On Wed, May 30, 2012 at 3:27 AM, Bruno Marchal <marc...@ulb.ac.be
<mailto:marc...@ulb.ac.be>> wrote:
On 29 May 2012, at 22:26, Jason Resch wrote:
On Tue, May 29, 2012 at 12:55 PM, Bruno Marchal <marc...@ulb.ac.be
<mailto:marc...@ulb.ac.be>> 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.
Not really. I pretend that this is the relative probability inferred by
the
person in front of you. But he is wrong of course. Each time the
probability
is 1/2, but his experience is "harry-Potter-like".
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%?
Yes.
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?
You cannot use absolute sampling. I don't think it makes any sense.
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),
OK.
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.
That is a different protocol. The one above is the one corresponding to
the
earth/mars experience.
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.
This is ambiguous.
What I mean is me stepping into the teleporter 5 times, with the net result
being
1 copy on Earth and 5 copies on Mars, seems just like stepping into the
teleporter
once, and the teleporter then creating 5 copies (with delay) on Mars.
Like the diagram on step 4 of UDA:
http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHAL_fichiers/image012.gif
<http://iridia.ulb.ac.be/%7Emarchal/publications/SANE2004MARCHAL_fichiers/image012.gif>
Except there is no annihilation on Earth, and there are 4 copies created
with
delay on Mars (instead of one with delay).
When stepping into the teleporter once, and having 5 copies created on Mars
(with
various delays between each one being produced) is the probability of
remaining on
Earth 1/6th?
