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Re: An ExperimentPosted by phobos on March 22, 19101 at 20:16:48: In Reply to: Re: An Experiment posted by jsodemann on March 22, 19101 at 16:29:32: No, no. The only existence of objects in the extra dimensions is in the form of the wavefunction. Consider the line segment from 0 to L. Now identify 0 and L as the same point. This space is identical to the circle. The setup you want is to say that molecules have some particular coordinate in this space in addition to those in spacetime. Fine. QM says that the atoms really have some wavefunction, but it's peaked around only a single point, the atom's classical position. What I'm telling you is the following: I'm going to make L sufficiently small that the Compton wavelength of the particle is of the order L (and in fact I'll make L much, much smaller). I can no longer treat this system classically, and I must solve something like a Schrodinger equation. It is no longer proper to speak of anything but the particle's wavefunction in this extra dimension. For something like a free particle, the wavefunction is like the ground state of the "particle in a box". The excitations of this configuration have energies which scale like E~1/(mL^2), so a very small extra dimension corresponds to huge excitation energies. Here's the rub: What you essentially want to do is take the chiral molecules and rotate them in the full space, changing their chirality. What I'm telling you is that this notion relies upon a having a well-defined definition of the position in such small dimensions, a definition which does not exist. In QM language, you would find that applying rotation operators to the wavefunctions of the compact directions gives either 0 (the wavefunction is symmetric) or a linear combination of the ground and excited states. These excited states are short-lived and decay rapidly, so that one ends up again with the ground state. It is thus impossible to effectively rotate the molecules in the extra dimensions with accessible energies. It's for this reason that physicists only look at compact extra dimensions as determining the spectrum of an effective theory in the unwrapped space only, using the geometry for the purpose of determing particle content. phobos
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