Re: Newbie Questions

[Michael Gough]

So you are saying the mass of the universe is infinite.

On Sat, Jan 17, 2009 at 4:40 PM, A. Wolf  wrote:

>
> > Yes, but space may be simply the coordinate system in which matter and
> > energy move. Even if the coordinate system is infinite, it doesn't matter
> > because the particles' occupy a finite (but growing) part of it.
>
> I don't think your conceptualization of an expanding universe is correct.
> No currently accepted model of the universe consists of a bunch of
> centrally-located matter with "empty space" surrounding it, and it's easy
> to
> see why: we can see the big bang (or at least, the moment when light
> decoupled from matter) from every direction in the sky.  This means that
> there is no center to the universe.  Matter is fairly uniformly distributed
> throughout the universe, and the universe is either finite but unbounded,
> or
> (as measurement of the CBR supports) infinite in both size /and/ content.
>
> So there is no "center" to the universe from which things are expanding
> into
> empty space.  Rather, everything is moving away from everything else.
> Evidence suggests there's an infinite amount of stuff out there, either
> way,
> because careful measurements of the visible universe show zero curvature as
> far back as is possible to see.
>
> Anna
>
>
> >
>

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Re: KIM 2.3 (was Re: Time)

[Brent Meeker]

Bruno Marchal wrote:
> 
> On 15 Jan 2009, at 22:50, Brent Meeker wrote:
> 
>>
>> Bruno Marchal wrote:
>>>
>>> On 14 Jan 2009, at 18:40, Brent Meeker wrote:
>>>
 Stathis Papaioannou wrote:
> 2009/1/14 Brent Meeker  > wrote:
> 
>>
>> in a computer program.  But a computer program requires a computer  
 to run
>>>
>>>
>>> This is true, but the word "run" is ambiguous. It could be a  
>>> mathematical run.
>>
>> But isn't that the crux of the question?  Mathematics is a set of logical
>> relations - which have no temporal component.  So a "mathematical run" 
>> can only
>> be analogous to a physical run.  So what is it in a mathematical run 
>> that makes
>> it a "run" instead of just a timeless Platonic object?
> 
> 
> The notion of step, and successor of a step.  For a mathematical run you 
> have a notion of first step, second step, etc.
> 
> 
> 
> 
> 
>>
>>
>>> It is digital some we can use the natural numbers  
>>> and the successor relation for the first order time of the UD run.  
>>
>> But if we look at the program for a UD the successor relation is not
>> implemented.  When it is run on a computer, the physics of the 
>> computer provides
>> the succession.
> 
> 
> That is based on your theory according to which there is a physical 
> reality. I have no problem with that, but the UDA has shown that you 
> have to say no to the doctor, 

Why?  The doctor proposes a physical implementation.

>or to point on the point that you don't 
> understand in the UDA.
> You told us you have a problem with the UDA 6, I have provided an 
> explanation, but then I am not sure if this satisfies you or not.
> Rfefrerring to the environment does not change the reasoning, unless you 
> put non-turing emulable feature in your brain/ environment (but then you 
> say no to the doctor).
> 
>>>
>>>

 In terms of Bruno's teleporter, one might say yes accepting that  
 there would be
 a one-time gap in consciousness (ever had a concussion?), but one  
 would probably
 hesitate if the there was to be a gap every 10ms.
>>>
>>>
>>> From the ultimate third point of view, there are no gap, or there are  
>>> gaps everywhere, that could depend on the topology or topologies you  
>>> will extract from the numbers.
>>
>> In order to teleport me, my state must be determined.  That means the 
>> values of
>> physical variables at disparate spacetime points (in my head or my galaxy
>> or...), but relativity makes it impossible to determine the state over an
>> extended region until some later time on the order of d/c where d is 
>> the size of
>> the region.  So in reproducing me in the teleporter this increment of 
>> time will
>> not be reproduced - I will experience a gap in consciousness, or a 
>> failure to
>> remember a certain interval just before the teleportation.  It's 
>> comparable to
>> the time it would take a computer to store an image of it's state.
> 
> 
> Are you stopping at UDA step 1? 

