Sunday, February 19, 2017

Cosmic Origami

When Einstein came along with his General Theory of Relativity, all of a sudden flat-earthers had a new justification for their loony argument. Einstein demonstrated that gravity comes about through the distortion that matter and energy produce in a four-dimensional spacetime “sheet.” If one looks at the universe as a two dimensional flat sheet of paper, then what we perceive as billions of clumps of matter that we call galaxies are no more than three-dimensional forms created out of a single flat universal sheet of paper into all manner of interesting shapes through a sort of grandiose cosmological origami. It is gravity itself that causes this infinite flat sheet consisting of dark matter pervading all of space to distort and fold into the three-dimensional bodies that we perceive to fill the universe.

From our observations of microwaves we know that just after the Big Bang there was a dark matter sheet laid out evenly throughout the universe whose density varied very little from point to point. However, there were tiny density fluctuations in the first instant of time that set up ripples in the field of dark matter. In these dense regions where the sheet contracted a bit, it bunched up, eventually forming structures like galaxies. In less-dense regions the sheet stretched out to form voids between the galaxies. The observable universe arose out of clumping along the folds created by the rippling.

If we take a three dimensional sheet of dark matter and expand it into a six dimensional position-velocity phase space, then each particle of matter may be plotted against it's 3D spatial coordinates and also the three coordinates of its velocity. Dark matter has a unique physical “collisionless” property in which its particles can all pass right through each other without any effect. In this 6D space phase, dark matter’s collisionlessness ensures that its sheet can never cross itself, or tear, just like a 2D paper-origami sheet is not allowed to cross itself or tear when it folds up. The creases and folds in dark matter are important because they mark the edges of structures like galaxies.

But the analogy to origami only goes so far. The cosmological origami sheet is stretchy, unlike in paper origami. And the cosmological sheet is three-dimensional, folding up in six dimensions, unlike 2D paper-origami sheets that fold up in 3D. The origami analogy helps explain why galaxies tend to form with filaments spreading out from them. Without stretching the paper, it is impossible to form a bunched up knot in the paper origami without producing filamentary folds at the same time. The origami viewpoint also helps us to understand the growth of complexity - how the complexity of a structure increases with the amount of “origami paper” that gets folded up to construct it.

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