Vinaire's Blog

Reference: http://www.relativitybook.com/resources/Einstein_space.html

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

THE ELECTROMAGNETIC FIELD ACTUALLY DESCRIBES THE STATES OF SPACE.

.

Previous: Relativity and the Problem of Space (Part 8)

Next:  Relativity and the Problem of Space (Part 10)

.

Reference: http://www.relativitybook.com/resources/Einstein_space.html

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

.

Science has taken over from pre-scientific thought the concepts space, time, and material object (with the important special case “solid body”) and has modified them and rendered them more precise. Its first significant accomplishment was the development of Euclidean geometry, whose axiomatic formulation must not be allowed to blind us to its empirical origin (the possibilities of laying out or juxtaposing solid bodies). In particular, the three-dimensional nature of space as well as its Euclidean character are of empirical origin (it can be wholly filled by like constituted “cubes”).

The subtlety of the concept of space was enhanced by the discovery that there exist no completely rigid bodies.

The axiomatic formulation of Euclidean geometry has brought precision to the concepts of space-time-event, which are an abstraction of material dimensions. But these material dimensions belong to bodies that are not totally rigid.

All bodies are elastically deformable and alter in volume with change in temperature. The structures, whose possible congruences are to be described by Euclidean geometry, cannot therefore be represented apart from physical concepts. But since physics after all must make use of geometry in the establishment of its concepts, the empirical content of geometry can be stated and tested only in the framework of the whole of physics.

In physics we study the elastic deformation of material bodies and the change in their volume with temperature. Such physical phenomena affects material dimensions. Hence it should be taken into account by the concepts of space-time-event.

In this connection atomistics must also be borne in mind, and its conception of finite divisibility; for spaces of sub-atomic extension cannot be measured up.

Atomistics also compels us to give up, in principle, the idea of sharply and statically defined bounding surfaces of solid bodies. Strictly speaking, there are no precise laws, even in the macro-region, for the possible configurations of solid bodies touching each other.

The atoms are not uniformly solid. They are made of frequency gradients from zero frequency of space to very high frequency of the nucleus of the atom. Thus material objects are not bound by sharply defined boundaries, and they do not exactly touch each other. This should also be taken into account by the concepts of space-time-event.

In spite of this, no one thought of giving up the concept of space, for it appeared indispensable in the eminently satisfactory whole system of natural science.

Mach, in the nineteenth century, was the only one who thought seriously of an elimination of the concept of space, in that he sought to replace it by the notion of the totality of the instantaneous distances between all material points. (He made this attempt in order to arrive at a satisfactory understanding of inertia).

Such minutiae in the concepts of space-time-event become important only when working with the concept of Inertia.

.

Earlier notes by Vinaire:

The fundamental ideas in natural science have been there all this time. We are simply looking at them more closely to free them of filters (biases, prejudices, fixed ideas, assumptions and blind faith) and make them logically consistent with reality.

Euclidean Geometry assumes completely rigid solid bodies to come up with its axiomatic structure. But there are no completely rigid bodies. When physics uses geometry to set up its concepts, it must take care in this regard.

Consider the following.

(1) We cannot keep dividing matter infinitely. Division of matter ultimately seem to emit electromagnetic waves.

(2) We cannot measure spaces of sub-atomic extension. Points in space are approximations.

(3) In reality, sharply defined bounding surfaces do not exist. Interface of space with solids is blurred.

(4) There is no precise definition for solid bodies touching each other.

If there is no way to define the dimensions of solids precisely, then there cannot be a precise concept of space. We associate inertia with motion of material points. So we need to look closely at how we define “material point”.

.

Previous: Relativity and the Problem of Space (Part 5 & 6)

Next:  Relativity and the Problem of Space (Part 8)

.

Reference: http://www.relativitybook.com/resources/Einstein_space.html

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

.

