Well, once again, language. We have dimensions of space. In that sense, duration is no natural universal dimension, at least in SR. It would be meaningful only in a world of objects all at rest with respect to a particular reference frame. On the other hand, we have dimensions/measures of events over physical intervals. But for these, duration is tautologically valid, because we define it as such. SR "only" tells us such a definition is always consistent and measurable in all reference frames. ...

... So yes, in a purely relational (but not in the coordinate-organization) sense, duration is the only consistent dimension.

@Void: "On the other hand, we have dimensions/measures of events over physical intervals." Why "on the other hand"? You don't agree with the common claim in contemporary physics that time is actually no different a dimension to physical ones? If it's fully "equivalent" then it should be treated the same here, shouldn't it?

@brightmagus "On the other" hand because I identify the "dimension of space" with a coordinate labeling of all events. Whereas the dimension of an "object $\to$ event" is the measure of it's extent. The "spatial" dimension talks about possible descriptions whereas the measure of event extent talks about the meaning of quantities obtained by measurement actions. We need four coordinate numbers for specifying an event, and we thus talk about four dimensions. But none of these can be even identified as either space or time. They are only space-time coordinates, there is no separation.

@Void: That's the kind of anwer I expected from current mathematical physics, ie. yes and no.

@brightmagus Well, in the end physics only tells you about physical actions and measurements. The language it provides for describing it is only a language, a code, or labeling useful for organization of observational knowledge. A question about the language itself is non-physical and will not have a distinct answer based on physics unless there is a hidden question about observable phenomena or physical actions underneath.

@Void: completely not true. Mislabeling leads to misusing and misunderstanding mathematics. And this is especially true for physics (not much so for mathematics, which is now pretending to be physics).

@brightmagus Can you give an explicit example? Obviously mislabeling has to be avoided and the organization must be sound, but I do not think that would counter my statement.

Sure, here is the derivation of the Virial Theorem: en.wikipedia.org/wiki/Virial_theorem#Statement_and_derivation. We are talking about the moment of inertia here, and therefore r is not only a position, as they stated. It is the radius, which means it is constant - by definition (as we are not constrained for instance to a gaseous object here).

Now, how can they call it a vector, and how can they differentiate it with respect to t, if it is not changing with respect to t (for a given particle)? Shocking, isn't it? Mislabeling, misunderstanding (cheating?) - what would you cal it?

And, by the way, this is not the only funny thing in this derivation. Look closely for yourself ... An there are other examples from other areas of physics: SR, GR, astrophysics ...