No.  There's a difference between your idea of running a world and making a 
copy 
of me within this world.  I think the latter will necessarily incur a gap in my 
consciousness because of the need to gather the information about my state 
(plus 
some environment), but not the former.

>  With some effort Stathis, Quentin or me, or some other will succeed in 
> making you say directly "no" to the doctor. 

Do I have to say "no" just because I suppose I'd incur a gap in consciousness? 
:-)

Brent

>In that case you just say no 
> to UDA step 0, that is to comp. I have no problem with that.
> 
>  I am personally not interested in discussing if comp is true or false 
> (except for debunking invalid reasoning which are ffrequent there). 
> My point is just that IF comp is true, THEN physics is a branch of 
> number theory, and I propose a constructive prove which shows how to 
> drive physics from numbers making the comp hyp. empirically refutable, 
> making comp a scientific theory, in the Popper sense of "scientific".
> 
> I have no doubt that digital mechanism and materialism are incompatible, 
> though.

Is that because, under materialism, consciousness depends on causal links?

Brent

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


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Re: Newbie Questions

[A. Wolf]

> Yes, but space may be simply the coordinate system in which matter and
> energy move. Even if the coordinate system is infinite, it doesn't matter
> because the particles' occupy a finite (but growing) part of it.

I don't think your conceptualization of an expanding universe is correct. 
No currently accepted model of the universe consists of a bunch of 
centrally-located matter with "empty space" surrounding it, and it's easy to 
see why: we can see the big bang (or at least, the moment when light 
decoupled from matter) from every direction in the sky.  This means that 
there is no center to the universe.  Matter is fairly uniformly distributed 
throughout the universe, and the universe is either finite but unbounded, or 
(as measurement of the CBR supports) infinite in both size /and/ content.

So there is no "center" to the universe from which things are expanding into 
empty space.  Rather, everything is moving away from everything else. 
Evidence suggests there's an infinite amount of stuff out there, either way, 
because careful measurements of the visible universe show zero curvature as 
far back as is possible to see.

Anna


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Re: Newbie Questions

[Michael Gough]

Thank you.

However, I don't understand your objection to an infinite number of states.
> The universe in which we live appears by current measurements to be
> infinite
> in size (because it is geometrically flat), and will last forever (because
> its expansion is hastening).


Yes, but space may be simply the coordinate system in which matter and
energy move. Even if the coordinate system is infinite, it doesn't matter
because the particles' occupy a finite (but growing) part of it.

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Re: Newbie Questions

[A. Wolf]

>I understand. I was trying ask about whether or not, if there were say
> 10^10^10 slits, would the electron go through all of them. Do we know for
> sure?

You can perform the experiment with a thin grid instead of slits and get 
similar patterns.  But 10^10^10 in the traditional top-down way is a googol, 
which is more than we can measure.  I mean, if you're asking "can we measure 
unbelievably large numbers directly", then no, of course we can't.  But 
theories would be pointlessly complicated if we restricted things that have 
no apparent limit to some arbitrary finite number.

> Also, I want the inside of time answer. Right now, in the multiverse, it
> seems like the number of differentiated states may be a very large number,
> but is it infinite? I expect the answer to be no, but I'm no expert.

The answer would not be infinite iff spacetime and mass were both quantized. 
This would restrict the possible number of states of a particle to a finite 
number.  Most theories of spacetime (with the exception of general 
relativity) quantize spacetime entirely, and in doing so quantize velocity 
(independent of relativistic movement), but the theory is inconsistent with 
relativity.  Mass is not known to be quantum, and we may never prove it one 
way or the other.  It is possible, though.

However, I don't understand your objection to an infinite number of states. 
The universe in which we live appears by current measurements to be infinite 
in size (because it is geometrically flat), and will last forever (because 
its expansion is hastening).  Trying to eliminate infinite numbers from math 
is like trying to keep the sun moving around the earth in physics.  It 
complicates prediction, and has no benefit.

