Henry Baker <hbaker1@pipeline.com> wrote:
This is the *quaternion universe*.
Egan mentions quaternions by name. And has one of the characters discover them, only with a different notation. But I think it would make more sense to view *our* universe as the quaternion universe. As soon as I learned about quaternions, about 40 years ago, I made the connection. Three dimensions that are just alike, and one that is different and has a direction associated with it. There is no way to define the units i, j, k, -i, -j, or -k except by reference to the other units. Your i could be my -j and our moderator's (j-k)/sqrt(2). Exactly as with space's x, y, and z axes. But there's no way to confuse 1 with -1 or with any of the imaginary units. Exactly like our t axis. There's a unique "arrow of time." Relativity can mix space and time to an extent, but every interval between two events is unabiguously either spacelike or timelike, depending on whether the invariant, x^2 + y^2 + z^2 - ct^2, is positive or negative. And if it's timelike, it's unambiguous which event is earlier and which is later. There's no frame of reference in which Macron's inauguration came before Trump's. (Disclaimer: That's special relativity. In general relativity, reverse causality appears to be possible under extreme conditions.) By contrast, in Egan's universe the four coordinates are completely interchangable. Once their spaceship reaches infinite speed, one of their planet's space axes is their spaceships's time axis, and one of their spaceship's space axes is their planet's time axis. There's no unique arrow of time. Each object carries its own arrow of time along with it. Hence it's possible to land on a time-reversed planet. But you had better bring a flashlight, since you won't be able to see by the light of its time-reversed sun. Also, watch out for the time-reversed dust that was in your spaceship before you landed, and you weren't able to remove it then. The good news is that it was all gone by the time you took off, as you had, without trying, tracked it all out. You also removed (by walking in them) all the footprints that were around your landing site when you landed.