Re: Are proofs equivalent to dovetailing computations?

[Jason Resch]

On Fri, Aug 16, 2019 at 6:31 PM Russell Standish 
wrote:

> On Fri, Aug 16, 2019 at 12:06:32PM -0500, Jason Resch wrote:
> >
> > Thanks for the background and explanation.  Is it the case then that any
> > undecidable (creative?) set is a compact description of universal
> dovetailing?
> > Would Chaitin's constant also qualify as a compact description of the
> universal
> > dovetailing (though being a single real number, rather than a set of
> rational
> > complex points)?
> >
>
> Related to this, on page 218 of Li and Vitanyi's "Introduction to
> Kolmogorov Complexity and it Applications", right under corollary 3.6.2 is
> the statement:
>
> "Moreover, for all axiomatic mathematical theories that can be
> extressed compactly enough to be conceivably interesting to human
> beings, say in fewer than 10,000 bits, [the first 10,000 bits of the
> Chatin probability Ω] can be used to decide for every statement in the
> theory whether it is the true, false or independent. ... Thus Ω is
> truly the number of Wisdom, and 'can be known of, but not known,
> through human reason' [C.H Bennett and M. Gardner, Sci
> Am. 241:11(1979),20-34]".
>
>
What an incredible and fascinating discovery/insight.  I couldn't
understand it at first but did some searching and reading and came across a
detailed explanation.  The quote above seems to be based on an earlier work
by Charles Bennett, in "On Random and Hard-to-Describe Numbers" (
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.214.7866=rep1=pdf
).  In it I found another nice quote:

Throughout history philosophers and mystics have sought a compact key to
universal wisdom, a finite formula or text which, when known
and understood, would provide the answer to every question. The Bible, the
Koran, the mythical secret books of Hermes Trismegistus, and the medieval
Jewish Cabala have been so regarded. Sources of universal wisdom are
traditionally protected from casual use by being hard to find, hard to
understand when found, and dangerous to use, tending to answer more
and deeper questions than the user wishes to ask. Like God the esoteric
book is simple yet undescribable, omniscient, and transforms all who know
It. The use of classical texts to foretell mundane events is considered
superstitious nowadays, yet, in another sense, science is in quest of its
own Cabala, a concise set of natural laws which would explain all
phenomena. In mathematics, where no set of axioms can hope to prove all
true statements, the goal might be a concise axiomatization of all
“interesting” true statements.

Ω is in many senses a Cabalistic number. It can be known of, but not known,
through human reason. To know it in detail, one would have to accept its
uncomputable digit sequence on faith, like words of a sacred text. It
embodies an enormous amount of wisdom in a very small space, inasmuch as
its first few thousand digits, which could be written on a small piece of
paper, contain the answers to more mathematical questions than could be
written down in the entire universe, including all interesting finitely
refutable conjectures. Its wisdom is useless precisely because it is
universal: the only known way of extracting from Ω the solution to one
halting problem, say the Fermat conjecture, is by embarking on a vast
computation that would at the same time yield solutions to all other
equally simply-stated halting problems, a computation far too large to be
carried out in practice. Ironically, although Ω cannot be computed, it
might accidentally be generated by a random process, e.g. a series of coin
tosses, or an avalanche that left its digits spelled out in the pattern of
boulders on a mountainside. The initial few digits of Ω are thus probably
already recorded somewhere in the universe. Unfortunately, no mortal
discoverer of this treasure could verify its authenticity or make practical
use of it.


Jason

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Re: STEP 3

[smitra]

On 16-08-2019 09:01, Bruce Kellett wrote:

On Fri, Aug 16, 2019 at 4:43 PM smitra  wrote:


On 16-08-2019 06:31, Bruce Kellett wrote:

On Wed, Aug 14, 2019 at 8:28 AM smitra  wrote:


On 13-08-2019 13:33, Bruce Kellett wrote:


Of course A(x) and B(x) refer to the same point on the screen.

That is

not a collapse, that is just what the notation means.


A(x) and B(x) considered as the representations of |A> and |B>

in

the
position basis, i.e. A(x) =  and B(x) =  are still
orthogonal
states, as they represent the orthogonal states |A> and |B>:

0 =  = Integral over x of d^3x = Integral over x

of


A*(x)B(x) d^3x


I don't think this really works out. You are claiming that the
integral of the interference terms over the whole screen

vanishes. If

we look at the usual derivation of the interference from two

slits, we

get something like

Intensity I = 2 A^2 (sin^2(beta)/beta^2) (1 + cos(delta))

where the term involving the angle beta is the superposed

diffraction

pattern from the finite width of the slits. The cos (delta) term

is

the interference, but it has this form only in a small angle
approximation, and the phase difference delta is, of course,

limited

by the separation of the slits. So, although the cos(delta) term

may

integrate to zero over small angles, the presence of the

diffraction

envelope, and the limitations of the small angle approximation,

mean

that is almost certainly will not vanish when integrated over the
whole screen.


