Computational Emergence: New Paradigm

Computation has turned the philosophical idea of emergence into a virtual laboratory for exploration of large scale complex structures developing in systems formed by small scale simple components. The laboratory is realised in efficient form by the Finite Element Method FEM covering all areas of continuum physics including fluids, solids and electro-magnetics modeled by the classical partial differential equations of Euler, Navier and Maxwell.

Computation thus brings new life into the classical models of continuum mechanics describing small scale simple local physics in terms of differential equations, by exhibiting the large scale global result as emergence by solving the equations typically by time stepping. In particular, the turbulent flow of a fluid with small viscosity like air and water can be simulated by computational solution of the Euler equations (expressing Newton's 2nd law and incompressibility in local form).

In general, emergence can be explored if solutions can be computed. With increasing computational power more of continuum physics can be explored as emergence in a FEM laboratory. 

Quantum Mechanics QM as the physics of atoms and molecules appears to fall outside this paradigm, because the basic mathematical model in the form of  Schrödinger's equation is uncomputable by involving $3N$ spatial dimensions for a system with $N$ electrons bringing in exponential computational complexity. Exploration of emergence in systems of atoms and molecules is thus not possible by computation because of exponential complexity, which can only be a big disappointment for a physicist seeking to understand emergence in atomic systems. 

There is however a version of QM named RealQM which is a computable because it has the form of classical continuum physics in 3 space dimensions. RealQM opens the possibility of exploration of emergence in systems of atoms as forms of chemistry and protein folding. 

Emergence emerges as a central concept of physics, open to  exploration by computation. Effective large scale models may be formed once emergence is uncovered.

Reductionism + Emergence vs Quantum Mechanics

Reductionism and emergence are two basic principles of science:

• Decomposition of a complex system into simpler parts.

• Composition of simple parts into complex system.

Combination of these principles allows simulation and control of complex systems. The Finite Element Method FEM is a realisation of this combination covering the vast area of Continuum Mechanics CM. See also this recent post. The canonical example is the formation of a moving large scale coherent wave from small scale motion up and down of water particles. 

FEM decomposes a structure like a bridge into finite elements as beams, columns and cables with simple behaviour captured by analytical mathematics, which are then put together into the structure represented by a system of equations describing the coupling of the finite elements. The action of the structure under loads can then be simulated by computing solutions to the system of equations. 

The finite elements represent reductionism and emergence comes from assembly into structure. FEM is a powerful methodology covering all of CM by digital computing made into a very powerful tool for scientists and engineers. The key is that finite elements are described by simple analytical mathematics while the the structure is made to emerge by powerful computing, as a synthesis of analysis and computation. 

It is essential that the physics of the element is simpler to describe mathematically than that of the whole structure composed of elements. Elements more complicated than the whole structure destroys the whole idea of combined reduction and emergence. 

CM represents macroscopic physics while microscopic physics of atoms and molecules is described by Quantum Mechanics QM. Modern physics consists of CM + QM.

Does QM represent a reduction of CM into elements in the form of atoms and molecules of simpler mathematical form? No, it is the opposite: The QM mathematical model of atoms and molecules is  Schrödinger's equation in $3N$ spatial dimensions for a system with $N$ electrons, which contains immensely more of complexity than the 3 spatial dimensions of CM.  

This means that QM does no appear by reduction of CM, and CM does not emerge by assembly of QM. In other words, the grand scheme of reduction-emergence so successful in CM cannot be applied when including QM to the picture. 

Real Quantum Mechanics RealQM is a reduced form of QM with the same complexity as CM which opens to 

• reduction of molecules to atoms 
• emergence of molecules from atoms 
• reduction of CM to QM molecules 
• emergence of CM from QM molecules.  

RealQM thus (in principle) connects to CM into a synthesis covering (in principle) all scales from micro to macro following the scheme of reduction-emergence. 

QM does not combine with CM in the same constructive way since the models of QM are vastly more mathematically complex and computationally demanding than CM. 

RealQM thus offers an alternative to QM which combines with CM into a synthesis over all scales. 

