The Universe is Round
The preceding three science articles have addressed progressively more deeply the question of what it is exactly that we mean, that is to say, what science means, with the use of the term "universe."
In the first of these articles, we explored the scientific origins of the use of the term universe, as well as the scientific revelations that were the consequence of the scientific efforts of the day. Next, in the second article, we explored the very shape of space itself (that is, the shape of the visible universe), discovering that what we ordinary call the universe is actually a four-dimensional sphere. In the most recent article, the one preceding this one, we explored the actual physical properties of a four-dimensional sphere, even analogizing these properties, through an illustration. (If you don't have the last illustration at hand, you can go to http://www.chongonation.com, click on either "Articles" or "Science Articles," page down and click on "The Shape of Space" article. The illustration is at the end of the article, at the bottom of the page.)
Now, in this article, we will explore just what the implications of a four-dimensional sphere are, and in particular, what these implications mean for each individual one of us; because, in actual physical fact, there is no single sphere that encompasses all, but instead, many.
Our individual light cone, our individual visible universe, being unique to its unique center, maps space and time, distances and angles uniquely with respect to the location of that unique center point, which is where each individual one of us, in either precise or general terms, always finds ourselves. Any other light cone, having a different center at a different location, will correspond to a different sphere and hence map all locations its own way, according to the displacement of its center point with respect to the location of any other center point.
A light cone's mapping differing from each and every other light cone's mapping, however slight that difference might be, means that what is mapped as the north pole according to one light cone's "globe," is never mapped exactly, as being the north pole according to another light cone's mapping, nor is the south pole or any other location mapped the same, either. Each cone locates everything wholly uniquely to it. Thus, no light cone ever encompasses exactly the same region of the universe, that is, its history, as any other cone does. The extent of each is likewise wholly unique too.
What this means is that part of what lies within the Big Bang, according to the mapping for one sphere, would already lie outside of the Big Bang according to the mapping for any other, and visa versa. Likewise, each one of us is always located closer to the Big Bang in one direction than in the opposite direction, according to our displacement, again, however slight that displacement might be, from the north pole center point corresponding to any other individual light cone globe's unique mapping. It should be noted that gasping these two final concepts is critical to fully understanding just what it means for each light cone (visible universe) to be unique from all others. It is an absolutely essential point.
Each physically existent light cone having its own unique mapping of space and time, distances and angles means that there physically exists no single unique mapping common to all globes, regardless of the fact that in practice, outside of the most precise science and engineering, we generally use what is effectively a common set of measures, absolute for all, because the difference between any individual cone's unique mapping is so slight as to generally be insignificant. Ignoring this, then because, each physically existent light cone being unique, there exists no physically existent mapping of space and time, distances and angles common to all globes, to use Einstein's well-chosen choice of terms, one must be stipulated, instead. And it is important not to erroneously confuse a stipulation with actually physically existing, like each individual light cone does, physically encompassing vast extents of time and space as well as its contents, reaching across billions of light years of space and billions of years of time. In contrast, a stipulation encompasses the meager extent of that time and space occupied only by the human brain, but is actually nonexistent beyond the shapes, as abstractions, that any stipulation is, residing in the mind alone, confined to its modest physical extents.
The geometric representation of the basis for the stipulation, as a stipulated mapping with respect to the north pole of any light cone's globe, comes in the form of something called a tangent. A line or lines stipulated as being straight, as defined by the tangent, can provide a basis for mapping space and time, distances and angles, with respect to many cones, albeit purely by means of a stipulation. Although it is nothing more than an abstraction, relativity's stipulated mapping, based upon a tangent, in fact, works impeccably. A tangent and the straight lines that are mapped with respect to it can be shared by different spheres, different light cones, and in this way provide the means for a common mapping of measures for all sharing the same unique motion (at rest, subject to the same gravity). Or, for different motion, provide a simple, universal means for translating the measures corresponding to the mapping for a common set of measures for one motion, to those of any other, which is an indispensable necessity for accurate physics.
A straight line, a flat surface, a flat three-dimensional space, or a flat four-dimensional combined space and time (called a frame of reference), etc., is 'tangent' to a curve at a single point and a single point alone, which is the single point where the straight line(s) of the tangent intersect(s) the curve. In two dimensions, a straight line can be tangent to a circle. In three dimensions, a flat (straight), stipulated two-dimensional surface can be tangent to a sphere. In four dimensions, a stipulated, flat three-dimensional spatial moment can be tangent to a three-dimensional spatial moment of an individual light cone. A stipulated four-dimensional mapping of time and space together (again, a frame of reference) can be tangent to a four-dimensional 'light cone' sphere.
For all light cones sharing the same motion, the intersecting stipulated straight line(s) of the tangent establishing the stipulated mapping of space and time, distances and angles always has/have the same number of dimensions (though it/they can have fewer) as does the curve that the tangent intersects, regardless of the number of dimensions involved. The intersection of the straight tangent and the curve is always at a single point alone, which is a single spa-tial location at a single moment, again, regardless of the number of dimensions involved. In the case of the mapping of a momentary three-dimensional space of a four-dimensional frame of reference, intersection is at the "point" (vicinity) of the observer at that moment, though it need not necessarily be (that is, it can be applied to another observer, an observed event, or a set of them, in a different motion, establishing unique measures corresponding to that motion).
This stipulated mapping of space and time, distances and angles, and the rules for its application are the utter substance of relativity's flawless accuracy at mirroring reality, because that is what relativity does, it maps reality's space and time, accurately; for the motions space and time, more accurately than any other body of ideas ever conceived. Indeed, this mere stipulation that is the substance of relativity, existing only within the mind and nowhere else beyond, is a fundamental foundation for describing everything in nature, space, time, and energy alike.
Isn't it just amazing what a mere stipulation can do? And, in case you don't know, it can put a satellite into orbit, allow us down here to use that satellite for pinpoint accuracy in a number of applications, and in their heyday, allow tube televisions to project a discernable image on a television screen, so that those of us who were fortunate enough, could watch Carl Sagan host one of the best television productions ever created, which was the series called "Cosmos." Indeed, this series provides the inspiration for many of the articles that will follow.