Is it possible to transmit some information faster than light 
and to modify the past ? These problems are raised by the following
thought experiment :

 Screen |        |
        |        | Slit 1
        |  			          +--------------+
        |        |                        | Measurement  |
        |        |            <- * ->     | device   / on|
        |        |            Source      |           off|
        |                                 +--------------+
        |        | Slit 2
        |        | 
 
A source emits pairs of particles in opposite directions. 
The particles on the left goes through 2 slits to the screen.
The particles on the right goes to a measurement device which records
their directions and keep the recording confined in the box in such a way
that no information concerning this recording goes out of the box.
First the measurement device is turned off, and the source is turned on.
The experimentator can see interference fringes on the screen.
Then the measurement device is turned on. The experimentator goes on
watching at the screen. Then he opens the measurement device and look at
the recording of the direction of the particles.

- When the measurement device is turned off, does the interference fringes
disappear immediately ? Is there some information transmitted faster than 
light from the measurement device to the screen ? 

- If not, what happens when the experimentator looks at the recording in
the measurement device ? Does it acts bact on the 
past, creating a world in which there are no interference fringes ?

- According to the theory of relativity, faster than light transmission
is equivalent to transmission to the past. What happens if we send
to the past an information different from the one we received ?

- What happens if we decide to look at the recording if we see interference 
fringes, and to erase it if we don't see fringes ?

- How could this experiment be interpreted in terms of Many-Worlds interpretation ?
According to Michael Clive Price's Everett FAQ (http://www.hedweb.com/manworld.htm)
	"The splitting is a local process that is causally transmitted from 
	system to system at light or sub-light speeds"
Does this mean that as long as the measurement information is kept in the device,
the splitting is confined in the device, so concerning the outside of 
the device, it is like if the measurement has not been done ?
Let us consider a point X located on a dark fringe.
According to the Many-Worlds interpretation, there is one world
in which the particle reaches X through slit 1 with amplitude Psi,
an d one world in which it reaches X through slit 2 with amplitude -Psi,
and the total makes 0, so this world is never observed. 
But what happens if some recording of which slit the particles went through 
is kept ? Does these two opposite worlds still annihilate them mutually ?
Do they become observable only when the experimentator looks at the recording ?

- How could this experiment be described with Dirac brackets notation ?
Let |X> represent the state in which a particle reaches a point X located
on a dark fringe, |S1> the state of the device recording that the particle
goes through slit 1, and |S2> same for slit 2. Then if we consider only this 
point X we would get 1/sqrt(2) * (|X>|S1> - |X>|S2>).
If we ignore |S1> and |S2> we get 1/sqrt(2) * (|X> - |X>) = 0, which
indicates that the particle never reaches X.
The problem with this notation is that a state such as |X>|S1> puts
together states of components |X> and |S1> located in different points of space.
How can we describe this composed state at instant t ? It is the 
tensorial product of states of components AT THE SAME TIME t, but 
this means nothing in the absolute according to the theory of 
relativity, since the notion of simultaneity is not absolute but
depends on the movement.

I would appreciate if you have some ideas about these problems.

        Jacques.
 
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