Does this mean that those arrays of mirrors that create the so-called infinity effect are actually windows into myriads of alternate universes? Maybe I should go read Feynmans book. If it is as good as his "Surely you Jest" book it'll be a good read even if I don't understand a word of it.
You are exactly correct that the real transformation is front-to-back. That is, if the plane of a vertical mirror is labeled X (horizontal) and Y (vertical) and the axis perpendicular to it Z, then the virtual image formed by the mirror is actually invariant in X and Y, but translated (moved to the other side of the mirror) and inverted (reversed front-to-back) in Z.
To achieve this transformation physically, you would have to take a very thin rubber mold of, for example, your own face. The mask would need to transfer colors and textures to both sides. Once made, you would next need to flip the mold inside out and force yourself to imagine the now-convex inside surface of the mask as the outer surface of a real face. Our brains don't readily accept that severe of a transformation to a solid face, unless maybe you are Hannibal Lecter, so they instead try more "reasonable" transformations such as left-to-right or up-to-down. The visual outcome is similar, at least if you don't worry about the lack of solidity behind the image.
Or for that matter, take a hand-lens and hold it close to your monitor. It magnifies, right? Now move it towards your eye; eventually you see an inverted image. (You may have to fuss with distances.) What's up with that?
I would say that mirrors do not transpose either left versus right, nor top versus bottom. Instead they transpose front versus back. Consider the image you would see if the mirror was not there, and you were behind it.
I tried to resist this very different topic offshoot, but I can't... :)
Using box-shaped room coordinates, stand near the back wall of a room that has some kind of text, say a poster, on the far wall in front of you.
Hold a flat mirror out to your left, keeping it parallel to the left wall of the room, and look at the poster image in the mirror. As you would expect, you will see the poster inverted left-to-right, and unchanged top-to-down. No big surprise there, right?
Now circle your arm upward in an arc until the flat mirror is instead parallel to the ceiling. Look at the image of the poster again. What do you see?
The same poster... only this time it is inverted up-to-down, and unchanged from left-to-right...
Uh, say what?
What's even more fun is that if you move your arm smoothly and keep the poster image centered within the mirror frame at all times, you can watch every step in the continuous transition between the "standard" left-to-right inversion and the unanticipated up-to-down inversion. Be sure to ask yourself when, exactly, the transformation takes place... }8^)>
(Meanwhile, if you like quantum stuff, don't forget my earlier reply below about how all forms of reflection and refraction require quantum mechanical "scoping out" of the human-scale shapes of large objects. The quantum world is always watching you, quite literally!)
As I touched on a couple of months ago (http://www.eetimes.com/messages.asp?piddl_msgthreadid=46313&piddl_msgid=322067#msg_322067):
because of our psychology and bilateral (near-) symmetry, we have a hard time understanding until we abstract the question into symbolic form.
While not strictly "mirror"-related, the geometry of (chemistry) chirality is as hard to believe: if any two bonds of a chiral atom are exchanged, the result is the mirror-image of the original; exchanging another random two returns it to the original state.
"Why does a mirror swap left and right but not up and down?"
A mirror swaps front and back.
The front (closest to the mirror) part of the object is the front (closest to the mirror) part of the reflected image. The back (farthest from the mirror) part of the object is the back (farthest from the mirror) part of the reflected image.
The left and right swap is our interpretation of the front and back swap. Due to gravity, we find rotating about our head to foot axis much more plausible than rotating about our left to right axis.
Max, you raised an interesting point earlier about how photons can reflect smoothly from a room temperature mirror. After all, at the atomic level the mirror surface should look like a chaotic jungle of wildly vibrating atoms and molecules, a chaotically kinetic kluge that should kick any particle-like photon off in a completely random direction.
In terms of QED, however, that is what happens. Feynman just doesn't get into that level of detail in that short, intentionally non-mathematical book.
That is, all of those "not really there" photons in the path integral really do end up bouncing randomly from all of those thermal atoms. However, since the total amplitude added by each such impact is proportional to the amount of turf occupied by the atom, the individual reflections are very weak. And while you might expect so many reflections to add up to a powerful overall effect, the fact that they are both random and complex (vs real) values means they tend very strongly to cancel each other. Only those components of the reflections that are in phase, e.g. due to long-range order (smoothness) in the mirror, will ever add up into a "signal" (amplitude, square root of the probability) that makes it likely the photon will travel in that direction. A fairly accurate classical analogy would be an ocean wave reflecting from a rough stone wall, with the wavelets bouncing from individual grains of the wall corresponding to the atomic-scale, non-reinforcing reflections of the mirror.
The answer I like best, however, is that neither reflection nor refraction are really classical phenomena. That is, all forms of smooth, optically coherent light bending are profoundly quantum mechanical in nature, even when their outcomes can be expressed in simple equations. That's way too much to get into here, but anyone interested can look up this short essay on Your Quantum Mechanical Eye.
ccorb: Madness indeed. My advisor, who was in a position to understand the answer (or how to get it) to Ag colour, repeatedly told me 'you don't really want to know at the cost it would take to find-out' or something to that effect. I found-out, and now, if someone asks me to explain, you can guess how I reply.