Yes, this is in the small angle approximation, if you go beyond
that
then the itnegral over the screen won't vanish.



So  will not vanish in general.

No, because  is the integral over all space and this is
exactly
zero. What happens is that when the small angle approximation
becomes
invalid and the integral over only the screen becomes nonzero, the
integrals over surfaces parallel to the screen will have a values
that
differ by a phase factor that depends on the distance in the
direction
orthogonal to the screen. This then causes the integral over all
space
to vanish.


I think you need to prove that. In my understanding, A(x) =  is
to be interpreted as the amplitude for a wave through slit A to get to
the screen at x. There is nothing 3-dimensional about this. The 'x' is
just the distance from the centre of the screen in the plane of the
screen. Nothing else is relevant. You do not have to integrate over
all space because you use a complete set of states in the x-direction:
 int |x>

A quantum state is defined in the position representation by assigning 
an amplitude to all points in space. It can be the case that the 
amplitude is zero outside of a narrow volume surrounding the the screen, 
in which case the integration can be approximated as an integral over 
the screen's surface.


The orthogonality can be rigorously proved as follows. If we have a 
single particle incident on the two slits described by a time dependent 
wave function psi(x,t) = 1/sqrt(2) [A(x,t) + B(x,t)] such that at A(x,0) 
is nonzero at one slit and B(x,0) at the other slit, then A(x,0) and 
B(x,0) are obviously orthogonal. Since time evolution will preserve 
inner products, A(x,t) and B(x,t) will remain orthogonal as a function 
of t. One can then describe the interaction with the screen as an 
effective collapse that will happen with the largest probability when 
the peak of the wavefunction has arrived at the screen.


Saibal

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Re: Are proofs equivalent to dovetailing computations?

[Russell Standish]

On Fri, Aug 16, 2019 at 12:06:32PM -0500, Jason Resch wrote:
> 
> Thanks for the background and explanation.  Is it the case then that any
> undecidable (creative?) set is a compact description of universal 
> dovetailing? 
> Would Chaitin's constant also qualify as a compact description of the 
> universal
> dovetailing (though being a single real number, rather than a set of rational
> complex points)?
> 

Related to this, on page 218 of Li and Vitanyi's "Introduction to Kolmogorov 
Complexity and it Applications", right under corollary 3.6.2 is the statement:

"Moreover, for all axiomatic mathematical theories that can be
extressed compactly enough to be conceivably interesting to human
beings, say in fewer than 10,000 bits, [the first 10,000 bits of the
Chatin probability Ω] can be used to decide for every statement in the
theory whether it is the true, false or independent. ... Thus Ω is
truly the number of Wisdom, and 'can be known of, but not known,
through human reason' [C.H Bennett and M. Gardner, Sci
Am. 241:11(1979),20-34]".

Cheers
-- 


Dr Russell StandishPhone 0425 253119 (mobile)
Principal, High Performance Coders
Visiting Senior Research Fellowhpco...@hpcoders.com.au
Economics, Kingston University http://www.hpcoders.com.au


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Re: Local Realism and Bell

[Bruce Kellett]

On Sat, Aug 17, 2019 at 12:21 AM Bruno Marchal  wrote:

> On 16 Aug 2019, at 13:30, Bruce Kellett  wrote:
>
> On Fri, Aug 16, 2019 at 9:23 PM Bruno Marchal  wrote:
>
>> On 16 Aug 2019, at 03:27, 'Brent Meeker' via Everything List <
>> everything-list@googlegroups.com> wrote:
>>
>> On 8/15/2019 5:06 PM, Bruce Kellett wrote:
>>
>> On Fri, Aug 16, 2019 at 9:25 AM Lawrence Crowell <
>> goldenfieldquaterni...@gmail.com> wrote:
>>
>>> I started reading this. It looks similar to the PR box argument.
>>>
>>
>> I have skimmed through it. It seems that Alice and Bob both split locally
>> according to the results they get, but then rely on magic to prevent the
>> incorrect pairs ever meeting.
>>
>>
>> I think you can interpret it as decoherence spreads at light speed from
>> Alice's measurement event and decoheres Bob's system when it comes within
>> the future light cone of Alice's measurementand vice versa, which is
>> why it needs to assume MWI to maintain symmetry between Alice and Bob.
>>
>>
>> That is my understanding. That explains entirely, it seems to me, the
>> violation of Bell’s inequality in a local, but multi-versal type of
>> reality. When Alice and Bob separates, they simply never meet again, but
>> both can meet their correlated counterparts. Each Alice and each Bob can
>> meet only their correlates, that they enforce by decoherence, at a speed
>> lower than light.
>>
>
>
> That doesn't explain anything.
>
>
> I know you’ve already try to expand on this, but it seems to me that this
> was based on some incorrect interpretation of the notion of worlds, like if
> a measurement made by Alice has to change the possible outcomes available
> to Bob, but that does not happen in the relative state view. Only a
> physical collapse would entail some “action at a distance”; without
> collapse anywhere, I don’t see how could such influence at a distance
> occurs. We did disagree also on the numbers of histories involved, which I
> take to be always infinite.
>

Clarify your argument, then, and remove the suggestion of magic.

