宇宙膨胀的几何驱动
Geometric Drive of the Universe's Expansion
摘要：
如果物理只是我们感知几何的方式呢？也就是说，如果几何学和物理学有一天会成为同一门学科呢？我相信这将意味着我们最终将真正理解物理学，除了那些定义物理剧表演的特定空间的假设之外，没有其他假设。在本文中，我使用5维时空作为出发点，并在坐标与物理距离和时间之间进行了非常特殊的分配。我假设存在一种超球面对称性，这是通过将超球面半径指定为适当的时间，将超球面上的距离指定为通常的三维距离而变得明显的。时间，或康普顿时间，以区别于宇宙时间是第0坐标，我能够通过施加零位移条件，将一切投影到四维中。令人惊讶的是，在不诉诸暗物质的情况下，解释哈勃膨胀定律并不需要其他任何东西;一个空的宇宙将以这种方式以一个统一的速率自然膨胀。然后，我讨论了一个小的质量密度在膨胀率的扰动效应在定性的方式;定量的结果要求解决方程，有时甚至没有明确制定，所以被推迟到以后的工作。对超球对称性对星系动力学的影响的简要展望允许导出恒定的旋转速度曲线，同样不需要诉诸暗物质。附录解释了电磁学是如何与这种几何方法相一致的，并证明了光子必须在超球面上运动，才能垂直于适当的时间。
英文摘要：
What if physics is just the way we perceive geometry? That is, what if geometry and physics will one day become one and the same discipline? I believe that will mean we will at last really understand physics, without postulates other than those defining the particular space where the physics play is performed. In this paper I use 5-dimensional spacetime as a point of departure and make a very peculiar assignment between coordinates and physical distances and time. I assume there is an hyperspherical symmetry which is made apparent by assigning the hypersphere radius to proper time and distances on the hypersphere to usual 3-dimensional distances. Time, or Compton time to distinguish from cosmic time is the 0th coordinate and I am able to project everything into 4-dimensions by imposing a null displacement condition. Surprisingly nothing else is needed to explain Hubble's expansion law without any appeal to dark matter; an empty Universe will expand naturally at a flat rate in this way. I then discuss the perturbative effects of a small mass density in the expansion rate in a qualitative way; quantitative results call for the solution of equations that sometimes have not even been clearly formulated and so are deferred to later work. A brief outlook of the consequences an hyperspherical symmetry has for galaxy dynamics allows the derivation of constant rotation velocity curves, again without appealing to dark matter. An appendix explains how electromagnetism is made consistent with this geometric approach and justifies the fact that photons must travel on hypersphere circles, to be normal to proper time.
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