Re: What day is it?

[Bruno Marchal]

On 23 Sep 2015, at 17:45, smitra wrote:
On 16-09-2015 16:24, Bruno Marchal wrote:
On 15 Sep 2015, at 22:33, smitra wrote:
On 12-09-2015 10:26, Bruno Marchal wrote:
On 11 Sep 2015, at 18:17, smitra wrote:
It seems to me that COMP should lead to MWI plus a preferred   
basis  where the latter derives from well defined computational   
states.  Many of the problems with the MWI should not arise  
here,  they are an  artifact of the theory never defining what  
an  observation is,  appealing to ad hoc intuitive notions that  
are  never formulated from  within the theory itself.
The notion that the environment plays a fundamental role should   
be  rejected on physical grounds, it just explains the  
effective  physics  we observe just like air resistance explains  
why Newton's  laws were  not all that obvious to people who  
lived many centuries  ago.
The only way you can explain Newton's law to students is by   
letting  them contemplate a perfect vacuum. It doesn't matter  
here  how  physically unrealistic that perfect vacuum is or  
isn't. The  same is  true for quantum mechanics. You'll never  
make process if  you always  invoke the environment and  
environment induced  decoherence to try to  define fundamental  
concepts, because Nature  cannot possibly work  that way on the  
fundamental level.
Instead, within quantum mechanics (i.e. if we forget about the    
desire to derive QM from COMP or some other deeper theory)   
defining  observers as computations,  means that they should be   
represented as  operators of the form:
sum over input of |output><input|
which leads to a preferred basis when you introduce an  
environment.
An environment or a universal machine, with or without oracle(s).
I think we agree.
I hope you agree that we agree here.
Yes, and I think you could make a lot of progress by trying to   
deconstruct QM in terms of algorithms.
Algorithm cannot be enough.
Assuming Mechanism, the doctrine that there is a physical universe is
deconstructed, and with Church thesis, the deconstruction is  
partially
constructive, as it shows what physics has to be given by the global
FPI calculus on the computations/sigma_1 sentences.
But the FPI calculus does not rely exclusively  on the computations
(modeled by the true sigma_1 sentences), but on the logic of correct
self-reference with respect to those propositions, or logic of
provability (and its intensional variants) with the atomic
propositions being the sigma_1 arithmetical sentences. Despite
provability, unlike computability,  is a relative notion, depending  
on
the machine or subject, as long as it is supportable by a machine,
and  arithmetically correct, the general laws of self-reference
(captured  by G*) will apply, and physics depends only on that.
And so I think that the work is entirely done, at least at the
propositional level. QM proposition calculus is entirely given by the
logics of []p & <>t (& p). The FPI is not algorithmic, even if the
distribution of probability is algorithmic with the simple protocol,
but even the simple FPI is no more algorithmic on the universal
dovetailing (or on the sigma_1 propositions) as we cannot recognize
them as such algorithmically. This makers very nice that the
propositional logic of observable is decidable (and close to a  
Quantum
Logic).
Note that the quanta appears at the star-level (in X1* minus X1),
making quanta into special case of qualia, which is coherent with
Everett's superposition of collection of people (first person plural)
and with the idea that the "absolute 3p reality is a multi-dreams  
(and
note a many-worlds). This shows that even with the Everett "MWI", we
don't have any world: only sharable first person experiences. If the
quanta would have appeared in Z1 or X1 (and not in the proper star-
extension) a notion of apparent global physical reality would have
made sense, but it looks we lost this.
I recall the 8 povs or "hypostases";
1) p   (truth of p)
2) [0]p = []p = bewesibar('p'), with p a (sigma_1) arithmetical   
sentence.
3) [1]p = []p & p  (the knower, or soul or inner god)
4) [2]p = []p & <>t (the observer, gambler, ...)
5) [3]p = [2]p & p  (the "senser").
which can be put in this diagram:
  1=1*
2        2*
  3=3*
4        4*
5        5*
We have that
  1=1*
2        2*
  3=3*
is the basic propositional theory of mind/soul  (1= One, 2 =
Intellect, 3 = Soul)
and
4        4*
5        5*
gives the "two sorts of matter": 4 = intelligible matter, 5 =  
sensible  matter.
Quantizations appear at 3*, 4*, and 5*. That suggests 3 sorts of
logics structuring (slightly?) differently the physical reality. I
guess that 3* is "heaven physics" (the physics of the soul which has
not yet felt), and 4*, like 5*, are the physics of "earth", when we
sin in the bet on the non justifiable "Reality" (<>t).
So we can not only test mechanism, but we can test if we are in  
heaven
or not :)
No need to take this too much seriously. A lot of research needs to
be pursued to clarify all this. At the quantified logical level, we
know that both 2 and 2* are highly undecidable, and I expect it to be
like that for 3, 3*, 4, 4*, 5 and 5* too.
That is technically annoying, but if the whole quantified logic were
decidable, I would have doubted that comp is true, because the whole
physics and theology would have become decidable, which I cannot
really imagine. In fact the miracle is that at the *propositional*
level, those logics *are* decidable.
Now I am aware that not much people have the background in logic, to
get this straight, and without asking question it is hard for me to
say much more. To get an intuition, I can only suggest to read the
neoplatonists or the mystics, or to try to find out by themselves by
meditation,  or other "perturbation of the brain" technic, in some
(non dangerous) way. People have to be careful because those technic
can also be used for brainwashing and to deepen the "illusion", but
then everything can be misused, even logic.
Bruno

