Einstein 1938: Field and Matter

Reference: Evolution of Physics

This paper presents Chapter III, section 14 from the book THE EVOLUTION OF PHYSICS by A. EINSTEIN and L. INFELD. The contents are from the original publication of this book by Simon and Schuster, New York (1942).

The paragraphs of the original material (in black) are accompanied by brief comments (in color) based on the present understanding.  Feedback on these comments is appreciated.

The heading below is linked to the original materials.


Field and Matter

We have seen how and why the mechanical point of view broke down. It was impossible to explain all phenomena by assuming that simple forces act between unalterable particles. Our first attempts to go beyond the mechanical view and to introduce field concepts proved most successful in the domain of electromagnetic phenomena. The structure laws for the electromagnetic field were formulated; laws connecting events very near to each other in space and time. These laws fit the frame of the special relativity theory, since they are invariant with respect to the Lorentz transformation. Later the general relativity theory formulated the gravitational laws. Again they are structure laws describing the gravitational field between material particles. It was also easy to generalize Maxwell’s laws so that they could be applied to any c.s. like the gravitational laws of the general relativity theory.

The mechanical view described simple forces acting between unalterable particles. It broke down because it was limited to a certain level of inertia. The electromagnetic phenomena went beyond that level of inertia. It could be explained better with field concepts. Speed of light in special relativity helped understand absolute motion and its relationship with inertia. Changing inertia in general relativity helped understand the laws of gravity on a broader basis.

We have two realities: matter and field. There is no doubt that we cannot at present imagine the whole of physics built upon the concept of matter as the physicists of the early nineteenth century did. For the moment we accept both the concepts. Can we think of matter and field as two distinct and different realities? Given a small particle of matter, we could picture in a naive way that there is a definite surface of the particle where it ceases to exist and its gravitational field appears. In our picture, the region in which the laws of field are valid is abruptly separated from the region in which matter is present. But what are the physical criterions distinguishing matter and field? Before we learned about the relativity theory we could have tried to answer this question in the following way: matter has mass, whereas field has not. Field represents energy, matter represents mass. But we already know that such an answer is insufficient in view of the further knowledge gained. From the relativity theory we know that matter represents vast stores of energy and that energy represents matter. We cannot, in this way, distinguish qualitatively between matter and field, since the distinction between mass and energy is not a qualitative one. By far the greatest part of energy is concentrated in matter; but the field surrounding the particle also represents energy, though in an incomparably smaller quantity. We could therefore say: Matter is where the concentration of energy is great, field where the concentration of energy is small. But if this is the case, then the difference between matter and field is a quantitative rather than a qualitative one. There is no sense in regarding matter and field as two qualities quite different from each other. We cannot imagine a definite surface separating distinctly field and matter.

Field and matter are split by a wide gulf of inertia and velocity. Both represent substance. Matter has high inertia but low velocity. Field has low inertia but high velocity. Physics views inertia as “mass” and velocity as “energy” but it does not see the reciprocal relationship between “mass” and “energy” as can be seen between inertia and velocity. Physics, however, does recognize some commonality between “mass” and “energy”. When it says, “Matter represents vast stores of energy,” it is comparing them as substance in terms of inertia. “Energy” has the sense of kinetic energy, which is perceived as velocity. Mass and energy equivalence is none other than inertia and velocity equivalence.

The same difficulty arises for the charge and its field. It seems impossible to give an obvious qualitative criterion for distinguishing between matter and field or charge and field.

Charge seems to be a transition phenomenon between matter and field. It has the characteristics of inertia and velocity that fall between matter and field.

Our structure laws, that is, Maxwell’s laws and the gravitational laws, break down for very great concentrations of energy or, as we may say, where sources of the field, that is electric charges or matter, are present. But could we not slightly modify our equations so that they would be valid everywhere, even in regions where energy is enormously concentrated?

We seem to have discontinuity between field and matter in terms of applicable laws.