Bruce

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Re: Local Realism and Bell

[Philip Thrift]

On Friday, August 16, 2019 at 3:26:47 PM UTC-5, Brent wrote:
>
>
>
> On 8/16/2019 4:23 AM, Bruno Marchal wrote:
>
>
> On 16 Aug 2019, at 03:27, 'Brent Meeker' via Everything List <
> everyth...@googlegroups.com > wrote:
>
>
>
> On 8/15/2019 5:06 PM, Bruce Kellett wrote:
>
> On Fri, Aug 16, 2019 at 9:25 AM Lawrence Crowell  > wrote:
>
>> I started reading this. It looks similar to the PR box argument.
>>
>
> I have skimmed through it. It seems that Alice and Bob both split locally 
> according to the results they get, but then rely on magic to prevent the 
> incorrect pairs ever meeting.
>
>
> I think you can interpret it as decoherence spreads at light speed from 
> Alice's measurement event and decoheres Bob's system when it comes within 
> the future light cone of Alice's measurementand vice versa, which is 
> why it needs to assume MWI to maintain symmetry between Alice and Bob.
>
>
> That is my understanding. That explains entirely, it seems to me, the 
> violation of Bell’s inequality in a local, but multi-versal type of 
> reality. When Alice and Bob separates, they simply never meet again, but 
> both can meet their correlated counterparts. Each Alice and each Bob can 
> meet only their correlates, that they enforce by decoherence, at a speed 
> lower than light.
>
>
> But as Bruce says, it's a kind of magic as stated.  To not be magic there 
> must be some physical interactions communicating Alice's result to Bob's 
> system: Photons would the obvious candidate, but how exactly do they 
> interact with Bob and his system to make them orthogonal to one of Alice's 
> results and not the other?  
>
> Brent
>



People were asking this question decades ago, and will still be asking it 
decades in the future.

@philipthrift 

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Re: Local Realism and Bell

['Brent Meeker' via Everything List]

On 8/16/2019 4:23 AM, Bruno Marchal wrote:


On 16 Aug 2019, at 03:27, 'Brent Meeker' via Everything List 
> wrote:




On 8/15/2019 5:06 PM, Bruce Kellett wrote:
On Fri, Aug 16, 2019 at 9:25 AM Lawrence Crowell 
> wrote:


I started reading this. It looks similar to the PR box argument.


I have skimmed through it. It seems that Alice and Bob both split 
locally according to the results they get, but then rely on magic to 
prevent the incorrect pairs ever meeting.


I think you can interpret it as decoherence spreads at light speed 
from Alice's measurement event and decoheres Bob's system when it 
comes within the future light cone of Alice's measurementand vice 
versa, which is why it needs to assume MWI to maintain symmetry 
between Alice and Bob.


That is my understanding. That explains entirely, it seems to me, the 
violation of Bell’s inequality in a local, but multi-versal type of 
reality. When Alice and Bob separates, they simply never meet again, 
but both can meet their correlated counterparts. Each Alice and each 
Bob can meet only their correlates, that they enforce by decoherence, 
at a speed lower than light.


But as Bruce says, it's a kind of magic as stated.  To not be magic 
there must be some physical interactions communicating Alice's result to 
Bob's system: Photons would the obvious candidate, but how exactly do 
they interact with Bob and his system to make them orthogonal to one of 
Alice's results and not the other?


Brent

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Re: The August 14 Black Hole - Neutron Star merger

[Lawrence Crowell]

On Friday, August 16, 2019 at 5:35:44 AM UTC-5, John Clark wrote:
>
> Yesterday August 14 2019 LIGO detected for the first time Gravitational 
> Waves coming from a Black Hole-Neutron Star merger; it was 900 million 
> light years away. They detected something like this a few months ago but 
> were only 13% confident it was real, this time the signal was much stronger 
> and they're 99% confident. They've narrowed the source down to a square 23 
> degrees on a side, so far they haven't detected any electromagnetic waves 
> from it but have just started looking. This type of merger produces a 
> cleaner signal that is easier to analyze than when two Black Holes merge 
> and can provide a more rigorous test of General Relativity, and if you 
> could spot a few dozen of these sort of mergers it could give us the best 
> value yet of the Hubble constant which has been in dispute lately and 
> perhaps tell us if we're heading for the Big Rip or not.
>
> LIGO and Virgo spotted the first black hole swallowing up a neutron star 
> 
>
> John K Clark
>

I am not sure how this is cleaner, for there is a lot of material dynamics 
that is complicated. Black hole coalescence is a pure vacuum problem. It is 
though interesting still. 

