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12 S. Saundersloops (postulated by Ampere) are oriented parallel to one another.However, subsequent results suggested a g-factor closer to two , a factthat received detailed discussion at the Solvay Conference of 1921.Einstein fo!Jowed the debates closely; by 1924 evidence for theanomaly was all but conclusive. As a result, Ampere's hypothesis is incrisis and with it the established theory of magnetization. By this timeBarnett, one of the leading experimentalists involved, had speculatedthat the converse process to the Einsteio-de Haas effect might haveestablished the magnetic field of the earth. He now considered thatthe anomalous g-factor might be related to the anomalous Zeemaneffect. Characteristically, Einstein looks to a new length-scale forclues for the needed modification of electrodynamics: be consideredthe hitherto unexplained magnetic field of the earth. That same yearGoudsmit and Uhlenbeck, with the introduction of electron spin,made an innovation more radical still. The complete theory of atomicg-factors rests on Dirac's 1928 synthesis of relativity and quantumtheory , constituting its earliest and most important success. (Fordetails 1 refer to Peter Galison's beautiful account in How Experi-ments End, University of Chicago Press, 1987: 27-74; for thecontemporary theory of the earth's magnetic field see Ronald Meniland Michael McElhjnny, The Earth's Magnetic Field: Its History,Origin, and Planetary Perspective, Academic Press, 1983.)

1On the EtherALBERT EINSTEIN

I f we are here going to talk about the ether, we are not, of course,talking about the physical or material ether of the mechanical theoryof undulations, which is subject to the laws of Newtonian mechanics,to the points of which are attributed a certain velocity. ThistheoretjcaJ edifice has , I am convinced, finally played out its role sincethe setting up of the special theory of relativity. I t is rather moregeneralJy a question of those kinds of trungs that are considered asphysically real, which play a role in the causal nexus of physics, apartfrom the ponderable matter that consists of electrical elementaryparticles. Therefore, instead ofspeaking ofan ether, one could equallywell speak of physical qualities of space. Now one could take theposition tbat all physical objects fall under this category, because inthe final analysis in a theory of fields the ponderable matter, or theelementary particles that constitute this matter, also have to beconsidered as fields' ofa particularkind, or as particular states' of hespace. But one would have to agree that, at the present state ofphysics, such a point of view would be premature, because up to nowall efforts directed to this aim in theoretical physics have led to failure.Jn the present situation we are de facto forced to make a distinctionbetween matte r and fields, while we hope that later generations will beable to overcome this dualistic concept, and replace it with a unitaryone, such as the field theory of today has sought in vain.It is generally assumed that Newtonian physics does nol recognizean ether, and that it is the undulatory theory of light that firstintroduced tills ubiquitous medium able to influence physicalphenomena. But this is not the case. N ewtonian mechanics has its'ether' in the suggested sense, whjch, however, is called 'absolutespace'. In order to understand trus clearly, and at the same time toOriginally published as 'Ober den Athcr", Sclrweizerische narurforschende Gesel/sc/rafi,Verhanjlungen (1924), 105: 85-93. This translalion S. W. Saunders 1991.

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14 A. Einsteinrender the ether concept more precise, we have to go back a littlefurther.

We consider first ofa ll a branch of physics that manages without anether, namely Euclidean geometry, which is conceived as the scienceof the possible ways of bringing bodies that are effectively rigid intocontact with one another. (We will disregard the light rays whichmight otherwise be involved in the origin of the concepts and laws ofgeometry.) The laws for the positioning of rigid bodies, excludingrelative mot ion, temperature, and deforming influences, such as theyare laid down in idealized form in Euclidean geometry, can make dowith the concept of a rigid body. Environmental influences of anykind, which are present independent of the bodies, which act upon thebodies, and which are to be considered as influencing the laws ofpositioning, are unknown to Euclidean geometry. The same is true ofnon -Euclidean geometries of constant curvature, if these are conceived as (possible) laws of nature for the positioning of bodies. I twould be ano ther matter if one considered it necessary to assume ageometry with variable curvature. This would mean that the possiblecontiguous positions of effectively rigid bodies in various differentcases would be determined by the environmental influences. In thesense considered here, in this case one would have to say that such atheory employs an ether hypothesis. This ether would be a physicalrea lity, as good as matter. If the laws of positioning could not beinfluenced by physical factors, such as the clustering or state ofmotion of bodies in the environmen t and so on , and were given onceand for all, such an ether would have to be described as absolute(i.e. independent of the influence of any other object).Just as the {physically interpreted) Euclidean geometry has no needof an ether, in the same way the kinematics or phoronomics ofclassical mechanics does not require one either. These laws have aclear sense in physics as long as one supposes that the influencesassumed in special relativity regarding rulers and clocks do not exist.

