On 5/31/2012 12:38 PM, Jason Resch wrote:
On Thu, May 31, 2012 at 2:09 PM, Bruno Marchal <[email protected]
<mailto:[email protected]>> wrote:
On 31 May 2012, at 18:29, Jason Resch wrote:
On Wed, May 30, 2012 at 3:27 AM, Bruno Marchal <[email protected]
<mailto:[email protected]>> wrote:
On 29 May 2012, at 22:26, 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.
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?
Yes.
That would be a good idea to enhance the probability to be the one, or a
one,
finding himself of mars. But again, the guy on earth will be in front of the
"looser", even if you multiply by 20. billions your delayed copies on mars.
Is the difference with the iterated example receiving the knowledge that
the other
copy made it to Mars before stepping into the Teleporter again?
I don't understand the sentence. It looks like what is the difference
between 24.
I apologize for not being clear. There are two different experiments I am
contrasting:
1. A person steps into a teleporter, and 5 copies (with varying delays) are reproduced
on Mars.
2. A person steps into a teleporter, and a duplicate is created on Mars. To increase
the chance of subjectively finding himself on Mars, he does it again (when he fails) and
the copy on Earth does so 5 times before giving up.
For experiment 1, you and I seem to agree that subjectively, that person person has a 1
in 6 chance of experiencing a continued presence on earth, and a 5/6 chance of finding
himself on mars.
For experiment 2, I believe you suggested there is a 1 in 32 (subjective chance) of
going through this exercise and not having the subjective experience of ending up on
Mars. Have I understood this correctly thus far?
If so, what accounts for these different subjective probabilities? How can it be that
there is a 31/32 chance of finding oneself on mars if there are just 5 copies there?
I think the latter is just wrong. It's an equivocation on who "you" are. The person who
supposedly has the 1/32 chance of going to Mars is the person identified as "the one who
doesn't go to Mars", so by definition his chance of going to Mars is zero. To make the
sense of "you" unequivocal would be to invoke as single "soul" that isn't duplicated but
instead either goes or stays on each try.
Brent
I hope I have been clear enough. Thanks again.
Jason
In this thought experience you were supposed to be an external observer on
earth,
not the candidate doing the duplication.
In your diary, you will always write things like, "he try to multiply the
copy on
mars, push on the button and told me "this fails again".
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