I don't agree with the prevailing belief on this list that one can only 
define probability mass over an discrete domain, just in case that's part of 
your objection.

Anna


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Re: Newbie Questions

[Michael Gough]

I understand. I was trying ask about whether or not, if there were say
10^10^10 slits, would the electron go through all of them. Do we know for
sure?

Also, I want the inside of time answer. Right now, in the multiverse, it
seems like the number of differentiated states may be a very large number,
but is it infinite? I expect the answer to be no, but I'm no expert.

On Sat, Jan 17, 2009 at 11:10 AM, Abram Demski wrote:

>
> Fragamus,
>
> That depends on definitions! What counts as a history, and "when" do
> we count them? In order for the number of histories to be "merely a
> fantastically large and growing number", we need to be inside of time
> when we count the number of histories-- otherwise it could not be
> growing. Personally I would prefer to count the *eventual* number of
> histories, rather than the number of histories at any given moment.
> This number will be infinite, but *which* infinity? The answer gives
> us some information. (I don't know if you are familiar with the
> different infinities, but there *are* smaller and larger infinities.)
> For example, if all universes end in finite time the number of
> histories may be smaller than if there are some that go on forever.
>
> -Abram
>
> On Fri, Jan 16, 2009 at 10:10 PM, fragamus
>  wrote:
> >
> > I would like to ask the board:
> >
> > Are ALL possible quantum histories realized in the multiverse?
> >
> > Is the number of possible histories infinite, or merely a
> > fantastically large and growing number?
> >
> > I don't like infinity so I'm hoping you say no.
> >
> > THANKS!
> > >
> >
>
>
>
> --
> Abram Demski
> Public address: abram-dem...@googlegroups.com
> Public archive: http://groups.google.com/group/abram-demski
> Private address: abramdem...@gmail.com
>
> >
>

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Re: Newbie Questions

[Abram Demski]

Fragamus,

That depends on definitions! What counts as a history, and "when" do
we count them? In order for the number of histories to be "merely a
fantastically large and growing number", we need to be inside of time
when we count the number of histories-- otherwise it could not be
growing. Personally I would prefer to count the *eventual* number of
histories, rather than the number of histories at any given moment.
This number will be infinite, but *which* infinity? The answer gives
us some information. (I don't know if you are familiar with the
different infinities, but there *are* smaller and larger infinities.)
For example, if all universes end in finite time the number of
histories may be smaller than if there are some that go on forever.

-Abram

On Fri, Jan 16, 2009 at 10:10 PM, fragamus
 wrote:
>
> I would like to ask the board:
>
> Are ALL possible quantum histories realized in the multiverse?
>
> Is the number of possible histories infinite, or merely a
> fantastically large and growing number?
>
> I don't like infinity so I'm hoping you say no.
>
> THANKS!
> >
>



-- 
Abram Demski
Public address: abram-dem...@googlegroups.com
Public archive: http://groups.google.com/group/abram-demski
Private address: abramdem...@gmail.com

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Re: Newbie Questions

[Abram Demski]

Fragamus,

That depends on definitions! What counts as a history, and "when" do
we count them? In order for the number of histories to be "merely a
fantastically large and growing number", we need to be inside of time
when we count the number of histories-- otherwise it could not be
growing. Personally I would prefer to count the *eventual* number of
histories, rather than the number of histories at any given moment.
This number will be infinite, but *which* infinity? The answer gives
us some information. (I don't know if you are familiar with the
different infinities, but there *are* smaller and larger infinities.)
For example, if all universes end in finite time the number of
histories may be smaller than if there are some that go on forever.

