The semantics of quantum mechanics, Copenhagen style

[Philip Thrift]

ref (article by Jim Baggott): 

      https://medium.com/@MassimoPigliucci/the-copenhagen-confusion-611f31cc27e1

https://twitter.com/philipcball/status/1268950876405850112

Jim Baggott Retweeted

Philip Ball @philipcball

·

"The “collapse of the wavefunction” was never part of the Copenhagen interpretation because the wavefunction isn’t interpreted realistically." I have been trying to get this point across for ages; I really hope Jim has more success.

Quote Tweet

Jim Baggott @JimBaggott

 

No, the Copenhagen interpretation does not entail the collapse of the wavefunction. 

@philipthrift

[Bruno Marchal]

Then, if I look at a spin in the 1/sqrt(2) (up + down), with a {up, down} measuring device, I am myself in a superposition state, if the wave does not collapse. 

Non collapse entails many world, or better many dreams. In that case there is no collapse, but also no waves needed, as it has to be explained by 2+2=4 & Co.

Bruno

@philipthrift

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[Philip Thrift]

On Saturday, June 6, 2020 at 6:10:46 AM UTC-5, Bruno Marchal wrote:

On 5 Jun 2020, at 23:36, Philip Thrift <cloud...@gmail.com> wrote:

ref (article by Jim Baggott): 

      https://medium.com/@MassimoPigliucci/the-copenhagen-confusion-611f31cc27e1

https://twitter.com/philipcball/status/1268950876405850112

Jim Baggott Retweeted

Philip Ball @philipcball

·

"The “collapse of the wavefunction” was never part of the Copenhagen interpretation because the wavefunction isn’t interpreted realistically." I have been trying to get this point across for ages; I really hope Jim has more success.

Quote Tweet

Jim Baggott @JimBaggott

 

No, the Copenhagen interpretation does not entail the collapse of the wavefunction. 

Then, if I look at a spin in the 1/sqrt(2) (up + down), with a {up, down} measuring device, I am myself in a superposition state, if the wave does not collapse. 

Non collapse entails many world, or better many dreams. In that case there is no collapse, but also no waves needed, as it has to be explained by 2+2=4 & Co.

Bruno

The best comment by a physicists (Associate Professor, Monash University) in the discussion thread:

The wavefunction is not a physical thing - so whether it collapses is irrelevant.

At least one physicist not  brainwashed into the current religion.

@hilipthrift

[Alan Grayson]

The WF transitions from a superposition of states, to an eigenstate of the eigenvalue measured. So it does seem to collapse whether it's "real" or not. AG

[John Clark]

On Sat, Jun 6, 2020 at 8:13 AM Philip Thrift <cloud...@gmail.com> wrote:

> The wavefunction is not a physical thing - so whether it collapses is irrelevant.

If the wavefunction is not a physical thing then it's just a useful calculating device. OK fine, but there are times, such as when an observation is made, when this calculating device stops producing useful data. Why? Call it collapse or call it anything you want, how do we know when we should stop paying attention to the calculating device called a "wavefunction"? And most important of all, what exactly is a "measurement"?

John K Clark

[Lawrence Crowell]

In some ways this is a no-brainer. The Copenhagen interpretation is ψ-epistemic which means there is fundamentally no wave function. The occurrence of eigenstates or their eigenvalues under certain operators in a measurement is then something that really has no collapse because the wave function has no existential content.

LC

[Brent Meeker]

Baggott and also Hosenfelder seem to be endorsing an epistemic interpretation like QBism, but they don't directly discuss the problems with it.

Brent

[scerir]

Il 6 giugno 2020 alle 14.13 Philip Thrift <cloud...@gmail.com> ha scritto:

The best comment by a physicists (Associate Professor, Monash University) in the discussion thread:

The wavefunction is not a physical thing - so whether it collapses is irrelevant.

At least one physicist not  brainwashed into the current religion.

@hilipthrift

----------

I personally like to regard a probability wave, even in 3N-dimensional space, as a real thing, certainly as more than a tool for mathematical calculations … Quite generally, how could we rely on probability predictions if by this notion we do not refer to something real and objective? [It is not me, it is Max Born]

 

[Philip Thrift]

As for Hossenfelder's fav quantum mechanics semantics, she has stated many times on her blog, it's superdeterminism.

https://arxiv.org/abs/1912.06462

"A superdeterministic theory is one which violates the assumption of Statistical Independence (that distributions of hidden variables are independent of measurement settings). Intuition suggests that Statistical Independence is an essential ingredient of any theory of science (never mind physics), and for this reason Superdeterminism is typically discarded swiftly in any discussion of quantum foundations. The purpose of this paper is to explain why the existing objections to Superdeterminism are based on experience with classical physics and linear systems, but that this experience misleads us. Superdeterminism is a promising approach not only to solve the measurement problem, but also to understand the apparent nonlocality of quantum physics. Most importantly, we will discuss how it may be possible to test this hypothesis in an (almost) model independent way."

@philipthrift

[Alan Grayson]

Can you list some of these problems? AG 

[Brent Meeker]

It makes the wave-function a description of personal knowledge of the system according to the PBR theorem https://arxiv.org/abs/1111.3328

Brent

[Philip Thrift]

As I pointed out, this is not the view Hossenfelder endorses at all, and I never saw Baggott endorse it.

He does like this quote though:

Thirty-one years ago, Dick Feynman told me about his 'sum over histories' version of quantum mechanics. "The electron does anything it likes," he said. "It just goes in any direction at any speed, forward or backward in time, however it likes, and then you add up the amplitudes and it gives you the wavefunction." I said to him, "You're crazy." But he isn't. 

Freeman Dyson (1980)

@philipthrift

 

[Bruno Marchal]

Physical ”thing” is an oxymoron, when we take Mechanism seriously. 

But collapsing or not remains relevant, to make sense of the behaviour of single particle, or more generally to get some meaning of the relative probabilities, experimentally, or in arithmetic.

Bruno

At least one physicist not  brainwashed into the current religion.

