- 654

- 148

Alice's dots are spaced further apart, too. But you have the right idea about pythagoras and subtracting, that is the essence of the relationship between time and space (the spacetime interval, to labour the point), notice we have a "3-5-4" triangle, not by accident! . Everyone has their own proper time, and you have worked out both Alice's and Bob's in this instance. I think you have it, just dont panic ;)we see that the traveling twin A (we’ll call her Alice)’s “path” through this ST diagram visually looks longer than Bob’s. However, the sides of the symmetrical stacked right triangles aresubtractingnot adding, as in the Euclidean case, and thus the magnitude of Alice’s resultant vector, or proper time/invariant interval, is actually shorter than Bob’s, not vice-versa. That is, for Alice’s journey out to her turnaround point 3 light years away, her time/age is (tau)^2=(5)^2-(3)^2= (tau)=4 years, whereas Bob’s is (tau)^2=(5)^2-(0)^2=(tau)=5 years.

Now I do have a little confusion here in the above example. That is, who’s proper time are we measuring or using here, Bob’s or Alice’s or both? (tau)=proper time is supposed to be invariant, right? But in the above example (tau) is 5 for Bob and 4 for Alice. Should I have re-arranged one of those equations?