-Abram

On Fri, Jan 16, 2009 at 10:10 PM, fragamus
 wrote:
>
> I would like to ask the board:
>
> Are ALL possible quantum histories realized in the multiverse?
>
> Is the number of possible histories infinite, or merely a
> fantastically large and growing number?
>
> I don't like infinity so I'm hoping you say no.
>
> THANKS!
> >
>



-- 
Abram Demski
Public address: abram-dem...@googlegroups.com
Public archive: http://groups.google.com/group/abram-demski
Private address: abramdem...@gmail.com

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Re: COMP, Quantum Logic and Gleason's Theorem

[Bruno Marchal]

On 17 Jan 2009, at 07:52, Brent Meeker wrote:

>
> Günther Greindl wrote:
>> Hi all,
>>
>> the question goes primarily to Bruno but all other input is  
>> welcome :-))
>>
>> Bruno, you said you have already arrived at a quantum logic in your
>> technical work?
>>
>> May I refer to the following two paragraphs?:
>>
>> We can read here:
>> http://plato.stanford.edu/entries/qt-quantlog/
>>
>> The Reconstruction of QM
>>
>> From the single premise that the “experimental propositions”  
>> associated
>> with a physical system are encoded by projections in the way  
>> indicated
>> above, one can reconstruct the rest of the formal apparatus of  
>> quantum
>> mechanics. The first step, of course, is Gleason's theorem, which  
>> tells
>> us that probability measures on L(H) correspond to density operators.
>> There remains to recover, e.g., the representation of “observables”  
>> by
>> self-adjoint operators, and the dynamics (unitary evolution). The  
>> former
>> can be recovered with the help of the Spectral theorem and the latter
>> with the aid of a deep theorem of E. Wigner on the projective
>> representation of groups. See also R. Wright [1980]. A detailed  
>> outline
>> of this reconstruction (which involves some distinctly non-trivial
>> mathematics) can be found in the book of Varadarajan [1985]. The  
>> point
>> to bear in mind is that, once the quantum-logical skeleton L(H) is in
>> place, the remaining statistical and dynamical apparatus of quantum
>> mechanics is essentially fixed. In this sense, then, quantum  
>> mechanics —
>> or, at any rate, its mathematical framework — reduces to quantum  
>> logic
>> and its attendant probability theory.
>>
>>
>> And here we read:
>>
>> http://en.wikipedia.org/wiki/Gleason%27s_theorem
>>
>> Quantum logic treats quantum events (or measurement outcomes) as  
>> logical
>> propositions, and studies the relationships and structures formed by
>> these events, with specific emphasis on quantum measurement. More
>> formally, a quantum logic is a set of events that is closed under a
>> countable disjunction of countably many mutually exclusive events.  
>> The
>> representation theorem in quantum logic shows that these logics  
>> form a
>> lattice which is isomorphic to the lattice of subspaces of a vector
>> space with a scalar product.
>>
>> It remains an open problem in quantum logic to prove that the field K
>> over which the vector space is defined, is either the real numbers,
>> complex numbers, or the quaternions. This is a necessary result for
>> Gleason's theorem to be applicable, since in all these cases we know
>> that the definition of the inner product of a non-zero vector with
>> itself will satisfy the requirements to make the vector space in
>> question a Hilbert space.
>>
>> Application
>>
>> The representation theorem allows us to treat quantum events as a
>> lattice L = L(H) of subspaces of a real or complex Hilbert space.
>> Gleason's theorem allows us to assign probabilities to these events.
>>
>>
>> END QUOTE
>>
>> So I wonder - how much are you still missing to construct QM out of  
>> the
>> logical results you have arrived at?
>>
>> Best Wishes,
>> Günther
>>
> I don't think this form of QM is consistent with Bruno's ideas.   
> Quantum
> logic takes the projection operation as be fundamental which is
> inconsistent with unitary evolution and the MWI.


But in QM the unitary evolution gives a third person point of view.

UDA shows (or is supposed to show) that Physics is first person  
(plural).  A logic of projection is interesting for just that reason.

Quantum logic and many world/dream are related by a relation akin to  
the difference between a ket Ia>, and a projection on that ket Ia>http://iridia.ulb.ac.be/~marchal/




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Re: COMP, Quantum Logic and Gleason's Theorem

[Bruno Marchal]

On 16 Jan 2009, at 22:04, Günther Greindl wrote:

>
> Hi all,
>
> the question goes primarily to Bruno but all other input is  
> welcome :-))
>
> Bruno, you said you have already arrived at a quantum logic in your
> technical work?



