I think this paper might be fodder for a nice discussion!


  About the Infinite Repetition of Histories in Space

Francisco José Soler Gil <http://arxiv.org/find/physics/1/au:+Gil_F/0/1/0/all/0/1>,Manuel Alfonseca <http://arxiv.org/find/physics/1/au:+Alfonseca_M/0/1/0/all/0/1> (Submitted on 22 Jan 2013 (v1 <http://arxiv.org/abs/1301.5295v1>), last revised 23 Jan 2013 (this version, v2))

    This paper analyzes two different proposals, one by Ellis and Brundrit, 
based on
    classical relativistic cosmology, the other by Garriga and Vilenkin, based 
on the DH
    interpretation of quantum mechanics, both of which conclude that, in an 
    universe, planets and living beings must be repeated an infinite number of 
times. We
    point to some possible shortcomings in the arguments of these authors. We 
    that the idea of an infinite repetition of histories in space cannot be 
    strictly speaking a consequence of current physics and cosmology. Such 
ideas should
    be seen rather as examples of {\guillemotleft}ironic 
science{\guillemotright} in the
    terminology of John Horgan.

The idea that there are infinitely many universe (or an infinitely big one) and therefore everything must be repeated infinitely many times is incoherent. If there's a copy of this universe, then it *IS* this universe by Leibniz's identity of indiscernibles. Similarly, if this universe is infinitely large it must have infinitely many different possible states - otherwise it would start repeating somewhere and, as I remarked above, a repeat is just the same thing double counted. So what makes sense is to say the universe (whether conceived as spacetime or as a Hilbert space) is unbounded, it can always get bigger and have more states - which seems to be supported by the expansion of the universe.


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