[extropy-chat] Re: Damien grants psi evidence

[scerir]

From: "Hal Finney"

> I disagree on what will happen in this experiment.  
> Eliezer asked a similar question once.  Unfortunately, 
> I've never found a definitive explanation online about 
> this seemingly paradoxical setup. [...]

Not sure there is a real disagreement, or a full
disagreement. Maybe I was obscure, my fault.
But these things are interesting and, imo, still not well 
fixed. (There is a strong disagreement even about
Heisenberg's microscope gedanken experiment). I'll try, 
here below, to keep things as simple as I can, and to 
avoid obscurity (as much as I can!).

Notice also that there is a wide range of "weird" effects,
all based on entagled pairs, and each one has its peculiarity.
This one (below) seems (to me) interesting, because it
is simple, or it seems so :-).

s      
c      |
r      
e      |  p1 <----- s -----> p2
e      
n      |

There is a source of entangled photons, p1 & p2.
The correlation between p1 & p2 is of the kind
"momentum/position". 

(For the other possible correlation, "time/energy", 
and related interesting interference experiments, see: 
http://techdigest.jhuapl.edu/td1604/Franson.pdf or
"High-Visibility Interference in a Bell-Inequality
Experiment for Energy and Time," by P. G. Kwiat,
A. M. Steinberg, and R. Y. Chiao, in Physical Review A, 
Vol.47, page R2472, 1993).

Now, p1 enters a two-slit interferometer, p2 goes left.

1) We decide not to perform measurements on p2. In this
case we can ask: what can we say about the "spot" of
p1 on the screen (of the two-slit interferometer)?
Specifically, can we say that this "spot" pertains to
some interference pattern or to some smooth distribution?
As far as I know, there is no theoretical treatment of
this question. Anyway the correct answer is the latter.
The "spot" pertains to some smooth distribution. And the
reason (I think you got this point perfectly) is that,
since we did not perform any measurements on p2, we could 
still perform measurements on p2, and specifically we 
could still register (observe, detect) p2 on an optical 
plane which "images" the two slits of the interferometer.
But - since there is a strict correlation between 
positions of p1 & p2 - knowing the position of p2, on
the optical plane "imaging" the two slits of the 
interferometer, means knowing "which slit" the photon
p1 entered. And knowing "which slit" p1 entered,
in turn means "distinguishability" and no interference
pattern.

2) We decide to perform a measurement on p2. Specifically 
we choose to register (observe, detect) p2 on an optical 
plane which "images" the two slits of the interferometer.
Since there is a strict correlation between positions of 
p1 & p2, knowing the position of p2, on the optical plane 
"imaging" the two slits of the interferometer, means knowing 
"which slit" the photon p1 entered. And knowing "which slit" 
p1 entered in turn means "distinguishability" and no interference
pattern. In this case we can ask: what can we say about the 
"spot" of p1 on the screen (of the two-slit interferometer)?
Specifically, can we say that this "spot" pertains to
some interference pattern or to some smooth distribution?
The correct answer is the latter. Obviously.

3) We decide to perform a measurement on p2. Specifically 
we choose to measure the momentum of p2 on a specific optical 
plane. Measuring momentum of p2 means projecting the momentum
state of p2 onto a momentum eigenstate and, since there is
a strict correlation between momenta of p1 and p2, it also
means projecting the momentum state of p1 onto a momentum
eigenstate. Being p1 and p2 in momentum eigenstates, any
possible information of positions vanished. Vanished, 
specifically, any possible information about "which slit"
photon p1 entered. In this case we can ask: what can we 
say about the "spot" of p1 on the screen (of the two-slit 
interferometer)? Specifically, can we say that this "spot" 
pertains to some interference pattern or to some smooth 
distribution? The correct answer is the first one. Obviously.
Since any possible information about the "which slit"
was washed out by the momentum measurement performed
on the photon p2.

4) Notice that since there is a symmetry between measurements
performed on the photon p2 and measurements performed
on photon p1 (they are entangled, strongly correlated both
in position and in momentum) we can "reverse" what we said
in the points above. In example a momentum measurement
performed on the photon p1 can produce an interferential
"spot" by p2. Etc. etc.

5) Notice also (but again I think you got this point
perfectly) that, from the above, the "interpretation"
of the "spot" on the screen depends strongly, or
completely, on the measurements non performed on the
photon p2 or, instead, on the measurements (position, 
or momentum) performed on the photon p2. (Notice also
that, after measurements performed, photon p2 is
destroyed). (All that just means that likewise ESP
experiments, also here there is a necessity of comparing
the outcomes registered at both "wings", for a correct
interpretation. The weirdness of these phenomena is
exactly in that comparation, since there is no possible,
or there is no evident, flux of informations).  

6) The point I was, perhaps, trying to make in the last 
post was: what if we implement a delayed choice in the 
situations above? That is to say: what. i.e., if the path 
of p2 is much longer than the path of p1?

s      
c      |
r      
e      |  p1 <----- s ------------------------> p2
e      
n      |

Something new? Well, the only thing which changes here
(i.e. the path of p2 is longer the path of p1) is that
for the correct "interpretation" of the spot on the
screen (interferential, or not) we must wait a longer time,
i.e. that a measurement of momentum, or a measurement
of position, will be performed, or _might_ be performed,
in the future, on the photon p2, maybe on another galaxy
(if there is enough coherence!). 

> I wrote a much more detailed analysis of this on this 
> list a couple of years ago.

I'll check it.

-serafino.