Quantum Immortality = no second law

[nichomachus]

On Apr 17, 5:17 am, Bruno Marchal <marc...@...> wrote:

> Le 16-avr.-08, à 15:13, nichomachus (Steve) a écrit :
>
> > The Prestige, with Christian Bale, Hugh Jackman, Michael Caine, Andy
> > Serkis.... and David Bowie as Nikola Tesla... I also highly recommend
> > this very entertaining movie that I saw last week.
>
> > Unfortunately, Bruno, I don't see the connection between this film and
> > the computationalist hypothesis.
>
> Hmmm.... I don't want to spoil the movie either ... Have you study the
> Universal Dovetailer Argument, or just the third key step?
>
> Note that from a purely strict logical point of view you don't need
> comp but a weakening of it. But the comp hyp makes something (in the
> movie) possible and even "real", and even already "real" in a sense
> made explicit in the movie.
>
> Perhaps I will say more later, when more people (of the list) will have
> seen the movie.

You're right, of course. Although I suppose we could just change the
subject to: "Spoiler Alert!!!!"  :)

>
> Bruno
>
> http://iridia.ulb.ac.be/~marchal/
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[nichomachus]

On Apr 17, 1:21 pm, Brent Meeker <meeke...@...> wrote:

> Telmo Menezes wrote:
> > On Thu, Apr 17, 2008 at 2:37 PM, Bruno Marchal <marc...@...> wrote:
>
> >>  Are you saying that the second law is verified in each of all
> >>  "branches" of the (quantum) multiverse?
>
> > I'm not saying that.
>
> >> I would say the second law is
> >>  statistical, and is verified in most branches. In the MWI applied to
> >>  quantum field it seems to me that there can be branches with an
> >>  arbitrarily high number of photon creation without annihilation, and
> >>  this for each period of time.
>
> I'm not sure what source of photon creation you have in mind, but QFT
> doesn't allow violation of energy conservation.

Maybe it was vacuum energy Bruno was referring to, or else perhaps the
creation of virtual particle pairs? Stephen Hawking (who by the way
apparently regards Everett's theory as trivally true, in other words,
instrumentalistic and without physical significance) used virtual
particles to explain how black holes may evaporate. But I don't want
to put words in anyone's mouth, and plus, I am not knowledgeable
enough on these matters to discuss them.

But if I may raise one possibility, it seems to me that despite the
existence of fluke branches in which the second law is not inviolate,
there are no possible branches that experience the outcome of a double
slit experiment that does not result in an interference pattern.

This is according to my understanding that the interference actually
takes place across branches, as each path of the photon interferers
constructively and destructively with itself.

The upshot of this is simply a recognition that not every outcome is
possible, and there remain situations that are not realized in any
extant universe.

>
> > Yes, I would tend to agree with that, although I can't say I'm 100%
> > convinced. Anyway I'm a relative newcomer to this list so I don't feel
> > I have an informed opinion yet. Need to catch up with all the
> > arguments. Also have a thesis to finish, which tends to get in the way
> > :)
>
> > I'm just arguing that the experiment with the rifle and the geiger
> > counter does not imply any second law anomaly. Yes, you are "forcing"
> > your consciousness to "move" to states where the atom never decays,
> > but if you consider the larger system, entropy is increasing as normal
> > because of the preparation and maintenance of the apparatus needed for
> > the experiment.
>
> > Do you think this makes sense?
>
> > Telmo Menezes.
>
> The idea of the multiverse derives from quantum mechanics, e.g. the
> Everett no-collapse interpretation.  But in that model the (microscopic)
> entropy never increases (or decreases), because QM evolution is unitary.
>   It is only the coarse-grained entropy, i.e. restricted to this branch,
> that increases.  Certainly within this branch you are correct that the
> entropy increase due to firing a gun is very much greater than the
> decrease due to an atom not decaying.

But the gun would only fire if the atom did in fact decay. It would
not fire in the branches where no decay was detected.

