Einsteins Electrodynamical Pathway to Special Relativity John D

Einstein’s Electrodynamical Pathway to Special Relativity John D. Norton Department of History and Philosophy of Science University of Pittsburgh 1

“…the seven and more years that the development of the Special Theory of Relativity had been my entire life. ” Einstein’s tribute to A. A. Michelson, Dec. 19, 1952. 7 and more years = 364 and more weeks What was Einstein doing for the remaining 364 - 5. 5 = 358. 5 and more weeks? …reflecting on electrodynamics in the context of Newtonian space and time. “The step” 5 -6 weeks before “On the electrodynamics. . . ” received by Annalen der Physik, Jun. 30, 1905 new considerations of space and time enter 2

We know. . . The Michelson-Morley experiment had no decisive presence in his deliberations. (Holton) Its importance was to affirm the principle of relativity, not the light postulate (Stachel). Einstein’s early deliberations were driven by the magnet and conductor thought experiment, which brought him the device of field transformations well before the Lorentz transformation of space and time. (Rynasiewicz et al. ) Einstein seriously investigated an emission covariant) akin to Ritz’s approach. (Stachel) theory of light (= Galilean …and very little more can be said if we demand unequivocal foundation in documentary evidence. 3

This talk will try nonetheless to answer… What could Einstein recover from the device of field transformations? What was Ritz’s emission “theory”? How might Einstein have used a Ritz type approach? What thought experiment shows its failure most cogently? How did Einstein make “the step”? Two partial theories of electrodynamics, jointly not adequate to the principle of relativity. Part polemic against Einstein and part program for finding Galilean covariant force laws. To construct a promising, Galilean covariant electrodynamics. Einstein’s chasing-a-light-beam thought experiment. Several possibilities; it may not have been by reflecting on light signals and clock synchronization. 4

Read all about it in: "Einstein's Investigations of Galilean Covariant Electrodynamics prior to 1905, " Archive for History of Exact Sciences, forthcoming. "Einstein's Special Theory of Relativity and the Problems in the Electrodynamics of Moving Bodies that Led him to it. " in Cambridge Companion to Einstein, M. Janssen and C. Lehner, eds. , Cambridge University Press. Links at www. pitt. edu/~jdnorton 5

The Magnet and Conductor Thought Experiment and the Device of Field Transformations 6

A device that reveals motion through the ether? H A magnet at rest in the ether is surrounded by a pure magnetic field H, but no electric field E. IMPROVED VERSION conductor moves with magnet E H A magnet moving through the ether creates in addition an induced magnetic field. Is this induced magnetic field the detectible mark of motion through the ether? 7

What is observable? no current conductor Einstein 1905 current due to electric field Observables obey principle of relativity. Theoretical account should as well. exactly balanced by current due to motion of conductor in magnetic field …but how? 8

Einstein’s 1920 recollection of his reaction: “The idea, however, that these were two, in principle different cases was unbearable for me. The difference between the two, I was convinced, could only be a difference in choice of viewpoint and not a real difference. Judged from the magnet, there was certainly no electric field present. Judged from the [resting observer], there certainly was one present. Thus the existence of the electric field was a relative one, according to the state of motion of the coordinate system used, and only the electric and magnetic field together could be ascribed a kind of objective reality, apart from the state of motion of the observer or the coordinate system. The phenomenon of magneto-electric induction compelled me to postulate the (special) principle of relativity. ” 9

The device of field transformations. “Judged from the magnet, there was certainly no electric field present. ” H E’ = - (1/c)vx. H H’ “Judged from the [resting observer], there certainly was one present. ” Pure magnetic field H change observer’s velocity by v Magnetic field H’ = H and Electric field E’ = - (1/c)vx. H 10

Which transformation for the general case? Lorentz transformation (First order) E = E’ + (1/c) ux. H’ H = H’ - (1/c) ux. E’ Simplified transformation E = E’ + (1/c) ux. H’ H = H’ Unusable without Lorentz’s local time. Einstein is still years from “the step. ” Unique, linear field transformation law under which Lorentz force law f/e = E + (1/c) ux. H is covariant 11

