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 > > 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 > > question. However, I just want to point out that an observer in relative > > motion observes the rotation in the complex plane of space-time > > geodesics. Could there be a connection between quantum and relativistic > > 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 > > > (Feinmann integrals). By substituting the time t with an (Euclidean) > > > 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 > > > 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 > > > black hole, and it should be the ultimate origin of Hawking radiation. > > > > > > I tried to derive this relation, or some kind of this, and I concluded > > > that it holds only at a formal level. Has anyone any idea about this > > > topic? > > > > > > Doriano Brogioli > > > > > > > > -- > > Joao Pedro Leao ::: [EMAIL PROTECTED] > 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 [EMAIL PROTECTED] Room 2075, Red Centre http://parallel.hpc.unsw.edu.au/rks International prefix +612, Interstate prefix 02 ----------------------------------------------------------------------------