LC 

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Re: Are proofs equivalent to dovetailing computations?

[Jason Resch]

On Wed, Aug 14, 2019 at 5:02 AM Bruno Marchal  wrote:

>
> On 12 Aug 2019, at 23:36, Jason Resch  wrote:
>
> In "The Universal Numbers. From Biology to Physics" Bruno writes
>
> "The universal dovetailing can be seen as the proofs of all true Sigma_1
> propositions there exists x,y,z such that P_x(y) = z, with some sequences
> of such propositions mimicking the infinite failing or proving some false
> Sigma_1 propositions."
>
> This is something I was thinking about recently in the context of
> universal Diophantine equations. It seems more correct to me to say these
> equations don't themselves represent the execution traces of the programs,
> but rather represent proofs of the outputs of programs.
>
> This can be seen from the fact that the work of verifying a Diophantine
> equation requires only a finite and constant number of arithmetical
> operations, while the computation itself could involve much more work, in
> terms of arithmetical steps.
>
>
>
>
> We have to distinguish
>
> - a computable function (from N to N, say), That is an *infinite* object,
> which can be represented by an infinite set (the set of input-output). That
> set is often called the “graph” of the function. We can show that if the
> function is computable, its graph is mechanically generable (recursively
> enumerable). Such a set can be described by a sigma_1 sentence (that is a
> sentence having the shape {y such that ExP(x, y)}.
>

Does the identity between a computation (in terms of discrete steps with
counterfactual behavior), and its representation as the set of all inputs
to outputs imply that the Blockhead (giant state table brain) possesses
consciousness of the same form as the incrementally processed computation?
Perhaps I just have too myopic of a view of what computation is from my
familiarity with programming.


>
> - The code of a computable function. That is a *finite* object
> (representable using some word or numbers, or finite set, …). I use usually
> the word “digital machine” for this. It is the (virtual) body of the
> machine. It is finitely describable.
>
> - a computation. That is either *a finite or an infinite* thing, usually
> representable by a sequence of numbers or words, called the trace of the
> computation). Some author call “computation” only the computations which
> halt, and thus are finite, like Martin Davis in the book “Computability and
> Unsolvability). Other like Daniel E. Cohen, and me most of the time, admits
> the term “computation” for non halting, and thus infinite, one.
>
> With, this you can guess that when you have an halting computation, you
> have automatically a proof of a sigma_1 sentence (like the sentence saying
> that some input-output (x,y) belongs to the graph of that function, or that
> x belongs to its domain).
>
> Unfortunately, the reciprocal is not necessarily true. We can find a proof
> of a sigma_1 sentence which would not be a computation, like an indirect
> proof by a reduction ad absurdum which can be a non constructive proof of
> an existential statement. Such a proof would state that a computation is
> halting, without executing that computation.
>
> So, proofs (of sigma_1 sentence) are not necessarily a computation, and as
> such will not belong to the universal dovetailing directly, although the
> universal dovetailing will emulate some subjects doing those
> non-constructive proof, but that gives a computation emulating a reasoning
> process, and that reasoning process does not need to be a computation.
>
> Inversely, as I said, a computation can be seen as a proof of a sigma_1
> sentence. There is a theorem which makes this precise: the normal form
> theorem of Kleene, which shows that there are computable (and elementary,
> primitive recursive, if people remember the definition) U and T such that
> if f(x) is a computable function, computed by the code z, then
>
>  y = f(x) = U(the least c (T(z, x, c)).
>
> T(z, x, c) is Kleene’s predicate. It says that z is the Gödel number of a
> (partial) computable function, x is the input given to the machine with
> code z, and y is an halting computation given by the machine with code z
> when applied to x.
> U is the result extracting function, which gives the output y from the
> computation c. Usually U just take the last line of the computation, for
> example. This results shows that you can always program a computable
> function with one “while”, or that you can always well structure a code
> (suppress all the “goto”-like instruction by just one “while”.
>

I think this fact (of implementing any program with a single loop) explains
both why recursive functions are Turing complete and why CPUs can work by
simply repeating the application of some electrical circuit over and over
again.


>
>
> So is it right to say that the proof of the result of some computable
> function is different from the computable function itself?
>
>
> So, the proof is different from the computable function, and from its
> code. But the 

Re: Standard Model & Higgs Boson

[Alan Grayson]

On Thursday, August 15, 2019 at 12:07:01 AM UTC-6, Alan Grayson wrote:
>
>
>
> On Sunday, August 11, 2019 at 9:40:45 PM UTC-6, Alan Grayson wrote:
>>
>>
>>
>> On Sunday, August 11, 2019 at 3:56:39 PM UTC-6, Lawrence Crowell wrote:
>>>
>>> On Saturday, August 10, 2019 at 10:43:39 PM UTC-5, Alan Grayson wrote:

 In what way does the Standard Model imply the existence of the Higgs 
 Boson? TIA.