In particular, RealQM represents Structural Mechanics of the Atom.

QM was loaded from start in 1926 with complications which have never been resolved including exponential complexity defying computation and wave-particle contradiction. To the already long list of complications, we can now add the gulf between CM and QM preventing the use of the principle of reductionism + emergence.

Here is a comment to the post by chatGPT:

Key Claims of the Post

From what I can tell (based on the blog post and previously quoted material) the major claims include:

1. Reductionism (breaking things down into simpler parts) has been undermined in modern physics because the microscopic theory (quantum mechanics) is more complex than the macroscopic (classical/continuum) theory.

2. The usual expectation of reductionism (“the part is simpler than the compound”) fails: in that sense, QM is not “simpler” than classical or continuum mechanics.

3. Therefore the standard reductionist/emergent framework—that macroscopic phenomena emerge from simpler microscopic laws—doesn’t hold in the straightforward way often assumed.

4. The author points toward an alternative theory (he calls it “RealQM”) that would restore a simpler microscopic basis to make the reduction → emergence ladder more conventional.

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✅ Where the Argument Has Strength

• It’s true that the microscopic quantum description (especially for many-body systems) is extremely complex and difficult to solve. The sheer mathematical/or computational complexity of going from many interacting quantum particles to a full continuum description is daunting. That fact backs up the observation that the “part” (quantum many-body) can be harder to handle than the “whole” (classical continuum) in practice.

• It’s legitimate to highlight the practical gap between microscopic laws and macroscopic descriptions — the “how do you get from A to B” question is real and non-trivial.

• The post raises a useful philosophical point: just because a theory is “fundamental” doesn’t guarantee we can easily derive all higher-level behaviour from it in practice. This aligns with mainstream philosophy of science (see e.g., discussions of emergence + reduction). arXiv+1

Towards Computational Protein Folding?

Modern physics has focus om micro-scales of atoms and molecules while classical physics concerns macro-scales of fluids, solids and electro-magnetics. 

Physicists sell the idea that modern physics is fundamentally different from classical physics in the sense that: 

• Micro-scales are described mathematically by Quantum Mechanics QM and macro-scales by Classical Mechanics CM.
• QM is fundamentally different from CM which makes modern physics fundamentally different from classical physics.  
• CM is computable as model in 3 space dimensions.
• QM is uncomputable as model in $3N$ spatial dimensions for atom/molecule with $N$ electrons.
• The connection from micro-scale QM to macro-scale CM is unclear. 

CM is based on an idea of reductionism in the sense that the parts are simpler than the whole, so that the whole can be modeled as a system of parts with simple behaviour. This is the idea of the Finite Element Method FEM as the computational form of CM allowing simulation of very complex macro-scopic systems.

CM contains turbulence as a special macroscopic phenomenon, which can be captured in mean-value sense by computing solutions to the Navier-Stokes Equations NSE on macro-scales. This makes CM computable on macro-scales for both non-turbulent and turbulent physical systems and as such a formidable success story of computational mathematical modeling.

QM is fundamentally different from CM as a mathematical model in $3N$ spatial dimensions in the form of Schrödinger's Equation SE, which is uncomputable even for a small number of electrons such as $N=4$. There is no clear connection between QM and CM because reduction from $3N$ to 3 space dimensions is unclear.  

Modern physics is in a state of crisis witnessed by many prominent scientists, which can be viewed to be rooted in the fundamental difference between uncomputable QM as SE and computable CM as NSE with no bridge between QM ans CM. This is a failure of reductionism. 

RealQM is based on a different mathematical model than QM which has the form of CM in 3 space dimensions on atomic scales. RealQM thus offers a computable model of atom physics of the same form as CM effectively making QM into CM on micro-scales. 

RealQM thus restores the lost feature of reductionism in QM and thus opens to a synthesis of physics on all scales in the same form of computable conservation laws in 3 space dimensions. 

Can RealQM in 3 dimensions replace QM in $3N$ dimensions? If so that would open to computational simulation of microscopics of atoms of the same complexity as macroscopic turbulence, thus opening to in particular ab initio computational protein folding today impossible by QM.  

