مرآة وعوالم متماثلة

a4111

Mirrors. "PT-theorem".

We found our first mirror in 2d world.
(142)

But the image of an image, through a succession of two mirrors, is identical to the initial object :
(143)

Same thing in 3d :
(144)

...We said that 4d-structure were comparable to animated holograms. In a way, you, me, are animated holograms. We are 4d structures. We are oriented in space ( if I remember, the liver in on the right ) and in time. We can appreciate what is "right", what is "left", what goes from past to future, avec what goes backwards in time.

If you meet an enantiomorphic human creature, the test is simple : look were is his liver.

...The chronologic test is more difficult. But, normally, if you talk with an antichron man, after a while, you will remark that :

• He knows enerything you are going to tell him.
• He ignores your precedent sentences. ( If he seems to know everything, he's God, by definition ). Suppose an animated hologram meets another animated hologram. He can look at it through an ordinary looking glass. He can look at it through a time mirror .
  See :
  [1] : J.P.Petit : Univers enantiomorphes à flèches du temps opposées. French Comptes Rendus de l'Académie des Sciences de Paris.t.284, serie A, 1977, p.1315 ( Enantiomophic universes with opposite time's arrows )
  [2] : J.P.Petit : Univers en interaction avec leur image dans le miroir du temps . French Comptes Rendus de l'Académie des Sciences de Paris.t.284, serie A, ( 6 june ) 1977, p.1413 (Universes interacting with their image in a time-mirror).

Consider the movement of the Moon around Earth :
(145)

Consider the mirror-image of this system :
(146)

Then reverse the time :
(147)

The movement of the Moon and its PT-symmetrical are identical.

...Physically : Imagine you can take a movie of it. You seat at distance and film the movement of the Moon around the Earth. Then you make a copy of the film. You use two projectors. In the first you introduce the film with correct orientation. In the second, you turn the film, reverse the space orientation of the frames :
(148)

Notice : this movie corresponds to a 3d space-time ( x, y, t ).
Then, when projecting the images of a screen, you reverse the chronology of the second series of frames.
(149)

God is a giant snail whose pedunclar eyes are each connected of half interacting brains, with opposite biologic clocks.

(If you have another definition, send ot by e-mail. We will publish it, mentioning the author, of course ).

Index Dynamic Groups Theory