Maxwell’s electrodynamics splits into two partial theories (“two charges partial theory”) (“magnet and conductor partial theory”) (M 1) . E = 4 pr (M 2) . H = 4 pr (M 3) x. H = (4 p/c)j + (1/c)(∂E/∂t) (M 4) x. E = - (1/c)(∂H/∂t) (L) f/e = E + (1/c) ux. H is covariant under t=t’ r=r’-ut E = E’ H = H’ - (1/c) ux. E’ t=t’ r=r’-ut E = E’ + (1/c) ux. H’ Full theory of Föppl’s (1894) two charges thought experiment, which violates the principle of relativity. Full theory of the magnet and conductor thought experiment. BUT A moving magnet does not induce an electric field. Lorentz force law not included. BUT A moving charge does not induce a magnetic field H = H’ 12

August Föppl’s Two Charges Thought Experiment from Einführung in die Maxwell’sche Theorie der Elektricität. Leipzig: B. G. Tuebner, 1894, Part 5, Ch. 1. To what extent is the principle of relativity respected in electrodynamics? It fails in the + case of the two charges thought experiment. - It holds in the case of the magnet and conductor thought experiment. Force between charges at rest in the ether is f. + - Force between same charges when they share a common motion in the ether is f’ = (1 -v 2/c 2)f. 13

What now? (“two charges partial theory”) (“magnet and conductor partial theory”) (M 1) . E = 4 pr (M 2) . H = 4 pr (M 3) x. H = (4 p/c)j + (1/c)(∂E/∂t) (M 4) x. E = - (1/c)(∂H/∂t) (L) f/e = E + (1/c) ux. H modify this? The two partial theories jointly entail the constancy of the velocity of light. How can it be extended to cover all electrodynamics? Supports an account of the magnet and conductor thought experiment fully in accord with the principle of relativity. Einstein concluded his 1920 recollections: “The difficulty to be overcome lay in the constancy of the velocity of light in a vacuum, which I first believed had to be given up. Only after years of groping did I notice that the difficulty lay in the arbitrariness of basic kinematical concepts. ” 14 keep this?

Ritz’s Emission “Theory” of Light 15

Ritz’s Emission “Theory” A modified electrodynamics in which the velocity of the light emitter is added vectorially to the velocity of light. Einstein to Ehrenfest, June, 1912 and elsewhere Reasons to take Einstein’s remark seriously. All Galilean covariant theories of light must be emission theories (but not conversely). Synonym for a Galilean covariant theory? “…Ritz’s conception, which incidentally was also mine before rel. theory. ” üCloseness of 1912 to actual events. üEinstein was defending his relativity theory from Ritz’s theory. Ehrenfest was proposing experimental tests. üEinstein knew Ritz and had co-authored a note with him. üEinstein won his first job in Zurich in 1909 only after the first choice, Ritz--Einstein’s critic, fell ill. 16

Ritz’s Negative Program “Recherches Critique sur l’Électrodynamique Génénerale, ” Annales des Chimie et de Physique, ” 13 (1908), pp. 145 -275. (and other works) Died July 1909, aged 31, from tuberculosis. üWe should be skeptical about many quantities used in electromagnetic theory, especially electric and magnetic fields. üFields laws should be eliminated in favor of action at a distance laws such as due to Weber and others. üThe ether should be eliminated from electrodynamics and the principle of relativity restored. üThe principle of relativity should not be restored by means of Einstein’s strange kinematical notions. üPresentations of electrodynamics should be given in terms of retarded potentials. The advanced potentials admitted by Maxwell’s equations are unphysical. 17

Ritz’s Positive Program To reconfigure and reformulate all of electrodynamics in terms of Galilean covariant, Weber-like action at a distance force laws. The program was not completed. Ritz developed many examples of such laws for special cases. The force F between two charges e, e’, moving with velocity u and acceleration w is given by: Fy = … Note the many undetermined constants! 18

Ritz’s Theory as reported in Pauli’s 1921 Relativitätstheorie Formulate electrodynamics in terms of scalar and vector potentials j, A E = - j - (1/c)∂A/∂t H = x. A “[…]” means a quantity is evaluated at event (x’, y’z’, t’) where the retardation time t’is t’ = t - r/c This time delay encodes the propagation of electromagnetic action at speed c in the ether. Replace the propagating retardation time t’=t-r/c by a Galilean covariant, projected retardation time t’=t-r/(c+vr) vr=speed of source in direction of point at r=(x, y, z). 19