@hilipthrift

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[Bruno Marchal]

Making things epistemic is the right move (provably so with mechanism), but it does not change the “many”, except that it go from many universes (which might be rather heavy to conceive) to many subjective experiences, which is already the case in arithmetic, and is rather natural among thinking beings.

The problem is that those who make the wave physically unreal”, is that they continue to think in terms of "real particles”, but that is logically incompatible with Mechanism. They go in the right direction but not far enough with respect to the mechanist constrains.

Bruno

Brent

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[Philip Thrift]

On Sunday, June 7, 2020 at 5:16:33 AM UTC-5, Bruno Marchal wrote:

But collapsing or not remains relevant, to make sense of the behaviour of single particle, or more generally to get some meaning of the relative probabilities, experimentally, or in arithmetic.

Bruno

 

There are so many "mechanisms" so many people have come up with over many decades now to "interpret" these "relative probabilities" that have been experimentally recored.

Sean Carroll has his "many worlds"

or (another "possibility"):

The offer wave going out in all directions and the many confirmation waves returning are a sort of subset of the infinite number of virtual photons traveling all possible paths between emitters and absorbers in Feynman's "sum-over-paths" path-integral formulation of quantum mechanics. Kastner proposes to regard the outgoing offer wave and many incoming confirmation waves as "possible" transactions, only one of which indeterministically becomes "actual."

Kastner is a possibilist who argues that OWs and CWs are possibilities that are "real." She says that they are less real than actual empirically measurable events, but more real than an idea or concept in a person's mind. She suggests the alternate term "potentia," Aristotle's that she found Heisenberg had cited. For Kastner, the possibilities are physically real as compared to merely conceptually possible ideas that are consistent with physical law (for example, David Lewis' "possible worlds." But she says the "possibilities" described by offer and confirmation waves are "sub-empirical" and pre-spatiotemporal (i.e., they have not shown up as actual in spacetime). She calls these "incipient transactions."

...

https://www.informationphilosopher.com/solutions/scientists/kastner/

@philipthrift

[Lawrence Crowell]

Superdeterminism is just a form of hidden variable theory. This invariant set theory of Palmer and Hossenfelder as a means of connecting nonlinearity with QM is interesting. The approach with Cantor sets connects with incomputability. I prefer a more standard definition of incomputability than what P&H appeal to. This works invariant set theory does imply a violation of statistical independence, but it does so as a hidden variable.

The complement of a fractal set is undecidable. A fractal set is recursively enumerable, which means we can compute it in a finite automata up to some point, and “in principle” a Turing machine that runs eternally could compute the whole thing. The complement of this is not computable. The complement of a recursive set is recursive, but the complement of a recursively enumerable set is not recursively enumerable and is incomputable. The invariant set in this superdeterminism is a form of Cantor set or related to a fractal. The results of Matiyasevich  showed that p-adic sets have no global solution method, where p-adic sets are equivalent to Diophantine equations. This means that dynamical maps from one point to another on the Cantor set are not given by the same quotient group and in general there is no single decidable system for such maps. In effect this means it is not observable.

So, while superdeterminism violates statistical independence this is all a nonlocal hidden variable and thus unobservable. In ways this is where I depart from Hossenfelder and Palmer, where Palmer uses a different concept of incomputability, based on the idea of Smale et al on the need to compute a fractal an infinite amount. I appeal to the complement of a fractal, a fractal being a recursively enumerable set and computable in a standard sense, but where the complement is not computable. The fractal emerges from QM in a singular perturbation series and the complement comes with the dual of a convex set with measure L^p is L^q with 1/p + 1/q = 1. 

LC

[John Clark]

On Sat, Jun 6, 2020 at 6:25 PM Philip Thrift <cloud...@gmail.com> wrote:

 > Superdeterminism is typically discarded swiftly in any discussion of quantum foundations.

Yes, and Superdeterminism is swiftly discarded for a very good reason. Occam's razor says the best physics theory that explains the facts is the one that's simplest, but that doesn't just mean the one that has the simplest laws but also has the simplest initial conditions. The initial conditions needed for Superdeterminism to work are as far from being simple as it is possible to get; out of the infinite number of ways the universe could have started out in only one of them is set up in exactly the right way such that things are really deterministic but fool us into thinking they are not even after 13.8 billion years of cosmic evolution.

Theosts answer the question "why does the universe exist?" by saying "because God created it", and I have a problem with that because it immediately suggests another obvious question that they have no answer for, "why does God exist?". I have pretty much the same problem with Superdeterminism; why did the universe start out in the only initial condition in which even after churning for 13.8 billion years it is still able to make fools of us? Superdeterministic theory is about as useful for increasing our understanding as saying things are the way they are now because things are the way they are now.

John K Clark

[Philip Thrift]

Statistical non-independence is less restrictive than statistical  independence 

       - or better -

Stochastic non-independence is less restrictive than stochastic independence

and is simpler

as argued in Huw Price's book Time's Arrow and Archimedes' Point.

@philipthrift

[John Clark]

On Sun, Jun 7, 2020 at 10:01 AM Philip Thrift <cloud...@gmail.com> wrote:

>> Yes, and Superdeterminism is swiftly discarded for a very good reason. Occam's razor says the best physics theory that explains the facts is the one that's simplest, but that doesn't just mean the one that has the simplest laws but also has the simplest initial conditions. The initial conditions needed for Superdeterminism to work are as far from being simple as it is possible to get; out of the infinite number of ways the universe could have started out in only one of them is set up in exactly the right way such that things are really deterministic but fool us into thinking they are not even after 13.8 billion years of cosmic evolution. Theosts answer the question "why does the universe exist?" by saying "because God created it", and I have a problem with that because it immediately suggests another obvious question that they have no answer for, "why does God exist?". I have pretty much the same problem with Superdeterminism; why did the universe start out in the only initial condition in which even after churning for 13.8 billion years it is still able to make fools of us? Superdeterministic theory is about as useful for increasing our understanding as saying things are the way they are now because things are the way they are now.