>
> Brent Meeker- Hide quoted text -
>
> - Show quoted text -- Hide quoted text -
>
> - Show quoted text -
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[Brent Meeker-2]

nichomachus wrote:

>
>
> On Apr 17, 1:21 pm, Brent Meeker <meeke...@...> wrote:
>> Telmo Menezes wrote:
>>> On Thu, Apr 17, 2008 at 2:37 PM, Bruno Marchal <marc...@...> wrote:
>>>>  Are you saying that the second law is verified in each of all
>>>>  "branches" of the (quantum) multiverse?
>>> I'm not saying that.
>>>> I would say the second law is
>>>>  statistical, and is verified in most branches. In the MWI applied to
>>>>  quantum field it seems to me that there can be branches with an
>>>>  arbitrarily high number of photon creation without annihilation, and
>>>>  this for each period of time.
>> I'm not sure what source of photon creation you have in mind, but QFT
>> doesn't allow violation of energy conservation.
>
> Maybe it was vacuum energy Bruno was referring to, or else perhaps the
> creation of virtual particle pairs? Stephen Hawking (who by the way
> apparently regards Everett's theory as trivally true, in other words,
> instrumentalistic and without physical significance) used virtual
> particles to explain how black holes may evaporate. But I don't want
> to put words in anyone's mouth, and plus, I am not knowledgeable
> enough on these matters to discuss them.
>
> But if I may raise one possibility, it seems to me that despite the
> existence of fluke branches in which the second law is not inviolate,
> there are no possible branches that experience the outcome of a double
> slit experiment that does not result in an interference pattern.
>
> This is according to my understanding that the interference actually
> takes place across branches, as each path of the photon interferers
> constructively and destructively with itself.

But that interference is of the wave-function with itself.  It's squared
modulus only determines a probability.  So, thru a fluke of probability,
the photons could strike the screen in a pattern that is arbitrarily close
to the naive no-interference pattern.  I say "arbitrarily close" since in
principle no photon could land where the probability was zero. But the zero
probability region is a line of measure zero.

It's not very clear to me how MWI accounts for the pattern.  Is it supposed
that there is a separate world for every point each photon could land; the
separate worlds having a certain probability weight.  Or are there multiple
worlds for each spot in order that the probability be proportional to the
number of worlds?  And what if the probability is an irrational number?

Brent Meeker


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[nichomachus]

On Apr 19, 2:17 am, Brent Meeker <meeke...@...> wrote:

> nichomachus wrote:
>
> > On Apr 17, 1:21 pm, Brent Meeker <meeke...@...> wrote:
> >> Telmo Menezes wrote:
> >>> On Thu, Apr 17, 2008 at 2:37 PM, Bruno Marchal <marc...@...> wrote:
> >>>>  Are you saying that the second law is verified in each of all
> >>>>  "branches" of the (quantum) multiverse?
> >>> I'm not saying that.
> >>>> I would say the second law is
> >>>>  statistical, and is verified in most branches. In the MWI applied to
> >>>>  quantum field it seems to me that there can be branches with an
> >>>>  arbitrarily high number of photon creation without annihilation, and
> >>>>  this for each period of time.
> >> I'm not sure what source of photon creation you have in mind, but QFT
> >> doesn't allow violation of energy conservation.
>
> > Maybe it was vacuum energy Bruno was referring to, or else perhaps the
> > creation of virtual particle pairs? Stephen Hawking (who by the way
> > apparently regards Everett's theory as trivally true, in other words,
> > instrumentalistic and without physical significance) used virtual
> > particles to explain how black holes may evaporate. But I don't want
> > to put words in anyone's mouth, and plus, I am not knowledgeable
> > enough on these matters to discuss them.
>
> > But if I may raise one possibility, it seems to me that despite the
> > existence of fluke branches in which the second law is not inviolate,
> > there are no possible branches that experience the outcome of a double
> > slit experiment that does not result in an interference pattern.
>
> > This is according to my understanding that the interference actually
> > takes place across branches, as each path of the photon interferers
> > constructively and destructively with itself.
>
> But that interference is of the wave-function with itself.  It's squared
> modulus only determines a probability.  So, thru a fluke of probability,
> the photons could strike the screen in a pattern that is arbitrarily close
> to the naive no-interference pattern.  I say "arbitrarily close" since in
> principle no photon could land where the probability was zero. But the zero
> probability region is a line of measure zero.
>
> It's not very clear to me how MWI accounts for the pattern.  Is it supposed
> that there is a separate world for every point each photon could land; the
> separate worlds having a certain probability weight.  Or are there multiple
> worlds for each spot in order that the probability be proportional to the
> number of worlds?  And what if the probability is an irrational number?

