It is remarkable thatBrown’s solution to the epistemological problem applies only to a few thought experiments,namely ‘Platonic’ ones. He seems not to be interested in the source of knowledge producedin other thought experiments; or, perhaps, he agrees with accounts of other philosophers inthese cases.

7.2 Intellectual perception

Like Norton, Brown acknowledges the epistemic problem too: “Thought experiments provideus with scientific understanding and theoretical advances which are sometimes quite signifi-cant, yet they do this without new empirical input, and possibly without any empirical inputat all. How is this possible?”113 As mentioned above, Brown’s answer to this question isonly applicable to Platonic thought experiments. Before I can fully state his solution, I mustexplain first how these thought experiments work, and, especially, why they are a priori. Iwill give three of Brown’s reasons for claiming these thought experiments provide a prioriknowledge.

The first reason is rather simple and straightforward. Although there may be some em-pirical input, there are no new experimental data being used in the transition from the oldto the new theory. “The old theory is not tossed out and the new instituted on the basis ofempirical observation.”114

Second, the conclusion of a Platonic thought experiment is not logically derived from givenempirical premisses. Nor is it any kind of analytic truth, because a tautology says nothingabout the world. Rather, Brown calls the new knowledge “synthetic a priori”, and explainsthat it is produced at once, when we see something clearly and distinctly.115 Brown showsthis by means of Galileo’s thought experiment, which he considers as the finest and mostinteresting thought experiment ever.116,117 Note, this refutation of a logical interpretation ofthought experiments directly contradicts Norton’s argument view.110Hereby, Brown challenges almost all philosophers, since throughout the history of western philosophy a

priori knowledge has been regarded as certain knowledge.111Brown (1986), p. 6; (2004), p. 1127; and (1991), p. 125112Brown (1986), p. 10113Brown (1992), p. 271114Brown (1986), p. 11115Brown (1991), p. 125116Idem, p. 122 and Brown (2004), p. 1129117Galileo’s thought experiment starts with the assumption held by Aristotle that heavy bodies (H) fall faster

than light ones (L) (Brown symbolizes this as H > L). Next, Galileo asks us to imagine a heavy ball attachedby a string to a light ball. What would happen if we drop these bodies from a great height, according toAristotle’s theory? On the one hand, the light ball will act as a drag on the heavy ball, so the compoundobject must fall slower than the heavy bodies alone (H+L < H). On the other hand, since the combined ballsare heavier than the heavy ball, the compound object should fall faster (H +L > H). This is in contradictionwith the former statement. Therefore, the Aristotelian assumption is incorrect and, moreover, a new account

33

The third consideration – “possibly the most interesting and most speculative”118 – dependson two things: mathematical Platonism and a realist view of laws of nature. First, I willdescribe the Platonistic framework of mathematics. In ‘Thought Experiments: a PlatonicAccount’ Brown explains:

“There are several ingredients involved in Platonism. (1) There are abstract objectsexisting outside of space and time. (2) The way these objects are is what makes ourmathematical statements true or false. (3) The mind can grasp or intuit (some of) them.(4) Our mathematical knowledge is a priori in the sense of being independent of thephysical senses; but it need not be infallible”.119

Therefore, mathematical knowledge is not about physical objects, but about abstract objects,such as numbers, existing independently from us in ‘another world’. This knowledge is ac-quired by some sort of ‘intellectual perception’. Correspondingly, thought experiments alsoinvolve some kind of intuition of the world by the mind. Thus, mathematical and thoughtexperimental truths are a priori in the sense that physical perception cannot fully account forthis knowledge acquisition.120

Secondly, Brown assumes a realism about the laws of nature. He associates himself withrecent thinking about the laws of nature and explains: “I take laws to be relations amongproperties. These are abstract entities, outside of space and time, that somehow necessitatethe regularities we experience in the empirical world.”121 Thus, laws of nature are relationsamong objectively existing abstract entities.

