Dear Organlearners,
Winfried Dressler <winfried.dressler@voith.de> writes, in reply to my:
>>Now, whether we measure with a two magnitude scale
>>or a million magnitude scale, both quantum mechanics
>>and irreversible thermodynamics have taught us a very
>>important lesson. Every measurement, how tiny it might
>>be, disturbs the system irreversibly. Measurement
>>changes the system.
Greetings Winfried,
Fellow learners will have difficulty in seeing the relationship
between diginity and changes brought about by measurements. It boils
down to this. Should we measure (with a meter, informed opinion or
wild guess) a person's dignity, we invoke a change on that person's
dignity, usually with detrimental effects.
Since Bruce Jones <brucej@nwths.com> in LO21732 also commented on this
changes brought about by measurements, I will discuss this issue
separately from the others points you have raised.
The question now is, why do such a change happen. As I have written,
Quantum Mechanics (QM) and Irreversible Thermodynamics (IT) give us
the answer that such a change will happen. But why does it happen. Let
us see what QM can tell us. In a next contribution I will discuss what
we can learn from IT.
You wrote:
>After my first read, I thought that you are talking about quantum
>mechanical disturbances. But these disturbances are a
>consequence of the complementarity of variables, which,
>according to a quick scan through my memory, has nothing to
>do with the number of possible output values.
Fellow learners who have a physics background and are interested in
the deeper meaning of QM, may study the book of
Bernard d' Espagnat's (1976) The conceptual foundations of quantum
mechanics (Benjamin, Masschusetts).
Unfortunately, the vast majority of fellow learners on this list do
not have such a background. Thus, if I want to exlain according to QM
why measurement disturbs the system, I must go beyond the formalism of
QM into everyday experiences of fellow learners. This will be
indicated by lines marked with an aterisk *. If not, then we have the
tyranny of the experts on our hands.
Winfried, you are right, the NUMBER of output values do not change.
But something do change. What?
A QM wave function V consists of many eigenfunctions v(i), say N in
number.
*Think of the V as a specific library and v(i) as its many
*books. The "i" is an index ranging from 1 (identifying the first
*book) to N (identifying the last book).
The complex wave function V is constructed in IMPLICATE (tacit,
antecedent) form from these elementary wave functions (eigenfunctions)
by
V = c(1)v(1)+c(2)v(2)+c(3)v(3)+...+c(i)v(i)+c(i+1)v(i+1)+...+c(N)v(N)
where c(i) squared, namely c(i)^2, is the probablity for the system to
have an energy (eigenvalue) E(i) corresponding to the eigenfunction
v(i). The shorthand notation for V is given by
V = SUM(i; 1 to N): c(i)v(i)
*Think of E as actual information on any specific topic, say
*cattle. We use "cattle" as topic so as to have no confusion
*with any other topic like "entropy production", "correspondence"
*or electrical "current" whch may have a bearing on our
*discussion. Then E(i) is the information in the i-th book
*on cattle. Thus the probability to find information on cattle
*in the i-th book is c(i)^2.
The energy density operator for the complex wave function
in implicate form is given by
R = SUM(i, j; 1 to N): c(i)xc(j)xv(i)Xv(j)
where x is multiplication of ordinary numbers (scalars) and X is
scalar multiplication of vectorial functions. For ortogonal
eigenfunctions the scalar product is zero.
*Think of the energy density operator R as an indication of all
*the information on cattle in all the books of the library. The
*scalar product of a physics book m and a husbandry book
*will be zero because a physics book and a husbandry book
*usually have nothing in common. They are ortogonal to or
*independent of each other. When the scalar product is not
*zero, it means that one book in husbandry has cross
*references to another book in husbandry which might or might
*not be in that library
When we make merely one measurement on the system, one of the energy
values E(i) and its corresponding eigenfunction v(i) become known. It
changes from the implicate (tacit, antecedent) state to the EXPLICATE
(objective, consequent) state. Say it is the case for the index i=1 to
make subsequent notations easier. The complex wave function V is still
given by
V = SUM(i; 1 to N): c(i)v(i)
*Note that, as Winfried has said, the wave function has still
*the same number of possible output values, namely N. It is
*still the same thing as before. Think of the meaurement in QM
*as going to the library, taking out any book and study it carefully
*to see what information it has on husbandry. To make things
*easy, give the book your own personal number by using the
*number 1. In our won library many books with information on
*cattle are in other sections than husbandry since cattle is a
*principal object in the culture of the Banthu people. Some of
*those books are in the law section, others in the anthropology
*section, etc.
