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

[Tim Gwinn <***>]

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 initial 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
>