Surely no discussion on cats is complete without the experiment first
proposed
by Schroedinger (Naturwiss 48.52 (1935) trans Jauch, Josef M (1965:125),
Foundations of Cat Mechanics (Reading, MA and Addison-Wesley)) cited in
Griffiths (1994), an experiment to my knowledge never performed, so that
the
cat concerned remains happily abstract, or possibly general, though
probably
not total.
"A cat is placed in a steel chamber, together with the following hellish
contraption...in a Geiger counter there is a tiny amount of radiocative
substance, so tiny that *maybe* within an hour of one of the atoms decays,
but
equally probably none of them decays. If one decays then the counter
triggers
and via a relay activates a little hammer which breaks a container of
cyanide.
If one has left this entire system for an hour, then one would say the cat
is
living if no atom has decayed. The first decay would have poisoned it. The
wave
function of the entire system would express this by containing equal parts
of
the living and dead cat" , (emphasis in original)
(for an alternative translation see Hughes, R.I.G (1989:280) who
substitutes
'diabolic' for 'hellish' and supplies the vital words so tellingly omitted
by
Griffiths: 'which must be secured against direct interference by the cat')
Griffiths (op cit) gives the cat wave function as
Psi = 1/sqrt(2)[Psi(alive) + Psi(dead)]
He comments:
"The cat is neither alive or dead, but rather a linear combination of the
two,
until a measurement occurs - until, say, you peek in the window to check.
At
that moment, your observation forces the cat to "take a stand": dead or
alive.
And if you find it to be dead, then it's really *you* who killed it by
looking
in the window."
Curiousity would thus, in this case, be a proximate cause of cat death,
though
not in the sense that this is normally understood.
There is a substantial debate around various interpretations of the
Schroedinger
text. All reduce to a single point, ignored until now:
Nobody ever thought to ask the cat.
The cat would know if it was alive. To prove this, assume a self-conscious
cat
(V=0 where V = unselfconsciousness) Such a cat could, until point of death,
reason as follows: I think, therefore I am. After the point of death, it
would
not reason at all and the question would (for the cat) be meaningless.
Since
moreover we must assume that if self-conscious, it would be a Cartesian
cat, its
knowledge would possess the status of absolute truth. This is a complete
refutation of von Neumann's (1932) 'no-go' theorem proving the
inconsistency of
hidden-variable-theories.
There is a case to be made that cat-ness is in complete contradiction with
self-consciousness. Also the possibility of Post-Modern cats is to be
considered, such cats being unable to deduce with certainty whether they
were
alive or dead. This corresponds to the modal quantum construction "Maybe I
think, so maybe I Am" or possibly "I think I Am, but you don't have to".
Indeed
empirical cat observation suggests that the actual state of general cat
consciousness corresponds to the deduction "I Know I Am, and I don't care
what the hell you think" (V = epsilon, where epsilon is very very very
large).
In this case we might as well pretend the cat is an ideal measuring
apparatus,
even though it isn't, because it makes no difference to us and the cat
doesn't
care anyhow because it exists in a Quantum World of its own.
On the connection between Quantum Logic and Post-Modernism cf Bub (1992)
and
Aaronovitch (RIP). Nevertheless, the balance of probability leads us to
conclude
that Schroedinger's cat could not possibly contribute to socially-necessary
abstract cat-time (SNAC) because after such a harrowing experience, it
would
be far too hungry.
And, indeed, the very same approach solves the great Kliman Cat Debate.
Ask the cat.
If it answers, it's part of abstract labour. If it don't, it ain't.
Alan