[FOM] The Lucas-Penrose Thesis vs The Turing Thesis

[scerir]

A.P. Hazen:
Suppose some version of the "many worlds" approach 
to quantum mechanics is true and that the universe 
"splits" every time a photon encounters a half-silvered 
mirror.  Might not human mathematicians come to accept 
different sets of set-theoretic sentences in the histories 
arising out of the two sides of a split?  But since 
the definition HAS to refer to an idealized, rather than 
a physically real, future development of mathematics (see below), 
perhaps this isn't important.

# H.Everett developed (1956/1957) the 'relative state' 
approach (essentially, the important thing is not the single
quantum state but the quantum state entangled with the resulting
detector state, and the resulting conscious state of the observer). 
Then the 'relative state' interpretation became the 'many worlds' 
interpretation (not sure about who gave, much later, this name, 
perhaps prof. deWitt). But H.Everett did not define what a 'world'
should be. Rather, according to Everett's paper on Rev.Mod.Phys.,
they are not 'worlds' but different 'orthogonal' memory states 
within the mind of the observer (which, in turn, has a limited 
memory capacity). This original interpretation of the 'many
worlds' interpretation it is also known as 'many minds'.
There are, for sure, many different interpretations of the 'many
worlds' interpretation (due to deWitt, Graham, Vaidman, Tegmark,
etc.). Sometimes those 'worlds' are different ontological entities,
sometimes they are just different 'histories' or different 'consistent 
histories'. 

I strongly recommend the paper ... 
Barrett, J. A. and D. Z. Albert  
"On What It Takes to Be a World" 
Topoi, 14(1): 35-37, 1995
on this page 
http://www.lps.uci.edu/home/fac-staff/faculty/barrett/papers.html
and you would realize that 'many worlds' is far to be
an easy and - what counts here - a consistent interpretation 
of quantum mechanics.

Regards,
scerir (Serafino Cerulli-Irelli)