We cannot build physics on the basis of the matter-concept alone. But the division into matter and field is, after the recognition of the equivalence of mass and energy, something artificial and not clearly defined. Could we not reject the concept of matter and build a pure field physics? What impresses our senses as matter is really a great concentration of energy into a comparatively small space. We could regard matter as the regions in space where the field is extremely strong. In this way a new philosophical background could be created. Its final aim would be the explanation of all events in nature by structure laws valid always and everywhere. A thrown stone is, from this point of view, a changing field, where the states of greatest field intensity travel through space with the velocity of the stone. There would be no place, in our new physics, for both field and matter, field being the only reality. This new view is suggested by the great achievements of field physics, by our success in expressing the laws of electricity, magnetism, gravitation in the form of structure laws, and finally by the equivalence of mass and energy. Our ultimate problem would be to modify our field laws in such a way that they would not break down for regions in which the energy is enormously concentrated.

We may look at matter as highly concentrated field. Here field is extremely dynamic, whereas, matter is nearly static. We need laws of physics to cover the structure of both field and matter.

But we have not so far succeeded in fulfilling this programme convincingly and consistently. The decision, as to whether it is possible to carry it out, belongs to the future. At present we must still assume in all our actual theoretical constructions two realities: field and matter.

Fundamental problems are still before us. We know that all matter is constructed from a few kinds of particles only. How are the various forms of matter built from these elementary particles? How do these elementary particles interact with the field? By the search for an answer to these questions new ideas have been introduced into physics, the ideas of the quantum theory.

These problems are taken forward to Quantum theory.


A new concept appears in physics, the’ most important invention since Newton’s time: the field. It needed great scientific imagination to realize that it is not the charges nor the particles but the field in the space between the charges and the particles which is essential for the description of physical phenomena. The field concept proves most successful and leads to the formulation of Maxwell’s equations describing the structure of the electromagnetic field and governing the electric as well as the optical phenomena.

The theory of relativity arises from the field problems. The contradictions and inconsistencies of the old theories force us to ascribe new properties to the time-space continuum, to the scene of all events in our physical world.

The relativity theory develops in two steps. The first step leads to what is known as the special theory of relativity, applied only to inertial co-ordinate systems, that is, to systems in which the law of inertia, as formulated by Newton, is valid. The special theory of relativity is based on two fundamental assumptions: physical laws are the same in all co-ordinate systems moving uniformly, relative to each other; the velocity of light always has the same value. From these assumptions, fully confirmed by experiment, the properties of moving rods and clocks, their changes in length and rhythm depending on velocity, are deduced. The theory of relativity changes the laws of mechanics. The old laws are invalid if the velocity of the moving particle approaches that of light. The new laws for a moving body as reformulated by the relativity theory are splendidly confirmed by experiment. A further consequence of the (special) theory of relativity is the connection between mass and energy. Mass is energy and energy has mass. The two conservation laws of mass and energy are combined by the relativity theory into one, the conservation law of mass-energy.

The general theory of relativity gives a still deeper analysis of the time-space continuum. The validity of the theory is no longer restricted to inertial co-ordinate systems. The theory attacks the problem of gravitation and formulates new structure laws for the gravitational field. It forces us to analyse the role played by geometry in the description of the physical world. It regards the fact that gravitational and inertial mass are equal, as essential and not merely accidental, as in classical mechanics. The experimental consequences of the general relativity theory differ only slightly from those of classical mechanics. Thy stand the test of experiment well wherever comparison is possible. But the strength of the theory lies in its inner consistency and the simplicity of its fundamental assumptions.

The theory of relativity stresses the importance of the field concept in physics. But we have not yet succeeded in formulating a pure field physics. For the present we must still assume the existence of both: field and matter.



Matter and field are two aspects of substance that remind us of particle and void; but there is no absolute void. Matter forms a high inertia and low velocity plateau; whereas, field forms low inertia and high velocity plateau. These two plateaus are separated by a sharp slope as shown in the following picture. Charge seems to be a transition phenomenon between matter and field.

Physics views inertia as “mass” and velocity as “energy”. The theory of relativity establishes equivalence between mass and energy. A very small amount mass is equivalent to a very large amount of energy. A similar relationship appears to exist between inertia and velocity. A large change in velocity in the material region has imperceptible change in mass (inertia).

The picture above shows that there is a reciprocal relationship between inertia and velocity. It will be helpful to find the exact mathematical relationship between them. This also shows that there exist absolute scales for both inertia and velocity.

Equivalence between gravity and acceleration means that a gravitational field shall consist of changing inertia. It will take an extremely small change in inertia to construct a gravitational field. This may help us develop a better understanding between field and matter.


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