Mutiple worlds for each spot on the screen, according to my
understanding of Feynman's explanation of the experiment. However, I
think it is important to distinguish between the probability function
that describes the interference pattern registering on the screen/
photodetector array, and the probability function that results from
the square of the psi modulus. IIRC, Feynman said that the
interference pattern from the double slit experiment (or equivalently,
the emergent probability function that is the same across branches)
results from the fact that for any point on the screen where a photon
may fall from the slits there are multiple paths that one photon may
take to get to that point. The next step is to say that there are
other branches (due to MWI), each of which describes another possible
path taken by that same photon, and that, depending on the relative
difference in path lengths to the point in question, summing over all
possible paths taken by a photon to that point results in a value
somewhere between completely desctructive interference and completely
constructive. I take this scenario to mean that the total interference
pattern is a probability function describing how likely it is to
measure a single photon at any point on the screen, and that this
probability function is an emergent property of light particles
interfering with parallel versions of themselves across branches.
Since they are summed across the branches, so to speak, the
interference pattern resulting from the double slit experiement is one
example of getting a deterministic result from probabilistic
interactions, and is in fact the same pattern across all branches
representing outcomes of the experiment. So the psi function may be
thought of as being proportional to the number of universes, but the
probability function representing the distribution of photons on the
screen is not.

This is what I was thinking when I first mentioned the experiment,
although I didn't express what I meant very well. I was also thinking
of a game show scenario thought experiment that arrives at the same
conclusion, i.e., that multiple probabilities may degenerate into
fewer unique branches, and that not every event actually happens
somewhere in the multiverse. For example, Lets say that a contestant
on Deal or No Deal gets down to the last briefcase, so that there is
only the case that she originally selected, or there is the other. All
other cases have been eliminated, so one of the remaining two has one
cent in it, and the other has one million dollars. The contestant has
to choose whether she wants to keep the one she originally selected,
or else switch with the last remaining case. The contestant, who
happens to read the Everything list, has brought along a qubit, a
particle in a superposition of spin states to help her with her
decision. If she measures the particle's spin as positive, she will
elect to switch cases, and if she measures it with a negative spin she
will keep the one she has. This is because she wants to be sure that,
having gotten to this point in the game, there will be at least some
branches of her existence where she experiences winning the grand
prize. She is not convinced that, were she to decide what to do using
only the processes available to her mind, she would guarantee that
same result since it is just possible that all of the mutiple versions
of herself confronted with the dilemma may make the same bad guess.

Is she correct to feel this way?
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[Telmo Menezes]

>  But the gun would only fire if the atom did in fact decay. It would
>  not fire in the branches where no decay was detected.

I am not proposing that it is the firing of the gun that causes the
entropy increase that compensates for the atom not decaying. What
increases entropy is the initial setup of the all experimental
apparatus (gun + geiger counter) plus operation and maintenance. The
geiger counter needs energy to operate and the apparatus needs
maintenance over larger periods of time.

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[nichomachus]

On Apr 19, 10:42 am, "Telmo Menezes" <te...@...> wrote:
> >  But the gun would only fire if the atom did in fact decay. It would
> >  not fire in the branches where no decay was detected.
>
> I am not proposing that it is the firing of the gun that causes the
> entropy increase that compensates for the atom not decaying. What
> increases entropy is the initial setup of the all experimental
> apparatus (gun + geiger counter) plus operation and maintenance. The
> geiger counter needs energy to operate and the apparatus needs
> maintenance over larger periods of time.

