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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When a smaller box s is situated, relatively at rest, inside the hollow space of a larger box S, then the hollow space of s is a part of the hollow space of S, and the same “space”, which contains both of them, belongs to each of the boxes. When s is in motion with respect to S, however, the concept is less simple. One is then inclined to think that s encloses always the same space, but a variable part of the space S. It then becomes necessary to apportion to each box its particular space, not thought of as bounded, and to assume that these two spaces are in motion with respect to each other.
Einstein makes the assumption that an impression of bounded space (s) is contained within the impression of larger bounded space (S). Both impressions are projected on a background SPACE. He then imagines spaces (s) and (S) to be unbounded and in motion relative to each other. This is all subjective based on abstraction of material dimensions.
Before one has become aware of this complication, space appears as an unbounded medium or container in which material objects swim around. But it must now be remembered that there is an infinite number of spaces, which are in motion with respect to each other.
The concept of space as something existing objectively and independent of things belongs to pre-scientific thought, but not so the idea of the existence of an infinite number of spaces in motion relatively to each other.
This latter idea is indeed logically unavoidable, but is far from having played a considerable rôle even in scientific thought.
Thus, Einstein’s spaces are the abstraction of “unbounded material objects”, which are in motion with respect to each other. There are infinite numbers of such spaces. This type of space is not a container in which material objects swim around. Only the background SPACE has that distinction, which, actually, provides an objective reference point of zero dimension and zero inertia.
But what about the psychological origin of the concept of time? This concept is undoubtedly associated with the fact of “calling to mind”, as well as with the differentiation between sense experiences and the recollection of these. Of itself it is doubtful whether the differentiation between sense experience and recollection (or simple re-presentation) is something psychologically directly given to us. Everyone has experienced that he has been in doubt whether he has actually experienced something with his senses or has simply dreamt about it. Probably the ability to discriminate between these alternatives first comes about as the result of an activity of the mind creating order.
Motion exists due to sequential changes in material extensions. While material extensions provide an impression of space, changes in these extensions provide the impression of time. Einstein’s space is subjective abstraction of unbounded material extensions. Changes in this abstraction of material extensions provide Einstein’s conception of time. This time is also subjective.
The physical reality exists only in terms of material extensions and changes in them. The objective reality of SPACE exists only as the background, which is best interpreted as “zero” of dimension and “zero” of inertia. The objective reality of TIME is also the same background viewed as “zero” of change.
An experience is associated with a “recollection”, and it is considered as being “earlier” in comparison with present “experiences”. This is a conceptual ordering principle for recollected experiences, and the possibility of its accomplishment gives rise to the subjective concept of time, i.e. that concept of time which refers to the arrangement of the experiences of the individual.
Our experience is made up of ordered perceptual elements that may be arranged in a matrix-like fashion. Many logical sequences exist in such a matrix from a point in different directions. Each of this logical sequence will represent the experience of time.
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Earlier notes by Vinaire:
To think that “the hollow space of s is a part of the hollow space of S” is treating space as matter. This is an example of “matter-centric” thinking. It introduces an arbitrary like “earth is at the center of the universe”. Logically space is simply the background. The idea of “an infinite number of spaces in motion relatively to each other” does not make sense.
In the Disturbance Theory of Space, pure space is simply the concept of undisturbed space that arises when there is disturbance. The disturbed space exists objectively as electromagnetic wave. We cannot say if undisturbed space exists by itself before there is any disturbance. The undisturbed space interfaces with the physical actuality of disturbed space only as a concept. We may say that undisturbed space is the limiting condition of electromagnetic wave of frequency zero.
The disturbance introduces the idea of time. Pure time is the background of all changes. It exists only as a concept. Actual time exists as change in the form of the “period” of the disturbance. More precisely, real space exists as the wavelength of the disturbance.
Diving into psychology simply means looking at the conceptual relationships that exist in the mind, as well as the physical relationships out there. “Calling to mind” is a process of reconstructing observations. Sense experience is direct observation that helps reconstruction. Any reconstruction involves ordering of events. This is essentially putting together a logical sequence of changes.
This brings time into view. Motion is changing relationships whether physical or conceptual.
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