By combining the two foregoing assumptions, one can, according to Brown, finally discoverhow (Platonic) thought experiments really work. Mathematical Platonism states we canperceive the abstract entities of mathematics. This implies it’s possible to perceive abstractentities, at least some. But, according to the realist view of laws of nature, laws are abstractentities, so they could be perceivable too. How could we have an intuition of these laws?Now, Platonic thought experiments form the missing link. In a similar way as we can perceivetruths about numbers via mathematics, we can have an intuition of a law of nature via thoughtexperiments. “Thought experiments are telescopes into the abstract realm. Not all laws canbe seen, but the odd one here and there can be perceived in this a priori way.”122 Thus,according to Brown, Platonic thought experiments provide us a priori knowledge of the lawsof nature, because they are vehicles for intellectually perceiving these abstract entities.

I will now return to the epistemological problem. How is it possible that Platonic thoughtexperiments teach us something new about the world? Brown’s answer: we can discoverthings about the world with the ‘mind’s eye’. The human mind can ‘see’ the laws of natureby performing a thought experiment. These laws may be (relations among) abstract entitiesoutside of space and time, but they actually represent principles which objects in the realworld have to obey. Thus, according to Brown, the epistemic source of new understanding inthought experiments is: intellectual perception. This makes Brown a rationalist, as opposedto an empiricist.

is established. Galileo’s thought experiment eventually leads to the conclusion that all bodies fall at the samespeed (H = L = H + L). This is a Platonic thought experiment since it simultaneously destroys Aristotle’stheory and establishes a new theory. (Brown (1986), pp. 9-10)118Brown (1991), p. 126119Idem, p. 122120Brown (2004), pp. 1130-1121Idem, p. 1131122Idem

34

7.3 Reviewing the epistemology of Platonic thought experiments

Does Brown’s account match with the four examples of Einstein’s thought experiments?They are not in contradiction with each other, but the four thought experiments are alsonot explicitly in favour of Brown. The main problem is that these thought experiments ofEinstein are either destructive or constructive, but not both at the same time. Brown’scentral epistemological claim is about Platonic thought experiments and, unfortunately, I didnot discuss any of these special thought experiments.

Can’t I say anything about Brown’s Platonism then? Although I cannot properly comparehis view with my thought experiments, I would like to make a few general remarks. Firstof all, I approve the fact that Brown takes the epistemological problem at face value. Heeschews the simple empiricist view of Norton, because he thinks thought experiments areneither based on new empirical data nor are they derived from old data. Therefore he isobliged to explain how we can gain knowledge of the world without relevant experience ofthe world. Only a radical, alternative epistemology will suffice. Brown advocates a particularkind of rationalism, which is quite a logical choice considering his assumptions.123

Secondly, however, I find Brown’s Platonism not very clear. Or, to put it more bluntly,his concepts are not well defined. He assumes the existence of a ‘Platonic world’ consisting of‘abstract entities’, ‘outside’ of space and time, which can be ‘perceived’ intellectually. What,or better where, is this world which is supposed to be outside of space? Why are laws of natureobjectively existing relations among abstract entities? How does intellectual perception work?Brown attempts to block these concerns by claiming that the mechanisms whereby physicalobjects are perceived are also poorly understood. But this does not justify the introductionof another world, existing outside of space and time.124

Thirdly, Brown does not explain why thought experiments, which are both destructive andconstructive, are so special. Why can’t, for example, constructive thought experiments giveus access to the Platonic world? I do not feel comfortable with the idea of a special class ofthought experiments. Although there may be some differences between thought experiments,I think all thought experiments are epistemically quite the same. Are all thought experimentsPlatonic then? It will become clear below that this question is to be answered negatively.