I understand, Telmo. But you must admit that those branches that
experience no atomic decay exist whether the suicider bothers to kill
himself or not. Those branches exist even if the experiment is not set
up. This follows necessarily from the MWI. Pick any date in history
that you like. There must exist fluke branches that have experienced
unlikely histories since that time. The example I mentioned previously
was no atomic decay since January 1, 1900.
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[Günther Greindl]

Bruno,

> more seriously imo. And then I tell you without further explanation
> that "the prestige" is truly more. We can come back on this later.

OK I cave in, I will watch this movie :-))

Cheers,
Günther

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[Telmo Menezes]

>  Those branches exist even if the experiment is not set
>  up. This follows necessarily from the MWI. Pick any date in history
>  that you like. There must exist fluke branches that have experienced
>  unlikely histories since that time. The example I mentioned previously
>  was no atomic decay since January 1, 1900.

Yes I agree. The second law is just a statistical property, is it not?
I believe it is possible to observe cases where the second law does
not hold, even for a long time. But it's extremely unlikely. That
being said, I would argue that it would be nice if we could come to
the conclusion that the quantum suicider experiment can work even
without the need to resort to an highly unlikely stacking of quantum
choices.

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[nichomachus]

On Apr 19, 11:51 am, "Telmo Menezes" <te...@...> wrote:

> >  Those branches exist even if the experiment is not set
> >  up. This follows necessarily from the MWI. Pick any date in history
> >  that you like. There must exist fluke branches that have experienced
> >  unlikely histories since that time. The example I mentioned previously
> >  was no atomic decay since January 1, 1900.
>
> Yes I agree. The second law is just a statistical property, is it not?
> I believe it is possible to observe cases where the second law does
> not hold, even for a long time. But it's extremely unlikely. That
> being said, I would argue that it would be nice if we could come to
> the conclusion that the quantum suicider experiment can work even
> without the need to resort to an highly unlikely stacking of quantum
> choices.

How would it work? The point of the suicider experiement is that the
suicider is able to prove to himself the reality of MWI by forcing
himself to experience only an absurdly low probability set of events.
Thus, he demonstrates to the few versions of himself who remain the
existence of fluke branches, and by extension the truth of the MWI.

Right, I agree that a universe in which entropy decreases
monotonically would be unlikely since it would only happen in those
exceedingly rare fluke branches. However, the point of the quantum
suicide experiment is to prove to the suicider the reality of the MWI
by verifying the existence of fluke branches, and by extension, all of
the other, more likely worlds as well. The suicider steps in for the
cat in the schrodinger experiment. The QTI suicide experiment simply
asks what its like for the cat, instead of the observers who open the
box. You can stay in that box for any length of time, and if MWI is
true, which implies the QTI, you won't die. this only works because we
are eliminating the consciousness of the observer in a great many more
branches.

But it isn't a healthy way to prove MWI in practice. "Don't try this
at home."  :)
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[Telmo Menezes]

>  How would it work? The point of the suicider experiement is that the
>  suicider is able to prove to himself the reality of MWI by forcing
>  himself to experience only an absurdly low probability set of events.
>  Thus, he demonstrates to the few versions of himself who remain the
>  existence of fluke branches, and by extension the truth of the MWI.
>
>  Right, I agree that a universe in which entropy decreases
>  monotonically would be unlikely since it would only happen in those
>  exceedingly rare fluke branches. However, the point of the quantum
>  suicide experiment is to prove to the suicider the reality of the MWI
>  by verifying the existence of fluke branches, and by extension, all of
>  the other, more likely worlds as well. The suicider steps in for the
>  cat in the schrodinger experiment. The QTI suicide experiment simply
>  asks what its like for the cat, instead of the observers who open the
>  box. You can stay in that box for any length of time, and if MWI is
>  true, which implies the QTI, you won't die. this only works because we
>  are eliminating the consciousness of the observer in a great many more
>  branches.
>
>  But it isn't a healthy way to prove MWI in practice. "Don't try this
>  at home."  :)