We still have something essential to add to this sketch concerning the psychological origin of the concepts space-time-event (we will call them more briefly “space-like”, in contrast to concepts from the psychological sphere). We have linked up the concept of space with experiences using boxes and the arrangement of material objects in them. Thus this formation of concepts already presupposes the concept of material objects (e.g. ”boxes”). In the same way persons, who had to be introduced for the formation of an objective concept of time, also play the rôle of material objects in this connection. It appears to me, therefore, that the formation of the concept of the material object must precede our concepts of time and space.

Objective formation of physical phenomena seems to start as electromagnetic disturbance of background SPACE, which then progresses into the formation of sub-atomic particles, atoms, molecules and matter. From this matter we abstract our concepts of space-time-event.

All these space-like concepts already belong to pre-scientific thought, along with concepts like pain, goal, purpose, etc. from the field of psychology. Now it is characteristic of thought in physics, as of thought in natural science generally, that it endeavours in principle to make do with “space-like” concepts alone, and strives to express with their aid all relations having the form of laws. The physicist seeks to reduce colours and tones to vibrations, the physiologist thought and pain to nerve processes, in such a way that the psychical element as such is eliminated from the causal nexus of existence, and thus nowhere occurs as an independent link in the causal associations. It is no doubt this attitude, which considers the comprehension of all relations by the exclusive use of only space-like concepts as being possible in principle, that is at the present time understood by the term “materialism” (since “matter” has lost its rôle as a fundamental concept).

We do not know exactly how matter emerges from the background of zero dimension, zero inertia and zero change. But once matter is formed we abstract from it not only the concepts of space-time-event, but other psychological concepts as well. This may be called a materialistic approach to the understanding of the universe. But there seems to be a spiritual element underlying the very formation of matter in the first place.

Why is it necessary to drag down from the Olympian fields of Plato the fundamental ideas of thought in natural science, and to attempt to reveal their earthly lineage? Answer: in order to free these ideas from the taboo attached to them, and thus to achieve greater freedom in the formation of ideas or concepts. It is to the immortal credit of D. Hume and E. Mach that they, above all others, introduced this critical conception.

It seems that life and thought evolve from matter. But we cannot just label it as materialism. Matter is also an evolutionary step. Spirituality underlies the very formation of matter.

.

Earlier notes by Vinaire (5):

Space is the background of objects. Time is the background of changes in objects. Changes are not independent of objects. Therefore, time is not absolute in itself but it is an aspect of space. We represent this as a four-dimensional continuum of “space-time”.

Objects are both material and conceptual. We use logical consistency as a gradient to form concepts out of material objects. Material and conceptual objects, therefore, appear as gradient of logical abstraction.

Thus we have a “dimension of abstraction” that starts from concrete and extends into abstraction. The key characteristic of this dimension is logical consistency. Abstraction is not independent of objects, therefore, it is also an aspect of space.  We may present this as a five dimensional continuum of space-time-abstraction.

Hopefully this would take care of the psychological origin.

Earlier notes by Vinaire (6):

By “space-like” concepts, Einstein refers to the simple fundamental concepts to which all other concepts reduce. Concepts from the field of psychology are quite complex but they do seem to reduce to space, time and abstraction.

Science focuses on space-like concepts to come up with fundamental relationships having the form of laws. What Einstein refers to as “elimination of psychical element” is actually the removal of logical inconsistencies in conceptualization. These logical inconsistencies come about as a result of “personal filters”, such as, biases, prejudices, fixed ideas, assumptions and blind faith.

When Einstein refers to “exclusive use of only space-like concepts”, he means“exclusive use of logic in conceptualization”, which is the characteristic of “Dimension of Abstraction”.

The word “materialism” is a misnomer. It does not mean the supremacy of the material world. It simply points to the objectivity brought about by the use of the 5-dimensional continuum of the universe.

.

Previous: Relativity and the Problem of Space (Part 4)

Next:  Relativity and the Problem of Space (Part 7)

.