(For more papers see the links in the Footer Bar)

Topology 101: Imagine Space Inside-Out – Dave Martsolf – 2020

The painting “Topology 101 : Imagine Space Inside-Out” is meant to encourage the observer to imagine our space-time and the objects within it (our universe) turned inside out and what the observable effects would be of such an inversion. To consider this state one must first accept currently held facts of the observable, and by extension the unobservable universe.

The expansion of the universe is one such apparent fact. Radiating objects such as galaxies that are located further and further away from us (verified in part by Hubble’s work with Cepheid variable stars) were also discovered to have had their radiation wavelengths elongated (redshifted), a phenomenon that is most easily reconciled by agreement that the object is moving away from us. Using this relationship it was also observed that objects further away from us were also receding from us at increased speeds proportional to their assumed distance.

It is currently surmised that this is due to the expansion of the intervening space itself. Measurements of the recession velocities of distant galaxies appeared to confirm that this expansion is universal. More recently, work with a class of supernovae in distant galaxies has discovered that the expansion rate is actually increasing over time. The science is still in the process of explaining how this could be, as a repulsive force working throughout the known universe has been postulated but not yet proven to exist.

In any case, the result of this expansion is that objects sufficiently distant from one another can theoretically (by general relativity) move away from each other at speeds greater than that of light. This means that for some objects that could be seen in the past, they cannot now be seen as their radiation at any wavelength will no longer be able to reach us.

If the expansion of the universe is relatively symmetrical, then an observer anywhere in the universe should find this “vanishing point” at a similar distance in all directions outward from that observer. In practical terms one can describe this border as an event horizon, similar to the term used to describe the outer ‘surface’ of black holes, but one where we are looking at it from the inside. Furthermore, every other point in the universe is also the center of its own black hole. In our case, we find ourselves looking outward toward an event horizon into which the entire observable universe is falling.

“Topology 101” with its inside-out examples of oranges, stars vs. traditional black holes, and interleaved hands suggests that we imagine turning our whole universe inside-out. If you invert this model you find a topologically equivalent traditional black hole, but one with a twist. Traditionally, a black hole is described as a singularity (at its center), and an event horizon at the singularity’s Schwarzschild radius. The problem is that a singularity is a mathematical concept of a non-dimensional point. All singularities should therefore be equivalent, and yet we know that black holes come in different sizes with different masses and correspondingly different Schwarzschild radii. Relativity solves this for our inverted model as it requires matter approaching light speed to become infinitely heavy with time slowing down to zero. Such a condition suggests a shell black hole where the singularity becomes a sphere with no thickness, but of varying surface area. This is the black hole in which we are at the center.

The mathematical representation of this “falling” should be an inverse equivalent to the equations describing universal space-time expansion. Differences could be used to better understand the relationship between gravitation and the observed expansion of space-time.

One other related concern - Special Relativity rules out objects traveling faster than light. As an observed radiating object recedes from us at speeds greater than that of light, could its radiation ever be observed again at 180 degrees from its point of origin, or does its elongated collection of various wavelengths all reaching infinity (zero energy) mean that the radiation has now truly vanished from our space-time? Wavelength elongation due to the expansion rate of space appears to support never seeing a 180 degree mirror as the expansion rate itself is limited to the speed of light. Once a wavelength reaches infinity it can never re-emerge from the opposite direction, or so it would seem. Is zero energy radiation hiding an attribute? Is it the underlying property of space itself?