On 5/29/2012 4:26 PM, Jason Resch wrote:
On Tue, May 29, 2012 at 12:55 PM, Bruno Marchal <[email protected]
<mailto:[email protected]>> wrote:
To see this the following thought experience can help. Some guy
won a price consisting in visiting Mars by teleportation. But his
state law forbid annihilation of human. So he made a teleportation
to Mars without annihilation. The version of Mars is very happy,
and the version of earth complained, and so try again and again,
and again ... You are the observer, and from your point of view,
you can of course only see the guy who got the feeling to be
infinitely unlucky, as if P = 1/2, staying on earth for n
experience has probability 1/2^n (that the Harry Potter
experience). Assuming the infinite iteration, the guy as a
probability near one to go quickly on Mars.
Bruno,
Thanks for your very detailed reply in the other thread, I intend to
get back to it later, but I had a strange thought while reading about
the above experiment that I wanted to clear up.
You mentioned that the probability of remaining on Earth is (1/2)^n,
where n is the number of teleportations. I can see clearly that the
probability of remaining on earth after the first teleportation is
50%, but as the teleportations continue, does it remain 50%? Let's
say that N = 5, therefore there are 5 copies on Mars, and 1 copy on
earth. Wouldn't the probability of remaining on Earth be equal to 1/6th?
While I can see it this way, I can also shift my perspective so that I
see the probability as 1/32 (since each time the teleport button is
pressed, I split in two). It is easier for me to see how this works
in quantum mechanics under the following experiment:
I choose 5 different electrons and measure the spin on the y-axis, the
probability that I measure all 5 to be in the up state is 1 in 32 (as
I have caused 5 splittings), but what if the experiment is: measure
the spin states of up to 5 electrons, but stop once you find one in
the up state. In this case it seems there are 6 copies of me, with
the following records:
1. D
2. DU
3. DDU
4. DDDU
5. DDDDU
6. DDDDD
However, not all of these copies should have the same measure. The
way I see it is they have the following probabilities:
1. D (1/2)
2. DU (1/4)
3. DDU (1/8)
4. DDDU (1/16)
5. DDDDU (1/32)
6. DDDDD (1/32)
I suppose what is bothering me is that in the Mars transporter
experiment, it seems the end result (having 1 copy on earth, and 5
copies on mars) is no different from the case where the transporter
creates all 5 copies on Mars at once. In that case, it is clear that
the chance of remaining on Earth should be (1/6th) but if the
beginning and end states of the experiment are the same, why should it
matter if the replication is done iteratively or all at once? Do RSSA
and ASSA make different predictions in this case?
Thanks,
Jason
--
Hi Jason,
Fascinating! This decrease in probability given an increase in the
number of copies would also hold if the copies had amnesia and could not
identify themselves with the "original"?
--
Onward!
Stephen
"Nature, to be commanded, must be obeyed."
~ Francis Bacon
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