WTF is Max Tegmark talking about? Can both be had together? The intuitive understanding seems to be that the shorter (space) the faster (time) but Fermat's principle shows that a shorter time may actually require a longer distance.
3h — TheMadFool
The shorter the faster has a relation to the uncertainty principle. The shorter the distance the greater the uncertainty in momentum (and thus velocity. Now velocity in relativity is velocity through spacetime. All particles move with the speed of light through spcetime. A particle standing still (which is impossible in QM) is moving with c through time. Time hasnt got a fixed pace in GR. If space is curved, then time is too (the space expansion metric, the FLMR metric, has constant time, already hinting at it being wrong wrong). In flat space time runs the fastest while in curve space it flows slower. Efficient time. You can use space efficiently but how to use time efficiently?
Of all possible paths between two spacetime points the most probable will probably be realized. If there are two particles starting from two fixed points (alwaya in spacetime or energy-momentum space) then they will arrive at their final points in phasespace by means of all intermediate interactions with the virtual field that takes care of the interactions. And there are infinite many. Each of these paths is comprised in Feynman diagrams, representing the path integrals of the Lagrangians. There is a zeroth order diagram. This one takes all non-interacting part of the parts into conseideratio. The first order diagram that of all paths of the two particles while interacting once. This is the popular view of, say, two electrons interacting by means of exchanging one photon. Etc.
So, what even means efficiency of space, let alone of time?