John K Clark

> Statistical non-independence is less restrictive than statistical  independence 

What are you talking about? If at the Big Bang the position or momentum of just one Quark or Gluon or Electron or Photon was out of place by even a infinitesimally small amount then today after 13.8 billion years of cosmic evolution the universe would be unable to fool us over and over and over again into thinking things were non-deterministic or non-local or non-realistic when in actuality that was not the case. That is as restrictive as a universe can be! Why is the universe putting such an immense effort into fooling us, what's the point of this HUGE cosmic conspiracy?

 John K Clark

[Lawrence Crowell]

On Sunday, June 7, 2020 at 6:56:04 AM UTC-5, John Clark wrote:

As I see it and explain above, superdeterminism is just a way of formulating nonlocal hidden variables, This means they have no causal or signalling properties that can be measured. This means if one takes a purely epistemic view of QM there is really nothing here that physically exists. 

LC 

[Philip Thrift]

As Hossenfelder commented on her paper

Rethinking Superdeterminism

S. Hossenfelder, T.N. Palmer

arXiv:1912.06462 [quant-ph]

http://backreaction.blogspot.com/2019/12/the-path-we-didnt-take.html :

"Ken Wharton and Nathan Argaman (see reference [ https://arxiv.org/abs/1906.04313 ] in our paper) don't assume that a superdeterministic theory is deterministic."

@philipthrift

[Bruno Marchal]

Kastner is a possibilist who argues that OWs and CWs are possibilities that are "real." She says that they are less real than actual empirically measurable events, but more real than an idea or concept in a person's mind. She suggests the alternate term "potentia," Aristotle's that she found Heisenberg had cited. For Kastner, the possibilities are physically real as compared to merely conceptually possible ideas that are consistent with physical law (for example, David Lewis' "possible worlds." But she says the "possibilities" described by offer and confirmation waves are "sub-empirical" and pre-spatiotemporal (i.e., they have not shown up as actual in spacetime). She calls these "incipient transactions.”

This looks like Popper's propensity. It leads to a dualism (and indeed, he wrote with Clles a book defending dualism in philosophy of mind).

It is conceptually more simple to consider an actuality as a possible seen from inside. Now, here, today are already indixicals,making sense.

That fits with the overall “everything is simpler than any thing” philosophy of this list, and is made obligatory with mechanism, except for adding ad hoc complexity or conspiracy à la Bostrom. It is definitely incompatible with Mechanism + very weak version of Occam Razor.

Bruno

...

https://www.informationphilosopher.com/solutions/scientists/kastner/

@philipthrift

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[Bruno Marchal]

On 7 Jun 2020, at 13:25, Lawrence Crowell <goldenfield...@gmail.com> wrote:

On Saturday, June 6, 2020 at 5:25:23 PM UTC-5, Philip Thrift wrote:

As for Hossenfelder's fav quantum mechanics semantics, she has stated many times on her blog, it's superdeterminism.

https://arxiv.org/abs/1912.06462

"A superdeterministic theory is one which violates the assumption of Statistical Independence (that distributions of hidden variables are independent of measurement settings). Intuition suggests that Statistical Independence is an essential ingredient of any theory of science (never mind physics), and for this reason Superdeterminism is typically discarded swiftly in any discussion of quantum foundations. The purpose of this paper is to explain why the existing objections to Superdeterminism are based on experience with classical physics and linear systems, but that this experience misleads us. Superdeterminism is a promising approach not only to solve the measurement problem, but also to understand the apparent nonlocality of quantum physics. Most importantly, we will discuss how it may be possible to test this hypothesis in an (almost) model independent way."

@philipthrift

Superdeterminism is just a form of hidden variable theory. This invariant set theory of Palmer and Hossenfelder as a means of connecting nonlinearity with QM is interesting. The approach with Cantor sets connects with incomputability.

The Mandelbrot Set (its complement) has been shown indecidable, but in a vary peculiar theory of computability, which has not so many relation with Turing. It is “computability in a ring”. 

In the Turing theory, it is an open problem if he complement of the rational-complex Mandelbrot set is undecidable. That is a conjecture in my long thesis. Penrose has come up with a similar (less precise) hypothesis.

I prefer a more standard definition of incomputability than what P&H appeal to. This works invariant set theory does imply a violation of statistical independence, but it does so as a hidden variable.

The complement of a fractal set is undecidable.

The complement of some fractal set have been shown undecidable in a theory of computability on a ring. This has been shown by Blum, Smale and Shub, if I remember well.

A fractal set is recursively enumerable, which means we can compute it in a finite automata up to some point, and “in principle” a Turing machine that runs eternally could compute the whole thing.

Yes, but it uses only the potential infinite. We get all element in the enumeration after a finite time (except that here we use computability on a ring, which is not so easy to compare with Turing computability). 

The complement of this is not computable. The complement of a recursive set is recursive, but the complement of a recursively enumerable set is not recursively enumerable and is incomputable.

You mean  “ … is not necessarily recursively enumerable”. Of course a complement of a recursively enumerable set can be recursively enumerable. That is always the case with recursive set.

The invariant set in this superdeterminism is a form of Cantor set or related to a fractal. The results of Matiyasevich  showed that p-adic sets have no global solution method, where p-adic sets are equivalent to Diophantine equations.

I would be interested in a precise statement of this, and some link to a proof. What has a p-adic set? Set of what?

Cantor sets are related to self-reference in many ways. For example through the topological semantic of G and S4Grz, but also through the “fuzzification” of Gödel or Löb theorem, like in a paper by Grim. 

This means that dynamical maps from one point to another on the Cantor set are not given by the same quotient group and in general there is no single decidable system for such maps. In effect this means it is not observable.

What is the relation between observable and decidable? If you study my papers, this is the most difficult thing to do. It is possible, and necessary, though, by the fact intensional variant of G and G*, which makes the logic of the observable/predictibvle obeying a quite different logic than G (indeed, a quantum logic).

So, while superdeterminism violates statistical independence this is all a nonlocal hidden variable and thus unobservable. In ways this is where I depart from Hossenfelder and Palmer, where Palmer uses a different concept of incomputability, based on the idea of Smale et al on the need to compute a fractal an infinite amount.

I thought you did this.