>>>
>>> I have been around the block on this. The Higgs field breaks the 
>>> electroweak symmetry U(2) = SU(2)xU(1) the transferring 3 Goldstone boson 
>>> components to the weak interaction bosons as longitudinal components. A 
>>> quantum field with a longitudinal component usually has a mass. 
>>>
>>> LC 
>>>
>>
>> Bear with me; what is electroweak symmetry, and why does it need to be 
>> broken? TIA, AG 
>>
>
> What is the contribution of the Higgs Field, as a per cent, to the vacuum 
> energy? Isn't the Higgs field, a defacto introduction to an ether theory? 
> Isn't the vacuum energy another name for the Cosmological Constant? TIA, AG 
>

It is an ether, but not specifically for light; ubiquitous, a limited 
explanation of mass, for some non composite particles. Can't you guys admit 
it? AG 

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Re: STEP 3

[Bruno Marchal]

> On 15 Aug 2019, at 23:22, Jason Resch  wrote:
> 
> 
> 
> On Sun, Aug 11, 2019 at 12:24 PM Bruno Marchal  > wrote:
> 
>> On 10 Aug 2019, at 20:34, Jason Resch > > wrote:
>> 
>> 
>> 
>> On Fri, Aug 9, 2019 at 10:20 AM Bruno Marchal > > wrote:
>> 
>>> On 9 Aug 2019, at 13:09, Jason Resch >> > wrote:
>>> 
>>> 
 
 Bruno,
 
 Forgive me if I have asked this before, but can you elaborate on the 
 how/why the math suggests negative interference?
 
 I currently have no intuition for why this should be.
 
 I recall reading something on continuous probability as being more natural 
 and leading to something much like the probability formulas in quantum 
 mechanics. Is that related?
>>> 
>>> 
>>> It is not intuitive at all. With the UDA, we can have have the intuition 
>>> coming from the first person indeterminacy on all all computational 
>>> continuation in arithmetic, but in the AUDA (the Arithmetical UDA), the 
>>> probabilities are constrained by the logic of self-reference G and G*. So 
>>> the reason why we can hope for negative amplitude of probability comes from 
>>> the fact that modal variant of the first person on the (halting) 
>>> computations, which is given by the arithmetical interpretation of:
>>> 
>>> []p & p
>>> 
>>>  or
>>> 
>>> []p & <>t
>>> 
>>> or
>>> 
>>> []p & <>t & p
>>> 
>>>  With, as usual, [] = Beweisbar, and p is an arbitrary sigma_1 sentences 
>>> (partial computable formula).
>>> 
>>> They all give a quantum logic enough close to Dalla Chiara’s presentation 
>>> of them, to have the quantum features like complimentary observable, and 
>>> what I have called a sort of abstract linear evolution build on a highly 
>>> symmetrical core (than to LASE: the little Schroeder equation: p -> []<>p, 
>>> which provides a quantisation of the sigma_1 arithmetical reality.
>>> 
>>> It is mainly the presence of this quantisation which justify that the 
>>> probabilities behave in a quantum non boolean way, but this is hard to 
>>> verify because the nesting of boxes in the G* translation makes those 
>>> formula … well, probably in need of a quantum computer to be evaluated. But 
>>> normally, if mechanism (and QM) are correct this should work.
>>> 
>>> This is explained with more detail in “Conscience et Mécanisme”.
>>> 
>>> Bruno
>>> 
>>> 
>>> Thank you Bruno for your explanation and references. 
>> 
>> Y’re welcome.
>> 
>> 
>>> Regarding “Conscience et Mécanisme”, is there a web/html or English version 
>>> available?  Unfortunately my browser cannot do translations of PDFs but can 
>>> translate web pages.  If not don't worry, I can copy and paste into a 
>>> translator.
>> 
>> Yes, There is no HTML page for the long text. But you can consult also my 
>> paper:
>> 
>> Marchal B. The Universal Numbers. From Biology to Physics, Progress in 
>> Biophysics and Molecular Biology, 2015, Vol. 119, Issue 3, 368-381.
>> https://www.ncbi.nlm.nih.gov/pubmed/26140993 
>> 
>> 
>> You will still need some background in quantum logic, like  the paper by 
>> Goldblatt which makes the link between minimal quantum logic and the B modal 
>> logic. 
>> 
>> There is also a paper by Rawling and Selesnick which shows how to build a 
>> quantum NOT gate, from the Kripke semantics of the B logic. It is not 
>> entirely clear if this can be used in arithmetic, because we loss the 
>> necessitation rule in “our” B logic. Open problem. A positive solution on 
>> this would be a great step toward an explanation that the universal machine 
>> has necessarily a quantum structure and can exploit the “parallel 
>> computations in arithmetic” in the limit of the 1p indeterminacy..
>> 
>> Rawling JP and Selesnick SA, 2000, Orthologic and Quantum Logic: Models and 
>> Computational Elements, Journal of the ACM, Vol. 47, n° 4, pp. 721-T51.
>> 
>> Ask question, online or here. It *is* rather technical at some point.
>> 
>> Bruno
>> 
>> 
>> 
>> I've been reading those references, and have found a few more which might be 
>> related and of interest.  Effectively, they provide arguments for the 
>> quantum probability theory based on the requirement for continuous 
>> reversible operations, or the juxtaposition between finite information-carry 
>> capacity and smoothness.
>> 
>> 
>> Lucien Hardy's "Quantum Theory From Five Reasonable Axioms" 
>> https://arxiv.org/abs/quant-ph/0101012 
>> 
>> 
>> The usual formulation of quantum theory is based on rather obscure axioms 
>> (employing complex Hilbert spaces, Hermitean operators, and the trace rule 
>> for calculating probabilities). In this paper it is shown that quantum 
>> theory can be derived from five very reasonable axioms. The first four of 
>> these are obviously consistent with both quantum theory and classical 
>> probability theory. Axiom 