It s otherwise in the mechanics of Galileo and Newton. T he law ofmotion, 'mass x acceleration=force', contains not only a state mentregarding material systems, but something more-even when, as inNewton's fundamental law of astronomy, the force is exp ressedthrough distances, i.e. through magnitudes, the real definitions ofwhich can be based upon measurements with rigid bodies. Fo r thereal definition of acceleration cannot be based entirely on observations with rigid bodies and clocks. It cannot be referred back to the

On the Ether 15measurable distances of the points that constitute the mechanicalsystem. Fo r its definition one needs in addition a system ofcoordinates, respectively a reference body, in a suitable state ofmotion. I f he state of mo tion of the system of coordinates is chosendifferently, then with respect to these the Newtonian equations ofmotion willnot be valid. ln these equations, the environment in whichthe bodies move appears somehow implicitly as a real factor in thelaw of motion, alongside the actual bodies themselves and theirdistances from one another, which are definable in terms of measuringbodies. In Newton's science of motion, space has a physical reality,and this is in strict contrast to geometry and kinematics. We are goingto ca!J this physical reali ty, which enters into Newton's law of motionalongside the observable ponderable bodies, the 'ether of mechanics'.The fact that centrifugal effects arise in a (rotating) body, the materialpoints of which do not cha nge their distances from one another,shows that this ether is not to be supposed a phantasy of theNewtonian theory, but that there corresponds to the concept acertain reality in nature.

We can see that. for Newton, space was a physical reality, in spite ofthe peculiarly indiiect manner in which this reality enters ourunderstanding. ErnstMa ch, who was the first person after Newton tosubject Newtonian mechanics to a deep and searching analysis,understood this quite clearly. He sought to escape the hypothesis ofthe 'et her of mechanics' by explaining inertia in terms of theimmediate interaction between the piece of matter under investigation and aU other matter in the universe. This idea is logicallypossible, but, as a theory involving action-at-a-dista nce, it does nottoday merit serious consideration. We therefore have to consider themechanical ether which Newton called 'Absoiute Space' as some kindof physica.l reality. The term 'ether', on the other band, must not leadus to understand something similar to ponderable matter, as in thephysics of the nineteenth century.UNewton caUed the space of physics 'absolute', he was thinking ofyet another property of that which we eaU 'e ther'. Each physicalobject influences and in generalis influenced in turn by others. Thelatrer, however, is not true of the ether ofNewtonian mechanics. Theinertia-producing property of this ether, in accordance with classicalmechanics, is precisely not to be influenced, either by the configuration of matter, or by anything else. Fo r this reason, one may call it'absolute'.

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16 A. EinsteinThat something real has to be conceived as the cause for thepreference of an inertial system over a non-inertial system is a fact thatphysicists have only come to understand in recent years. Hi storically,the ether hypothesis, in its present-day form, arose out of themechanical ether hypothesis of optics by way of sublimation. Afterlong and fruitless efforts, one came to the conviction that light could

not be explained as the motion of an elastic medium with inertia, thatthe electromagnetic fields of the Maxwellian theory cannot in generalbe explained in a mechanical way. Under this burden of failure, theelectromagnetic fields were gradually cons idered as final, irreduciblephysical realities, which are not to be further explained as states of theether. The only thing that remained to the ether of the mechanicaltheory was its definite state of motion. I t represented, so to speak, an'absolute rest'. I f all inertial systems are on a par in the Newtonianmechanics, therefore also in the Maxwell- Lorentz theory, the state ofmotion of the preferred frame of coordinates (at rest with respect tothe ether) appeared to be ful1y determined. One tacitly assumed thatthis preferred system would, at the same time, be an inertial system,i.e. that the principle of inertia would bold in relation to theelectromagnetic ether.There is a second way in which the rising tide of the MaxwellLorentz theory shifted still further the fundamental concepts ofphysicists. On ce the electromagnetic fields had been conceived of asfundamental, irreducible entities, it seemed they were entitled to robpondera ble inertial massof ts fundamental significance in mechanics.I t was concluded from the Maxwell equations that an electricallycharged body in motion would be surrounded by a magnetic field th eenergy of which would, to a first approximation, depend on thesquare of the velocity. What could be more obvious than to conceiveof all kinetic energy as electromagnetic energy? In this way one couldhope to reduce mechanics to electromagnetism, having failed to referelectromagnetic processes back to mechanical ones. This appeared tobe all the more promising as it became more and more likely that allponderable matter was constituted of electrical elementary particles.At the same time, there were two difficulties which one could notmaster. First, the Maxwell-Lorentz equations could not explain howthe electrical charge that constitutes an electrical elementary particlecould exist in equilibrium in spite of the electromagnetic forces ofrepulsion. Second, the electromagnetic theory could not explaingravitation in a reasonably natural and satisfactory manner. In spite