I appeal to the complement of a fractal, a fractal being a recursively enumerable set

Set of what?

and computable in a standard sense, but where the complement is not computable.

The complement of a creative set (the set-definition of a universal machine, due to Emil Post, and done before Church and Turing) is always non recursively enumerable. 

The complement of any set of all theorems of an axiomatic rich enough to prove the axiom of RA is automatically non recursively enumerable. 

Thanks to the work of Myhill, we know that a theory is Turing complete (Turing universal) iff and only the complement in N of the set of (Gödel number of) its theorem is constructively not recursively enumerable. 

A set S of numbers is constructively not recursively enumerable, or called also productive, means that for any W_i subset of S, you can find some x in S, but not in W_i.. That x serves as counter-example of the recursive enumerability of S. You can extend the extension of S in the constructive transfinite, by reiterating this trasnfinitely (on the recursive ordinals, or beyond).

A Recursively enumerable set with a productive complement is called creative, by Emil Post, and is the set theoretical definition of Turing universality, by a result of Myhill.

The fractal emerges from QM in a singular perturbation series and the complement comes with the dual of a convex set with measure L^p is L^q with 1/p + 1/q = 1. 

I fail to see what are the elements of the sets you are talking. The standard notion of computability concerns set of natural numbers (or of things encodable into finite numbers, like strings (the computer science one!), words, formula, etc.

Bruno

LC

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[Bruno Marchal]

I agree with most of this. Superdeterminism is like abandoning trying to understand. It is almost worst than “shut up and calculate”, because it is that idea transformed into a general principle. Superdeterlinism is a high price to keep on our unicity, which already makes no sense when we postulate Mechanism (which presupposes the elementary arithmetical truth (i.e 0 + 0 = 0, etc.) and entails the running of all computations (really *all* with Church’s Thesis).

To be sure, not many theologians would say that “God created the universe” is an explanation of the origin of the universe. An expert in both Theology and Astrophysics, like the bishop or priest (abbé) Lemaître insisted a lot about this.

When asked if his theory or “primordial atom” (which has become the Big Bang theory) gives a clue that the bible is correct. His answer was that to relate  the big bang with the bible is as much dishonest in theology than in physics. Things are a bit more subtle than that, even in the catholic Aristotelian theology. I have discovered this recently. That guy was rather honest, which is not so frequent in the post +500 theologies. De Chardin, which I like very much, was not that honest apparently.

Bruno

John K Clark

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[Brent Meeker]

On 6/8/2020 7:13 AM, Bruno Marchal wrote:

On 7 Jun 2020, at 12:39, Philip Thrift <cloud...@gmail.com> wrote:

On Sunday, June 7, 2020 at 5:16:33 AM UTC-5, Bruno Marchal wrote:

But collapsing or not remains relevant, to make sense of the behaviour of single particle, or more generally to get some meaning of the relative probabilities, experimentally, or in arithmetic.

Bruno

 

There are so many "mechanisms" so many people have come up with over many decades now to "interpret" these "relative probabilities" that have been experimentally recored.

Sean Carroll has his "many worlds"

or (another "possibility"):

The offer wave going out in all directions and the many confirmation waves returning are a sort of subset of the infinite number of virtual photons traveling all possible paths between emitters and absorbers in Feynman's "sum-over-paths" path-integral formulation of quantum mechanics. Kastner proposes to regard the outgoing offer wave and many incoming confirmation waves as "possible" transactions, only one of which indeterministically becomes "actual."

Kastner is a possibilist who argues that OWs and CWs are possibilities that are "real." She says that they are less real than actual empirically measurable events, but more real than an idea or concept in a person's mind. She suggests the alternate term "potentia," Aristotle's that she found Heisenberg had cited. For Kastner, the possibilities are physically real as compared to merely conceptually possible ideas that are consistent with physical law (for example, David Lewis' "possible worlds." But she says the "possibilities" described by offer and confirmation waves are "sub-empirical" and pre-spatiotemporal (i.e., they have not shown up as actual in spacetime). She calls these "incipient transactions.”

This looks like Popper's propensity. It leads to a dualism (and indeed, he wrote with Clles a book defending dualism in philosophy of mind).

I don't see that it entails dualism, even though Popper may have defended it.  Have you read the propensity theory of Paul Humphreys

https://pdfs.semanticscholar.org/57cd/976f12b84c660a78d21c3cd207530a7fd82d.pdf

or the book "Causality" by Judea Pearl, which takes similar approach to inference?

Brent

It is conceptually more simple to consider an actuality as a possible seen from inside. Now, here, today are already indixicals,making sense.

That fits with the overall “everything is simpler than any thing” philosophy of this list, and is made obligatory with mechanism, except for adding ad hoc complexity or conspiracy à la Bostrom. It is definitely incompatible with Mechanism + very weak version of Occam Razor.

Bruno

...

https://www.informationphilosopher.com/solutions/scientists/kastner/

@philipthrift

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[Lawrence Crowell]

On Monday, June 8, 2020 at 9:39:30 AM UTC-5, Bruno Marchal wrote:

On 7 Jun 2020, at 13:25, Lawrence Crowell <goldenfield...@gmail.com> wrote:

On Saturday, June 6, 2020 at 5:25:23 PM UTC-5, Philip Thrift wrote:

As for Hossenfelder's fav quantum mechanics semantics, she has stated many times on her blog, it's superdeterminism.

https://arxiv.org/abs/1912.06462

"A superdeterministic theory is one which violates the assumption of Statistical Independence (that distributions of hidden variables are independent of measurement settings). Intuition suggests that Statistical Independence is an essential ingredient of any theory of science (never mind physics), and for this reason Superdeterminism is typically discarded swiftly in any discussion of quantum foundations. The purpose of this paper is to explain why the existing objections to Superdeterminism are based on experience with classical physics and linear systems, but that this experience misleads us. Superdeterminism is a promising approach not only to solve the measurement problem, but also to understand the apparent nonlocality of quantum physics. Most importantly, we will discuss how it may be possible to test this hypothesis in an (almost) model independent way."

