🚀 go-pugleaf

In article <31JUL199217054379@zeus.tamu.edu>, dwr2560@zeus.tamu.edu
(RING, DAVID WAYNE) writes:
|>johncobb@ut-emx.cc.utexas.edu (John W. Cobb) writes...

[Musings on fate of Scrodinger's Cat]

|>>If you accept the definition that measurement occurs when the "irreversible
|>>act of amplification" (Is this a Bohr quote?) occurs then I would say that
|>>the wavefunction collapsed when the silicon detector INSIDE the box fired
|>>amplifying the decay event from a single particle to a stream of millions
|>>or billions of electrons cascading across the potential.
|>
|>I have no problem with this so long as 'collapse' just means that a coherent
|>superposition becomes incoherent.
That is what I mean. the cat lives or dies when the detector fires, not
when the lid is opened.
|>
|>>I developed an intuition to explain this "curious world". The detector
|>>amplifies small events to create vastly different time asymptotic states
|>>(no current flow/current flow). So the detector is unstable and right at
|>>a bifurcation point. Thus its global behavior is determined by small
|>>perturbations. So very small perturbations can be measured by the
|>>effect they have on the measuring apparatus. This is "the irreversible
|>>act of amplification". It makes great sense when I 'fess up to my
|>
|>But you are amplifying an event which can go either way with equal
|>probability. 
Yep.

|>Something which 'seeds' this choice is called a hidden
|>variable. 
Not at all. How does normal quantum uncertainty occur? It is an
intrinsic randomness. I could say that the event is governed by
uncontrolled "hidden variables" that most experimentalists usually
call experimental noise. However, in this case we are bumping up
against quantum limits, so I will instead invoke the empirically
supported, no hidden variables, randomness of quantum fields.
However, if we had been discussing a classical problem, then I
would have agreed, except I would have called the "hidden variables"
unknown degrees of freedom not controlled by the experiment. The law
of equal a priori probabilities would then prevent me from saying
anything about the "seed" a priori, althouth I might be able to
a posterieri after the amplification has occurred.

|>Look at it this way: You prepare the system in a state which
                                                  ^
                                                 macro
|>_rigorously_ has equal chances to go either way. How can the probability
|>change if you don't open the box?

I look at classical statistical physics for an analogy. When you contrast
the classical viewpoint with the quantum viewpoint, the result flows for
me. classically I would say that I prepare my system so that it occupies
a point in phase space that is consistent with my imposition of macro
constraints like temperature, density, center or mass, etc. Now my
specification usually does not restrict phase space to a single point.
the are many micro-states of the system that are consistent with the
macroscopic constraints. So I use a classical probability density
distribution and say that there is an equal probability that the
actual system is in any one of the multitude of allowable micro-states.
This is the state of my experiment at time t=0. Now if the system is
such that it amplifies uncertainties (i.e. is unstable) then the state
of the system at a later time may be different for different micro states,
even if those micro-states obeyed the same initial macro constraints.
Moreover, a macroscopic observable may also depend on the exact initial
micro-state. 

For example, use the Bernoulli shift as an example. Consider the set of points 
on the real unit [0,1]. Define time evolution as a mapping from the real
numbers tothe real numbers where evolution forward one unit of time corresponds
to shifting the decimal representation one place to the right. That is
f(x) = 10*x, with the understanding that f drops the part to the left of
the decimal so that its range is less than one. Now suppose you prepare
your system so that you localize the position to 0.001. Say You require
the initial position to be 0.123. Now since this is a macro constraint, you
system will have an initial value in the range [0.1225,0.1235]. After two
iterations, the time evolution of the system says that your position will
now be in the range [0.25,0.35]. Now you can distinguish between states and
if you make a measurement and find that the position is 0.278 you will
then gain knowledge about the initial state that is was actually in the
range [0.12275,0.12285]. So a posteriori you gain knowledge about the
initial state. However, this knowledge was unknowable (even in this
classical system) until the measurement was taken.

So in the classical system, eventhough I do my darndest with the macro-
state specifiers I have available, I cannot pinpoint the initial 
condition. Moreover the system has an equal chance to go in many different
directions. However, in the classical system, there is no problem with
non-commuting observables, so I could, in principle, refine my macro-tools
of state preparation to become more precise and then have more a-priori
knowedge (although this process cannot proceed indefinitely). Thus the
classical system does have hidden variables. That is my measurement not only
tells me the macro-state of the system at this time, but it provides
extra information that can be used to devise additional information about
the initial state. Sometimes this information pertains to which particular
micro-state (or states) the system was actually in at t=0. However, in the
quantum case, there is no definite initial micro-state.  That is by the
time we have gotten to quantum measurements, we have lumped all possible
ways of preparing the system into the set of parameters called "macro
parameters". The set of undetermined micro-parameters is now null. However,
the curious nature of quantum physics says that the phase space has not
collapsed to a point but it is instead still of finite size determined by
Planck's constant. Now if the dynamics is again unstable, this initial
phase space will expand. We will then have a much larger possible hyper-volume
where our system can be located. At some point we find that the wavefunction
has evolved to the point that there are uncertainties in knowledge about
the system that can be distinguished by measurement. So again we measure
and when find out new information. However, now we don't interpret this
as the addition of information about the initial state, but rather as a
perturbation of the evolving system. While this is very curious, experimentally
that is what appears to be occurring. For some reason, the act of measurement
itself is what causes the decoherence.

So the heart of the question is that usually when we are presented with the
Cat paradox, we are told that the coherent superposition is maintained
until the measurement is made. Then we distinguish between possible
macro-states at that time. Really the only point that I was making in
my previous post was that I would argue that the act of measurement actually
occurs when the detector fires and not when we open the lid. That is I call
the detector the measuring device, and not our eyes.

The physics question is whether the difference between calling the
measurement the detector firing or opening the lid makes any difference in any 
physically testable way. I do not know. If it doesn't, then it is just a
different interpretation. If it does, then perhaps it is an interesting
area of investigation.
 
|> Who decides which way it will go?

??? I don't know, the same person who decides whether the cat is alive 
    or dead.

|>Does the universe really have 'free will'?
ONly if it wants to. :)
|>
john w. cobb
jwc@fusion.hp.utexas.edu