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 Field
In Newtonian mechanics, space and time play a dual rôle. First, they play the part of carrier or frame for things that happen in physics, in reference to which events are described by the space co-ordinates and the time. In principle, matter is thought of as consisting of “material points”, the motions of which constitute physical happening. When matter is thought of as being continuous, this is done as it were provisionally in those cases where one does not wish to or cannot describe the discrete structure. In this case small parts (elements of volume) of the matter are treated similarly to material points, at least in so far as we are concerned merely with motions and not with occurrences which, at the moment, it is not possible or serves no useful purpose to attribute to motions (e.g. temperature changes, chemical processes).
In Newtonian Mechanics space and time act as the frame of reference in which matter is treated as a point and its motion is described by space and time coordinates. It is not possible to describe changes, such as, chemical and temperature, that cannot be represented as physical motions.
The second rôle of space and time was that of being an “inertial system”. From all conceivable systems of reference, inertial systems were considered to be advantageous in that, with respect to them, the law of inertia claimed validity.
Within the space-time reference frame the material points have inertia, which follows certain laws of motion.
In this, the essential thing is that “physical reality”, thought of as being independent of the subjects experiencing it, was conceived as consisting, at least in principle, of space and time on one hand, and of permanently existing material points, moving with respect to space and time, on the other. The idea of the independent existence of space and time can be expressed drastically in this way: If matter were to disappear, space and time alone would remain behind (as a kind of stage for physical happening).
Here space and time are assumed to be independent of the material points that are existing permanently within it.
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Earlier notes by Vinaire:
The Euclidean geometry is matter-centric as Einstein describes it so nicely here, “In this case small parts (elements of volume) of the matter are treated similarly to material points…”
We may define the matter-centric viewpoint as, “Unconsciously using material characteristics as one’s reference to understand what is there.” This is the case with Euclidean geometry. This has also been the case with most of science.
We assume that “physical reality” is independent of the subjects experiencing it. But the subjects experiencing it are also part of existence. Therefore, we need to expand definition of existence to include not only matter but also the awareness of matter. This adds to existence another dimension. This dimension is abstraction. Conceptualizing is part of abstraction. The last abstraction shall be the ability to conceptualize.
Space forms the background of “existence”. Time forms the background of “change in existence”. We may say that abstraction forms the background of “nature of existence”. There seems to be a whole gradient of existence from matter to awareness. Awareness seems to be a subtle form of motion. This needs to be explored further.
Thus, if matter were to disappear, there still may remain a finer form of existence.
The existence has a tendency to stay as it is, for it resists change. This is the law of inertia. Space and time form an “inertial system” as the basis of this law. Where does the change come from that is resisted by the law of inertia? It may be the change due to restoring forces as described at The Logical Structure of the Universe (Part 1) – Static to Kinetic.
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