论M理论、量子粒子和新相对论
On M Theory, Quantum Paradoxes and the New Relativity
摘要：
最近，一位作者提出了一个新的相对性原理，作为弦理论和{ \bf M}理论的物理和几何基础。结果表明，在新相对论的框架下，某些量子力学参量如Einstein-Rosen Podolsky和黑洞信息损失等是容易解决的.这样的新相对论需要引入一个无限维的量子时空，正如我们中的一个人最近所证明的那样。这可以被看作是另一种看待费曼路径积分公式的量子力学。在一个有限维时空中，在$all$路径上的无穷维泛函积分是平滑的，在时间上是向前和向后的，是随机的和分形的，而在一个无限维量子时空中，我们有有限数量的路径。我们提出了一个几行证明，为什么没有这样的事情作为一个{ \bf EPR}粒子在这个新的相对论。原因是{ \bf不是}由于超光速信息速度而是由于{ \bf发散}信息电荷密度。在无限维极限中，由于伽马函数的性质，由具有有限非零半径的$D$ -dim超球包围的超体积收缩为零：收缩为{ \bf hyperpoint}，即点的无限维模拟。由于这个原因，信息在瞬间流过半径非零但大小为零的无限维超曲面，即超点。以这种方式，我们赋予一个抽象的数学“点”以真正的物理意义：它是无限维中的实体，在非零半径处具有零超体积。提出了黑洞中信息损失问题的一个合理的解决方案。
英文摘要：
Recently a New Relativity Principle has been proposed by one of the authors as the underlying physical and geometrical foundations of String and {\bf M} Theory. It is explicitly shown that within the framework of the New Relativity Theory, some Quantum Mechanical Paradoxes like the Einstein-Rosen Podolsky and the Black Hole Information Loss, are easily resolved. Such New Relativity Theory requires the introduction of an Infinite Dimensional Quantum Spacetime as has been shown recently by one of us. This can be viewed as just another way of looking at Feynman's path integral formulation of Quantum Mechanics. Instead of having an infinite dimensional funcional integral over $all$ paths, smooth, forwards and backwards in time, random and fractal, in a finite-dimensional spacetime, one has a finite number of paths in an Infinite Dimensional Quantum Spacetime. We present a few-lines proof why there is no such a thing as an {\bf EPR} Paradox in this New Relativity theory. The reason is {\bf not} due to a superluminal information speed but to a {\bf divergent} information charge density. In the infinite dimensional limit, due to the properties of gamma functions, the hypervolume enclosed by a $D$-dim hypersphere, of finite nonzero radius, shrinks to zero : to a {\bf hyperpoint}, the infinite-dimensional analog af a point. For this reason, Information flows through the infinite-dimensional hypersurface of nonzero radius, but zero size, the hyperpoint, in an instant. In this fashion we imbue an abstract mathematical "point" with a true physical meaning : it is an entity in infinite dimensions that has zero hypervolume at nonzero radius . A plausible resolution of the Information Loss Paradox in Black Holes is proposed.
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