NOTE: Einstein’s statements are in black italics. My understanding follows in bold color italics.
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From “Relativity and the Problem of Space” Albert Einstein (1952)
It is characteristic of Newtonian physics that it has to ascribe independent and real existence to space and time as well as to matter, for in Newton’s law of motion the idea of acceleration appears. But in this theory, acceleration can only denote “acceleration with respect to space”. Newton’s space must thus be thought of as “at rest”, or at least as “unaccelerated”, in order that one can consider the acceleration, which appears in the law of motion, as being a magnitude with any meaning. Much the same holds with time, which of course likewise enters into the concept of acceleration.
Newtonian physics describes velocity as the rate of change of the distance of a body with respect to another body. Such distances are interpreted in terms of the material dimensions. This constitutes the understanding of space in terms of material dimensions.
Newtonian physics describes acceleration as the rate of change of the velocity of a body. Acceleration is a change relative to the inertia of a body itself, and not relative to another body. This constitutes the understanding of background SPACE in terms of inertia.
Newton himself and his most critical contemporaries felt it to be disturbing that one had to ascribe physical reality both to space itself as well as to its state of motion; but there was at that time no other alternative, if one wished to ascribe to mechanics a clear meaning.
The physical reality of space exists in terms of material dimensions. The physical reality of the state of motion (acceleration) exists in terms of material inertia. Here SPACE acts as the background of zero inertia and zero dimension.
It is indeed an exacting requirement to have to ascribe physical reality to space in general, and especially to empty space. Time and again since remotest times philosophers have resisted such a presumption. Descartes argued somewhat on these lines: space is identical with extension, but extension is connected with bodies; thus there is no space without bodies and hence no empty space. The weakness of this argument lies primarily in what follows. It is certainly true that the concept extension owes its origin to our experiences of laying out or bringing into contact solid bodies. But from this it cannot be concluded that the concept of extension may not be justified in cases which have not themselves given rise to the formation of this concept. Such an enlargement of concepts can be justified indirectly by its value for the comprehension of empirical results.
Since the concept of space depends on material dimensions, it cannot be conceived in the absence of matter. Descartes was, therefore, correct. “Empty space” cannot be conceived when material dimensions do not exist. Any concept of “empty space” shall only be subjective. Objectively, we may conceive of background SPACE only as a reference point of zero dimension.
The assertion that extension is confined to bodies is therefore of itself certainly unfounded. We shall see later, however, that the general theory of relativity confirms Descartes’ conception in a roundabout way.
According to mindfulness, extension and inertia is confined to material bodies. Descartes argument that space is identical with extension is similar to the argument that it is identical with inertia. In reality, the background SPACE is neither identical with extension nor with inertia. It is simply the background reference point of zero inertia and zero dimensions.
What brought Descartes to his remarkably attractive view was certainly the feeling that, without compelling necessity, one ought not to ascribe reality to a thing like space, which is not capable of being “directly experienced”.
Our reality starts with physical perceptions. It is extended by the mental derivations as abstractions. We view zero as an absence of quantity. We may view background SPACE as the absence of the direct experience of physical perceptions.
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Earlier notes by Vinaire:
Newtonian physics treats space, time and matter to be independent of each other. This brings into question the physical reality of space. Newtonian physics does not offer answer to this question.
The basic concept of space comes from the dimensions suggested by objects. Space is not considered by philosophers to have a physical reality of its own.
We ascribe physical reality to those things that we can experience directly. When there appears discontinuity in physical reality we look at it more closely to set up a precise logical continuity. The scientific thought evolves in this way.
Descartes is logical in arguing that space and bodies should be continuous. The Disturbance theory establishes this continuity of space with matter through energy. When matter is absent there seems to be “empty space”, but that space is actually filled with energy.
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