The energy density operator R after the first measurement is
given by
R = c(1)xc(1)xv(1)Xv(1) + SUM(i, j; 2 to N): c(i)xc(j)xv(i)Xv(j)
Since the term c(i)xc(j)xv(i)Xv(j) has moved out of the implicate
SUM(i, j), scrapping i=j=1 to become an explicate value.
*The point now is that by taking out the first book and study
*(measuring it), the density of information on cattle has changed.
*We do not expect any more book 1 to have some information
*on cattle. We know explicitly what information on cattle it has,
*namely its E(1) value. We know explicitly what section it
*belongs to. In the case of physics its probablity c(1)^2 will be
*very small. In the case of law its probability will be much
*higher in our library, but lower in yours where cattle are not
*principal objects of culture.
The energy density operator is now said to be of a MIXED form.
It is also said to be of REDUCED form. It is also said that the
wavepacket is of reduced and mixed form.
*By studying the exact content of the first book, the libary is
*not a pure unknown (pure implicate form) to us.
*One book is now known as a consequence of our study
*(measuring). Also, since all products v(i)Xv(j) which contain
*i=1 or j=1 disappear, the tacit SUM(i,j) has much less terms
*(2N -1 exactly). By taking one book of the library, we have
*reduced the number of combinations we can make between
*the remaining books (implicate or not yet studied).
When we make the second measurement on the system, another of the
energy values E(i) and its corresponding eigenfunction v(i) become
known. It also changes from an implicate to an explicate. Say it is
the case for the index i=2 to make subsequent notations easier. The
complex wave function V is still given by
V = SUM(i; 1 to N): c(i)v(i)
But the energy density operator R after the second measurement
is given by
R = SUM(k;1 to 2): c(k)xc(k)xv(k)Xv(k)
+ SUM(i, j; 3 to N): c(i)xc(j)xv(i)Xv(j)
*The mixture and reduction is now to be seen clearly.
*The first SUM(k) is the explicate sum while the second
*SUM(i, j) is the implicate sum. The explicate SUM(k) has
*only one index k to run through while the implicate SUM(i, j)
*has two indexes to run through.
Likewise the energy density operator R after the third measurement
is given by
R = SUM(k;1 to 3): c(k)xc(k)xv(k)Xv(k)
+ SUM(i, j; 4 to N): c(i)xc(j)xv(i)Xv(j)
Eventually the energy density operator R after all possible
measurements is given by
R = SUM(k; 1 to N): c(k)xc(k)xv(k)Xv(k)
*What happens here is that the explicate SUM(k) grows in
*terms of the implicate SUM(i, j) which decreases. In other
*words, as we study the books in the library, our formal
*knowledge grows as the number of books unknown to us
*decreases. In other words, what we have here, is the
*Digestor action in a most revealing manner. Obviously,
*the kind of learning needed to go into a library and study
*book after book without an expert to teach, is
*what I call self-learning based on the two tenets
*TO LEARN IS TO CREATE
*CREATIVITY IS THE RESULT OF ENTROPY PRODUCTION
*Self-learning meanders between emergent learning and
*digestive learning as its two asymptotes.
Compare the pure implicate form
R = SUM(i, j; 1 to N): c(i)xc(j)xv(i)Xv(j)
with the pure explicate form
R = SUM(k; 1 to N): c(k)xc(k)xv(k)Xv(k)
to see what disturbance measurement has brought into the system. The
pure implicate form has NxN combinations of which N of them is
reflexsive (i=j). The pure explicate form has only N combinations,
namely the N reflexsive combinations.
