![]() ![]() We now understand the Newtonian model as approximate. It does an excellent job as a model, but it isn't reality. But always remember: this is a theoretical model, an abstraction that exists only in the human mind. If the model had more than one time dimension, it would need some other barrier to rotation in timelike planes. And then, with only one time dimension, it is impossible to reverse a timelike interval, as the phenomena demand. While space and time may be partially interchanged through "rotation" (acceleration), timelike intervals may never become spacelike, and vice versa. Minkowski's spacetime accommodates the arrow of time through its metric signature. Electrodynamics is theoretically simpler in Minkowski's four dimensional spacetime (although we mostly do our approximate practical calculations assuming Newtonian space and time). However, this approach struggles with electromagnetic phenomena. The geometry of Newtonian physics manages this with three spatial dimensions kept completely separate from a single time dimension. One consequence of this is that any geometric model that includes time must have only one time dimension. On the other hand, we cannot rotate ourselves to exchange "past" and "future". Any geometric model of space must accommodate this possibility. In space, we may rotate ourselves to interchange spatial directions: "forward" may become "backward". The observed fact that the past is different from the future constrains any model of spacetime. ![]() It is a product of the human imagination, like all of our models of physics. Minkowski spacetime is a mathematical model constructed to capture aspects of the phenomena we observe. Is there anything inconsistent or problematic about a universe whose asymptotic metric signature is (-1, 1, 1, 1) where the -1 direction is unbounded but one or more of the 1 directions are bounded from below (or equivalently, from above) and the metric becomes singular as that special coordinate approaches the origin? Or is it just random luck, like we had a 1 in 4 shot of the bounded dimension being the -1 and that just happened to be the case? ![]() While the 4th is unbounded only in the positive direction, and therefore strictly non-negative if you choose its lower bound as the origin. To put it another way, 3 of the dimensions are unbounded in both the positive and the negative direction. where I think the last one is probably right. or maybe neither of them necessarily must have an arrow. But I've never heard anyone explain whether living in a universe with two time dimensions would mean only one of them has an arrow, or both of them have an arrow. I know these have come up now and then in string theory and other approaches to quantum gravity. I've also wondered about theories with more than one time dimension. Where the usually distinction between a spacial and a temporal dimension is which sign it contributes to the metric signature. One of them is generally believed to have to do with special boundary conditions at the beginning of time.īut if you knew nothing about our universe, and you were constructing one from scratch, it seems just as logically possible that you could put the special boundary condition at the edge of any spacial dimension instead. Time is different from space in these two seemingly independent ways. ![]()
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