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.

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What is the position of the special theory of relativity in regard to the problem of space? In the first place we must guard against the opinion that the four-dimensionality of reality has been newly introduced for the first time by this theory. Even in classical physics the event is localised by four numbers, three spatial co-ordinates and a time co-ordinate; the totality of physical “events” is thus thought of as being embedded in a four-dimensional continuous manifold. But on the basis of classical mechanics this four-dimensional continuum breaks up objectively into the one-dimensional time and into three-dimensional spatial sections, only the latter of which contain simultaneous events. This resolution is the same for all inertial systems. The simultaneity of two definite events with reference to one inertial system involves the simultaneity of these events in reference to all inertial systems. This is what is meant when we say that the time of classical mechanics is absolute. According to the special theory of relativity it is otherwise.

The problem of space is that it is an abstraction only. The three spatial coordinates apply to the extension of the bodies. The time dimension applies to the changes in the bodies. These dimensions do not exist in the absence of the bodies. The theory of relativity deals with the subjective abstraction of space and time.

“The sum total of events which are simultaneous with a selected event exist, it is true, in relation to a particular inertial system, but no longer independently of the choice of the inertial system. The four-dimensional continuum is now no longer resolvable objectively into sections, all of which contain simultaneous events; “now” loses for the spatiaIly extended world its objective meaning. It is because of this that space and time must be regarded as a four-dimensional continuum that is objectively unresolvable, if it is desired to express the purport of objective relations without unnecessary conventional arbitrariness.

Objectivity comes from what can be sensed physically. The objectivity of space and time comes from looking directly at material objects. It changes as we look at field instead of matter. The objectivity of inertia is tied closely to the objectivity of space and time. It also changes from matter to field.

Since the special theory of relativity revealed the physical equivalence of all inertial systems, it proved the untenability of the hypothesis of an aether at rest. It was therefore necessary to renounce the idea that the electromagnetic field is to be regarded as a state of a material carrier. The field thus becomes an irreducible element of physical description, irreducible in the same sense as the concept of matter in the theory of Newton.

The background SPACE of zero inertia is “at rest” in all inertial systems. This is misinterpreted as aether being at rest. Inertia manifests as the fundamental characteristic that underlies both electromagnetic and inertial fields. Inertia consolidates itself as the electromagnetic field condenses into the inertial field of mass. Space and time are aspects of this inertia. They manifest as space-time dimensions for the inertial field, but as frequency for the electromagnetic field.

Up to now we have directed our attention to finding in what respect the concepts of space and time were modified by the special theory of relativity. Let us now focus our attention on those elements which this theory has taken over from classical mechanics. Here also, natural laws claim validity only when an inertial system is taken as the basis of space-time description. The principle of inertia and the principle of the constancy of the velocity of light are valid only with respect to an inertial system. The field-laws also can claim to have a meaning and validity only in regard to inertial systems.

The inertial field of matter is considered to have inertia because its “velocity” maintains itself. This inertia is overcome by force, which then manifests “acceleration”. Similarly, the electromagnetic field has inertia because it’s “frequency” maintains itself. This inertia is overcome by force that changes this frequency.

Inertia changes with changes in frequency for the field, and changes in velocity for the matter; but these changes are very small.

Thus, as in classical mechanics, space is here also an independent component in the representation of physical reality. If we imagine matter and field to be removed, inertial-space or, more accurately, this space together with the associated time remains behind. The four-dimensional structure (Minkowski-space) is thought of as being the carrier of matter and of the field. Inertial spaces, with their associated times, are only privileged four-dimensional co-ordinate systems, that are linked together by the linear Lorentz transformations. Since there exist in this four-dimensional structure no longer any sections which represent “now” objectively, the concepts of happening and becoming are indeed not completely suspended, but yet complicated. It appears therefore more natural to think of physical reality as a four-dimensional existence, instead of, as hitherto, the evolution of a three-dimensional existence.

Einstein says, “If we imagine matter and field to be removed, inertial-space or, more accurately, this space together with the associated time remains behind.” This is an abstraction and a subjective interpretation of reality. The objectively reality consists only of the background SPACE of no inertia, no dimensions and no change when matter and field are removed. The Minkowski space is a mathematical abstraction and it is not an actuality that can be sensed physically.

Einstein’s theory correctly postulates the reality of the field, but it does not deal with it objectively. It has no way to account for the reference point of zero inertia for the matter and field that is present. It does not acknowledge the reality of the background SPACE of zero inertia and zero dimension. Therefore, it has no objective sense of “now” either.

This rigid four-dimensional space of the special theory of relativity is to some extent a four-dimensional analogue of H. A. Lorentz’s rigid three-dimensional aether. For this theory also the following statement is valid: The description of physical states postulates space as being initially given and as existing independently. Thus even this theory does not dispel Descartes’ uneasiness concerning the independent, or indeed, the a priori existence of “empty space”. The real aim of the elementary discussion given here is to show to what extent these doubts are overcome by the general theory of relativity.

The general theory of relativity is a four dimensional analogue of the three-dimensional aether theory. It does not dispel Descartes’ uneasiness concerning the independent, or indeed, the a priori existence of “empty space”, because it does not acknowledge that when matter and field are removed, their abstractions are also removed.

The reality postulated by Descartes aligns with the background space of no inertia, no dimensions and no change.

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Earlier notes by Vinaire:

Time was held absolute in classical mechanics, but it is no longer so in the special theory of relativity. But “space-time” was still being held absolute and independent with respect to matter.

The electromagnetic field could no longer be regarded as a state of a material carrier, such as, aether at rest. The field thus becomes an irreducible element of physical description.

Concept of motion arises as the “evolution” of three-dimensional space with respect to absolute time. But when existence is looked upon as four-dimensional space-time with respect to absolute matter, how does it “evolve”?

The Disturbance Theory regards that field (energy) and matter arise as the “evolution” of four-dimensional space-time.

The Disturbance Theory looks at Space-Energy-Matter as three states of INERTIA, just like Classical Mechanics looks at gas-liquid-solid as the three states of matter.

Time seems to appear as the continuously varying parameter underlying the spectrum of “space-energy-matter”.

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

Next:  Relativity and the Problem of Space (Part 12)

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

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

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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.

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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.

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

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

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

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

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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.

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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”.

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

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

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