The Instantaneous Creation of Infinite Space

Eugene Shubert

The 3-space in which we live is one of an infinite variety of possible geometries. [1]. No mortal can identify the right spatial form. The Big Bang creation story comes in two incomprehensible versions. No human knows which version is correct. This thread is a request that knowledgeable mathematicians answer questions as simply as possible on the very essence of mathematical cosmology and what is knowable and provable.

The most delightful creation story is that, in an instant, out of nothing, infinite space suddenly came to be. The infinite and everywhere appeared instantly, inexplicably; and time was also born. The second creation story is a plain and simple alternative to the first. Space (the everywhere) was born finite, with zero volume and grew from that; and time also came to be.

The birthing of geometry in time has associated with that space and time, a flow of idealized, mathematical trajectories. Each trajectory is easily pictured as the spatial trace of an abstract idealized clock moving effortlessly through that geometric space, parameterized by its own clock time. Each clock, therefore, is defined by a timelike geodesic.

The most glaring fact that I see in the simultaneous emergence of space and time is the existence of the above mentioned global flow of abstract coordinate clocks, all initially synchronized by God Himself. Obviously, attempting mathematical physics by coordinatizing space and time, if space is infinite and flat, can not produce the Lorentz transformation. It isn't the Creator's choice. It doesn't harmonize with creation. Going the route of conventional special relativity would imply that imagining an event at some time in one frame of reference would necessarily translate to the same event happening in another frame before time even began. It's against nature. The implications are clear. The instantaneous creation of space and time identifies an absolute frame of reference.

Imagine the second creation story and the birthing of a hypersphere (or projective 3-space if you prefer) from an initial inexplicable point. The symmetry of this space demands a corresponding symmetry in the global multidirectional flow of abstract coordinate clocks. To understand this symmetry physically, I wish to understand motion generally. My most stubborn and longstanding expectation is that all motions in spatially compact spacetimes have extremely absolute characteristics, whereas, all motion in spatially infinite spacetime is relative.

Therefore: I would like to define a geodesic coordinate system in space as a flow of our abstract idealized clocks such that all those clocks travel the same distances as a function of clock time. I also like the requirement that nearby clocks in the flow all move in approximately the same direction. What are all the geodesic coordinate systems for an expanding circle, sphere and hypersphere?