Fourthly, I believe that the method of thought experimenting is epistemically unremark-able. This is in agreement with what Norton thinks: “For in one of his Platonic thoughtexperiments, the outcome is supposed to arise almost miraculously from an act of Platonicperception quite unlike the mundane operation of ordinary inference. If it turns out – as thereconstruction thesis asserts – that the same outcome can be achieved by ordinary means, wemay well begin to wonder if we need the mysteries of Platonic perception to explain thoughtexperiments.” Later on he concludes that thought experiments “can do no more than canordinary thinking with its standard tools of assumption and argument. They open no newchannels of access to the physical world.”125 I agree that thought experiments work thesame as ordinary thinking. Therefore, the epistemological problem does not only apply tothought experiments in particular, but to the scientific method in general. An epistemologyof thought experiments should be an epistemology of science at the same time. To conclude, Ido not think Brown’s Platonism is eligible for such an epistemology, because it only describesa special, unclear method of acquiring knowledge.

123Norton (2004c), p. 56124Cooper (2005), p. 333; Norton (1996), pp. 358-65; and Norton (2004c), p. 57125Norton (1996), pp. 339 and 366

35

Conclusion

In Part I of this thesis I have discussed four thought experiments in Einstein’s work. Allfour of the thought experiments could be reconstructed as arguments. Like every otherargument, they were implicitly or explicitly founded on assumptions. In all four examplesI discovered (hidden) assumptions based on earlier made observations and/or on physicaltheories corroborated by experience. Furthermore, each argument leads to a conclusion viainferences of a recognized sort, for example induction or deduction. In three of the thoughtexperiments Einstein (or Bohr) performed an inductive step to go from a concrete example toa general principle. Therefore, the four thought experiments revealed two epistemic resources:earlier made observations and inductive inferences. This is where the new knowledge of thesethought experiments comes from.

In Part II, I have analysed two solutions to the epistemological problem these experimentspose: Norton’s argument view and Brown’s Platonism. Norton holds that thought experi-ments are picturesque, disguised arguments of a hypothetical or counterfactual nature. Heindicates the same epistemic sources I do: ordinary experiences and the inferences we drawfrom them. Brown thinks this is not the full account. Some thought experiments, whichdestroy an old theory and establish a new one, could not be reconstructed as arguments.These so-called Platonic thought experiments are vehicles for seeing the laws of nature withthe mind’s eye. According to Brown, new understanding is created in thought experimentsby intellectual perception.

My own sympathies lie more with Norton than with Brown for two reasons. The firstreason is based on the scientific practice. The thought experiments which I discussed re-vealed exactly what Norton predicted. The second reason for supporting Norton is of a morephilosophical nature. I do not feel comfortable with the idea of a special class of thought ex-periments with almost magical powers. I agree with Norton that thought experiments are notextraordinary from an epistemological point of view. Thought experiments work epistemicallythe same as other scientific methods of acquiring knowledge.

As a consequence of this last point, one’s solution to the epistemological problem dependsstrongly on one’s epistemic scheme. An empiricist, like Norton, would state that thoughtexperimental knowledge of the world is derived from sensory experience. A rationalist, likeBrown, would argue that an act of the understanding is needed in order to produce knowl-edge. According to the Kantian scheme to which I adhere, both sensory experience andunderstanding are epistemic sources of thought experimental knowledge. But the most im-portant thing to note is that a solution to the epistemic problem should not be restricted tothought experiments, but should be made from a broader philosophical perspective.

36

References

Bohr, Niels (1949). ‘Discussion with Einstein on Epistemological Problems in ModernPhysics’. In: Schilpp, Paul A. (ed.). Albert Einstein: Philosopher-Scientist. 3rd ed. LaSalle, Illinois: Open Court, pp. 199-241.

Brown, James R. (1986). ‘Thought Experiments Since the Scientific Revolution’. In:International Studies in the Philosophy of Science. Vol. 1, No. 1, pp. 1-15.

———— (1991). ‘Thought Experiments: a Platonic Account’. In: Horowitz, Tamara, andMassey, Gerald J. (eds.). Thought Experiments in Science and Philosophy. Savage,MD: Rowman and Littlefield, pp. 119-28.

