[FOM] The Strong Free Will Theorem
kochen at math.princeton.edu
Mon Jan 26 12:01:58 EST 2009
This is a reply to Timothy Chow's letter about our "strong free will
He makes three points. First, that although relativity is not
explicitly presumed, it is implicit in the mention of "spacelike
separate" in the third axiom. We use this term only as a shorthand
for "a separation of experiments for which light would take longer to
travel than the duration of the experiments" (for example, two
Stern-Gerlach type experiments on the Earth and Moon). As we said
we used relativity to justify the third axiom (MIN), but it is not
needed in the statement of the axiom or its use.
Secondly, he asks "what is new?" In our referenced original
Foundations of Physics paper, we give a detailed history of "No-Go
theorems" which addresses this point. The new result is a sharpening of
the original Kochen-Specker paradox, which prohibited only
"non-contextual" hidden-variable theories. We now prove that
this restriction is unnecessary. Bell's theorem uses "Bell locality,"
about which there is some disagreement - Redhead's book "Incompleteness,
Non-locality and Realism," discusses nine different versions of
locality, whereas we use only the axiom MIN, which is justified by
Lorentz invariance (and we repeat, this is the only place Lorentz
invariance is used).
Bell's locality axiom also involves probability (roughly, that two
remote events are probabilistically independent), and its conclusion is
also stated in probabilistic terms. The fact that our argument makes no
use of probability makes it apply to theories that the earlier theorems
didn't prohibit - for instance relativistic GWR theories (see the
appendix to the paper).
His third point is our use of the word "theorem" for a result in
mathematical physics rather than mathematics proper. We thought it
appropriate precisely because of the trouble we took to reduce the
physical assumptions to just SPIN, TWIN, and MIN. In any case, such use
is hardly new -- we have many distinguished predecessors, of which we
can instance Bell's theorem above, Liouville's and Boltzman's theorems
in thermodynamics, Araki's in field theory. There can be no precise
use of the word "theorem" in phyics until Hilbert's problem of
formalizing physics is realized.
John Conway and Simon Kochen
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