user104694

What specifically are the "direct implications on physics" the "metaphysics of time will have", i.e., in what way would physics differ or haw would you do better physics if you thought about these things? Would you be better at running a restaurant if you thought about whether chairs exist?

In classical Newtonian mechanics and gravity, causation is instataneous, and this is a clearly defined theory. Do you consider thet to be logically inconsistent?

Sure, typo. Should be $\mathbf[j}/\mathbf{i}$.

The website picks some convention. For them, $\mathbf{i}/\mathbf{j}=-\mathbf{k}$ (if I didn't make a mistake), so $\mathbf{i}/\mathbf{j}=\mathbf{i}^{-1}\mathbf{j}$.

This may be mostly about terminology. In quaternions, division is well -defined in the sense that for any $p$, $q\neq0$ the expressions $pq^{-1}$ and $q^{-1}p$ exist. On the other hand, the expression $p/q$ (and the wordy expression "$p$ divided by $q$") are ambiguous and thus probably best avoided.