These are really postulates of physics in general, but is aimed mostly toward the dynamics of space and time and of motion, specifically to that which is necessary to derive Special Relativity. This is not a theory, but a collection of postulates which serve as the foundation of many such theories, put together here in the fashion that they might normally be used in physics. As such, this thread is of course open to any discussion as to how they might be made more rigorous or to the consideration of any further postulates that might be added.
1) Local - It will be assumed that identical experiments can and will be performed under identical conditions at any location in any inertial frame, locally to the experiment, as with setting temperature for example, by applying the same local methods for achieving these conditions.
2) Ideal - It is assumed that the effects of any phenomenon that cannot be locally controlled and which might affect the experiment in some way but are not meant to do so, such as cosmic background radiation or universal expansion, will be negligible.
3) Homogeneity - Any identical experiments performed under the same conditions and with the same dynamics applied in any direction relative to an inertial observer at any location in any inertial frame will attain the same results according to that observer.
4) Volume - If a large container of any shape is filled separately with two different sets of naturally occuring physical entities that take up space, such as between different types of atoms, then the average number ratio or proportion between those two sets will remain the same at any location in any inertial frame when placed under the same conditions.
5) Rigidity - Any sturdy materials, regardless of composition, will retain the same proportions to each other no matter which direction they are turned locally within a frame.
Test - This can easily be tested by placing two rigid rods of different composition side by side and cutting them to the same length, defined simply by having their ends meet, then turning them in various directions to test whether the ends no longer both meet.
A) Coordinate choice for rulers - As per postulate 5, even if rods were to contract or expand in different directions, they would all do so in the same way regardless of composition, so we could not directly measure a difference, so we will consider them to be rigid and to remain the same length in any direction. As per postulate 4, we will make a ruler according to a particular number of such physical entities placed one after another along a straight line (a staight line to be defined), and this shall be done the same in every frame.
6) Circle - In accordance with the third postulate of Euclidean geometry, a circle can be described with any center and radius.
B) Coordinate choice for spheres - We will apply postulates 5 and 6 to extend to spheres, whereby after identifying two random points upon a rigid body of any shape, we can then rotate the body in all directions about one of the points and mark the places in space that the second point coincides, which will enclose the surface of a sphere.
7) Line - In accordance with the first postulate of Euclidean geometry, a straight line can be drawn between any two points.
C) Coordinate choice for lines - We will define a straight line as the shortest distance between two points. Since distance is determined by a ruler and we have not yet determined how to make a straight line ruler to begin with yet, the procedure is as follows. We will identify two points in space which will be the endpoints of our ruler. We will then make many identical infinitesimal spheres which have been fashioned in the manner described by coordinate choice B and connect them along their outer surfaces as would be a string of beads. The path that lies between the two points in space that can be found by placing the least number of spheres between them will define a straight line between those two points, and that shall also be the edge of our ruler.
8) Periodicity - All physical processes, whether they be periodic as with atomic vibrations or a measure of change as with radioactive decay, for examples of such, will occur at the same rate locally in proportion to each other at any location in any inertial frame.
9) Locality - Identical physical processes will occur at the same rate at any location within the same inertial frame.
Test - We can test this by having two sets of identical periodic processes, then moving one to another location within the same frame while continuing to count its periodic rate of each, and after some time has passed, moving the other set to the same location in the same manner as the first while still continuing to count the periodic rates while doing so, and determining that the same count has occurred for both sets.
D) Coordinate choice for clocks - In accordance with postulates 8 and 9, since all local periodic processes occur at the same rate in proportion to each other, and since clocks should connect with these processes in order to have any physical meaning, we will set the timing of clocks in accordance with local natural periodic processes.
10) Dynamics - An inertial body will travel at a constant and steady pace unless otherwise acted upon, as observed by an inertial observer.
11) Path - An inertial body will continue to travel in the same direction along a straight line as observed by an inertial observer.
12) Aberration - If a light pulse is emitted from each of two sources as they coincide at the same point in space and the light pulses then travel to an observer at any other location in any frame, that observer will receive both pulses simultaneously, regardless of the motions of the sources.
13) Isotropy - It is assumed that the speed of light is not directly affected in any measurable way by any discernable medium. As such, postulates 2 and 3 will apply, whereby if a clock is placed at the end of a rigid rod and a light pulse is propagated from the clock to the other end of the rod and back, it will do so in the same two way time according to the difference in readings upon the clock, regardless of the direction of the rod in space.
14) Speed - When the lengths of identical rigid rulers and the timing of clocks are set according to the natural physical processes as per coordinate choices A and D, then by applying the method as described in postulate 13, the same difference in readings will be found to pass upon the clock at the end of the rod at any location in any inertial frame.