———— (1992). ‘Why Empiricism Won’t Work.’ In: PSA: Proceedings of the BiennialMeeting of the Philosophy of Science Association. Vol. 2, pp. 271-79.

———— (2004). ‘Peeking Into Plato’s Heaven’. In: Philosophy of Science. Vol. 71, No. 5,pp. 1126-1138.

————, and Fehige, Yiftach (2010). ‘Thought Experiments’. In: Zalta, Edward N. (ed.).The Stanford Encyclopedia of Philosophy. URL = <http://plato.stanford.edu/archives/win2010/entries/thought-experiment/>.

Cooper, Rachel (2005). ‘Thought Experiments’. In: Metaphilosophy. Vol. 36, No. 3, pp.328 - 47.

Einstein, Albert (1905). ‘On the Electrodynamics of Moving Bodies’. Reprinted in: Ein-stein, Albert, et al. (1952). The Principle of Relativity: A Collection of OriginalMemoirs on the Special and General Theory of Relativity. Perrett, Wilfrid, and Jeffery,George B. (transl.). New York: Dover Publications, pp. 37-65.

———— (1907). ‘On the Relativity Principle and the Conclusions Drawn from It’. Reprintedin: Stachel, John, et al. (eds.). The Collected Papers of Albert Einstein. Vol. 2, Doc.47, pp. 433-88.

———— (1911). ‘On the Influence of Gravitation on the Propagation of Light’. Reprintedin: Einstein, Albert, et al. (1952). The Principle of Relativity: A Collection of OriginalMemoirs on the Special and General Theory of Relativity. Perrett, Wilfrid, and Jeffery,George B. (transl.). New York: Dover Publications, pp. 97-108.

———— (1912). ‘To Wilhelm Wien, 10 July 1912’. In: Klein, Martin J., et al. (eds.). TheCollected Papers of Albert Einstein. Vol. 5, Doc. 413, pp. 497-8.

————, and Grossmann, Marcel (1913). ‘Outline of a Generalized Theory of Relativityand of a Theory of Gravitation’. Reprinted in: Klein, Martin J., et al. (eds.). TheCollected Papers of Albert Einstein. Vol. 4, Doc. 13, pp. 302-43.

———— (1920). Relativity: The Special and The General Theory. Lawson, Robert W.(transl.). New York: Henry Holt and Company.

37

————, and Infeld, Leopold (1938). The Evolution of Physics: The Growth of Ideas fromEarly Concepts to Relativity and Quanta. 2nd ed. re-issued. Cambridge: CambridgeUniversity Press.

———— (1949). ‘Autobiographical Notes’. In: Schilpp, Paul A. (ed.). Albert Einstein:Philosopher-Scientist. 3rd ed. La Salle, Illinois: Open Court, pp. 1-94.

———— (1954). Ideas and Opinions. New York: Crown Publishers.

———— (1956). ‘Autobiographische Skizze’. In: Seelig, Carl (ed.). Helle Zeit - DunkleZeit. Zurich: Europa Verlag, pp. 9-17.

————, and Born, Max (1971). The Born-Einstein Letters: Correspondence betweenAlbert Einstein and Max and Hedwig Born from 1916-1955, with commentaries by MaxBorn. Born, Irene (transl.). London: Macmillan.

———— (1989). The Collected Papers of Albert Einstein. Volume 2. The Swiss Years:Writings, 1900-1909. Stachel, John, et al. (eds.). Princeton: Princeton UniversityPress.

———— (1993). The Collected Papers of Albert Einstein. Volume 5. The Swiss Years:Correspondence, 1902-1914. Klein, Martin J.; Kox, Anne J.; and Schulmann, Robert(eds.). Princeton: Princeton University Press.

