Thursday 6 March 2008
K-Pax, Eternal Return, Poincare
Hurly Burly has mentioned on various occasions the similarities between CTF and the final speech of the K-Pax character Prot, played, curiously enough by Kevin Spacey (what is it with Kevin Spacey and 'end of film 'talk-overs and CTF?).
In this Prot explains that the K-Paxians have been around long enough to know that the universe will expand, stop expanding, collapse back on itself and then expand again. as such we will all live our lives again. However everything will be the same, every action and mistake of our lives will be repeated. Prot says:
"Whatever mistakes you make in this life you will live through in the next pass, every mistake you make you will live through again, and again, and again, for ever."
This is a description of a scientific/mathematical principle known as Poincare's Recurrence Theorem. This has been defined as:
"For a (time-dependent) Hamiltonian system a trajectory returns to a given neighbourhood of a point given a sufficiently long (or an infinite) time."
( The Laws of Nature by Peter Mittelstaedt & Paul Weingartner, page 162 - Spinger 2005).
In simple terms this means, as I understand it, that if we live in a finite universe with boundaries then once the universe has expanded into all the available 'space' then it can expand no further and deflates back to the 'big crunch'. I am aware that the latest research from COBE implies that the universe will go on expanding forever (but if this is the case then given an infinite amount of time the universe will become so diffuse that it will cease to exist as a coherent entity).
So if Poincare's Recurrence Theorum (and Prot's suggestion) has any validity then we are back facing what I term the 'Strong Cheating The Ferryman' Interpretation (SCTF) that we all are doomed to live the same life as Nietzsche suggested in his famous 'demon' analogy (see my next posting). However WCTF (the 'Weak Cheating The Ferryman') proposes that Daemon-induced warnings and interventions can change events and as such contribute to a far more evolutionary Bohmian IMAX within Everett's Many-Worlds (Many-Minds) Interpretation.
(note my use of 'Weak' and 'Strong' - this is deliberate and reflects two other fascinating theories of modern cosmology, the 'Strong Anthropic Principle' (SAP) and 'Weak Anthropic Principle (WAP). These are well worth a posting in their own right).
If you are interested the K-PAX Prot speech can be viewed on YouTube by following this link (you need to go in for about two minutes):