@philipthrift

Superdeterminism is just a form of hidden variable theory. This invariant set theory of Palmer and Hossenfelder as a means of connecting nonlinearity with QM is interesting. The approach with Cantor sets connects with incomputability.

The Mandelbrot Set (its complement) has been shown indecidable, but in a vary peculiar theory of computability, which has not so many relation with Turing. It is “computability in a ring”. 

In the Turing theory, it is an open problem if he complement of the rational-complex Mandelbrot set is undecidable. That is a conjecture in my long thesis. Penrose has come up with a similar (less precise) hypothesis.

The p-adic ring is what determines the trajectory of a point. where in the case of a Cantor set the divisor of the quotient ring is the map from one point to another. The Cantor set then has a set of orbits given by a set of p-adic rings. The result of Matiyaesivich is there is no global method for solving these or the Diophantine equations they correspond to. This is the approach that I take. With the Mandelbrot set the "black bit" has periodic orbits or maps which correspond to periods of Julius sets. The points outside are chaotic and are in a sense "beyond chaos" and are not computable.

 

I prefer a more standard definition of incomputability than what P&H appeal to. This works invariant set theory does imply a violation of statistical independence, but it does so as a hidden variable.

The complement of a fractal set is undecidable.

The complement of some fractal set have been shown undecidable in a theory of computability on a ring. This has been shown by Blum, Smale and Shub, if I remember well.

The incomputability if with the fractal set itself. The incomputability occurs because with a finite cut off you have uncertainty whether points or regions are in or outside the Mandelbrot set. In this somewhat different meaning the Mandelbrot set is considered incomputable by Blum, Smale and Shub,

 

A fractal set is recursively enumerable, which means we can compute it in a finite automata up to some point, and “in principle” a Turing machine that runs eternally could compute the whole thing.

Yes, but it uses only the potential infinite. We get all element in the enumeration after a finite time (except that here we use computability on a ring, which is not so easy to compare with Turing computability). 

The complement of this is not computable. The complement of a recursive set is recursive, but the complement of a recursively enumerable set is not recursively enumerable and is incomputable.

You mean  “ … is not necessarily recursively enumerable”. Of course a complement of a recursively enumerable set can be recursively enumerable. That is always the case with recursive set.

Yes, if the RE set is recursive.

 

The invariant set in this superdeterminism is a form of Cantor set or related to a fractal. The results of Matiyasevich  showed that p-adic sets have no global solution method, where p-adic sets are equivalent to Diophantine equations.

I would be interested in a precise statement of this, and some link to a proof. What has a p-adic set? Set of what?

Cantor sets are related to self-reference in many ways. For example through the topological semantic of G and S4Grz, but also through the “fuzzification” of Gödel or Löb theorem, like in a paper by Grim. 

A p-adic set is a quotient ring with the Z_p for p a prime. The Chinese remainder theorem guarantees that all quotient rings are equivalent to the product of quotient rings with primes that are the prime decomposition of the quotient ring. In other words for the quotient group ℤ_n = ℤ_{p1}×ℤ_{p2}× … ×ℤ_{p} for n = {p1}×{p2}× … ×{p} the prime factorization. There is a lot there and quotient rings define an elementary aspect of cohomology that leads to p-adic topology and with complex rings algebraic geometry.

 

This means that dynamical maps from one point to another on the Cantor set are not given by the same quotient group and in general there is no single decidable system for such maps. In effect this means it is not observable.

What is the relation between observable and decidable? If you study my papers, this is the most difficult thing to do. It is possible, and necessary, though, by the fact intensional variant of G and G*, which makes the logic of the observable/predictibvle obeying a quite different logic than G (indeed, a quantum logic).

That is a part of the issue, and as I have worked things, hidden variables are unobservable and incomputable. The superdeterminism 'tHooft advanced and that others have taken up is really a form of hidden variable, and is not computable.

 

So, while superdeterminism violates statistical independence this is all a nonlocal hidden variable and thus unobservable. In ways this is where I depart from Hossenfelder and Palmer, where Palmer uses a different concept of incomputability, based on the idea of Smale et al on the need to compute a fractal an infinite amount.

I thought you did this.

I worked this in a way similar to Hossenfelder and Palmer, but with out the appeal to Blum, Smale and Shub. 

 

I appeal to the complement of a fractal, a fractal being a recursively enumerable set

Set of what?

A fractal is a region of space that has a boundary with a Hausdorff dimension that is not integral. So it is a set of points or orbits under maps.

 

and computable in a standard sense, but where the complement is not computable.

The complement of a creative set (the set-definition of a universal machine, due to Emil Post, and done before Church and Turing) is always non recursively enumerable. 

The complement of any set of all theorems of an axiomatic rich enough to prove the axiom of RA is automatically non recursively enumerable. 

Thanks to the work of Myhill, we know that a theory is Turing complete (Turing universal) iff and only the complement in N of the set of (Gödel number of) its theorem is constructively not recursively enumerable. 

A set S of numbers is constructively not recursively enumerable, or called also productive, means that for any W_i subset of S, you can find some x in S, but not in W_i.. That x serves as counter-example of the recursive enumerability of S. You can extend the extension of S in the constructive transfinite, by reiterating this trasnfinitely (on the recursive ordinals, or beyond).

A Recursively enumerable set with a productive complement is called creative, by Emil Post, and is the set theoretical definition of Turing universality, by a result of Myhill.

This I am not that familiar with. I tend to prefer to stay as much as possible within more standard mathematics instead of set theory. Set theory I will appeal to somewhat, but I prefer to stay more within algebra and geometry.

 

The fractal emerges from QM in a singular perturbation series and the complement comes with the dual of a convex set with measure L^p is L^q with 1/p + 1/q = 1. 

I fail to see what are the elements of the sets you are talking. The standard notion of computability concerns set of natural numbers (or of things encodable into finite numbers, like strings (the computer science one!), words, formula, etc.

Bruno

The set of maps for any point is something computable or not. The Cantor set is not because there is not a single algorithm for solving all orbits that hop from one point to the other. This is because there is no global solution method for all p-adic quotient rings. The elements are really maps, maps that take a point here to there and then to elsewhere in an iterative manner. 

