Comment by simiones

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.