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Albert Einstein

Maxwell’s Influence
on the Development
of the Conception of Physical Reality

Written for the centenary of Maxwell’s birth [1931]

The belief in an external world independent of the observing subject lies at the foundation of all natural science. However, since sense-perceptions only inform us about this external world, or physical reality, indirectly, it is only in a speculative way that it can be grasped by us. Consequently our conceptions of physical reality can never be final. We must always be ready to change these conceptions, i.e. the axiomatic basis of physics, in order to do justice to the facts of observation in the most complete way that is logically possible. In actual fact, a glance at the development of physics shows that this axiomatic basis has met with radical changes from time to time.

The greatest change in the axiomatic basis of physics, and correspondingly in our conception of the structure of reality, since the foundation of theoretical physics through Newton, came about through the researches of Faraday and Maxwell on electromagnetic phenomena. In what follows we shall try to present this in a more precise way, while taking the earlier and later development into account.

In accordance with Newton’s system, physical reality is characterised by concepts of space, time, the material point and force (interaction between material points). Physical events are to be thought of as movements according to law of material points in space. The material point is the only representative of reality in so far as it is subject to change. The concept of the material point is obviously due to observable bodies; one conceived of the material point on the analogy of movable bodies by omitting characteristics of extension, form, spatial locality, and all their ‘inner’ qualities, retaining only inertia, translation, and the additional concept of force. The material bodies which had psychologically given rise to the formation of the concept of ‘material point’ had now for their part to be conceived as a system of material points. It is to be noted that this theoretical system is essentially atomistic and mechanistic.

All happening was to be conceived of as purely mechanical, that is, merely as motions of material points according to Newton’s laws of motion.

The most unsatisfactory aspect of this theoretical system — apart from the difficulty relating to the concept of ‘absolute space’ which has recently been brought back into the discussion — lay mainly in the doctrine of light, which Newton quite logically had also thought of as consisting of material points. Even at that time the question must already have been felt acutely: What happens to the material points that constitute light, when light itself is absorbed? Moreover, it is altogether unsatisfactory to introduce into the discussion two quite different kinds of material points which had to be put forward to represent ponderable matter and light. Then later on electrical corpuscles were added as a third sort with fundamentally different properties. Besides, it was a weakness in the basic structure that interacting forces had to be postulated quite arbitrarily to account for what happens. Nevertheless, this conception of reality accomplished a lot. How, then. did the conviction arise that it should be abandoned?

In order to give his system mathematical form at all, Newton had first to invent the concept of the differential quotient, and to draw up the laws of motion in the form of total differential equations — perhaps the greatest intellectual step that it has ever been given to one man to take. Partial differential equations were not needed for this, and Newton did not make any methodical use of them. Partial differential equations were needed, however, for the formulation of the mechanics of deformable bodies; this is bound up with the fact that in such problems the way and the manner in which bodies were thought of as constructed out of material points did not play a significant part to begin with.

Thus the partial differential equation came into theoretical physics as a servant, but little by little it took on the role of master. This began in the nineteenth century, when under the pressure of observational facts the undulatory theory of light asserted itself. Light in empty space was conceived as a vibration of the ether, and it seemed idle to conceive of this in turn as a conglomeration of material points. Here for the first time partial differential equations appeared as the natural expression of the primary realities of physics. In a particular area of theoretical physics the continuous field appeared side by side with the material point as the representative of physical reality. This dualism has to this day not disappeared, disturbing as it must be to any systematic mind.

If the idea of physical reality had ceased to be purely atomistic, it still remained purely mechanistic for the time being. One still sought to interpret all happening as the motion of inert bodies: indeed one could not at all imagine any other way of conceiving of things. Then came the great revolution which will be linked with the names of Faraday, Maxwell, Hertz for all time. Maxwell had the lion’s share in this revolution. He showed that the whole of what was known at that time about light and electromagnetic phenomena could be represented by his famous double system of partial differential equations, in which the electric and the magnetic fields made their appearance as dependent variables. To be sure Maxwell did try to find a way of grounding or justifying these equations through mechanical thought-models. However. he employed several models of this kind side by side, and took none of them really seriously, so that only the equations themselves appeared as the essential matter. and the field forces which appeared in them as ultimate entities not reducible to anything else. By the turn of the century the conception of the electromagnetic field as an irreducible entity was already generally established and serious theorists had given up confidence in the justification, or the possibility, of a mechanical foundation for Maxwell’s equations. Soon. on the contrary an attempt was made to give a field-theoretical account of material points and their inertia with the help of Maxwell’s field theory, but this attempt did not meet with any ultimate success.

If we disregard the important particular results which Maxwell’s life work brought about in important areas of physics, and direct attention to the modification which the conception of physical reality experienced through him, we can say: Before Maxwell people thought of physical reality — in so far as it represented events in nature — as material points, whose changes consist only in motions which are subject to total differential equations. After Maxwell they thought of physical reality as represented by continuous fields, not mechanically explicable, which are subject to partial differential equations. This change in the conception of reality is the most profound and the most fruitful that physics has experienced since Newton; but it must also be granted that the complete realisation of the programme implied in this idea has not by any means been carried out yet. The successful systems of physics, which have been set up since then, represent rather compromises between these two programmes, which because of their character as compromises bear the mark of what is provisional and logically incomplete, although in some areas they have made great advances. - Of these the first that must be mentioned is Lorentz’s theory of electrons, in which the field and electric corpuscles appear beside one another as equivalent elements in the comprehension of reality. There followed the special and general theory of relativity which — although based entirely on field theory considerations — hitherto could not avoid the independent introduction of material points and total differential equations.

The last and most successful creation of theoretical physics, quantum mechanics, differs fundamentally in its principles from the two programmes which we will briefly designate as Newton’s and Maxwell’s. For the quantities which appear in its laws lay no claim to describe physical reality itself but only the probabilities for the occurrence of one of the physical realities to which attention is being directed. Dirac, to whom in my judgement. we are indebted for the most logically complete account of this theory rightly points to the fact that it would not be easy, for example. to give a theoretical description of a photon in such a way that there would be comprised in the description sufficient reason for a judgement as to whether the photon will pass a polarisator set obliquely in its path or not.

Nevertheless. I am inclined to think that physicists will not be satisfied in the long run with this kind of indirect description of reality, even if an adaptation of the theory to the demand of general relativity can be achieved in a satisfactory way. Then they must surely be brought back to the attempt to realise the programme which may suitably be designated as Maxwellian: a description of physical reality in terms of fields which satisfy partial differential equations in a way that is free from singularities.

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