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That seems like a form of solipsism for intergalactic travelers. Wherever you go, there you are. If you have a point of origin or a destination, you can define your speed relative to either of those points. And if you are at rest with respect to another object, you will both have the same velocity vector for (x,y,z,t) = (0,0,0,c) or maybe (0,0,0,-c). You both move at the same velocity through time, so you age at the same rate. Now, if you throw that object away from you, in your frame of reference, you are at (0,0,0,c) and the object is satisfying something like sqrt(x^2+y^2+z^2-t^2)=c (real physics is more complicated, naturally). You age normally, and the object ages more slowly. From the object's frame of reference, it is aging normally, and you age more slowly, because you're the one moving fast. Now as that spatial component approaches c, it becomes more and more difficult to hang a left at Betelgeuse. So you can usually treat all the dimensions that square to a positive number as the magnitude of their combined vector (let's call it s). The dimension that squares to a negative number, t, could be the magnitude of a vector in multiple dimensions that all square to a negative number (let's call them u, v, and w). So a photon might prefer to see its spacetime vector as (s,u,v,w) = (c,0,0,0) or maybe (-c,0,0,0), provided that x^2+y^2+z^2=s^2 and u^2+v^2+w^2=t^2 (or similar equivalent constraints that change the signs around). And whatever happens that might appear to us as though the photon is traveling at less than c is actually the photon stepping sideways through temporal dimensions orthogonal to our own hard-to-divert movements through time. If you look at dual quaternions or geometric algebra, the math for systems with dimensional signatures (+,+,+,-) and (+,-,-,-) are often nearly identical, with a few sign flips here and there. And it would allow for odd things like imaginary mass and imaginary energy. We simply might not notice the additional temporal dimensions, for the same reason that it is difficult for us to change the direction of a massless, chargeless photon without touching it. |