I believe this thread started with an attempt do disprove MWI by
stating that the quantum suicider would violate the second law of
thermodynamics. Although I do believe that the MWI logically leads to
universes where the second law is violated and am fine with that, I'm
just proposing that in the case of the quantum suicider no violation
is observed at the macroscopic level. The macroscopic level is where
the second law makes sense anyway, because of its statistical nature.
I am prepared to agree that this is a pointless exercise because MWI
leads to second law violations anyway. :)

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[Günther Greindl]

Dear Nichomachus,

> decision. If she measures the particle's spin as positive, she will
> elect to switch cases, and if she measures it with a negative spin she
> will keep the one she has. This is because she wants to be sure that,
> having gotten to this point in the game, there will be at least some
> branches of her existence where she experiences winning the grand
> prize. She is not convinced that, were she to decide what to do using
> only the processes available to her mind, she would guarantee that
> same result since it is just possible that all of the mutiple versions
> of herself confronted with the dilemma may make the same bad guess.


I have also thought along these lines some time ago (to use a qubit to
ensure that all outcomes are chosen, because one should not rely on
one's mind decohering into all possible decisions).

The essential question is this: what worlds exist? All possible worlds.
But which worlds are possible? We have, on the one hand, physical
possibility (this also includes other physical constants etc, but no
totally unphysical scenarios).

I have long adhered to this "everything physically possible", but this
does break down under closer scrutiny: first of all, physical relations
are, when things come down to it, mathematical relations.

So we could conclude with Max Tegmark: all possible mathematical
structures exist; this is ill defined (but then, why should the
Everything be well defined?)

Alastair argues in his paper that everything logically possible exists
(with his non arbitrariness principle) but, while initially appealing,
it leads to the question: what is logically possible? In what logic?
Classical/Intuitionist/Deviant logics etc etc...then we are back at
Max's all possible structures.

For all this, I am beginning very much to appreciate Bruno's position
with the Sigma_1 sentences; but I still have to do more reading and
catch up on some logic/recursion theory for a final verdict ;-))

One objection comes to mind immediately (already written above): why
should the Everything be well defined?

To go back to your original question: to consider if both variants are
chosen by the player of the game by herself (without qubit) seems to
depend on which kind of Everything you choose. And that, I think, is the
crux of the matter.

Cheers,
Günther

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[Brent Meeker-2]

nichomachus wrote:

>
>
> On Apr 19, 2:17 am, Brent Meeker <meeke...@...> wrote:
>> nichomachus wrote:
>>
>>> On Apr 17, 1:21 pm, Brent Meeker <meeke...@...> wrote:
>>>> Telmo Menezes wrote:
>>>>> On Thu, Apr 17, 2008 at 2:37 PM, Bruno Marchal <marc...@...> wrote:
>>>>>>  Are you saying that the second law is verified in each of all
>>>>>>  "branches" of the (quantum) multiverse?
>>>>> I'm not saying that.
>>>>>> I would say the second law is
>>>>>>  statistical, and is verified in most branches. In the MWI applied to
>>>>>>  quantum field it seems to me that there can be branches with an
>>>>>>  arbitrarily high number of photon creation without annihilation, and
>>>>>>  this for each period of time.
>>>> I'm not sure what source of photon creation you have in mind, but QFT
>>>> doesn't allow violation of energy conservation.
>>> Maybe it was vacuum energy Bruno was referring to, or else perhaps the
>>> creation of virtual particle pairs? Stephen Hawking (who by the way
>>> apparently regards Everett's theory as trivally true, in other words,
>>> instrumentalistic and without physical significance) used virtual
>>> particles to explain how black holes may evaporate. But I don't want
>>> to put words in anyone's mouth, and plus, I am not knowledgeable
>>> enough on these matters to discuss them.
>>> But if I may raise one possibility, it seems to me that despite the
>>> existence of fluke branches in which the second law is not inviolate,
>>> there are no possible branches that experience the outcome of a double
>>> slit experiment that does not result in an interference pattern.
>>> This is according to my understanding that the interference actually
>>> takes place across branches, as each path of the photon interferers
>>> constructively and destructively with itself.
>> But that interference is of the wave-function with itself.  It's squared
>> modulus only determines a probability.  So, thru a fluke of probability,
>> the photons could strike the screen in a pattern that is arbitrarily close
>> to the naive no-interference pattern.  I say "arbitrarily close" since in
>> principle no photon could land where the probability was zero. But the zero
>> probability region is a line of measure zero.
>>
>> It's not very clear to me how MWI accounts for the pattern.  Is it supposed
>> that there is a separate world for every point each photon could land; the
>> separate worlds having a certain probability weight.  Or are there multiple
>> worlds for each spot in order that the probability be proportional to the
>> number of worlds?  And what if the probability is an irrational number?
>
> Mutiple worlds for each spot on the screen, according to my
> understanding of Feynman's explanation of the experiment. However, I
> think it is important to distinguish between the probability function
> that describes the interference pattern registering on the screen/
> photodetector array, and the probability function that results from
> the square of the psi modulus. IIRC, Feynman said that the
> interference pattern from the double slit experiment (or equivalently,
> the emergent probability function that is the same across branches)
> results from the fact that for any point on the screen where a photon
> may fall from the slits there are multiple paths that one photon may
> take to get to that point. The next step is to say that there are
> other branches (due to MWI), each of which describes another possible
> path taken by that same photon, and that, depending on the relative
> difference in path lengths to the point in question, summing over all
> possible paths taken by a photon to that point results in a value
> somewhere between completely desctructive interference and completely
> constructive. I take this scenario to mean that the total interference
> pattern is a probability function describing how likely it is to
> measure a single photon at any point on the screen, and that this
> probability function is an emergent property of light particles
> interfering with parallel versions of themselves across branches.
> Since they are summed across the branches, so to speak, the
> interference pattern resulting from the double slit experiement is one
> example of getting a deterministic result from probabilistic
> interactions, and is in fact the same pattern across all branches
> representing outcomes of the experiment. So the psi function may be
> thought of as being proportional to the number of universes, but the
> probability function representing the distribution of photons on the
> screen is not.

But <psi*|psi> is the probability function.  And the some pattern does not
occur across all branches.  The patterns are only "the same" in the
statistical sense of having the same limit as the number of particles goes
to infinity; which is to say "in theory", since in practice the number is
always finite.  Feynman's multiple-path formulation is mathematically
identical to the Schroedinger equation for and Heisenberg matrix form -
there is nothing new in it except the mental image evoked.

>
> This is what I was thinking when I first mentioned the experiment,
> although I didn't express what I meant very well. I was also thinking
> of a game show scenario thought experiment that arrives at the same
> conclusion, i.e., that multiple probabilities may degenerate into
> fewer unique branches, and that not every event actually happens
> somewhere in the multiverse. For example, Lets say that a contestant
> on Deal or No Deal gets down to the last briefcase, so that there is
> only the case that she originally selected, or there is the other. All
> other cases have been eliminated, so one of the remaining two has one
> cent in it, and the other has one million dollars. The contestant has
> to choose whether she wants to keep the one she originally selected,
> or else switch with the last remaining case.

I'm not familiar with "Deal or No Deal", but if it's like the old "Let's
Make a Deal" with the three doors, the contestant should consult quantum
mechanics, he should always switch.

