On 1/15/2014 4:32 PM, Stephen Paul King wrote:
Yes, GR assumes smooth Riemannian manifolds. The mapping works for them wonderfully. That fact was proven by the people that discovered Fiber Bundles. The hard thing to grasp is how the mapping between separable QM systems and the infinitesimal points of the smooth
Maybe it's hard to grasp because it's wrong. Almost the first thing Kitada writes:"The problem is that if the notion of time is given a priori , the velocity is definitely determined when given a position, which contradicts the uncertainty principle of Heisenberg."
First, makes no sense since determining a position at a time doesn't determine velocity (you have to do it twice). Second, the HP doesn't prohibit measuring both p_x and x, it just says that you get random variation in their values.
I'll leave to Bruno Kitada's proof that set theory is inconsistent. Given the above I'm not inspired to wade through 168 pages of dense notation. A quick perusal indicates that he just attaches a Hilbert space for particle energy to each spacetime world line - nothing amazing there, but it is similar to Edgar's idea of having separate little frames that get 'aligned' at interactions. He draws conclusions like:
Riemannianmanifold works and how to interpret what that tells us about QM systems.Basically, it tells us that the realm of QM and the realm of GR are separate forever, there is not a way to map QM rules onto the smooth Riemannian manifold in a global way. To do so makes time vanish. Wheeler and DeWitt proved this long ago with their W-D equation. Until Prof Kitada analyzed the W-D equation using results from scattering theory, it was assumed that it was not possible to make time pop back out of the theory, but he found a mathematically consistent way to do it. But his results disallow for the kind of concepts that Edgar and many others are advocating.
No such thing was proved by WD. The WD implies a static universe, but that's consistent with a block universe picture, and Don Page and William Wooters showed that events in such a universe can still be assigned dynamics relative to clocks in the universe.
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