A Universe of Infinite Spacetime

Context: What is the shape of the Universe ?

Cosmologists believe that they have successfully measured the curvature of the large scale structure of the Universe and that it has returned a result of zero.  To understand curvature in this context – consider a triangle on a flat sheet of paper: its angles always add up to exactly 180°.  If you draw the triangle on an object which possesses positive curvature, such as a sphere or a balloon – the angles will always add up to more than 180°.  If you draw the triangle on a surface with negative curvature, the angles will always equal less than 180°.

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Positive and negative spatial curvature where the sum of angles in a triangle is not equal to 180°.

The curvature of space (actually – of space and time combined, of spacetime) is what we experience as a constant acceleration towards the surface of our planet, that is – gravity.  As a whole, the Universe has a gravitational influence on itself and this is the curvature that we are primarily concerned with here.

Observations which cosmologists have been seeking to interpret imply that the Universe is on the grandest of scales a structure which has zero curvature.  If the Universe is flat and due to this – infinite, there are some interesting logical consequences. Infinity as a word is often thrown around without much thought for its depth and profound implications. If the Universe is infinite in spatial and temporal extension and is populated more or less uniformly by matter and energy, this is stunning. It is a mathematical fact that in an infinite Universe, anything that can happen will happen, and further to this: anything that can happen will happen an infinite number of times. All possible configurations of matter, energy, life, civilisation – infinitely replicated an infinite number of times, unending, and with all possible variations existing somewhere in the unutterably vast infinity of all existence.

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