Kind of trivial result, but thought it might be interesting. This is part of a wider development which will be described further, either here or in another thread. Statement: "A Point in Spacetime has the Cardinality of the Continuum" Justification: Time can play a really neat trick !! To observe time you must have some type of motion or physical activity of some kind. Without some kind of motion it is impossible to observe time. Motion does not create time or cause it to occur. But without some type of motion it becomes impossible to observe or measure time. By hypothesis, there are motions in the universe which are so vast (relative to an observer on our scale) that these motions are impossible to observe. Hence, very large scale motions cannot be used to obsere time relative to an observer on our scale. Time becomes impossible to measure or observe in that context, and therefore ceases to exist relative to an observer. The converse also holds for the quantum scale. The point is that time ceases to exist relativistically on the largest and smallest of scales. There is an important distinction. Neglecting to observe time will not cause it to cease to exist. But if it is utterly impossilbe to observe or measure in a given context, then indeed it does not exist relative to you - in that context. [ seems to agree with Planck] If time ceases to exist relative to an observer, then 4D Minkowski spacetime (3+1) loses one of it's dimensions to become the 3rd dimension (3+0). This defines the edges of our universe. Keeping in mind that this effect is relativistic, you immediately derive that the universe is both open and closed. An observer on our scale will think observe that it is closed, but in an absolute sense it is really open. Hence, it is open AND closed, simultaneously. [ Having the 3rd dimension also allows you to explain, easily, all kinds of QM weirdness.] The fine structure of Minkowski spacetime is therefore a composite of 4D and 3D "points" of some kind, and the only difference between these two types of points is relativistic. The universe has two boundaries, one on the astronomical scale, and one on the quantum scale. These boundaries exist relativistically. Knowing that the universe is both open and closed simultaneously, consider a 4D point, P1, in spacetime. Since 3D points may be considered to be "relativistically nonexistent", you can even say that you have uncountably many such points at P1. Such additional points could become existent depending on how P1 is observed, and so a point in spacetime really can be said to have the cardinality of the continuum. Discussion 1: You can easily say that I bent the rules here because I invoked points which are nonexistent relative to an observer, but by altering the observation, those points could become existent, so it's only partially cheating. Also, you could argue that I have "assumed" continuity by stating that the manifold has cardinality of continuum. This would be a difficult statement to make if we were talking about points which are strictly existent, but since we are talking about points which are relativistically nonexistent there is no reason why you cannot define them to be continuous. Continuity in spacetime is a relativistic phenomena, and with luck we'll get a little closer to proving it. Discussion 2: I know that these ideas are extremely bizarre, perhaps especially the part about the "relativistic nonexistence". But I will prove this with one short addendum. This is very easy to grasp, so please read on. Consider the double-slit quantum-interference experiment . http://physicsweb.org/articles/news/9/3/1/1?rss=2.0 This experiment is easily explained. Time ceases to exist on the quantum scale (relative to an observer), and so the individual wavecrests in this experiment cannot be separated by time. The wavecrests must, therefore, be separated only by distance. The experiment becomes identical to the classical double slit. This experiment appears to be something very new. But because time does not exist on that scale, the arrangement MUST be identical to the classical double slit. The difference between successive wavecrests cannot be time, but distance ! :surprised Je le vois, mais je ne le crois pas !! Regards - The Average Joe.