On the Ether 17of all this, the consequences of the electromagnetic theory were soimportant that it was considered an utterly secure possession ofphysics-indeed, as one of its best founded acquisitions.In this way the Maxwell- Lorentz theory finally influenced ourunderstanding of the theoretical foundations of physics to such anextent that it led to the founding of the special theory of relativity. Itwas realized that the electromagnetic equations do not in truthdetermine a particular state of motion, but that, in accordance withthese equations- just as in classical mechanics- there is an infinitemanifold of coordinate systems, moving uniformly with respect toeach other, and all on a par, so long as one applies suitabletransformation formulae for the space coordinates and the time. I t iswell known that this realization brought about a deep modification ofkinematics and dynamics as a result. The ether of electrodynamicsnow no longer had any special or particular stateof motion. I t had theeffect, like the ether of classical mechanics, of giving preference not toa particular state of motion, but only to a particular state ofacceleration. Because it was no longer possible to speak ofsimultaneous states in different places in the ether in any absolutesense, the ether became, so to speak, four-dimensional, because therewas no objective arrangement of its space in accordance with timealone. Also, following the special theory of relativity, the ether wasabsolute, because its influence on inertia and light propagation wasthought to be independent of physical influences of any kind. While inclassical physics the geometry of bodies is presumed to be independent of the state of motion, in accordance with the special theory ofrelativity, the laws of Euclidean geometry for the positioning ofbodies at rest in relationship to one another are applicable only i fthese bodies are in a state of rest relative to an inertial system; 1 thiscan easily be concluded from the so-called Lorentz contraction.Therefore the geometry of bodies is influenced by the ether as well asthe dynamics.The general theory of relativity removes a defect of classicaldynamics: in the latter, inertia and weight appear as totally differentmanifestations, quite independent of one another, in spite of the factthat they are determined by the same body-constant, i.e. the mass.The theory of relativity overcomes this deficiency by determining the

1 For example, in accordance with the special theory of relativity, the Euclideangeometry does not apply to a system of bodies that are at rest relative to one another,but which in their totality rotate in relation to an inertial system.

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18 A. Einsteindynamical behaviour of the electrically neutral mass-point by meansof the law of the geodesic line, in which the inertia and weight effectscan no longer be distinguished. Thereby it attributes to the ether,varying from point to point, the metric and the dynamical propertiesof the points of matter, which in their turn are determined by physicalfactors, to wit the distribution of mass or energy respectively. Theether of the general theory of relativity therefore differs from that ofclassical mechanics or the special theory of relativity respectively, inso far as it is not 'absolute', but is determined in its locally variableproperties by ponderable matter. This determination is complete ifthe universe is closed and spatiaiJy finite. The fact that the generaltheory of relativity has no preferred space-time coordinates whichstand in a determinate relation to the metric is more a characteristic ofthe mathematical form of the theory than of its physical content.Even the application of the formal apparatus of the general theory'of relativity was no t able to reduce all mass-inertia to electromagneticfields or fields in general. Furthermore, in my opinion, we havenot asyet succeeded in going beyond a superficial integration of theelectromagnetic forces into the general scheme of relativity. Themetric tensor which determines both gravitational and inertialphenomena on the one hand, and the tensor of the electromagneticfield on the other, still appear as fundamentally different expressionsof the state of the ether; but their logical independence is probablymore to be attributed to the imperfection of our theoretical edificethan to a complex structure of reality itself.

I admit that Weyl and Eddington have, by means of a generalization of Riemann geometry, found a mathematical system that allowsboth types of field to appear as though united under one single pointof view. But the simplest field equations that are yielded by thattheory do not appear to me to lead to any progress in theunderstanding of physics. Altogether it would today appear that weare much further away from an understanding of the fundamentallaws of electromagnetism than it appeared at the beginning of thecentury. To support this opinion,1would here like briefly to pointou tthe problem of the magnetic fields of the earth and sun as well as theproblem of light quanta, which problems concern, so to speak, thelarge-scale structure and the fine structure of the electromagneticfield.

The earth and the sun have magnetic fields, the orientation andsense of which stand in approximate relationship to the axes of

On the Ether 19rotation of these heavenly bodies. In accordance with the Maxwelltheory these fields could be produced by electrical current s which flowin the opposite direction to the rotational movement around the axesofthe heavenly bodies. The sunspots too, which for good reasons arelooked upon as vortices, possess analogous and very strong magneticfields. But it is hard to imagine that, in all these cases, electricalconduction or convection currents of sufficient magnitude are reallypresent. It rather looks as if cyclic movements of neutral masses areproducing magnetic fields. The Maxwell theory, neither in its originalform, nor as extended by the general theory of relativity, does notallow us to anticipate field generation of this kind. It would appearhere that nature is pointing to a fundamental process which is not yettheoretically understood. 2