Re: Local Realism and Bell

[Bruno Marchal]

> On 16 Aug 2019, at 13:30, Bruce Kellett  wrote:
> 
> On Fri, Aug 16, 2019 at 9:23 PM Bruno Marchal  > wrote:
> On 16 Aug 2019, at 03:27, 'Brent Meeker' via Everything List 
> mailto:everything-list@googlegroups.com>> 
> wrote:
>> On 8/15/2019 5:06 PM, Bruce Kellett wrote:
>>> On Fri, Aug 16, 2019 at 9:25 AM Lawrence Crowell 
>>> >> > wrote:
>>> I started reading this. It looks similar to the PR box argument.
>>> 
>>> I have skimmed through it. It seems that Alice and Bob both split locally 
>>> according to the results they get, but then rely on magic to prevent the 
>>> incorrect pairs ever meeting.
>> 
>> I think you can interpret it as decoherence spreads at light speed from 
>> Alice's measurement event and decoheres Bob's system when it comes within 
>> the future light cone of Alice's measurementand vice versa, which is why 
>> it needs to assume MWI to maintain symmetry between Alice and Bob.
> 
> That is my understanding. That explains entirely, it seems to me, the 
> violation of Bell’s inequality in a local, but multi-versal type of reality. 
> When Alice and Bob separates, they simply never meet again, but both can meet 
> their correlated counterparts. Each Alice and each Bob can meet only their 
> correlates, that they enforce by decoherence, at a speed lower than light.
> 
> 
> That doesn't explain anything.

I know you’ve already try to expand on this, but it seems to me that this was 
based on some incorrect interpretation of the notion of worlds, like if a 
measurement made by Alice has to change the possible outcomes available to Bob, 
but that does not happen in the relative state view. Only a physical collapse 
would entail some “action at a distance”; without collapse anywhere, I don’t 
see how could such influence at a distance occurs. We did disagree also on the 
numbers of histories involved, which I take to be always infinite.

Bruno




> 
> Bruce 
> 
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Re: Local Realism and Bell

[Bruce Kellett]

On Fri, Aug 16, 2019 at 9:23 PM Bruno Marchal  wrote:

> On 16 Aug 2019, at 03:27, 'Brent Meeker' via Everything List <
> everything-list@googlegroups.com> wrote:
>
> On 8/15/2019 5:06 PM, Bruce Kellett wrote:
>
> On Fri, Aug 16, 2019 at 9:25 AM Lawrence Crowell <
> goldenfieldquaterni...@gmail.com> wrote:
>
>> I started reading this. It looks similar to the PR box argument.
>>
>
> I have skimmed through it. It seems that Alice and Bob both split locally
> according to the results they get, but then rely on magic to prevent the
> incorrect pairs ever meeting.
>
>
> I think you can interpret it as decoherence spreads at light speed from
> Alice's measurement event and decoheres Bob's system when it comes within
> the future light cone of Alice's measurementand vice versa, which is
> why it needs to assume MWI to maintain symmetry between Alice and Bob.
>
>
> That is my understanding. That explains entirely, it seems to me, the
> violation of Bell’s inequality in a local, but multi-versal type of
> reality. When Alice and Bob separates, they simply never meet again, but
> both can meet their correlated counterparts. Each Alice and each Bob can
> meet only their correlates, that they enforce by decoherence, at a speed
> lower than light.
>


That doesn't explain anything.

Bruce

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Re: Local Realism and Bell

[Bruno Marchal]

> On 16 Aug 2019, at 03:27, 'Brent Meeker' via Everything List 
>  wrote:
> 
> 
> 
> On 8/15/2019 5:06 PM, Bruce Kellett wrote:
>> On Fri, Aug 16, 2019 at 9:25 AM Lawrence Crowell 
>> mailto:goldenfieldquaterni...@gmail.com>> 
>> wrote:
>> I started reading this. It looks similar to the PR box argument.
>> 
>> I have skimmed through it. It seems that Alice and Bob both split locally 
>> according to the results they get, but then rely on magic to prevent the 
>> incorrect pairs ever meeting.
> 
> I think you can interpret it as decoherence spreads at light speed from 
> Alice's measurement event and decoheres Bob's system when it comes within the 
> future light cone of Alice's measurementand vice versa, which is why it 
> needs to assume MWI to maintain symmetry between Alice and Bob.

