In Brian Greene's book "The Fabric of the Cosmos," he says "For an object's trajectory through spacetime to be straight, the object must not only move in a straight line through space, but its motion must be uniform through time; that is, both its speed and direction must be unchanging and hence it must be moving with constant velocity." This makes perfect sense but there's something that I don't get. Lets say I'm accelerating but moving in a perfectly straight line through space, wouldn't that also mean my trajectory through spacetime would be straight as well? Ofcourse, I understand that I am not moving uniformly through time and therefore if you were to plot my motion on a graph of space and time, it would obviously be curved, implying acceleration. But as far as my trajectory through spacetime goes, I can't see it being any other way than straight. How can it be a curved trajectory if I am moving perfectly straight through space? Clearly I must be missing something. Please help.