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From: Russell Standish <R.Standish.domain.name.hidden>

Date: Wed, 25 Jun 2003 13:04:40 +1000 (EST)

There is another interesting piece of the puzzle. Laurent Nottale has

developed an interesting unification of Relativity and Quantum Physics

using the notions of Fractal Spacetime. IIRC, particles move in a 2D

time manifold (which is fractal, not Euclidean ie think "plane filling

curves") and this seems to tend to a QM limit ine one direction, and a

classical relativistic limit in the other.

Being 2D, this does imply that "complex time" might have some legs in

it.

More info at http://www.daec.obspm.fr/users/nottale/.

Cheers

Joao Leao wrote:

*>
*

*> The so-called "Wick rotation" which is often employed to turn the
*

*> unruly measure of path integrals into a regular summable measure
*

*> and is represented as
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*>
*

*> t ---> -it
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*>
*

*> has no direct relation with the so-called "Weyl unitarity trick"
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*> which is used to turn the bilinear anti-symmetric non-positive definite
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*> Lorentz metric dt^2 - dx^2- dy^2 - dz^2 to a unitary one:
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*> -dt^2-dx^2 - etc...
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*>
*

*> though they have the same flavor as mathematical expedients
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*> without physical (empirical) meaning. The formal analogy
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*> between Quantum Field Theory and Stat Mech depends indeed on
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*> the first of these tricks. Unless, of course, if you believe
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*> in "imaginary time" it will be hard for you to know what
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*> you are talking about when you speak of a rotation "in the
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*> complex plane of t". We would most likely need 4-dimensional
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*> wrist watches to display the "current iTime" ( though Apple is
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*> probably at work on an iClock as we speak !).
*

*>
*

*> -Joao Leao
*

*>
*

*>
*

*>
*

*> George Levy wrote:
*

*>
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*> > Hi Doriano,
*

*> >
*

*> > Welcome to the list.
*

*> >
*

*> > You raise an interesting problem and. I don't know the answer to your
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*> > question. However, I just want to point out that an observer in relative
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*> > motion observes the rotation in the complex plane of space-time
*

*> > geodesics. Could there be a connection between quantum and relativistic
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*> > rotations?
*

*> >
*

*> > George
*

*> >
*

*> > Doriano Brogioli wrote:
*

*> >
*

*> > > Hi to everybody. I subscribed to this mailing list yesterday, but I'd
*

*> > > like to pose a question since I think it _must_ be the right place.
*

*> > >
*

*> > > Quantum mechanics can be formulated in terms of path integrals
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*> > > (Feinmann integrals). By substituting the time t with an (Euclidean)
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*> > > immaginary time i s, that is, a real value s times the imaginary root
*

*> > > mean square of -1, the path integral changes to the Boltzmann
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*> > > distribution, where the energy is the (classical) energy of a
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*> > > continuum (classical) mechanical system, at temperature 1/h.
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*> > >
*

*> > > From this fact, someone claims that quantum world is simply a
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*> > > classical world, but rotated by pi/2 in the complex plane of t: the
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*> > > real world is classical, but we see it at the wrong angle. In
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*> > > particular, something similar happens near the event horizon of a
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*> > > black hole, and it should be the ultimate origin of Hawking radiation.
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*> > >
*

*> > > I tried to derive this relation, or some kind of this, and I concluded
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*> > > that it holds only at a formal level. Has anyone any idea about this
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*> > > topic?
*

*> > >
*

*> > > Doriano Brogioli
*

*> > >
*

*> > >
*

*>
*

*> --
*

*>
*

*> Joao Pedro Leao ::: jleao.domain.name.hidden
*

*> Harvard-Smithsonian Center for Astrophysics
*

*> 1815 Massachussetts Av. , Cambridge MA 02140
*

*> Work Phone: (617)-496-7990 extension 124
*

*> VoIP Phone: (617)=384-6679
*

*> Cell-Phone: (617)-817-1800
*

*> ----------------------------------------------
*

*> "All generalizations are abusive (specially this one!)"
*

*> -------------------------------------------------------
*

*>
*

*>
*

*>
*

----------------------------------------------------------------------------

A/Prof Russell Standish Director

High Performance Computing Support Unit, Phone 9385 6967, 8308 3119 (mobile)

UNSW SYDNEY 2052 Fax 9385 6965, 0425 253119 (")

Australia R.Standish.domain.name.hidden

Room 2075, Red Centre http://parallel.hpc.unsw.edu.au/rks

International prefix +612, Interstate prefix 02

----------------------------------------------------------------------------

Received on Tue Jun 24 2003 - 23:14:25 PDT

Date: Wed, 25 Jun 2003 13:04:40 +1000 (EST)

There is another interesting piece of the puzzle. Laurent Nottale has

developed an interesting unification of Relativity and Quantum Physics

using the notions of Fractal Spacetime. IIRC, particles move in a 2D

time manifold (which is fractal, not Euclidean ie think "plane filling

curves") and this seems to tend to a QM limit ine one direction, and a

classical relativistic limit in the other.

Being 2D, this does imply that "complex time" might have some legs in

it.

More info at http://www.daec.obspm.fr/users/nottale/.

Cheers

Joao Leao wrote:

----------------------------------------------------------------------------

A/Prof Russell Standish Director

High Performance Computing Support Unit, Phone 9385 6967, 8308 3119 (mobile)

UNSW SYDNEY 2052 Fax 9385 6965, 0425 253119 (")

Australia R.Standish.domain.name.hidden

Room 2075, Red Centre http://parallel.hpc.unsw.edu.au/rks

International prefix +612, Interstate prefix 02

----------------------------------------------------------------------------

Received on Tue Jun 24 2003 - 23:14:25 PDT

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