LC

 

LC

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[Bruno Marchal]

On 8 Jun 2020, at 23:47, 'Brent Meeker' via Everything List <everyth...@googlegroups.com> wrote:

On 6/8/2020 7:13 AM, Bruno Marchal wrote:

On 7 Jun 2020, at 12:39, Philip Thrift <cloud...@gmail.com> wrote:

On Sunday, June 7, 2020 at 5:16:33 AM UTC-5, Bruno Marchal wrote:

But collapsing or not remains relevant, to make sense of the behaviour of single particle, or more generally to get some meaning of the relative probabilities, experimentally, or in arithmetic.

Bruno

 

There are so many "mechanisms" so many people have come up with over many decades now to "interpret" these "relative probabilities" that have been experimentally recored.

Sean Carroll has his "many worlds"

or (another "possibility"):

The offer wave going out in all directions and the many confirmation waves returning are a sort of subset of the infinite number of virtual photons traveling all possible paths between emitters and absorbers in Feynman's "sum-over-paths" path-integral formulation of quantum mechanics. Kastner proposes to regard the outgoing offer wave and many incoming confirmation waves as "possible" transactions, only one of which indeterministically becomes "actual."

Kastner is a possibilist who argues that OWs and CWs are possibilities that are "real." She says that they are less real than actual empirically measurable events, but more real than an idea or concept in a person's mind. She suggests the alternate term "potentia," Aristotle's that she found Heisenberg had cited. For Kastner, the possibilities are physically real as compared to merely conceptually possible ideas that are consistent with physical law (for example, David Lewis' "possible worlds." But she says the "possibilities" described by offer and confirmation waves are "sub-empirical" and pre-spatiotemporal (i.e., they have not shown up as actual in spacetime). She calls these "incipient transactions.”

This looks like Popper's propensity. It leads to a dualism (and indeed, he wrote with Clles a book defending dualism in philosophy of mind).

I meant Eccles (not Clles).

I don't see that it entails dualism, even though Popper may have defended it.  Have you read the propensity theory of Paul Humphreys

https://pdfs.semanticscholar.org/57cd/976f12b84c660a78d21c3cd207530a7fd82d.pdf

I took a look at it just now. I tend to agree with him. 

As far as I understand “propensity”, I find rather normal that Bayes theorem does not apply, and that propensity is not probability. It remind me of the Shafer-Dempster theory of evidence, or Smets' Transferable Belief Model”. It might be close to the logic of []p & <>t, thanks to the lack of necessitation rules at the G* level. Now, all this seems to avoid the metaphysical issue. Popper used it to avoid the many-world, but eventually it leads to some action of consciousness on matter: a dualist interactionist theory, which makes not much sense to me.

or the book "Causality" by Judea Pearl, which takes similar approach to inference?

Ah! I read many papers by Pearl when working with Smets on its belief theory (many years ago). Eventually the modal logic where based on the deontic axiom ([]p -> <>p), which is recovered by the []p & <>t mode of self-reference. But I have not read his book on “causality”. I tend to agree with such treatment of inference, but not when this is used to hide the metaphysical problem.

Most of those approach avoid the metaphysical question. It is more artificial intelligence than philosophy of mind. 

Bruno

Brent

It is conceptually more simple to consider an actuality as a possible seen from inside. Now, here, today are already indixicals,making sense.

That fits with the overall “everything is simpler than any thing” philosophy of this list, and is made obligatory with mechanism, except for adding ad hoc complexity or conspiracy à la Bostrom. It is definitely incompatible with Mechanism + very weak version of Occam Razor.

Bruno

...

https://www.informationphilosopher.com/solutions/scientists/kastner/

@philipthrift

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[Bruno Marchal]

On 9 Jun 2020, at 02:27, Lawrence Crowell <goldenfield...@gmail.com> wrote:

On Monday, June 8, 2020 at 9:39:30 AM UTC-5, Bruno Marchal wrote:

On 7 Jun 2020, at 13:25, Lawrence Crowell <goldenfield...@gmail.com> wrote:

On Saturday, June 6, 2020 at 5:25:23 PM UTC-5, Philip Thrift wrote:

As for Hossenfelder's fav quantum mechanics semantics, she has stated many times on her blog, it's superdeterminism.

https://arxiv.org/abs/1912.06462

"A superdeterministic theory is one which violates the assumption of Statistical Independence (that distributions of hidden variables are independent of measurement settings). Intuition suggests that Statistical Independence is an essential ingredient of any theory of science (never mind physics), and for this reason Superdeterminism is typically discarded swiftly in any discussion of quantum foundations. The purpose of this paper is to explain why the existing objections to Superdeterminism are based on experience with classical physics and linear systems, but that this experience misleads us. Superdeterminism is a promising approach not only to solve the measurement problem, but also to understand the apparent nonlocality of quantum physics. Most importantly, we will discuss how it may be possible to test this hypothesis in an (almost) model independent way."

@philipthrift

Superdeterminism is just a form of hidden variable theory. This invariant set theory of Palmer and Hossenfelder as a means of connecting nonlinearity with QM is interesting. The approach with Cantor sets connects with incomputability.

The Mandelbrot Set (its complement) has been shown indecidable, but in a vary peculiar theory of computability, which has not so many relation with Turing. It is “computability in a ring”. 

In the Turing theory, it is an open problem if he complement of the rational-complex Mandelbrot set is undecidable. That is a conjecture in my long thesis. Penrose has come up with a similar (less precise) hypothesis.

The p-adic ring is what determines the trajectory of a point. where in the case of a Cantor set the divisor of the quotient ring is the map from one point to another. The Cantor set then has a set of orbits given by a set of p-adic rings.

Do you mean the triadic Cantor set? It is a set of reals. This play some role for the isolation of the measure, thanks to relation between Baire Space, Cantor triadic set. This requires ZF + Projective Determinacy (the existence of some winning strategy for some infinite game). It is not directly related to computability theory, except that we get them from the union of all sigma_set relative to all oracles. That leads to complex set theory. Here, I use only N, never R, nor bare space.

