Reply-To: "Kevin Aylward"
From: "Kevin Aylward"
Subject: Re: OT: Chiao's experiment
X-Newsreader: Microsoft Outlook Express 6.00.2600.0000
Date: Thu, 12 Sep 2002 19:54:24 +0100
NNTP-Posting-Date: Thu, 12 Sep 2002 19:54:25 BST
"Dirk Bruere" wrote in message
> "Kevin Aylward" wrote in message
> > The Schroedingers cat dilemma, isn't. It was simple a misapplication
> > QM when QM first came about. A *correct* interpretation of QM does
> > require a cat two be in two states at once.
> There is *no* 'correct interpretation'.
There are however, interpretations that can be demonstrated to be
incorrect because the result in a contradiction with experiment. For
example, Ballentine's "Quantum
Mechanics", page 342, watched pot paradox:
Noted here is A, interpretation that leads to the split cat, and B that
A. A pure state |y> provides a complete and exhaustive description on an
_individual_ system. A dynamical variable represented by the operators Q
value (q, say) if and only if Q|y>=q|y>
B. A pure state describes the statistical properties of an ensemble of
The "watched pot" paradox
This paradox is amusing, but also instructive since it has implications
interpretation of quantum mechanics. This paradox arise within the
interpretation (A) in section 9.3, according to which a state vector is
attributed to each individual system. If any system is observed to be
it will be assigned the state vector |y_u>, within that interpretation.
that interpretation has superficial plausibility, and was once widely
it has been rejected in this book. Some of the reasons were given in
this paradox provides further evidence against it.
Suppose that an unstable system, initially in the state |y_u>, is
times in a total interval duration t; that is to say, it is observed at
t/n, 2t/n...t. Since t/n is very small, the probability that the system
undecayed at the time of the first observation is given by (12.21) to be
P_u(t/n)=1-(qt/n.hbar)^2, where q^2=<(H - )^2>. Now according to the
interpretation (A), whose consequences are being explored, the
observation of no
decay at time t/n implies that the state is still |y_u>. Thus the
of survival between the second observation will also be equal to
on for each successive observations. The probability of survival in
at the end of this sequence of n independent observations is the product
probabilities for surviving each of the short intervals, and thus
P_u(t)= [P_u(t/n)]^n = [1-(qt/n.hbar)^2]^n (12.30)
We now pass to the limit of contineous observation by letting n become
The limit of the logarithm of (12.30) is
log (P_u(t)) = n.log[1-(qt/n.hbar)^2] -> 0 for n->inf
Thus we obtain P_u(t) = 1 in the limit of contineous observation. Like
saying "A watched pot never boils", we have been led to the conclusion
contineously observed system never changes its state!
This conclusion is, of course false. The fallacy clearly results from
assertion that if an observation indicates no decay, then the state
be |y_u>. Each successive observation in the sequence would then
state back to its initial value |y_u>, and in the limit of continuous
observation there could be no change at all. The notion of "reduction of
state vector" during measurement was criticized and rejected in Sec 9.3.
detailed critical analysis, with several examples, has been given by
(190). Here we see that it is disproven by the simple empirical fact
continuous observation does not prevent motion. It is sometimes claimed
rival interpretations of quantum mechanics differ only in philosophy,
not be experimentally distinguished. That claim is not always true. as
Some background to this is:
The *whole" concept of collapse of the wave function" is *completely*
the Ballentine approach, which I might add is not of his origination, it
way back to people like Einstein.
The basic concept, in essence, is that the wave function does not apply
single experiment or individual particles at all, but only to an
experiments/systems or particles. There is *no* system in a *real* |a>
state. This is just a lose way of notation for what is really happening.
Saying that a wavefuntion collapses is just as silly as saying because
an average of 2.4 children to a family, that when I make a particular
measurement on a specific family, the wave function collapses on a
to say, 2 boys and a girl. The fundamental point is that the QM wave
only applies to a statistical ensemble, or collection of experiments,
Consider a classical dice. If this is expressed in QM notation, it could
written so that there is a wave function describing the probability of
outcome given by:
psy= |1> + |2> + |3> + |4> +|5> + |6>
It is obvious here that on each throw, only one of the states will be
but there is no requirement for any notion of collapse of the wave
for the dice to *physically* exist in the summed state! It a nonsense
The wave function is a statistical function. It does not directly apply
single experiment, only the statistical results of many. Fundamentally,
to understand exactly what psy= |1> + |2> means. It simple does not mean
here is a *real* system state of that sum. That's why it can not
was never in that state to begin with. Its just notation for a method
has real meaning in calculating a *final* result.
I must stress here that the Ballintine view is not a classical ensemble,
it is a
> As for things being in multiple states at the same time, a quantum
> would not work if it were not possible.
Not really. I think you misunderstand what is going on. No part of QM
requires this concept. QM computing is completely explained by the
statistical ensemble of quantum states as noted above.
> Things as large as buckyballs have been shown to exhibit interference
Again you misunderstand. Of course there are effects equivalent to
interference effects. However, one needs to be clear on what
interference means. Interference manifests itself by the pattern of
discrete, localised effects building over time. Its only when you stand
back a bit the it looks like a real wave pattern. The classic two slit
diffraction pattern can be built up slit with time such that only one
photon goes through a slit at a time. Its only *after* waiting for many
to hit that you actually see any pattern at all.
> Whether cats can, and for how long, remains an open question.
Not as far as I, Ballentine and Einstein are concerned. Its a dead issue
that won't die.
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