That is my understanding. That explains entirely, it seems to me, the violation 
of Bell’s inequality in a local, but multi-versal type of reality. When Alice 
and Bob separates, they simply never meet again, but both can meet their 
correlated counterparts. Each Alice and each Bob can meet only their 
correlates, that they enforce by decoherence, at a speed lower than light.

Bruno



> 
> Brent
> 
>> 
>> Not convincing.
>> 
>> Bruce
>>  
>> LC
>> 
>> On Thursday, August 15, 2019 at 10:56:24 AM UTC-5, Jason wrote:
>> From: https://www.mdpi.com/1099-4300/21/1/87/htm 
>> 
>> 
>> Abstract: We carry out a thought experiment in an imaginary world. Our world 
>> is both local and realistic, yet it violates a Bell inequality more than 
>> does quantum theory. This serves to debunk the myth that equates local 
>> realism with local hidden variables in the simplest possible manner. Along 
>> the way, we reinterpret the celebrated 1935 argument of Einstein, Podolsky 
>> and Rosen, and come to the conclusion that they were right in their 
>> questioning the completeness of the Copenhagen version of quantum theory, 
>> provided one believes in a local-realistic universe. Throughout our journey, 
>> we strive to explain our views from first principles, without expecting 
>> mathematical sophistication nor specialized prior knowledge from the reader.
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>>  
>> .
> 
> 
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The August 14 Black Hole - Neutron Star merger

[John Clark]

Yesterday August 14 2019 LIGO detected for the first time Gravitational
Waves coming from a Black Hole-Neutron Star merger; it was 900 million
light years away. They detected something like this a few months ago but
were only 13% confident it was real, this time the signal was much stronger
and they're 99% confident. They've narrowed the source down to a square 23
degrees on a side, so far they haven't detected any electromagnetic waves
from it but have just started looking. This type of merger produces a
cleaner signal that is easier to analyze than when two Black Holes merge
and can provide a more rigorous test of General Relativity, and if you
could spot a few dozen of these sort of mergers it could give us the best
value yet of the Hubble constant which has been in dispute lately and
perhaps tell us if we're heading for the Big Rip or not.

LIGO and Virgo spotted the first black hole swallowing up a neutron star


John K Clark

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Re: Local Realism and Bell

[Philip Thrift]

On Thursday, August 15, 2019 at 8:27:23 PM UTC-5, Brent wrote:
>
>
>
> On 8/15/2019 5:06 PM, Bruce Kellett wrote:
>
> On Fri, Aug 16, 2019 at 9:25 AM Lawrence Crowell  > wrote:
>
>> I started reading this. It looks similar to the PR box argument.
>>
>
> I have skimmed through it. It seems that Alice and Bob both split locally 
> according to the results they get, but then rely on magic to prevent the 
> incorrect pairs ever meeting.
>
>
> I think you can interpret it as decoherence spreads at light speed from 
> Alice's measurement event and decoheres Bob's system when it comes within 
> the future light cone of Alice's measurementand vice versa, which is 
> why it needs to assume MWI to maintain symmetry between Alice and Bob.
>
> Brent
>
>
>

All of this is well-established physics.

@philipthrift 


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Re: STEP 3

[Bruce Kellett]

On Fri, Aug 16, 2019 at 4:43 PM smitra  wrote:

> On 16-08-2019 06:31, Bruce Kellett wrote:
> > On Wed, Aug 14, 2019 at 8:28 AM smitra  wrote:
> >
> >> On 13-08-2019 13:33, Bruce Kellett wrote:
> >>>
> >>> Of course A(x) and B(x) refer to the same point on the screen.
> >> That is
> >>> not a collapse, that is just what the notation means.
> >>
> >> A(x) and B(x) considered as the representations of |A> and |B> in
> >> the
> >> position basis, i.e. A(x) =  and B(x) =  are still
> >> orthogonal
> >> states, as they represent the orthogonal states |A> and |B>:
> >>
> >> 0 =  = Integral over x of d^3x = Integral over x of
> >>
> >> A*(x)B(x) d^3x
> >
> > I don't think this really works out. You are claiming that the
> > integral of the interference terms over the whole screen vanishes. If
> > we look at the usual derivation of the interference from two slits, we
> > get something like
> >
> >  Intensity I = 2 A^2 (sin^2(beta)/beta^2) (1 + cos(delta))
> >
> > where the term involving the angle beta is the superposed diffraction
> > pattern from the finite width of the slits. The cos (delta) term is
> > the interference, but it has this form only in a small angle
> > approximation, and the phase difference delta is, of course, limited
> > by the separation of the slits. So, although the cos(delta) term may
> > integrate to zero over small angles, the presence of the diffraction
> > envelope, and the limitations of the small angle approximation, mean
> > that is almost certainly will not vanish when integrated over the
> > whole screen.
>
> Yes, this is in the small angle approximation, if you go beyond that
> then the itnegral over the screen won't vanish.
>
> >
> > So  will not vanish in general.
> No, because  is the integral over all space and this is exactly
> zero. What happens is that when the small angle approximation becomes
> invalid and the integral over only the screen becomes nonzero, the
> integrals over surfaces parallel to the screen will have a values that
> differ by a phase factor that depends on the distance in the direction
> orthogonal to the screen. This then causes the integral over all space
> to vanish.
>

