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.


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. :-)

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