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The existence is an ergodic and complete phase space

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05/21/2014 05:58 AM
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The existence is an ergodic and complete phase space
The whole existence is a multidimensional phase space [1]. Phase space denotes to an abstract space that records all possible states of a system. Each possible state corresponds to one unique point. The abstract phase space approach does away with the traditional location, velocity, energy and momentum involved with individual particles (or, for instance, galaxies), thus allowing us to understand the existence (not just our universe) as a whole.

Phase spaces are widely used in analytical mechanics. For an example of a very simple phase space, take a look at the phase space diagrams for a 1D oscillator [2]. Undamped and damped oscillators produce nice phase space curves (on the right) in two dimensions (position, velocity) that capture the essentials of the physical system. It's certainly overkill when you're dealing with such a simple system, but when your system has more degrees of freedom (more dimensions), it becomes truly useful. For instance, if you're dealing with a three dimensional oscillator, your phase space becomes six dimensional. While this sounds daunting, but it actually simplifies the mathematics: all the relevant physical quantities can be calculated as simple multidimensional volume and surface integrals or partial differentials without even thinking about the actual physical configuration. Writing the explicit non-phase space equations in the traditional way you learnt in school, by calculating forces, velocities and accelerations, is much more complicated and eventually becomes impossible. Yes, multidimensional volume integrals are easier.

Now, it is my belief that the phase space of the existence is ergodic [3] and the phase space structure is complete [4]. In non-mathematical terms that means that there are no "empty spaces" in the phase space and that every point of the phase space will be visited at least once. Now you see the power of the phase space approach. Without considering individual creatures, humans, galaxies or stars, it can be deduced that in such a system, every possible scenario will become reality at some point or another.

You will live every possible life (e.g. in one universe your friend here is you), all the possible variations of the earth exist (e.g. one with Mount Everest and one without it), there exists an improbable universe where all the galaxies have clustered right next to each other, and so on. Now, of course, this can't be sequential. We can't first have an earth with Mount Everest and then another earth without it.

The logical conclusions is that they have to exist in parallel. Hence, when the existence is exploring every possible point in the phase space, it generates an infinite number of parallel universes where the alternatives are explored. Satisfying ergodicity this way is possible, because the universes do not have to communicate with each other - in fact, satisfying the ergodicity requirement dictates that the parallel universes CANNOT communicate with each other.

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