The result of Matiyaesivich is there is no global method for solving these or the Diophantine equations they correspond to. This is the approach that I take.

I would like to see a pair on this. Matiyasevic’s paper and books do not refer to p-adic structure, nor to real numbers. There is no Church’s thesis for the notion of computability with real number. Constructive reals can be represented by total computable functions (with a computable modulus so that + and * remain computable).

With the Mandelbrot set the "black bit" has periodic orbits or maps which correspond to periods of Julius sets. The points outside are chaotic and are in a sense "beyond chaos" and are not computable.

That is proved with the notion of computability on a ring, but like you, I prefer to not use such notion. I see some application in theoretical numerical analysis, but not much for computability theory in general. Then the measure problem is enforce to use all set of (usual) real numbers, except that we can make the closed set “perfect”, which helps to neglect the infinite countable set of “isolated points”, but I am not there already.

 

I prefer a more standard definition of incomputability than what P&H appeal to. This works invariant set theory does imply a violation of statistical independence, but it does so as a hidden variable.

The complement of a fractal set is undecidable.

The complement of some fractal set have been shown undecidable in a theory of computability on a ring. This has been shown by Blum, Smale and Shub, if I remember well.

The incomputability if with the fractal set itself. The incomputability occurs because with a finite cut off you have uncertainty whether points or regions are in or outside the Mandelbrot set. In this somewhat different meaning the Mandelbrot set is considered incomputable by Blum, Smale and Shub,

But only that meaning makes sense to me, and is of no use with respect to the problem I am working on. I have only numbers (natural numbers!), and a real number is (coddle by) any subset of N.

 

A fractal set is recursively enumerable, which means we can compute it in a finite automata up to some point, and “in principle” a Turing machine that runs eternally could compute the whole thing.

Yes, but it uses only the potential infinite. We get all element in the enumeration after a finite time (except that here we use computability on a ring, which is not so easy to compare with Turing computability). 

The complement of this is not computable. The complement of a recursive set is recursive, but the complement of a recursively enumerable set is not recursively enumerable and is incomputable.

You mean  “ … is not necessarily recursively enumerable”. Of course a complement of a recursively enumerable set can be recursively enumerable. That is always the case with recursive set.

Yes, if the RE set is recursive.

OK.

 

The invariant set in this superdeterminism is a form of Cantor set or related to a fractal. The results of Matiyasevich  showed that p-adic sets have no global solution method, where p-adic sets are equivalent to Diophantine equations.

I would be interested in a precise statement of this, and some link to a proof. What has a p-adic set? Set of what?

Cantor sets are related to self-reference in many ways. For example through the topological semantic of G and S4Grz, but also through the “fuzzification” of Gödel or Löb theorem, like in a paper by Grim. 

A p-adic set is a quotient ring with the Z_p for p a prime. The Chinese remainder theorem guarantees that all quotient rings are equivalent to the product of quotient rings with primes that are the prime decomposition of the quotient ring. In other words for the quotient group ℤ_n = ℤ_{p1}×ℤ_{p2}× … ×ℤ_{p} for n = {p1}×{p2}× … ×{p} the prime factorization. There is a lot there and quotient rings define an elementary aspect of cohomology that leads to p-adic topology and with complex rings algebraic geometry.

OK. I like very much the Chinese lemma, if only through its use by Gödel to code “digital machine” into numbers, without using exponentiation. But it is basically only a representation trick. What you say here seems to have some interest, but cohomology is a complex matter. Keep in mind that everything I say can be translated faithfully in the elementary arithmetic of the natural numbers, or in combinator theory. I avoid algebra, category theory, set theory, even if those comes back at some point in the phenomenology. But I did not have to use this to get the quantum phenomenology from arithmetic.

 

This means that dynamical maps from one point to another on the Cantor set are not given by the same quotient group and in general there is no single decidable system for such maps. In effect this means it is not observable.

What is the relation between observable and decidable? If you study my papers, this is the most difficult thing to do. It is possible, and necessary, though, by the fact intensional variant of G and G*, which makes the logic of the observable/predictibvle obeying a quite different logic than G (indeed, a quantum logic).

That is a part of the issue, and as I have worked things, hidden variables are unobservable and incomputable.

Here you are too much quick. Keep in mind that I have only natural numbers, and that the observable is defined by what digital machine (number) can predict about their accessible computational states. The point is that we cannot invoke an ontological universe, given that we have arithmetic (just to define what is a digital machine), and then we are confronted to the fist person indeterminacy on all computations (in arithmetic) going through our actual states. 

The superdeterminism 'tHooft advanced and that others have taken up is really a form of hidden variable, and is not computable.

 

So, while superdeterminism violates statistical independence this is all a nonlocal hidden variable and thus unobservable. In ways this is where I depart from Hossenfelder and Palmer, where Palmer uses a different concept of incomputability, based on the idea of Smale et al on the need to compute a fractal an infinite amount.

I thought you did this.

I worked this in a way similar to Hossenfelder and Palmer, but with out the appeal to Blum, Smale and Shub. 

You will need to define “computable” in the context of the real number, for which there is no CT thesis. I refer to avoid this. The real numbers exists in arithmetic only as a kind of whole.

 

I appeal to the complement of a fractal, a fractal being a recursively enumerable set

Set of what?

A fractal is a region of space that has a boundary with a Hausdorff dimension that is not integral. So it is a set of points or orbits under maps.

To solve the mind-body problem, such a notion of space can only be phenomenological. It belongs to the imagination of the natural numbers, and this has to be taken into account (and indeed that plays the main role in making the logic of the observable into a quantum logic. My approach has to be bottom up, where the bottom is elementary arithmetic. 

 

and computable in a standard sense, but where the complement is not computable.

The complement of a creative set (the set-definition of a universal machine, due to Emil Post, and done before Church and Turing) is always non recursively enumerable. 

The complement of any set of all theorems of an axiomatic rich enough to prove the axiom of RA is automatically non recursively enumerable. 