———— (1995). The Collected Papers of Albert Einstein. Volume 4. The Swiss Years:Writings, 1912-1914. Klein, Martin J.; Kox, Anne J.; Renn, Jurgen; and Schulmann,Robert (eds.). Princeton: Princeton University Press.

Eotvos, Lorand (1890). ‘Uber die Anziehung der Erde auf verschiedene Substanzen.’ In:Mathematische und Naturwissenschaftliche Berichte aus Ungarn. Vol. 8, pp. 65-8.

Griffiths, David J. (1981). Introduction to Electrodynamics. 3rd ed. Upper Saddle River,New Jersey: Prentice Hall.

Hartle, James B. (2003). Gravity: An Introduction to Einstein’s General Relativity. SanFrancisco: Addison Wesley.

Kant, Immanuel (1781/1787). Critique of Pure Reason. Reprinted in: The Cambridgeedition of the works of Immanuel Kant (1998). Guyer, Paul and Wood, Allen W.(transl.). Cambridge: Cambridge University Press. Cited as (CPR, A/B page).

Kuhn, Thomas S. (1964). ‘A Function for Thought Experiments’. Reprinted in: Kuhn,Thomas S. (1977). The Essential Tension: Selected Studies in Scientific Tradition andChange. Chicago: University of Chicago Press, pp. 240-265.

Kumar, Manjit (2008). Quantum. Einstein, Bohr and the Great Debate About the Natureof Reality. London: Icon Books.

Lorentz, Hendrik A. (1916). The Theory of Electrons and Its Applications to the Phenom-ena of Light and Radiant Heat. 2nd ed. Leipzig: Teubner.

38

Moue, Aspasia S. et al. (2006). ‘Tracing the Development of Thought Experiments in thePhilosophy of the Natural Sciences’. In: Journal for General Philosophy of Science.Vol. 37, pp. 61-75.

Norton, John D. (1985). ‘What was Einstein’s Principle of Equivalence?’. In: Studies inHistory and Philosophy of Science Part. Vol. 16, pp. 203-46.

———— (1991). ‘Thought Experiments in Einstein’s Work’. In: Horowitz, Tamara, andMassey, Gerald J. (eds.). Thought Experiments in Science and Philosophy. Savage,MD: Rowman and Littlefield, pp. 129-48.

———— (1996). ‘Are Thought Experiments Just What You Thought?’. In: CanadianJournal of Philosophy. Vol. 26, No. 3, pp. 333-66.

———— (2003). ‘Einstein’s Special Theory of Relativity and the Problems in the Elec-trodynamics of Moving Bodies that Led him to it’. In: Janssen, Michel, and Lehner,Christoph (eds.). Cambridge Companion to Einstein. Cambridge: Cambridge Univer-sity Press.

———— (2004a). ‘Einstein’s Investigations of Galilean Covariant Electrodynamics prior to1905’. In: Archive for History of Exact Sciences. Vol. 59, pp. 45-105.

———— (2004b). ‘On Thought Experiments: Is There More to the Argument?’. In: Phi-losophy of Science. Vol. 71, No. 5, pp. 1139-1151.

———— (2004c). ‘Why Thought Experiments Do Not Transcend Empiricism’. In: Hitch-cock, Christopher (ed.). Contemporary Debates in the Philosophy of Science. Blackwell,pp. 44-66.

———— (2010). ‘Chasing the Light: Einstein’s Most Famous Thought Experiment’, pre-pared for Brown, James R.; Frappier, Melanie; and Meynell, Letitia (eds.). ThoughtExperiments in Philosophy, Science and the Arts. London: Routledge.

Pais, Abraham (1982). ‘Subtle is the Lord...’: The Science and the Life of Albert Einstein.Oxford: Clarendon Press.

———— (1991). Niels Bohr’s Times, In Physics, Philosophy, and Polity. Oxford: Claren-don Press.

Ryden, Barbara S. (2003). Introduction to Cosmology. San Francisco: Addison Wesley

39