When Alice went through the looking glass, she found a whole different world with different rules on the other side. Such stories are very common. There is something about that virtual image in the mirror which makes it seem, not exactly half-real, but super-real or differently-real. I cite a few examples before discussing some scientific implications.

In a movie I vaguely remember (but not by name), the main character looked in the mirror in the wall of his new house, and saw in it a very different room. It turned out that it was the room as it had been furnished and arranged by its previous occupier, who had come to a violent end. The room and the mirror “remembered” that intense emotional experience, and was plotting revenge on the innocent new occupier. He got out of there fast.

In the French movie “Orphee”, the woman representing Death was able to enter the underworld through a mirror when wearing a certain pair of gloves. Her extended gloved hands went through the glass and the rest of her could follow; the glass started to ripple like water when touched by the gloves. (The visual trick was reportedly performed with a pool of liquid mercury.) When Orpheus hung on to Death, he was able to follow her into the underworld through that rippling mirror while still alive.

In a story of spirit possession by Cynthia Asquith, the main character Margaret did not see herself in the mirror any more, nor did she cast a shadow, when the evil Elspeth (long since dead) took possession of her body.

Yesterday again, as I often do, I sat on a bus by the window and watched the phantom cars, reflected from the other side of the bus, mingle and interpenetrate with the real cars on my side. The reflected and the real vehicles were going in opposite directions, but did not collide — they passed right through each other. The only way I could tell which ones were real and which were virtual (apart from knowing that highway) was to see which ones vanished when they got beyond the line of reflection. Until then, both looked equally and completely real.

Mirror images are truly “sinister” (meaning “left” in Latin), in the sense that the mirror image of a right hand is a left hand (and vice versa, of course). The relationship of the right hand to the left hand is called “chirality”, and plays an important role both in organic and bio chemistry and in nuclear particle physics. The basic fact is that the right and left hand (or any other chiral pairs, called “enantiomers”) are not super-imposable on each other by any combination of translations, rotations, or flippings in three-dimensional space. (I wonder what happens in four or more dimensions?)

Chemical enantiomers are usually organic (Le. carbon) compounds in which a central carbon atom is bound to four different groups or atoms. Enantiomers have exactly the same chemical properties, but one is a levo (1) form and the other is a dextro (d) form, so called because l-enantiomers rotate the plane of polarized light to the left and d-enantiomers by an equal amount to the right. In ordinary chemical reactions, both enantiomers form in equal proportions, and the resulting 50-50 mixture of I and d-enantiomers is called a racemic mixture, which does not rotate the plane of polarized light; we call it “optically inactive”.

However, there is an important exception: biological enzymes are specific for only one of any pair of enantiomers, both in forming them and in using them in further reactions. The “lock and key fit” of enzymes which is responsible for their catalytic activity is specific to only one of these forms.

Because of the enantiomeric specificity of enzymes, all the amino acids that constitute proteins are I-forms, and all the sugars in polysacharides and various glyco-complexes (including RNA and DNA) are d-forms. In principle this could be otherwise; life could have developed with d-amino acids and 1-sugars, or the other two 1- and d- combinations; but it could not have been a mixture — it was one OR the other, though neither was in principle preferred, like the choices in so-called coordination games. A symmetry-breaking choice had to be made, arbitrarily, at some point.

We cannot even digest I-sugars or d-amino acids — they pass right through. (Ideal for diet foods, except that they cause diarrhoea.) Extra-terrestrial life, if any, may use the opposite configurations; but then, even if there are mirror-image humans in that other world, we could never mate with them to produce offspring. (At least we would not both explode on touching, as we would if they were made of anti-matter.)

When you look in the mirror, you see a different face than other people see when they look at you. (Try a double mirror, front and back, or a photograph where the negative was reversed. It’s a real surprise!) Your right hand becomes your left hand, and — I think — your amino acids and sugars reverse their optical activities. You become like a being from another planet. Exactly like what we have always known about mirrors.