Yes.  The hypostases, with p restrict to the Sigma-1 sentences (the  
UD)  given by

Bp & p  (the knower certainty)
Bp & Dp (the observer certainty)
Bp & Dp & p (the "feeler" certainty), with B the Godel Beweisbar  
predicate, and Da = ~B~a.

gives rise to Brouwersche like modal logics with natural quantization  
(BDp) which act like quantum projector, except that I loose the  
Brouwersche necessitation rule, which formally makes things more  
complex, more rich also.




>
>
> May I refer to the following two paragraphs?:
>
> We can read here:
> http://plato.stanford.edu/entries/qt-quantlog/
>
> The Reconstruction of QM
>
> From the single premise that the “experimental propositions”  
> associated
> with a physical system are encoded by projections in the way indicated
> above, one can reconstruct the rest of the formal apparatus of quantum
> mechanics. The first step, of course, is Gleason's theorem, which  
> tells
> us that probability measures on L(H) correspond to density operators.
> There remains to recover, e.g., the representation of “observables” by
> self-adjoint operators, and the dynamics (unitary evolution). The  
> former
> can be recovered with the help of the Spectral theorem and the latter
> with the aid of a deep theorem of E. Wigner on the projective
> representation of groups. See also R. Wright [1980]. A detailed  
> outline
> of this reconstruction (which involves some distinctly non-trivial
> mathematics) can be found in the book of Varadarajan [1985]. The point
> to bear in mind is that, once the quantum-logical skeleton L(H) is in
> place, the remaining statistical and dynamical apparatus of quantum
> mechanics is essentially fixed. In this sense, then, quantum  
> mechanics —
> or, at any rate, its mathematical framework — reduces to quantum logic
> and its attendant probability theory.



Very nice text. I agree, but it is a difficult matter. You can extract  
the quantum of 1 bit, but the quibit needs a good tensor product,  
which is not easy to derive (unless in ad hoc way) from quantum logic.
With comp, I think we will need the first order extension of the  
"hypostases", and it could be that special feature of computability  
theory will need to be discovered to complete the derivation. In my  
1991 paper I sum by saying that comp is in search of its Gleason  
theorem".  A lot of work remains, of course.



>
>
>
> And here we read:
>
> http://en.wikipedia.org/wiki/Gleason%27s_theorem
>
> Quantum logic treats quantum events (or measurement outcomes) as  
> logical
> propositions, and studies the relationships and structures formed by
> these events, with specific emphasis on quantum measurement. More
> formally, a quantum logic is a set of events that is closed under a
> countable disjunction of countably many mutually exclusive events. The
> representation theorem in quantum logic shows that these logics form a
> lattice which is isomorphic to the lattice of subspaces of a vector
> space with a scalar product.
>
> It remains an open problem in quantum logic to prove that the field K
> over which the vector space is defined, is either the real numbers,
> complex numbers, or the quaternions. This is a necessary result for
> Gleason's theorem to be applicable, since in all these cases we know
> that the definition of the inner product of a non-zero vector with
> itself will satisfy the requirements to make the vector space in
> question a Hilbert space.
>
> Application
>
> The representation theorem allows us to treat quantum events as a
> lattice L = L(H) of subspaces of a real or complex Hilbert space.
> Gleason's theorem allows us to assign probabilities to these events.
>
>
> END QUOTE
>
> So I wonder - how much are you still missing to construct QM out of  
> the
> logical results you have arrived at?


I have the formal systems. In a sense, nothing is missing. Except  
enough competent and interested people in those weird self-referential  
logics. It is a sequence of open math problems. It is normal. When the  
research is driven by high level question, you don't choose the  
mathematical objects you have to handle. You discover them.

I could later give more explanation, but here we are at the end of the  
AUDA (!). It would be too much technical right now.
you can take a look at  Goldblatt 1974, one or the clearest paper on  
the Brouwersche Modal "quantum" logic.


Best,

Bruno

http://iridia.ulb.ac.be/~marchal/




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