Mauro Lacy wrote: > Jones Beene wrote: >> -----Original Message----- >> From: Mauro Lacy >> >> >>> Please take into account that when Hotson says 'imaginary direction' you >>> >> can read '4th spatial dimension'. >> >> Are you familiar with the Dirac concept of "reciprocal space"? >> > > No, but I'll read about it. Reciprocal space sounds like a mirror > space to me. By example, using the fourth dimension, you can invert a > tridimensional sphere without breaking it. That is, you can put the > inside out and viceversa, through a rotation over a fourth dimensional > space, in the same way as you can invert a bidimensional figure by > rotating it in a three dimensional space. Reciprocal space then can be
Just for clarity: How it'll look like? Tridimensionally, you'll see that the sphere starts shrinking, until becoming a point, and then starts growing again, but this time the inside is outside, and viceversa. It has inverted, like you can invert a glove. Suppose initially the sphere is painted blue in the inside, and red on the outside. After the fourth dimensional rotation, you'll get a blue sphere with a red interior. That's a fourth dimensional (semi) rotation. And that can be probably understood as "reciprocal spaces". A full rotation will bring you the original sphere again. Mauro > understood as the mirror image of a n-dimensional space, rotated in > one higher (n+1) dimensional space. >> ... or rather, like so many things that have been updated in order to bring >> Dirac into the 21st Century, are you familiar with how this conception can >> be reconciled with a '4th spatial dimension'? (even if others have rejected >> that as a possible implication) >> > > No, I'm not familiar with that at all(although I would read about it > as soon as possible). Anyways, see above for a possible method of > reconciliation or equivalence between these concepts. > > Mauro
