Re: Quantum Physics, Robert's models, sensory perception

[Ionel <***>]

Tim:

I seem to have anticipated your question; please note my new posting today
on some different views by other notable workers in the area of "Quantum
Theory". Hence, I will avoid repeating that posting here , but it contains
views expressed fairly recently by David Bohm and Mackay in their separate
books on Quantum Theory (no TQFT here yet!)  TQFT provides much more than
that: a means to reconcile relativistic motions of microscopic particles
and gravity with quantum theory, hence also the suggestive name of "Quantum
Gravity". The generalized 'spaces' involved are permitting the trick.
However, I believe that we'd have to wait for Topos tools in this field,
and especially some form of generalization of Hopf Algebras. I am working
closely with some Logician-categorical theory colleagues/ maths experts on
some of these problems. Werner Heisenberg in his book (1951) points out the
well known difficulties and problems in these areas. There are also
the 'knotty' problems of string theories that are also topological in form.
In a previous posting I pointed out that Heyting Logic (infinite,
distributive lattice logic) involved in defining Topos does 'entail'
morphisms in appropriate models, avoiding impredicative boolean logic,
for example NonNonX does not have to take the value zero typically in the
Heyting logic but it does so in Boolean Logic. Furthermore, as Robert
pointed out in his "Essays..." book, even if a function is 'entailed' in N,
if we want to 'make'/fabricate such an entailed system EN, we still have to
get through the 'difficult representation stage' as Robert calls it:

N----> EN--->(R(--->N). This is where having the 'right logic' helps!
Last point: technically the "operators" that Robert introduces in his
discussion of entailing of (M,R)-systems in his "Essays..." are not very
different, except in mathematical structure and/or generality from the
concept of observable-related operators in Quantum Theory. Last-but-not-
least, David Bohm's idea of a whole entire universe connected at the
quantum/microscopic level, goes beyond Robert's idea of linking measurement
systems to the observed system, and 'inseparability' of arbitrary chunks
out of an organism. But... Werner Heisenberg disagrees with the idea of a
whole connected Universe in the measurement process!! He has some strong
points that are not easy to ignore.

My own concept of an organismic "state" is in fact explained in my 68-73
papers published in BMB, and is defined as a "generating diagram of
functional 'relationships' " that entail the system. The basic concepts, as
is the preferrence now, and was then in mathematics and logic, are
introduced axiomatically, such as the axiomatic self-reproducing pi-objects
of Lofgren, that are "equivalent" to a complex (M,R)-system from the
standpoint of entailing, but do not have the restriction
to ...structureless sets, Boolean logic and impredicativities in boolean
logic. At the quantum level, I suggested to introduce a "Quantum Automaton"
whose 'quantum states' , could for example encode in a genetic network or
genome, relational 'oscillations', patterns of processes repeating through
the cell cycle of a dividing cell. The key question is then, as in "What is
Life?" , "Life Itself..." by F. Crick, Robert's 1956 "Quantum Genetics",
and in his "Essays..." , how does the germ cell avoid the 'unavoidable'
irreversibility of quantum measurement when the genome is duplicated, or
when beta is replicated, or reverse-transcribed for that matter.  Because
that would mean that the genome is a "catalist"-- like molecule-- behaves
like an enzyme, not just like any substrate, i.e. it exits the many cyscles
of duplication of a germ cell, or "immortal"--perpetually dividing cell
many, many times without any observable phenotypic change. The alternative.
more likely, is that changes that occur are reversed by the repair system
entailed already in the (M,R)-system, subsequent to cell division. In
molecular biology terms, tumor suppressor gene, TP-53, and the protein "it
makes" p-53, control the quality of the genome replication, and if it cannot
repair the found faults through a signalling chain of proteins then in will
order 'self-destruct', or apoptosis/dismantling of the cell by the caspase
enzyme system. Anyway, I taught this entire process to our freshmen at UIUC.
National Cancer Institute and a similar institute in France, have beautiful
websites (such as CGAP_)that one might be tempted to
call 'reductionsitic'(?). There has been great progress in experimental
biology , genomics, proteomics and bioinformatics, since Robert wrote the
book and nobody who's serious about Life's complexity can now ignore that.
For example, in his article in 2003, J.C. Letelier et al. draw on such new
knowledge in genomics and proteomics, and so do I, in the posted
summary on "Natural Transformations in Molecular Biology.", written
originally in 1994, communicated at the joint SIAM-SMB joint meeting, and
updated this year. We will also have soon a preprint on "Cancer
Interactomics from the standpoint of Metabolic--->Repair--->Reverse
Transcription--->Replication Systems." It's 70% there but it needs
important additions before it's posted here. I'm also almost done with
thinking on Robert's exciting "Essays..." and will begin writing my review
for posting soon, in June '04.