Brent Meeker

>The contestant, who
> happens to read the Everything list, has brought along a qubit, a
> particle in a superposition of spin states to help her with her
> decision. If she measures the particle's spin as positive, she will
> elect to switch cases, and if she measures it with a negative spin she
> will keep the one she has. This is because she wants to be sure that,
> having gotten to this point in the game, there will be at least some
> branches of her existence where she experiences winning the grand
> prize. She is not convinced that, were she to decide what to do using
> only the processes available to her mind, she would guarantee that
> same result since it is just possible that all of the mutiple versions
> of herself confronted with the dilemma may make the same bad guess.
>
> Is she correct to feel this way?
> >
>

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[Brent Meeker-2]

nichomachus wrote:

> On Apr 19, 11:51 am, "Telmo Menezes" <te...@...> wrote:
>>>  Those branches exist even if the experiment is not set
>>>  up. This follows necessarily from the MWI. Pick any date in history
>>>  that you like. There must exist fluke branches that have experienced
>>>  unlikely histories since that time. The example I mentioned previously
>>>  was no atomic decay since January 1, 1900.
>> Yes I agree. The second law is just a statistical property, is it not?
>> I believe it is possible to observe cases where the second law does
>> not hold, even for a long time. But it's extremely unlikely. That
>> being said, I would argue that it would be nice if we could come to
>> the conclusion that the quantum suicider experiment can work even
>> without the need to resort to an highly unlikely stacking of quantum
>> choices.
>
> How would it work? The point of the suicider experiement is that the
> suicider is able to prove to himself the reality of MWI by forcing
> himself to experience only an absurdly low probability set of events.
> Thus, he demonstrates to the few versions of himself who remain the
> existence of fluke branches, and by extension the truth of the MWI.
>
> Right, I agree that a universe in which entropy decreases
> monotonically would be unlikely since it would only happen in those
> exceedingly rare fluke branches.

If it were also expanding in spacetime it would be exactly like our universe.

Brent Meeker


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[Brent Meeker-2]

Günther Greindl wrote:

> Dear Nichomachus,
>
>> decision. If she measures the particle's spin as positive, she will
>> elect to switch cases, and if she measures it with a negative spin she
>> will keep the one she has. This is because she wants to be sure that,
>> having gotten to this point in the game, there will be at least some
>> branches of her existence where she experiences winning the grand
>> prize. She is not convinced that, were she to decide what to do using
>> only the processes available to her mind, she would guarantee that
>> same result since it is just possible that all of the mutiple versions
>> of herself confronted with the dilemma may make the same bad guess.
>
>
> I have also thought along these lines some time ago (to use a qubit to
> ensure that all outcomes are chosen, because one should not rely on
> one's mind decohering into all possible decisions).
>
> The essential question is this: what worlds exist? All possible worlds.
> But which worlds are possible? We have, on the one hand, physical
> possibility (this also includes other physical constants etc, but no
> totally unphysical scenarios).
>
> I have long adhered to this "everything physically possible", but this
> does break down under closer scrutiny: first of all, physical relations
> are, when things come down to it, mathematical relations.
>
> So we could conclude with Max Tegmark: all possible mathematical
> structures exist; this is ill defined (but then, why should the
> Everything be well defined?)

There's no compelling reason the everything, or "The Everything", should be
well defined.  In fact all our theories to date have contingent aspects,
usually in the form of boundary conditions, that are not defined by the
theory.  But mathematical structures are different, they don't have
contingent parts.  So if a mathematical set is not well defined then we
don't know what we're talking about when we discuss it.

Brent Meeker

>
> Alastair argues in his paper that everything logically possible exists
> (with his non arbitrariness principle) but, while initially appealing,
> it leads to the question: what is logically possible? In what logic?
> Classical/Intuitionist/Deviant logics etc etc...then we are back at
> Max's all possible structures.
>
> For all this, I am beginning very much to appreciate Bruno's position
> with the Sigma_1 sentences; but I still have to do more reading and
> catch up on some logic/recursion theory for a final verdict ;-))
>
> One objection comes to mind immediately (already written above): why
> should the Everything be well defined?
>
> To go back to your original question: to consider if both variants are
> chosen by the player of the game by herself (without qubit) seems to
> depend on which kind of Everything you choose. And that, I think, is the
> crux of the matter.
>
> Cheers,
> Günther
>
> >
>

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