Propagation versus Projection Propagation Electromagnetic action propagates from fixed point in space that is left behind by a moving source. Projection The apparent source of electromagnetic action is boosted, and moves with uniformly moving source. Ritz imagined that charges emit fictitious particles that are projected by ordinary rules of Galilean kinematics. 20

Propagation versus Projection Propagation Electromagnetic action propagates from fixed point in space that is left behind by a moving source. Projection The apparent source of electromagnetic action is boosted, and moves with uniformly moving source. 21

My conjecture: This is also theory Einstein hit upon and associated with Ritz’s name. “Ritz’s ideas on electrodynamics and optics are not so far developed that one can call them a ‘theory. ’ What is special in them is that there does not exist a definite speed for light propagation at a position and in a given direction, but that this [speed] depends on the state of motion of the light source. Then one cannot trace light propagation back to differential equations, but one must introduce “retarded potentials, ” which is a kind of action at a distance. Before setting up the special theory of rel. , I had myself thought of investigating such a possibility. ” Draft of a response written on the back of a letter dated 1 February 1952 to Einstein from C. O. Hines. (Einstein Archive 12 250, 12 251. ) 22

Why Einstein might think of “investigating such a possibility”: Galilean covariant, magnet and conductor partial theory Necessary and sufficient for existence of scalar and vector potentials E = - j - (1/c)∂A/∂t (M 2) . H = 4 pr (M 4) x. E = - (1/c)(∂H/∂t) H = x. A Retarded integrals capture content of remaining Maxwell equations (M 1) and (M 3). (L) f/e = E + (1/c) ux. H t=t’ r=r’-ut E = E’ + (1/c) ux. H’ H = H’ Might we render theory Galilean covariant by replacing propagating retardation times by projected retardation times? Promising, BUT… H = H’ still precludes magnetic fields induced by charge currents. Transformations for A must conform, so A=A’ under which is not covariant. Might some other variant of this theory escape these troubles? Is any Galilean covariant electrodynamics admissible? 23

Einstein’s Objections to All Emission Theories of Light. Collected from remarks in many places. The physical state of a light ray is determined completely by its intensity and color [and polarization]. “ I decided [against an emission theory], since I was convinced that each light [ray] should be defined by frequency and intensity alone, quite independently of whether it comes from a moving or a resting light source. ” Einstein to Ehrenfest, mid June 1912 The theory cannot be formulated in terms of differential equations. Different velocities entail that light can back up on itself (later parts overtakes earlier). e. g. Einstein to Shankland, 1950 s; to Hines Feb. 1952 e. g. Einstein to Shankland, 1950 s Problems with shadow formation by a moving screen. e. g. To Mario Viscardini, April 1922 24

Einstein Chases a Beam of Light 25

Einstein, Autobiographical Notes, 1946 “After ten years of reflection such a principle resulted from a paradox upon which I had already hit at the age of sixteen: If I pursue a beam of light with the velocity c (velocity of light in a vacuum), I should observe such a beam of light as an electromagnetic field at rest though spatially oscillating. There seems to be no such thing, however, neither on the basis of experience nor according to Maxwell’s equations. From the very beginning it 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, relative to the earth, was at rest. For how should the first observer know or be able to determine, that he is in a state of fast uniform motion? One sees in this paradox the germ of the special relativity theory is already contained. ” 26

Albert Einstein, “Autobiographical Sketch” published 1956 “During this year in Aarau the following question came to me: if one chases a light wave with the speed of light, then one would have before one a time independent wave field. But such a thing appears not to exist! This was the first child-like thought experiment related to the special theory of relativity. Discovery is not a work of logical thought, even if the final product is bound in logical form. ” As recounted to Max Wertheimer in 1916 “The problem began when Einstein was sixteen years old, a pupil in the Gymnasium (Aarau, Kantonschule)… The process started in a way that was not very clear, and is therefore difficult to describe —in a certain state of being puzzled. First came such questions as: What if one were to run after a ray of light? What if one were riding on the beam? If one were to run after a ray of light as it travels, would its velocity thereby be decreased? If one were to run fast enough, would it no longer move at all? …[W’s ellipses] To young Einstein this seemed strange. …When I asked him whether, during this period, he had already had some idea of the constancy of light velocity, independent of the movement of the reference system, Einstein answered decidedly: ‘No, it was just curiosity. That the velocity of light could differ depending upon the movement of the observer was somehow characterized by doubt. Later developments increased that doubt. ’” 27

