mj<p><span class="h-card"><a href="https://mastodon.sdf.org/@defrisselle" class="u-url mention" rel="nofollow noopener noreferrer" target="_blank">@<span>defrisselle</span></a></span> <span class="h-card"><a href="https://fribygda.no/@Mizmar" class="u-url mention" rel="nofollow noopener noreferrer" target="_blank">@<span>Mizmar</span></a></span> </p><p>Yeah, if we were only talking about the theory of <a href="https://c.im/tags/GR" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>GR</span></a>, then we'd have an open & shut case against my vague use of "dimensions in quotation marks".</p><p>Since reality is only poked at with <a href="https://c.im/tags/models" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>models</span></a> we know to be inconsistent (big picture) and incomplete (like all), I think there's nothing but room to wonder what a better theory would look like. One thing we do know, it will require a different approach to <a href="https://c.im/tags/time" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>time</span></a> & dynamics, for at least one of the discrepant models on the table. Regardless of whether or not any of us have a better solution, GR's combining of space & time plus use of curvature of 4D is putting time on each spatial dimension. Are they independent? It depends. </p><p>For what reason would they be included, if not to have specific instances where they were needed to be calculated separately? There's a lot of translation/transforming between "every day physics" and GR; momentum & stress tensors, etc. Other work has shown that the curvature is not required in the way postulated by GR. There are also other geometries, <a href="https://c.im/tags/symmetries" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>symmetries</span></a>, manifolds, etc. In SR, there's a 10D Poincare group, which includes 4 spacetime translations. The reality is, that physicists jump back & forth between models based on context & convenience. Euclidean 4D (3+1) is not the same as Minkowski 4D.</p><p>There are different types of mass, from context, and I'd argue the same holds for Time. (I'm happy to expound..)</p><p>At any rate, time dilation & length contraction work together in all directions, to satisfy the conflict between individual perception (I'd argue that conscious observers anthropocentrically use a Cartesian coordinate system centered on themselves) and a consistency of explanatory power of the model, for all frames of reference. There would be fewer problems if we only had to contend with mass & gravity, but <a href="https://c.im/tags/SR" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>SR</span></a> is based around light, so conflicts with <a href="https://c.im/tags/QM" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>QM</span></a> cannot be avoided.</p><p>The velocity 4 vector in GR uses dt for dx, dy, and dz. In SR, this 4-velocity cannot be defined, as the 'proper time' between events (d\_tau) is zero. QM has to input time to 3D, and doesn't even have a position operator for the photon. The list of differences goes on, of course, but I think this is enough to resolve the disagreement at hand. All of these things are just ways we try to measurably explain events/interactions between objects/observers.</p>