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