The Thought A frozen waveform! 28

The thought experiment generates no trouble for an ether based Maxwell electrodynamics. “…I should observe such a beam of light as an electromagnetic field at rest though spatially oscillating. There seems to be no such thing, however, neither on the basis of experience nor according to Maxwell’s equations. From the very beginning it 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, relative to the earth, was at rest. For how should the first observer know or be able to determine, that he is in a state of fast uniform motion? ” …but only because we have no experience of moving at the speed light in the ether. …but it is allowed by Maxwell’s equations through the simplest transformation. …but the observer would know he is moving rapidly because the light would appear frozen. 29

Why does the thought experiment merit pride of place in Einstein’s defining autobiography? Is it merely the recording of the visceral hunches of a precocious sixteen year old, who did not study Maxwell’s theory until two years later? Or does it have a cogency that extends beyond Einstein’s final high school year? Einstein (16 yrs) in 1896 in the cantonal school of Aarau 30

The Thought Experiment succeeds against an emission theory of light. i. e. a theory that conforms to the principle of relativity using Newtonian notions of space and time. Frozen lightwaves? “…There seems to be no such thing, however, neither on the basis of experience. . . ” A light source receding at c leaves a frozen wave behind. We should expect to experience these frozen waves if there are rapidly receding light sources. There is no need for us to move at c. 31

“…or according to Maxwell’s equations…” Frozen electromagnetic waves are possible in any inertial frame of reference. Frozen electromagnetic waves must be admissible in electrostatics and magnetostatics. Electrostatics and magnetostatics of an emission theory should agree with the electrostatics and magnetostatics of Maxwell’s theory. (Oldest and most secure part of theory. ) BUT Maxwell’s equations prohibit frozen waves. 32

“…For how should the first observer know or be able to determine, that he is in a state of fast uniform motion? ” A light wave of definite color, amplitude, polarization. Is it a propagating wave? Or a frozen wave? An extra property is needed to separated the two cases. (Equivalent to: Is the observer moving rapidly with respect to the source? ) But color, amplitude and polarization are the only properties light has. 33

An emission theory of light cannot be formulated in terms of differential field equations. Field theory formulated with differential equations: present, local state of the field determines its future time development. Precluded in an emission theory of light. An extra property is needed to distinguish frozen from propagating waves. Example: Maxwell’s theory x. H = (1/c)(∂E/∂t) x. E = - (1/c)(∂H/∂t) Present state of field Rate of change of field Future time development of field. 34

The obvious escape… A field theory in which the color of a wave fixes its velocity of propagation. Example: The differential field equation (∂2/∂t 2 - ∂2/∂x 2 -m 2) j(x, t)= 0 admits waves j(x, t)= exp i (wt-kx) where m 2=k 2 -w 2 Color (wave number k) fixes velocity v = w/k = (1 - m 2/ k 2) 1/2 k = m --> v=0 “But the strongest argument [against an emission theory] seemed to me: If there is no fixed velocity for light at all, then why should it be that all light emitted by “stationary” bodies has a velocity completely independent of the color? This seemed absurd to me. Therefore I rejected this possibility as a priori improbable. ” Einstein to Hines, Feb. 1952, 35

Pathways to “the Step” 36

Did Einstein actually discover Or was the celebrated analysis of the relativity of simultaneity by reflecting on clocks and their synchronization by light signals? clock synchronization a convenient way to present a result already found by other means? Light enters virtually everywhere as an electromagnetic waveform and not a spatially localized signal. Other pathways are possible: e. g. aberration, Einstein unaware that Fresnel drag coefficient can be derived by velocity addition on light pulses. The aberration of starlight and the Fresnel drag in Maxwell-Lorentz electrodynamics is a manifestation of Lorentz’s local time. Reverse the derivation to read relativity of simultaneity from observations. Simple thought experiments show field transformations can force the relativity of simultaneity. 37

Conclusion 38

What could Einstein recover from the device of field transformations? What was Ritz’s emission “theory”? How might Einstein have used a Ritz type approach? What thought experiment shows its failure most cogently? How did Einstein make “the step”? Two partial theories of electrodynamics, jointly not adequate to the principle of relativity. Part polemic against Einstein and part program for finding Galilean covariant force laws. To construct a promising, Galilean covariant electrodynamics. Einstein’s chasing-a-light-beam thought experiment. Several possibilities; it may not have been by reflecting on light signals and clock synchronization. 39