*Some fellow readers may have read books by the
*physicist David Bohm (for example, Wholeness and the
*Implicate Order) and wondered why he was so keen on the
*implicate structure. The more the books of that specific
*library we study, the more our knowledge density
*becomes a mixture of tacit (implicate) and formal
*(explicate) knowledge. We also reduce our tacit
*knowledge with respect to that library. But what happens
*when we sustain our creativity by the five elementary
*sustainers of creativity? We again grow in tacit knwledge.
*Hopefully this also explains to you why Bohm was so
*keen on the dialogue (one of the five elementary sustainers).
The expert physicist John von Neumann has expressed (1955) this
difference between the implicate SUM(i, j) and the explicate SUM(k) in
a most startling manner by saying that "entropy is created" when we go
from a pure implicate state
R = SUM(i, j; 1 to N): c(i)xc(j)xv(i)Xv(j)
to a mixed state
R = SUM(k;1 to M): c(k)xc(k)xv(k)Xv(k)
+ SUM(i, j; M+1 to N): c(i)xc(j)xv(i)Xv(j)
and finally the pure explicate and equilibrium state
R = SUM(k; 1 to N): c(k)xc(k)xv(k)Xv(k)
This entropy production in the energy density operator R gave Ilya
Prigogine the vital idea to search for the entropy operator in QM. He
eventually found it (together with the time operator so much searched
for in vain in ordinary hermitian QM) and so opened up a totaly new
leg of quantum mechanics called star-hermitian QM.
Winfried, you also wrote:
>A second read made clear, that you are talking of disturbances
>due to irreversible thermodynamics. Hmm.
No. I talked of both Quantum Mechanics and Irreversible
Thermodynamics. The viewpoint which QM offers us, is that we disturb
the system in such a way that we mix the implicate order of the system
with our own explicate order while simultaneously reducing the
richness of its implicate order. This reduction is inevitable if we
want to emerge into the explicate order through our measurements. The
viewpoint which IT offers us, will be discussed on another occasion.
The correspondence to measurements in human organisations is too
compelling to deny. As we measure the organisation increasingly, the
organisation become more characterised by our explicate measurements
than its own implicate order. It may appear to be a fine development
for people bent on measurement. However, by reducing the implicate
order of the organisation, the creativity of each members is seriously
impaired when such a member has no other means to sustain his/her
creativity. In other words, excessive measurement causes the
organisation to grind to a deadly stand still. What I cannot
understand, is why so many managers and consultants shut their eyes to
this impairing of creativity. The organisation worst afflicted by it,
is our formal institutions (schools, colleges and univeristies) for
education. It makes me mad when I think of what it does to the
creativity of learners.
Winfried, just to wet your appetite for the seven essentialities once
again. Each essentiality may be directly impaired in terms of itself.
But by overstressing one to the detriment of the other six, is another
way of impairing them. You seem to be one of the few who understand
this over reaction. In this case of excessive measurement, there is an
over reaction to the essentiality spareness. (For fellow learners who
have jumped the first time in our dialogue on "deep creativity", see
Essentiality - "quantity-limit" (spareness) LO20541
<http://www.learning-org.com/99.02/0009.html>)
To end this contribution with a view to its topic heading:
Dignity is an implicate property which has to reamin as such.
Explicate dignity is an oxymoron.
Best wishes
--At de Lange <amdelange@gold.up.ac.za> Snailmail: A M de Lange Gold Fields Computer Centre Faculty of Science - University of Pretoria Pretoria 0001 - Rep of South Africa
[Host's Note: In association wtih Amazon.com, this link...
Conceptual foundations of quantum mechanics by Bernard d'. Espagnat http://www.amazon.com/exec/obidos/ASIN/080532383X/learningorg
...but it's out of print. ...Rick]
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