It's been a very fruitful year, and really wish Robert was with us to see
all this ...unfolding.

I do appreciate, Tim, your well-put questions and answers/ discussions, etc.



Ionel


On Fri, 28 May 2004 21:55:39 -0400, Tim Gwinn <***> wrote:

>Ionel,
>
>Regarding TQFT, I have read only bits about it. From an Introduction to
>TQFT:
>[http://www.math.lsa.umich.edu/~ruthjl/papers/itft.html]
>        "In classical mechanics, there are two ways of describing the
possible
>evolutions of a system. The first is to specify the equations of motion,
>which will determine the state of a system at any time (as a point in phase
>space) once it is given at some initia time; this is known as the
>Hamiltonian approach. The second description proceeds on the assumption
that
>the worldline followed is one which minimises a certain functional, known
as
>the action. This minimisation takes place over all possible paths in the
>configuration space, beginning and ending at given points, and is known as
>the Lagrangian approach. In quantum theory, the phase space is replaced by
a
>Hilbert space of possible states, and dynamical variables are replaced by
>observables, which are operators on the Hilbert space and have expectation
>values. In a quantum field theory, the states of the system studied are
>specified by fields on the background manifold. The Hamiltonian approach
>leads to the consideration of operators on Hilbert space which describe the
>evolution of the state of the system. In the Lagrangian approach, the basic
>object which arises is the partition function of the theory which can be
>expressed as a Feynman integral.
>        As for any quantum theory, the ouput from a quantum field theory
is a
>collec­tion of expectation values and correlation functions of observables.
>A topological field theory is a theory in which the output is unchanged
>under a variation of the metric on the background manifold, so that
>expectation values of observables must give rise to topological invariants
>of the manifold."
>
>As best I can tell, TQFT provides an alternate approach for describing
>systems states, as do the other approaches mentioned above. Each approach
>offers ways of searching for particular kinds of patterns within those
state
>sets. However, it does not seem to me that TQFT is any different insofar as
>they all rest entirely on a state-based paradigm. Each approach mentioned
>above provides information already present in the states - these approaches
>seek to extract particular patterns of that information, but none of them
>includes information that is not reducible to, or already present in, the
>state information.
>
>I can't really speak to your other examples. Does either one of them take
us
>outside of the state-based paradigm?
>
>Regards,
>Tim
>
>
>> -----Original Message-----
>> From: ROSEN Forum [mailto:*** Behalf Of Ionel
>> Sent: Friday, May 28, 2004 12:33 AM
>> To: ***
>> Subject: Re: Quantum Physics, Robert's models, sensory perception
>>
>>
>> Tim and Howard:
>>
>> I would agree with most things Howard said , and add some more about the
>> status of fundamental theories in Physics today ... For example,
>> theoreticians in the fields of string theory or Topological Quantum Field
>> Theories (TQFT) are attempting to describe Quantum Gravity using
>> N-categories and special topological manifolds treated with categorical
>> tools.
>>
>> After all, Prigogine who did receive the Sweedish prize, dealt with open
>> systems, and I have the strong feeling from what Robert wrote about his
>> work that he was positive about Prigogine's contributions, and that's
part
>> of modern Physics, too!
>>
>> Another example:  Werner Heisenberg in his early book on "Principles of
>> Quantum Mechanics" gives strong reasons why putting together the
measuring
>> system and the observed system is not such a good idea, at least for
>> treating microscopic, or quantum, systems. He also leaves the door open
to
>> future developments in Physics and points out problems in Quantum Field
>> Theory that have only been partially resolved by Feynman and John
Wheeler.
>>
>> Ionel
>>