If  some simplified model can be constructed based on these ideas  
that demonstrates that it indeed yields physics then that would be  
helpful.


The demonstration that *IT HAS* to describe physics is normally  
provided by the UDA. I can come back on this.

The demonstration that IT indeed DOES begin to describe physics is  
suggested by the fact that the "measure one" on the consistent  
extensions "existing if they exist (as we can't prove that they  
exist", leads to a quantum logic and some rather well behaved many- 
histories logic with some quantization, so we can see if it emulates a  
quantum computer).

The measure one is naturally  given by the modality []p & <>t (or the  
stronger []p & p, or the weaker []p & <>t & p), with "[]" = Gödel  
beweisbar (and thus obeying G and G*) and p being a sigma_1  
arithmetical proposition). It gives a notion of observable, with a  
justification of why it remains observable in "my" neighborhood.

When physics is "discovered" by pure introspection, the discovery  
begin by the many-worlds, and the question is how finite machine does  
the filtering and why the physical universe looks so much computable.

I use all the time both
1) the completeness theorem, which says that if <>t is true about a  
(reasonable) machine/theory/set-of-beliefs, then the machine/theory/ 
set-of-beliefs has a model, which can serve as a ultimate (non  
computable) consistent extension.
2) the incompleteness theorem, which says that if <>t is true about a  
machine/theory/set-of-beliefs, then the machine/theory/set-of-beliefs  
cannot prove it.
That is what explain that despite []p and []p & <>t proves exactly the  
same propositions, they obey very different logic. The UDA view of  
what is physics (a statistics on consistent continuations) should  
explain why the measure one is given by []p & <>t.

By completeness we have also that if []p is true for the machine, that  
is, the machine does prove p, then p is true in all models (that is in  
all consistent extensions, or here continuations). But due to  
incompleteness we have cul-de-sac world, which prevents []p to play  
the role of measure one ([]p is trivially true in cul-de-sac, yet all  
probabilities are null there), so adding consistency in the definition  
of the (physical) modality is equivalent as deciding to not count the  
cul-de-sac worlds in the probabilities (which is coherent with the UDA  
redefinition of physics.

Completeness and incompleteness of theories like PA is well explained  
in good textbook, like Mendelson, or Franzen's "inexhaustibility" book.
G is well explained in Bollos 79, 93, and in Smorinsky 1980.