I think you need to prove that. In my understanding, A(x) =  is to be
interpreted as the amplitude for a wave through slit A to get to the screen
at x. There is nothing 3-dimensional about this. The 'x' is just the
distance from the centre of the screen in the plane of the screen. Nothing
else is relevant. You do not have to integrate over all space because you
use a complete set of states in the x-direction:  \int |x> > Which is what I would have
> > thought because the paths through the separate slits are not
> > independent -- each particle essentially has to see both slits (go
> > through both slits) in order to maintain coherence. So they cannot be
> > orthogonal (independent).
>
> Coherence and orthogonality have nothing to do with each other.
>
> >
> > In practice, to see the interference pattern you need coherent
> > illumination over both slits. This is easy these days with lasers, but
> > in older books, coherence was ensured by having a preparatory single
> > slit followed by suitable condenser lenses. If the slits could be
> > treated as independent entities, this would not have been necessary.
>
> This has nothing to do with orthogonality of the states. What matters is
> that the interference pattern shouldn't get washed out due to each
> wavefunction of each particle near the screen having its peaks and
> fringes at different places. This can be prevented by using an
> approximate monochromatic light source and making sure that the light
> passes through a collimator. Without a collimator, the interference
> pattern due to the light from one part of the source will be shifted
> w.r.t. to the other part causing the pattern to get washed out.
>
> Saibal
>
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Re: STEP 3

[smitra]

On 16-08-2019 06:31, Bruce Kellett wrote:

On Wed, Aug 14, 2019 at 8:28 AM smitra  wrote:


On 13-08-2019 13:33, Bruce Kellett wrote:


Of course A(x) and B(x) refer to the same point on the screen.

That is

not a collapse, that is just what the notation means.


A(x) and B(x) considered as the representations of |A> and |B> in
the
position basis, i.e. A(x) =  and B(x) =  are still
orthogonal
states, as they represent the orthogonal states |A> and |B>:

0 =  = Integral over x of d^3x = Integral over x of

A*(x)B(x) d^3x


I don't think this really works out. You are claiming that the
integral of the interference terms over the whole screen vanishes. If
we look at the usual derivation of the interference from two slits, we
get something like

 Intensity I = 2 A^2 (sin^2(beta)/beta^2) (1 + cos(delta))

where the term involving the angle beta is the superposed diffraction
pattern from the finite width of the slits. The cos (delta) term is
the interference, but it has this form only in a small angle
approximation, and the phase difference delta is, of course, limited
by the separation of the slits. So, although the cos(delta) term may
integrate to zero over small angles, the presence of the diffraction
envelope, and the limitations of the small angle approximation, mean
that is almost certainly will not vanish when integrated over the
whole screen.


Yes, this is in the small angle approximation, if you go beyond that 
then the itnegral over the screen won't vanish.




So  will not vanish in general.
No, because  is the integral over all space and this is exactly 
zero. What happens is that when the small angle approximation becomes 
invalid and the integral over only the screen becomes nonzero, the 
integrals over surfaces parallel to the screen will have a values that 
differ by a phase factor that depends on the distance in the direction 
orthogonal to the screen. This then causes the integral over all space 
to vanish.



Which is what I would have
thought because the paths through the separate slits are not
independent -- each particle essentially has to see both slits (go
through both slits) in order to maintain coherence. So they cannot be
orthogonal (independent).


Coherence and orthogonality have nothing to do with each other.



In practice, to see the interference pattern you need coherent
illumination over both slits. This is easy these days with lasers, but
in older books, coherence was ensured by having a preparatory single
slit followed by suitable condenser lenses. If the slits could be
treated as independent entities, this would not have been necessary.


This has nothing to do with orthogonality of the states. What matters is 
that the interference pattern shouldn't get washed out due to each 
wavefunction of each particle near the screen having its peaks and 
fringes at different places. This can be prevented by using an 
approximate monochromatic light source and making sure that the light 
passes through a collimator. Without a collimator, the interference 
pattern due to the light from one part of the source will be shifted 
w.r.t. to the other part causing the pattern to get washed out.


Saibal

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