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From: Joao Leao <jleao.domain.name.hidden>

Date: Mon, 23 Jun 2003 13:44:06 -0400

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

t ---> -it

has no direct relation with the so-called "Weyl unitarity trick"

which is used to turn the bilinear anti-symmetric non-positive definite

Lorentz metric dt^2 - dx^2- dy^2 - dz^2 to a unitary one:

-dt^2-dx^2 - etc...

though they have the same flavor as mathematical expedients

without physical (empirical) meaning. The formal analogy

between Quantum Field Theory and Stat Mech depends indeed on

the first of these tricks. Unless, of course, if you believe

in "imaginary time" it will be hard for you to know what

you are talking about when you speak of a rotation "in the

complex plane of t". We would most likely need 4-dimensional

wrist watches to display the "current iTime" ( though Apple is

probably at work on an iClock as we speak !).

-Joao Leao

George Levy wrote:

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

*> >
*

*> > Quantum mechanics can be formulated in terms of path integrals
*

*> > (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
*

*> > continuum (classical) mechanical system, at temperature 1/h.
*

*> >
*

*> > From this fact, someone claims that quantum world is simply a
*

*> > classical world, but rotated by pi/2 in the complex plane of t: the
*

*> > real world is classical, but we see it at the wrong angle. In
*

*> > 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
*

*> >
*

*> >
*

Date: Mon, 23 Jun 2003 13:44:06 -0400

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

t ---> -it

has no direct relation with the so-called "Weyl unitarity trick"

which is used to turn the bilinear anti-symmetric non-positive definite

Lorentz metric dt^2 - dx^2- dy^2 - dz^2 to a unitary one:

-dt^2-dx^2 - etc...

though they have the same flavor as mathematical expedients

without physical (empirical) meaning. The formal analogy

between Quantum Field Theory and Stat Mech depends indeed on

the first of these tricks. Unless, of course, if you believe

in "imaginary time" it will be hard for you to know what

you are talking about when you speak of a rotation "in the

complex plane of t". We would most likely need 4-dimensional

wrist watches to display the "current iTime" ( though Apple is

probably at work on an iClock as we speak !).

-Joao Leao

George Levy wrote:

-- 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!)" -------------------------------------------------------Received on Mon Jun 23 2003 - 13:45:57 PDT

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