Re: [Vo]:Casimir force at slab edges

[Mauro Lacy]

Stephen A. Lawrence wrote: Frank Roarty wrote: s identified this incoming email as possible spam. The original message has been attached to this so you can view it (if it isn't spam) or labelNo, 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. But you can't -- not just by rotating it. Hi Of course you can't do that in three dimensions. That's the whole point of using a fourth. I was drawing an analogy. The bidimensional equivalent will be the following (please excuse my "ascii art"). Suppose you have an asymetrical figure, like to one below: original figure: ---------- |____    |      |   |      |   |      |   |      |   |      ----- No matter how you rotate it in two dimensions, you can't construct its mirror image. But if you leave the second dimension, you can rotate it through the third, and obtain it mirror image easily: ----------------   axis of symmetry (and rotation)  -------------------- mirror image:        -----      |   |      |   |      |   |      |   | |-----   | |________| Do you see what I mean? I'll send some real drawings for clarity later. Mauro Look at the attached 2D figure. How would you *rotate* it in order to put the blue ring on the outside and the red ring on the inside? Of course, if you cut it out of paper and tried it, you wouldn't be able to do it. If it were made of rubber, you could turn it inside out in 3 dimensions, which you can't do in 2 dimensions, but that involves considerable stretching as well as rotating. If it's made of paper you'll tear it if you try to do that; it's not a simple rotation. You can flip chirality with a simple 4-d rotation but not inside/outside. 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. Again, you're turning the sphere inside out, which you can do in 4 dimensions (if the sphere is stretchable) but you're not doing it with a simple rotation, in any number of dimensions. 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