Hi Bruno
As a variation of my last post, I would like to use your teleportation
experiment rather than Q-suicide to illustrate the First and Third
Person concept, in a manner that parallels Einstein's scenario in which
two observers in different inertial frames of reference observe that the
length of an object is a relative quantity.
Let's consider a teleportation/duplication experiment in which 100
copies of a volunteer are sent.from Brussel to Washington and to Moscow.
Let's say that A copies are send to Washington and 100-A copies are sent
to Moscow where 0<A<100. In addition let us say that the value of A is a
random process generated by the multiple throw of a dice for example,
and is uniformly distributed between 0 and 100.
The expected value of A for a Third Person observer would be exactly 50
since A is uniformly distributed. However, the expected value of A for a
First Person who ends up in Washington is >50 and for a First Person who
ends up in Moscow is <50.
The actual expected value of A for the First Person going to Washington
is 67 and for the one going to Moscow is 33.
This can be calculated by assuming for example 100 such experiments with
A uniformly distributed such that A takes on a different value for each
experiment such as A = 1,2,3,4,5,...100. The value of A as seen by the
First Person in Washington is a weighted sum of the value of A
multiplied by the number of observers, and normalized by the total
number of observers in the 100 experiments:
(100x100 + 99x99 + 98x98....2x2 + 1x1) / ( (100x(100+1)/2)
= ((100)(100+1)(2x100+1)/6) / ( (100x(100+1)/2) = 67
Similarly for the one in Moscow.
We see here that the expected value of A is relative to the observers in
Washington or Moscow and the frame of reference is defined by the
contigency that A imposes on their destination Washington/Moscow.
George
PS. I just saw the title of Stephen's post, and I assume it implies
trouble for duplication experiments in general... Anyways I am sending
this post. :-)
Received on Tue Jun 15 2004 - 04:52:47 PDT