The concept of distance is simple; distance is one dimensional space. One dimensional space is a specific distance between two points in space. Two dimensional space is an area of space. Three dimensional space is a volume of space. Three dimensional space is infinite in magnitude. Three dimensional space covers all of the infinite points, lines, areas, and volumes of space! Those are the dimensions of space. There is no mention of light, or objects of mass. Space is simply the concept as described above. Without mentioning objects as of yet, we can go into the mathematics of light travel time to lay the grid of distance in the infinite three dimensional space.
Without associating your grid to any frame of reference, or naming any points as yet, you already have one. It is your intersection of x, y, z. Otherwise there is no math. You also already have three lines, otherwise it could not be called space, or three dimentional. What next? What do you want to do with your grid
You also used the term grid, and want to use light/time as a unit to discuss math. So, you also now have an infinite amout of lines, based on whole numbers, with an infinite amount of intersesting lines filling the entirety of your infinite space. Your grid is in limbo and infinite motion waiting for a beginning, because without deciding wether we are moving through it, it moves through us, or where it is then there is no math to be expressed.
In order to have an x,y,z you have to have picked a starting point. That starting point is a point in the infinite volume of space.
Yes, x,y,z are coordinates used to describe the location of points within a 3 dimensional region. Allowing notions of vectors, combinations of vectors, movement, paths, and distances involves adding additional structure. A space parametrised by some coordinates doesn't automatically have a notion of distance. This is the difference between a space and a metric space (or in regards to relativity a manifold and a Riemannian manifold). Even in 1 dimension a space with locations defined by numbers doesn't automatically possess a notion of distance, by specifying such a notion you add additional structure.
It is not the same question as asking if an object is moving or not. Space is simply infinite volume. Volume is not an object. Volume doesn't move because if it did that would mean volume would be moving in another volume. There is no other volume, there is space, which is infinite volume.
What object? What matter? An infinite grid, can move about freely through and about and around and in between any other mathmatical volume, until you have identified what your space is made of, or your frame of reference is in reference to.
The grid is incapable of motion. The grid is a mathematical depiction of distance in space. Distance in space is defined by light travel time. You are trying to say it is possible that somehow if light travels in space, that it is also possible that that space could be traveling in another space at the same time. There is no other space, 3 dimensional space is all encompassing. Did you miss that part?
Are we talking about a hypothetical space or actual space? Of course you can define a rigid Euclidean space but there are other spaces you can define what the grid is capable of motion. No, the grid is a manifestation of coordinates. Distance is something else. More formally distance between points A and B in space S is defined by a function \(d : S \times S \to \mathbb{R}^{+}\), ie it takes in two points and returns a non-negative number defined as the distance between the points. The grid defines how you describe the points, not the distance between them. A rigid grid can have many different distances defined on it, this is why a metric space is more elaborate than just a space. More formally again, if you have two points in N dimensional space \(\mathbf{a} = (a_{1},\ldots,a_{N})\) and \(\mathbf{b} = (b_{1},\ldots,b_{N})\) then we can define an infinite family of metric spaces via the \(l_{p}\) norm, \(d_{p}(\mathbf{a},\mathbf{b}) = \left( \sum_{i=1}^{N}|a_{i}-b_{i}|^{p} \right)^{\frac{1}{p}}\). For p=2 you get the usual Euclidean distance. And these are by no means all the possible metrics. Now you're going even further, adding in a notion of time and light and motion. Are you talking about an abstract space or actual space? If the former then you are welcome to assert anything you like, you are merely defining the space you talk about. If the latter then it is by no means true simply because you assert it. If you're talking about actual space then you are asserting things without justification. Why should anyone think what you're proclaiming about space is accurate? What experimental evidence do you have that 3d space is all encompassing? Although there is no evidence for extra dimensions there's no evidence against such notions. There is a difference between saying "I do not believe there are other dimensions" and "I believe there are no other dimensions". The former requires no evidence to say as it is a disbelief in a claim. The latter requires evidence since it makes a claim.
There is no difference in measurements between an actual space and a hypothetical space other than that if the space contains matter light will take more time to traverse a distance than it would the same distance if no matter is present (vacuum). You automatically define distance in an infinite volume when you make coordinates. There is 1 light second distance in the x direction between the coordinate (0,0,0) and (1,0,0). Those were the two points in 3 dimensional space to measure a distance in that 3 dimensional space. It is non-negotiable at that point, 1 light second is 1 light second by any stretch of the imagination. When you choose a starting point in 3 dimensional space you have just defined a distance to every point in the grid from that chosen point, whether you realized or measured it or not. Three dimensional space is abstract. The reality of 3d space is objects residing in an infinite volume of space. Can you describe your "actual" space differently?
I didn't say anything about light traveling anywhere. That was your unit to measure distance. You have not yet grasped what infinite means. Until you lay out some perameters to share whatever it is you would liketo discuss the unit used is meaningless, as would be time or any other unit. You never said real space, or reality is what you're trying to discuss. Even then, your grid moves about wildly and infinitely until you decide where 0 is, or decide where any number is. If your zero point is in your imagination that's fine too, but that will have to be established to be able to apply rules.
If I am to measure distance according to light travel time in the grid, then time is started at the start point of the grid in space when the light starts traveling, and time stops when light stops traveling at the chosen destination. The "zero point" is where in the infinite 3d grid that the light starts traveling and the clock starts.
As well, if you assert that your grid us stationary, i have no problem with that. Its a good place to start, but lets establish something ti discuss. What is your alternate theory and how does it apply to the space you are creating?
