Dear Ian,
"...Actually, special relativity can be derived without reference to the transforms. Not to beat a dead horse, but Moore does it graphically in his text. .."
I haven't seen all the sources there are to learn from; however, I would suspect that he probably went to advanced theory or end points of theory, conservation type properties, and worked his way back from them. If I am wrong than I apologize for misrepresenting what he has done. I was prompted to say this because every explanation I have seen of Relativity Theory, other than its original type derivation, usually begins with theoretically advanced properties that owe their origin to the assumed adoption of Relativity Theory. It is a practice of beginning at the end and working back toward some set of 'fundamental properties' as established by theory. .
"...Can you clarify one thing for me that seems to be hindering my full understanding of what you're saying: when you say equations in physics don't have "causes" what do you mean exactly by "cause" in this case? If it means what I think it means, I would say that most of these "causeless" equations are empirically derived, i.e. they are the way they are because that's what experiment seems to indicate. Maybe this is the point you are trying to get at but I'm not sure. ..."
Thank you for this question. I spent the weekend thinking over what I had said. It seemed clear to me; however, when I thought in terms of explaining it to someone else in detail, I had to think about it a lot. I am still thinking about it and now also writing about it. We do not know what cause is and yet it must be indicated by empirical properties, not theoretical ones, somewhere in the equations. I have already been challenging myself to support what I said. When I can say something more clear about it, or perhaps modify or rescind it, then I will respond.
I also thought that I was once again veering off into my own ideas about possible solutions. The point I really wanted to make, in answer to your original question, was that I think mathematics leaves reality behind when the theorist begins to guess about new extra givens and interjects them into the original equations by identifying unverifiable properties and even more than this, interjecting indefinable units into the otherwise empirically clean equations.
You certainly are patient with me. I acknowledge that I know less than do you about complex theoretical physics and the fullness of empirical knowledge. I do think something is fundamentally wrong; however, I know and appreciate the necessity for demonstrating it and having it challenged. Thank you for your time.
James