This is from a paper I recently submitted to Synthese.
ABSTRACT
I am proposing a new order to dimensional ontology that considers motion to be the fourth spatial dimension. Having established that, force can even be seen to be the fifth and final spatial dimension that forms physical reality. Beyond that, as a sixth dimension, or first non-spatial dimension, is possibility, that dwells within consciousness, or non-spatial existence.
INTRODUCTION
Personal speculation has led me to consider motion as the fourth order of spatial dimension after a simple thought experiment.1 I started by describing the progression of lower spatial dimensions to seemingly be copies of the lower dimension ‘stretched’ in some new direction. The line is the measurement between two points, or we may say it is the point ‘stretched’ or replicated into a new direction. From there a line can be ‘stretched’ into a two-dimensional shape by replicating itself in some new direction, and finally a cube can be seen as a square ‘stretched’ into a three-dimensional object by replicating itself in some new direction.
From there, there are no new directions to ‘stretch’ the cube. There are no observable fourth ‘perpendicular’ spatial dimensions as proposed by modern theories, but if we continue with my original pattern of progression, we can think of a cube replicating or changing itself, not in some new direction but within any of the present three directions. That action is known as motion.
As motion is introduced, we can imagine a trail of cubes following wherever the original cube goes, a visualization which instantly brings to mind the concept of the object’s path and history of motion through space. The shape of that path of motion itself can be represented geometrically in up to three dimensions, and will also have to include the metric of time.
THEORY DEVELOPMENT
As space is needed for the lower three dimensions to occur, so is it needed for motion to occur, making them all intrinsically inherent. Space is needed for a point to exist somewhere, the concept of points is needed for the line to be formed, lines are needed for shapes to be formed, shapes are needed for three-dimensional objects to be formed and motion only occurs in three-dimensional space by three-dimensional objects.2
Time has been commonly proposed as the fourth dimension, but I think it can be more simply understood as a metric of measuring motion’s duration. Like with space, motion and time are also intrinsic, making motion seem to possibly be an integral manifestation of what is called ‘space-time’.
DISCUSSION
Let’s consider the common representation of the fourth spatial dimension, the tesseract.
Considering the ‘trail of cubes’ visualization that my description of progression from the third to the fourth spatial dimension produces, a cube’s path of motion of contracting or expanding a certain amount would look exactly like a tesseract.
This is what the “shadow of a hypercube” as described by Carl Sagan looks like. I propose that it is instead a collection of “shadows” or “snapshots” of parts of its path of motion superimposed upon each other.
The same can be seen in other common representations of a four-dimensional cube. As an article on the Duke University ‘Research Blog’ states, “to create a hypercube, we move identical 3D cubes parallel to each other, and then connect them with four lines, as depicted in the image below.”3
This, also, can be seen as a representation of a possible path of motion as we take an initial or ‘starting’ object at a location and move it to a position as represented by the second or ‘ending’ object’s location. We then connect the paths of motion that occurred, typically between very recognizable properties such as the corners on the cube, and those pathways will form shapes as seen by the lines ‘connecting’ the two cubes. The lines could just as easily be curved or distorted in any way two-dimensionally and even three-dimensionally. In this case, the starting and ending objects share the same form.
Any change in form of the object would incorporate the properties seen as displayed by the tesseract, while changes only in position can be geometrically represented by the second example.