I f we have just dealt with a case where the field t heory in its presentshape does not appear to be adequate, the facts and ideas thattogether make up the quantum theory threaten to blow up the edificeof field theory altogether. Indeed, the arguments are growing that thelight quantum should be considered a physical reality, and that theelectromagnetic field may not be looked upon as an ultimate realityby means of which other physical objects can be explained. Thetheory of the Planck formula has already shown that the transmissionof energy and impulse by means of radiation takes place in such amanner as if the latter consisted of atoms moving with the velocity oflight c and with the energy hv, and with an impulse hvjc; by means ofexperiments on the scattering of X-rays by matter, Compton nowshows that scattering events occur in which light quanta collide withelectrons and transmit part of their energy to the latter, whereby thelight quanta change their energy and direction. So much is factuallycertain: the X-rays undergo such changes of frequency in theirscattering as are required by the quantum hypothesis, as predicted byDebye and Compton.

2 Th e electrodynamic analogy would suggest the assumption of a relationship of theform dH = - C dm v x r/r 3 , in which dm is a mass moving with the velocity 'V , and r,respectively r= JJ , is the distance of the origin from this mass. (This formula can,however. at best be considered only for cyclic motion, and then only as a firstapproximation.) The relationship between the magnetic fields of the earth and of thesun is in this way correctly given as far as the order of magnitude is concerned. Th econstant C has the dimension (gravitational constant) 10j(speed of light). From Ibisone can estimate the order of magnitude of the constant C. If one puts this numericalmagnitude into the above formula, it will, applied to the rotating earth, give the rightorder of magnitude for the magnetic field. These relationships deserve consideration,but could be accidental.

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20 A. EinsteinFurthermore, a paper has recently appeared by the Indian scientistBose, regarding the derivation of the Planck formula, which isparticularly important for our theoretical understanding for thefollowing reason. Hitherto, all derivations of Planck's formula havesomewhere made use of the hypothesis of the undulatory structure ofradiation; for example, the factor 8rr.v2/c 3 of this formula, in thewell-known derivation of Ehrenfest and Debye, was obtained bycounting the number of eigenvibrationsoftbe cavity that occur in thefrequency range dv. This counting, which was based on the concepts

of the wave theory, is replaced by Bose by a gas-theoreticalcalculation, which he applies to a light quan tum situated in the cavityin the manner of a molecule. The question now arises whether itwould not one day be possible to connect the diffraction andinterference phenomena to quantum theory in such a way that thefield-like concepts of the theory would represent only the expressionsof the interactions between quanta, whereby no longer would anindependent physical reality be ascribed to the field.The important fact that, according to the theory of Bohr, the

frequency of the radiation is not determined by electrical masses thatundergo periodical processes of the same frequency can only increaseour doubts as to the independent reality of the undulatory field.But even if hese possibilities should mature into genuine theories,we will not be able to do without the ether in theoretical physics, i.e. acontinuum which is equipped with physical properties; for the generaltheory of relativity, whose basic points of view physicists surely willalways maintain, excludes direct distant action. But every contiguousaction theory presumes continuous fields, and therefore also theexistence of an 'ether'.

2The Mass of the Classical Vacuum

R. PENROSEThere is something a bit paradoxical in the lessons classical physicshas to teach us about the physical n_ture of matter. We may ask,What indeed is 'matter'? The commonsense reply might be that it isthe real substance of which actual physical objects- the 'things' ofthis world-are composed. It is what you, I, and our houses are madeof. How, then, does one actually quantify this substance? Ourelementaryphysics textbooks provide us with Newton's clear answer:it is the mass of an object, or system of objects, that measures thequantity of matter that it contains. This, indeed, now seems right;there is no other physical quantity that can seriously compete withmass as the true measure of total substance. Moreover, it isconserved-so that the mass of any system whatever must beunchanging with time.Yet Einstein's famous (1905) formula from special relativity,

E=mcl,tells us that mass and energy are interchangeable with one another.Mass is still conserved, but now it seems less clearly to be the truemeasure of actual substance. Energy, after all, depends upon thespeed with which tha t substance is seen to be travelling. The energy ofmotion in an express train is considerable, but if we happen to besitting in that train, then, according to our own reference frame, thetrain possesses no motion at all. The energy of that motion (thoughnot the heat energy of the individual particles, nor the rest-massenergy of those particles) is now reduced to zero by our particularchoice of frame. The total mass of the express train, beingproportional to its energy, appears to be less to a traveller on the trainthan to someone who remains stationary on the ground as the trainspeeds by.@ R. Penrose 1991This article is based largely on a passage (the final section or eh. 5) from TheEmperor's New Mind, by R. Penrose (Oxford University Press, 1989).