Can you expand on this? I’m guessing that it’s something to do with preservation of mass & energy? Like mass doesn’t have to be preserved over a spatial dimension (eg rotating an object) but does over time.
I explained in another comment, but it's more fundamental than that.
In pure mathematical terms, the vector space used in special relativity (and in theories compatible with it, such as QM/QFT), while being 4 dimensional, is not R^4, it's not a 4D cartesian vector space.
Specifically, the scalar product of two vectors in R^4 (4D space) is [x1,y1,z1,h1] dot [x2,y2,z2,h2] = x1x2 + y1y2 + z1z2 + h1h2. You can order the coordinates however you like - you could replace x with h in the above and nothing would change.
However, SR space-time is quite different. The scalar product is defined as [x1,y1,z1,t1] dot [x2,y2,z2,t2] = c^2 * t1t2 - x1x2 - y1y2 - z1z2. You can still replace x with y without any change with the result; but you can't replace x with t in the same way. This makes it clear from the base math itself that the time dimension is of a different nature than the 3 space dimensions in this representation. This has a significant impact on how distances are calculated, and how operations like rotations work in this geometry.
In pure mathematical terms, the vector space used in special relativity (and in theories compatible with it, such as QM/QFT), while being 4 dimensional, is not R^4, it's not a 4D cartesian vector space.
Specifically, the scalar product of two vectors in R^4 (4D space) is [x1,y1,z1,h1] dot [x2,y2,z2,h2] = x1x2 + y1y2 + z1z2 + h1h2. You can order the coordinates however you like - you could replace x with h in the above and nothing would change.
However, SR space-time is quite different. The scalar product is defined as [x1,y1,z1,t1] dot [x2,y2,z2,t2] = c^2 * t1t2 - x1x2 - y1y2 - z1z2. You can still replace x with y without any change with the result; but you can't replace x with t in the same way. This makes it clear from the base math itself that the time dimension is of a different nature than the 3 space dimensions in this representation. This has a significant impact on how distances are calculated, and how operations like rotations work in this geometry.