where c is the speed of light, ds is the interval in both time and space, dt is the change in time, and dr is the change in space coordinates (x, y, and z). It’s basically just saying that moving in time and space can be written in a combined manner to give the total “interval” that you moved. We can see that space and time are treated differently just by a quick look at the equation: the interval of time is multiplied by c, and it doesn’t have a negative sign like the spatial interval does.

*grid*(see picture). Let’s say we can only move forward along each dimension of time (into the future). So for time 2, t

_{2}, time must move up (that is the forward direction) and for time 1, t

_{1}, time must move to the right (also the forward direction). But if the times are

*combined*, where can you move? There are plenty of options depending on how fast you go, for example, see the lines on the grid. In each case, you’re moving forward in t

_{1}and t

_{2}, but for some, you’re going faster in t

_{1},

_{ }and for others, you’re going faster in t

_{2}. Only the blue arrow has you going forward in time at the same speed in each time.

_{1 }passing more quickly than t

_{2}, or vice versa. The orange line in the picture has t

_{2 }passing more quickly, since for every step through t

_{1}, you go forward 2 steps in t

_{2}. The green one is the opposite: for every step in t

_{2}, you go forward 2 steps in t

_{1}. But you could also have more fanciful patterns on the grid like the pink line: here, although you’re going forward in both times, the speeds at which you move forward in each time keeps changing.

_{2}(call it O2) appear to someone two travels through both t

_{1}and t

_{2 }(call them P12)? I think there are a few options. The first is that O2 appears stationary for P12: the object would appear to be “locked” in one direction. Since it doesn’t travel along t

_{1}, it could be just stationary at all points in t

_{1. }This is hard to imagine: what would an object travelling along one time appear to someone travelling in two times? Would it appear “blurred” in part, or somehow less substantial? I really don’t know. This requires a great stretch of the imagination!

_{1}. Why not shifted to another time? Since it isn’t travelling in the t

_{1}direction, that time is meaningless to it, so it shouldn’t prefer to be at one time rather than another.

_{2 }while you only travelled in t

_{1}, they would either appear to you to be stationary, since you can’t perceive their motion in the other dimension, or you just wouldn’t see them at all (like in the first example).

Tweet