I think that's a fairly accurate summary. The Lorentz transformation predates relativity. Einstein's genius was taking it seriously.
People who get too attached to the idea that the he must have created the theory from whole cloth might be offended by that idea, but... honestly, that really was a stroke a genius. A lot of very smart people had the mathematics all but yelling at them that the model of rigidly separate space and time wasn't working, and when you dig back into it, it was "yelling" for decades. (For instance, Maxwell's equations, first published 1861, have a speed of light that is simply a constant, not a function based on the velocity of the observer or anything else like that. In hindsight, this is obviously a Big Clue.) It really was a stroke of genius that he put it together.
Had he not, I guarantee somebody else would have. It may have been years later, or possibly even a decade later, but probably not much more than that. Eventually evidence would have started stacking up and the conclusion would have become inevitable. Einstein did it off of not a lot of concrete evidence. But we certainly would not be living in a world in which nobody had ever come up with the idea or anything stupid like that.
If you want to dig through it, I find http://mathpages.com/rr/rrtoc.htm Reflections on Relativity to be a dense, but fantastic book on the topic. (Ooo, this is the first time I've ever clicked through that link and seen the physical book finally exists, after years of me wishing for it. Nice.) RoR even digs back and shows how the Greeks had paradoxes that demonstrated the impossibility of a rigidly separated space and time, and had we taken those paradoxes seriously much earlier, who knows what we might have done.
(I do find it intriguing how much math from that era can be framed in terms of taking the ancient paradoxes seriously, really really seriously, and not just as wordplay. One of the biggest moments in 20th-century math history, Godel's Incompleteness Theorem, can be viewed as "simply" taking the ancient Epimenides paradox seriously. http://en.wikipedia.org/wiki/Epimenides_paradox )
People who get too attached to the idea that the he must have created the theory from whole cloth might be offended by that idea, but... honestly, that really was a stroke a genius. A lot of very smart people had the mathematics all but yelling at them that the model of rigidly separate space and time wasn't working, and when you dig back into it, it was "yelling" for decades. (For instance, Maxwell's equations, first published 1861, have a speed of light that is simply a constant, not a function based on the velocity of the observer or anything else like that. In hindsight, this is obviously a Big Clue.) It really was a stroke of genius that he put it together.
Had he not, I guarantee somebody else would have. It may have been years later, or possibly even a decade later, but probably not much more than that. Eventually evidence would have started stacking up and the conclusion would have become inevitable. Einstein did it off of not a lot of concrete evidence. But we certainly would not be living in a world in which nobody had ever come up with the idea or anything stupid like that.
If you want to dig through it, I find http://mathpages.com/rr/rrtoc.htm Reflections on Relativity to be a dense, but fantastic book on the topic. (Ooo, this is the first time I've ever clicked through that link and seen the physical book finally exists, after years of me wishing for it. Nice.) RoR even digs back and shows how the Greeks had paradoxes that demonstrated the impossibility of a rigidly separated space and time, and had we taken those paradoxes seriously much earlier, who knows what we might have done.
(I do find it intriguing how much math from that era can be framed in terms of taking the ancient paradoxes seriously, really really seriously, and not just as wordplay. One of the biggest moments in 20th-century math history, Godel's Incompleteness Theorem, can be viewed as "simply" taking the ancient Epimenides paradox seriously. http://en.wikipedia.org/wiki/Epimenides_paradox )