On Jul 8, 2:19 pm, harald <h...@swissonline.ch> wrote: > On Jul 8, 4:40 am, Immortalist <reanimater_2...@yahoo.com> wrote: > > > What sort of things are they if they are things? > > > One natural answer is that they comprise continua, three-dimensional > > in the case of space, one-dimensional in the case of time; that is to > > say that they consist of continuous manifolds, positions in which can > > be occupied by substances and events respectively, and which have an > > existence in their own right. > > "Existence in their own right"? First of all they are human concepts, > based on physical phenomena. See for example, "The evolution of space > and time" of Paul Langevin (translation is still work-in-progress): >http://searcher88.wikispaces.com/Langevin1911 > Our universe exists in a three dimensional space, and experiences continuous changes with the 'passage' of time. We can only depict the history or record of such changes (or make predictions of some futuristic changes) with the aid of a four dimensional space-time manifold as a mathematical model. Spacetime is not a physical entity. https://sites.google.com/a/fundamentalphysics.info/book/Home/book_files/chapter8.pdf?attredirects=0&d=1
Introduction. Most followers of Relativity theories consider the spacetime continuum to be a physical entity which can even be deformed and curved. This misconception is quite deep rooted in the metaphysical eternalist viewpoint of existence in contrast to the logical presentist viewpoint. As per the eternalist viewpoint, a so- called material object in a spacetime world is a continuous series of spacetime events, each of which exists eternally as a distinct part of the world. There is no distinction between the past, present and future. We may refer to it as a block view of spacetime. As per the presentist viewpoint, the present moment is different from the past and future and that physical entities exist only in the present. The physical phenomenon does not exist in the past and the future regions of time. The foundations of General Theory of Relativity (GR) are critically dependent on the integrity of the notion of spacetime continuum. Actually, spacetime is just a mathematical notion which has no physical existence.
The Coordinate Space. The association of the set of points P on coordinate line X with the set of real numbers x, constitutes a coordinate system of the one-dimensional space, once the notion of certain unit length has been defined. The one-to-one correspondence of ordered pairs of numbers with the set of points in the plane X^1X^2 is the coordinate system of the 2D space consisting of points in the plane. Similarly, with a predefined notion of unit length, an essential feature of 3D space is the concept of one-to-one correspondence of points in space with the ordered sets of real numbers. The predefined notion of unit length or scale for different coordinate axes constitutes the metric of space for quantifying the notion of distance and the position measurements of the sets of points in this coordinate space.
We define a space (or manifold) of N dimensions as any set of objects that can be placed in a one-to-one correspondence with the ordered sets of N numbers x^1, x^2,..., x^N. Any particular one-to-one association of the points with the ordered sets of numbers is called a coordinate system and the numbers x^1, x^2, ...., x^N are termed the coordinates of points. In all coordinate spaces that are metricized, we associate the notion of unit length along all coordinate axes and a metric tensor gij with each coordinate system. All essential metric properties of a metricized space are completely determined by this tensor.