Wuwei
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- Apr 18, 2015
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I just wanted to expand on potential a bit as it relates to a topic in string theory called landscape and possibly multiverse as well. As you pointed out, every object has potential. This potential can be plotted on a multi-dimensional graph. The object's initial state or position on the graph is called minima. The object needs additional energy to move to the next state. If it does not find that additional energy then it can get stuck in a given minima and fail to move to the next state. Similarly our universe too can get stuck at a given minima. The different versions of string theory simply describe different sates of the universe. We simply have not yet theorized a version of string theory which describes the current state of our universe. These different states of the universe have very different properties. For example in one state, the space can be three dimensional and in another state, space can be of more dimensions (up to 10 dimensions). This is where string theory start to converge with the idea of multiverses each with their own unique properties.
I haven't heard of the local minimum aspect in multiverses. I have read that shortly after the big bang there were possibilities of different phases, similar to the solid state phases of carbon (graphite, diamond, etc). After a point when the temperature of the universe dropped to a certain point, the laws of physics were frozen into it's current form (or phase). That is the same concept as annealing some types of metals: a hot metal is cooled in a way to lock in a particular phase. It now makes sense, the local minima mathematically represent the different phases our universe can (could) be in. As you say, since the universe is much cooler now, we are stuck in our current local minimum.
As far as the dimensionality of space-time, if there were more or less than 3 space-like dimensions, the inverse square law would no longer be valid in gravity or EM theory.
One interesting thing about string theory is that all 10 dimensions are closed – circular. Space and time are huge circles encompassing the closed universe. The remaining dimensions are tiny circles;10^20 times smaller than the diameter of a proton. It would be interesting to see what a universe would be like where some of the large dimension circles are interchanged with smaller dimensional circles. I assume that what you meant by different states of the universe.