Bruno





Saibal


Saibal
Bruno
Saibal
On 11-09-2015 17:07, Bruno Marchal wrote:
On 11 Sep 2015, at 03:10, Bruce Kellett wrote:
On 11/09/2015 5:00 am, Bruno Marchal wrote:
On 10 Sep 2015, at 01:20, Bruce Kellett wrote:
On 10/09/2015 7:42 am, Brent Meeker wrote:
On 9/9/2015 10:27 AM, Bruno Marchal wrote:
On 09 Sep 2015, at 07:55, Quentin Anciaux wrote:
As for Bruce, could you then be honest, and simply say   
you   don't believe in the many world interpretation and   
don't  want  to explore it... yes we're talking mostly   
metaphysics  on this  list, if you dislike it, I wonder   
what you're doing  here.
Indeed the point is notably that we can reason about  
this,   that  is doing science, so that we never disagree  
except  about  the  choice of the assumptions.
Now, I disagree with Bruce, and I guess many philosophers   
and   scientists, except Deutsch (on this), but I do  
think  that QM   (without collapse) is a theory of many  
worlds (in  a perhaps   admittedly more abstract than  
usual notion of  world).
If we define a physical world by a set of events close  
for    interaction,
But can computationalism give a coherent account of this?    
Doesn't  the UD imply at every set of events will have  
many   (countably  many?) causal histories and infinitely  
many  causal  futures.
then the "many-world" is a consequence of the linearity  
of   the  wave evolution together with the linearity of  
the  tensor  product.
But they are only "many" FAPP.  Decoherence suppresses   
cross   terms in the density matrix, but it doesn't make  
them  zero -  and  I don't think it's even provable that  
there is a  unique  basis in  which it diagonalized FAPP.   
And of course  we have no  theory of  quantum spacetime.   
QM assumes a  continuous  spacetime, so QM is  not the last  
word and if  computationalism  only reproduces QM it  will  
fail when QM  fails.
I think it is clear that Bruno does not understand either  
QM  or   the MWI. MWI is not a consequence of the linearity  
of the  wave   function.
It is when you define a world by the maximal consistent    
extension  close for the local observable interactions.
That is not a consequence of linearity. Linearity gives     
superpositions. You only escape from the superpositions to    
distinct  non-interacting worlds by imposing some non- 
linearity   somewhere. In  MWI this is hidden in the trace  
over  environmental  states. But this  is just as much a non- 
linear  collapse as in any  other collapse model.
On the contrary, linearity of the tensor product gives the
superposition, and linearity of the wave evolution assures that  
the
terms of the superposition behaves like we see pure states,  
when in
fact we are ourself superposed. It assures also the non   
interaction  of
the terms, but it does not imply the lack of interference. Then
decoherence explains the *hardness* (and the need of amnesia) of
realizing the interference of the branches in which we "belong".
Superposition is the consequence of linearity,
OK. And if the computations done can interfere, they have  
an    equivalent physical reality, and determined alternate   
accessible   realities, but if entangling oneself with them,  
we  loss or make   very hard the ability to see the  
interference.
Just because you can't see it it does not follow that it is  
not   there.
Yes. That's my point.
and superposition implies interactions between outcomes.
?
I would say interference between the outcomes.
Many-worlds requires decoherence in a preferred basis,
I would say that classical macroscopic brain or universal    
machine  requires a classical-enough base, which benefits  
of   that  decoherence, although with quantum computing we  
can  exploit  the  ignorance by changing the base (which is  
still  rather  mysterious  from the comp pov).
There is no such thing as a "classical" basis for Hilbert   
space.   Quantum computing is irrelevant here.
?
All linear space have bases (if you are OK with the axiom of   
choice).
A basis is a classical notion. All basis are classical.
with actual zeroing of the off-diagonal terms in the  
density    matrix. Indeed, this latter step is just the  
standard   "collapse"  postulate in a different guise. So,  
far from   eliminating  "collapse", MWI relies on it as much  
as any  other  interpretation  of QM.
Not at all. There is no physical collapse, just an    
epistemological  differentiation when one get entangled in  
the   other's business.
You appear to be referring to Everett's original 'relative   
state'   interpretation,
I refer (here) to any theory which assumes that the SWE apply  
to  both
the particles and the observers.
Well, to tell you the truth, I believe that just computationalism
implies the "many-dreams" in arithmetic. No need to know quantum
mechanics. I do not assume quantum mechanics at all once we  
assume
computationalism. I just say that the SWE (or MWI, which is   
logically
equivalent) confirms the many-dreams theory (arithmetic "seen  
from
inside") up to now.
in which there was only ever one world --
... or zero world. "world" are never really defined.
the other parts of the wave function played no role. But this   
was   soon realized to be unworkable. You really should read  
up  on  modern  versions of MWI. I recommend Shlosshauer, Rev.  
Mod.  Phys.  76 (2004)  1267. Or
http://arxiv.org/abs/quant-ph/0312059
or his book on the subject.
I have no problem with that paper. It looks it confirms what I   
said.
Maybe you can elaborate, as I am not sure why you refer to it.  
I  read
most of Griffith papers, and Omnes' books. I agree with a lot  
in   them,
except that they lost me very often in the philosophical
conclusion(s)  where they lack rigor, and seems to believe in  
some
primary universe,  which is useless, and contradicted (my job) by
computationalism (which  is my starting hypothesis).
Bruno
Bruce
The real difference between interpretations is whether  
this    "collapse" is a physical process or merely an  
epistemological  one.
In the MWI, actually in Everett theory, there is only the   
SWE.   Sating "there is no collapse", means, for a logician,   
that we  don't  add the collapse postulate (unlike many   
textbook). So the  collapse  is necessarily an  
epistemological,  even indexical, and  relative,  notion.
In MWI, which reifies the wave function
Which is indeed an error, at least with the mind-body  
problem  in   mind, but physicists do this very often.
and the elements of the superposition, the collapse is    
definitely  physical.
?
So it is, after all, no different in this respect from the   
von   Neumann Copenhagen interpretation.
I have a problem. In Everett theory there is no postulation   
of   collapse. The collapse is explained by the postluation  
of   universal  machine, or at least good approximation of   
universal  machine.
Copenhague:
- SWE
- Collapse
- Dualist theory of mind and matter
Everett:
- SWE
- COMP
And what I try to explain is that COMP   ->.   [](COMP ->  
SWE)  &   (COMP -> SWE), so "my" theory is just
- COMP
Formally it is just any theory which is Turing universal,  
and    observation is defined by the logic of self-reference  
(of  rcher   entities living there) and the intensional  
variants.
This is not supposed to compete with physics, but to supply   
the   qualia, and the range of non communicable, but true,   
realities.
Bruno
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