Tricky question, Ender. I like it.
One possible answer involves different reference frames. Every time you travel through time, your enter a new frame, and the propagation delay is only evident from within the frame of the traveller who made the change, which is shared by everyone and everything he brought with him. That leaves Doc in a history-altering frame, while Marty remains in his initial frame. When Doc sends his letter (the primary change), he causes a ripple that propagates down the timestream and causes the letter to be delivered to Marty. If he had a picture of Marty standing on the road a few minutes downstream from his own abrupt departure, he would have seen the delivery guy and the letter slowly fade into view at some point long after he sent the letter; in fact, given his life expectancy at the time, he probably wouldn’t have seen the photo change at all. For Marty, locked into his 1955 frame, the change would be effectively instantaneous. That letter had been waiting for him for 70 years. This gets really sticky, though, when you consider that Old Biff’s alteration to the past didn’t seem to affect Doc, Marty, and Jennifer immediately in 2015. I don’t have a glib answer for that (yet–one may yet come to me). There must be some element of this at work to explain the unaltered memories of the travellers, though. Perhaps there are only two frames, traveller and non-traveller, and things in the travelling frame are only affected by changes that would prevent them from entering the travelling frame entirely (such as not being born).
I think a better answer is the one I alluded to in my summation above: propagation rates differ between primary and secondary (and presumably tertiary) changes. As a refinement of my earlier handwaving, say that the propagation rate of the changewave is a function of the number and degree of the changes it causes. That would explain why secondary changes (those triggered by the primary wave) seem to propagate faster; they necessarily have lesser effects than the primary. Each wave initially has a very rapid propagation, and it slows down as it causes changes. The greater the impact of the secondary change, the more it slows the primary. This would explain the dramatic slowing of the wave Marty caused by preventing his parents’ from meeting. It caused minor secondary effects quickly (Lorraine not going to the dance with George, no wedding, and so forth), which slowed it to an average rate of 1 year/hour by the time it reached David’s birth, 7 years downstream. The two major secondaries (the births of David and Linda, which would also cause tertiary effects as they were erased) and many minor secondaries slowed the primary wave dramatically before it reached Marty’s birth 14 years downstream. The drag bought him time to fix things.
Now, consider Doc’s letter. What secondary changes did it cause? It moved a tiny amount of money into Western Union’s coffers, then sat in a vault for 70 years. For the sake of convenience, let’s assume that over that period, the cumulative effects of that changed bank balance and any other minor impacts are roughly equivalent to all the secondary changes caused by Marty’s primary change up to the time of David’s birth (roughly 7 years downstream). That gives us an average propagation rate of about 1 year/hour across seventy years for Doc’s letter. Doc would have seen a photo begin to change in about 3 days, if he had had one. The secondary change would have been the Western Union guy setting out to deliver the letter, with the actual delivery as a tertiary effect. The secondary change would propagate quickly, slowed only by minor effects like the guy’s influence on traffic…on a quiet road late on a Saturday night. Most of the effects would be off-screen (since we weren’t watching a movie about a Western Union delivery guy). The first sign of the tertiary change that would have been noticeable from Marty’s perspective is the the guy’s headlights in the fog. Even if we assume that the secondary wave propagated at roughly the same rate as the primary, 1 year/hour still equates to about 2.4 hours/second. That means that if the Western Union office was less than two hours away, the change would take place in under a second. Say, during the time when the headlights were fading into view. We may have seen the change happening, but misinterpreted it as the headlights advancing through a thick patch of fog, rather than fading into existence. If the guy had been running late, he would have suddenly appeared out of nowhere in front of (an undoubtably startled) Marty.
I’m enjoying this far too much. I am such a geek.
