Relativity and the Problem of Space (Part 9)

NOTE: Einstein’s statements are in black italics. My understanding follows in bold color italics.


The surmounting of this standpoint resulted from a development which, in the first place, appeared to have nothing to do with the problem of space-time, namely, the appearance of the concept of field and its final claim to replace, in principle, the idea of a particle (material point). In the framework of classical physics, the concept of field appeared as an auxiliary concept, in cases in which matter was treated as a continuum. For example, in the consideration of the heat conduction in a solid body, the state of the body is described by giving the temperature at every point of the body for every definite time. Mathematically, this means that the temperature T is represented as a mathematical expression (function) of the space co-ordinates and the time t (Temperature field). 

The law of heat conduction is represented as a local relation (differential equation), which embraces all special cases of the conduction of heat. The temperature is here a simple example of the concept of field. This is a quantity (or a complex of quantities), which is a function of the co-ordinates and the time. Another example is the description of the motion of a liquid. At every point there exists at any time a velocity, which is quantitatively described by its three “components” with respect to the axes of a co-ordinate system (vector). The components of the velocity at a point (field components), here also, are functions of the co-ordinates (x, y, z) and the time (t).

With the development of the concept of field, the idea of an inertial field provides a more accurate picture of physical reality than the concept of a material point.

The concept of field came about with the development of thermodynamics and fluid dynamics. The fields described by these disciplines are made up of quantities, such as, temperature and velocity, which are a function of the co-ordinates of space and time (x, y, z, t).

In principle, then it is possible to replace the concept of material point with the concept of a field, where that field describes inertia as a function of space and times at every point.

It takes differential equations to completely describe the complexity of temperature and velocity fields. Similar complexity may arise in completely describing an inertial field that may replace the concept of material point.

It is characteristic of the fields mentioned that they occur only within a ponderable mass; they serve only to describe a state of this matter. In accordance with the historical development of the field concept, where no matter was available there could also exist no field. But in the first quarter of the nineteenth century it was shown that the phenomena of the interference and motion of light could be explained with astonishing clearness when light was regarded as a wave-field, completely analogous to the mechanical vibration field in an elastic solid body. It was thus felt necessary to introduce a field, that could also exist in “empty space” in the absence of ponderable matter.

The classical fields occur only within a ponderable mass, as they describe a state of this matter. Where no matter was available there could also exist no field.

But the work of Faraday and Maxwell showed that light, while being completely analogous to the mechanical vibration field, could also exist as a wave-field in “empty space”. In other words, light was a wave-field that could exist independent of matter in the background of SPACE of zero dimension, zero inertia and zero change.

Matter consists of mass that is abstracted as inertia. The material point is the concept of mass concentrated at a point. The reality is closer to inertia of mass distributed in the background SPACE as a function of x, y, z, and t. In other words, mass can be described better as an inertial field.

This state of affairs created a paradoxical situation, because, in accordance with its origin, the field concept appeared to be restricted to the description of states in the inside of a ponderable body. This seemed to be all the more certain, inasmuch as the conviction was held that every field is to be regarded as a state capable of mechanical interpretation, and this presupposed the presence of matter. One thus felt compelled, even in the space which had hitherto been regarded as empty, to assume everywhere the existence of a form of matter, which was called “aether”.

But since space was viewed as abstraction of material extensions, it was considered to be similar to matter in its properties. Therefore, the background space was believed to be the so-called “aether” having mechanical properties.

The emancipation of the field concept from the assumption of its association with a mechanical carrier finds a place among the psychologically most interesting events in the development of physical thought. During the second half of the nineteenth century, in connection with the researches of Faraday and Maxwell it became more and more clear that the description of electromagnetic processes in terms of field was vastly superior to a treatment on the basis of the mechanical concepts of material points. By the introduction of the field concept in electrodynamics, Maxwell succeeded in predicting the existence of electromagnetic waves, the essential identity of which with light waves could not be doubted because of the equality of their velocity of propagation. As a result of this, optics was, in principle, absorbed by electrodynamics. One psychological effect of this immense success was that the field concept, as opposed to the mechanistic framework of classical physics, gradually won greater independence.

But with the development of electrodynamics by Faraday and Maxwell, The concept of “aether” came under question, and it was ultimately replaced by the concept of space that was more like the electromagnetic wave-field, and not like matter having mechanical properties. 

Nevertheless, it was at first taken for granted that electromagnetic fields had to be interpreted as states of the aether, and it was zealously sought to explain these states as mechanical ones. But as these efforts always met with frustration, science gradually became accustomed to the idea of renouncing such a mechanical interpretation. Nevertheless, the conviction still remained that electromagnetic fields must be states of the aether, and this was the position at the turn of the century.

We are now in a position to evaluate electromagnetic wave-field against background SPACE of zero dimension, zero inertia and zero change.

An atom is made up of electrons and a nucleus. It may, therefore, be represented by electromagnetic wave-fields condensing into inertial fields. The boundary of the atom may be visualized as extending out all the way to the background SPACE of zero frequency.

This makes the atom continuous with space at its “boundary”. Thus, matter does not have absolutely sharp boundaries because there exists a continuity from space to matter.


Earlier notes by Vinaire:

The above is an excellent description by Einstein of evolution of scientific thought from the idea of a particle (material point) to the concept of field.

Field can exist in “empty space” in the absence of ponderable matter. The electromagnetic field is not a property of some matter called “aether”. The electromagnetic field is “matter of a finer form”. This broadens the mechanistic framework into a field concept. From this point it is easy to see that



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