Thanks to the work of Myhill, we know that a theory is Turing complete (Turing universal) iff and only the complement in N of the set of (Gödel number of) its theorem is constructively not recursively enumerable. 

A set S of numbers is constructively not recursively enumerable, or called also productive, means that for any W_i subset of S, you can find some x in S, but not in W_i.. That x serves as counter-example of the recursive enumerability of S. You can extend the extension of S in the constructive transfinite, by reiterating this trasnfinitely (on the recursive ordinals, or beyond).

A Recursively enumerable set with a productive complement is called creative, by Emil Post, and is the set theoretical definition of Turing universality, by a result of Myhill.

This I am not that familiar with. I tend to prefer to stay as much as possible within more standard mathematics instead of set theory. Set theory I will appeal to somewhat, but I prefer to stay more within algebra and geometry.

I have no other choice (given my goal and methodology) to never go outside arithmetic. (Algebra and geometry use already to much of (naive) set theory. 

 

The fractal emerges from QM in a singular perturbation series and the complement comes with the dual of a convex set with measure L^p is L^q with 1/p + 1/q = 1. 

I fail to see what are the elements of the sets you are talking. The standard notion of computability concerns set of natural numbers (or of things encodable into finite numbers, like strings (the computer science one!), words, formula, etc.

Bruno

The set of maps for any point is something computable or not. The Cantor set is not because there is not a single algorithm for solving all orbits that hop from one point to the other. This is because there is no global solution method for all p-adic quotient rings. The elements are really maps, maps that take a point here to there and then to elsewhere in an iterative manner. 

I can understand that the complex-rational Mandelbrot set is or not computable, but once real numbers are considered, I am lost. Just lost. You need a definition of computability for real. I can imagine why you avoid Blum, Shub and Small, but I have no real clue which notion you are using. It might be interesting, we will see, or not.

Bruno 

LC

 

LC

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[Lawrence Crowell]

On Tuesday, June 9, 2020 at 5:57:38 AM UTC-5, Bruno Marchal wrote:

On 9 Jun 2020, at 02:27, Lawrence Crowell <goldenfield...@gmail.com> wrote:

On Monday, June 8, 2020 at 9:39:30 AM UTC-5, Bruno Marchal wrote:

On 7 Jun 2020, at 13:25, Lawrence Crowell <goldenfield...@gmail.com> wrote:

On Saturday, June 6, 2020 at 5:25:23 PM UTC-5, Philip Thrift wrote:

As for Hossenfelder's fav quantum mechanics semantics, she has stated many times on her blog, it's superdeterminism.

https://arxiv.org/abs/1912.06462

"A superdeterministic theory is one which violates the assumption of Statistical Independence (that distributions of hidden variables are independent of measurement settings). Intuition suggests that Statistical Independence is an essential ingredient of any theory of science (never mind physics), and for this reason Superdeterminism is typically discarded swiftly in any discussion of quantum foundations. The purpose of this paper is to explain why the existing objections to Superdeterminism are based on experience with classical physics and linear systems, but that this experience misleads us. Superdeterminism is a promising approach not only to solve the measurement problem, but also to understand the apparent nonlocality of quantum physics. Most importantly, we will discuss how it may be possible to test this hypothesis in an (almost) model independent way."

@philipthrift

Superdeterminism is just a form of hidden variable theory. This invariant set theory of Palmer and Hossenfelder as a means of connecting nonlinearity with QM is interesting. The approach with Cantor sets connects with incomputability.

The Mandelbrot Set (its complement) has been shown indecidable, but in a vary peculiar theory of computability, which has not so many relation with Turing. It is “computability in a ring”. 

In the Turing theory, it is an open problem if he complement of the rational-complex Mandelbrot set is undecidable. That is a conjecture in my long thesis. Penrose has come up with a similar (less precise) hypothesis.

The p-adic ring is what determines the trajectory of a point. where in the case of a Cantor set the divisor of the quotient ring is the map from one point to another. The Cantor set then has a set of orbits given by a set of p-adic rings.

Do you mean the triadic Cantor set? It is a set of reals. This play some role for the isolation of the measure, thanks to relation between Baire Space, Cantor triadic set. This requires ZF + Projective Determinacy (the existence of some winning strategy for some infinite game). It is not directly related to computability theory, except that we get them from the union of all sigma_set relative to all oracles. That leads to complex set theory. Here, I use only N, never R, nor bare space.

Yes it is that sort of construction.

 

The result of Matiyaesivich is there is no global method for solving these or the Diophantine equations they correspond to. This is the approach that I take.

I would like to see a pair on this. Matiyasevic’s paper and books do not refer to p-adic structure, nor to real numbers. There is no Church’s thesis for the notion of computability with real number. Constructive reals can be represented by total computable functions (with a computable modulus so that + and * remain computable).

Matiyasevich showed the Hilbert's 10 problem can't be solved. This was the existence of a global single solution system for Diophantine equations. DIophantine equation are equivalent to p-adic sets by Robinson, Davis and others. 

 

With the Mandelbrot set the "black bit" has periodic orbits or maps which correspond to periods of Julius sets. The points outside are chaotic and are in a sense "beyond chaos" and are not computable.

That is proved with the notion of computability on a ring, but like you, I prefer to not use such notion. I see some application in theoretical numerical analysis, but not much for computability theory in general. Then the measure problem is enforce to use all set of (usual) real numbers, except that we can make the closed set “perfect”, which helps to neglect the infinite countable set of “isolated points”, but I am not there already.

As a physicist I tend to have my heaviest foot on the side of Babylonian math, which is more applied and something of a tool. I have some weight on a foot on the Greek math side as well, which is the axiomatic, theorem and proof mathematics. 

As for further down, Godel's theorem works with reals. In effect Cantor diagonization shows the set of reals are not enumerable, and the people who get into set theory deeply use the concept of forcing. This takes one from integers or natural numbers to the reals, and the same concept can lead to complex numbers and so forth. Bernays and Cohen used Godel's theorem in this form to show the continuum hypothesis is consistent with ZF set theory. However, it is not provable. Don't ask me details on this because I am no expert.

LC

 

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