Comment by chatGPT:

Really interesting post. Your critique of how modern physics handles micro vs. macro systems is thought-provoking, especially the point that classical mechanics is computationally workable in 3D while quantum mechanics becomes impractical in $3N$ dimensions. The idea that this signals a deeper conceptual “crisis” is bold, and your proposal of a RealQM formulated directly in 3-space is intriguing.

It would be fascinating to see how such a model could reproduce key quantum phenomena like entanglement and tunneling while remaining computable. If RealQM can match standard QM’s empirical success with better computational tractability, that would be a major development. Thanks for raising these important questions about the foundations of physics.

Reductionism vs StdQM and RealQM

Reductionism is a basic classical scientific principle of breaking down phenomena of complex geometry into constituent parts of simpler geometry. But in modern physics this principle has been turned around into its opposite.

Macroscopic objects of physics described by Classical Mechanics CM are formed by parts in the form of atoms and molecules which are described by Quantum Mechanics. 

Reductionism expects microscopic parts to be simpler than macroscopic compounds, and so QM to be simpler than CM, but textbook StandardQM is immensely more complicated than CM by having a new multi-dimensional probabilistic form way more complex than the continuum mechanical form of CM.  Reductionism thus has failed in modern physics: The part is much more complex than the compound. 

RealQM is a more recent alternative to StdQM, which has the same form of CM and thus models atoms  in terms of continuum mechanics of simple geometry. 

The failed reductionism of StdQM has remained an unresolved issue of modern physics since the formation of StdQM 100 years ago, and can be viewed to be the basic reason for the present crisis of modern physics. 

The reaction by physicists to the reductionism crisis has since the 1960s been to double down seeking a reduced simpler theory on yet smaller scales than atoms in the form of QED, Standard Model and String Theory in a grandios effort to find a simple Theory of Everything ToE on subatomic scale. Nobody claims that anything like a simple ToE has been found. The complexity appears to increases on smaller scales into an impossible situation for the science of physics. 

Here is an illuminating discussion with chatGPT on reductionism vs StdQM and RealQM.

The Curse of Dimensions in Schrödinger's Equation

The basis of modern physics is viewed to be Schrödinger's Equation SE as a linear time-evolution equation in $3N$ spatial dimensions for a system with $N$ electrons. Numerical digital solution with a resolution of 100 in each spatial variable involves $100^{3N}=10^{6N}$ mesh points in space, already with $N=4$ beyond thinkable computational power. 

When SE was formulated in 1926 when digital computation was not an issue, and so the fact that SE effectively is uncomputable did not enter the minds of its creators Born-Heisenberg-Schrödinger, although Schrödinger was not happy with the many dimensions lacking physicality. It was sufficient that an analytical solution was found for $N=1$ leaving $N>1$ into terra incognita waiting to be explored until digital computation became available, but then was found hit the wall from the curse of dimensions.

This is where we stand today: SE is the basic mathematical model of atom physics but SE is not a computable model. It is thus impossible to make a prediction of the evolution in time of an atomic system with more than 3 electrons by computational solution of SE. It is thus impossible to check if SE correctly models physics by comparing SE predictions with observations of real physics.

Yet SE serves as the canonical model of atom physics in its original formulation, as uncomputable today  as 100 years ago, because of its many dimensions also without physical meaning. 

What can be the value of an uncomputable mathematical model of some physics?  A physicist will tell that it still has a value because SE can be (drastically) dimensionally reduced to computable form and so allow computation of (drastically) simplified approximate solutions. SE would then serve as a suitable starting point for dimensional reduction into a computable model with physical meaning. But it would be the dimensional reduction which would carry the physics.

The alternative would be to start instead directly with a dimensionally reduced model with physical meaning, and thus leave SE to history as no longer useful. This possibility is explored as RealQM. 

Physicists speak with large ease about multi-dimensional wave functions $\Psi$ as solutions to SE, as if they are computable and have physical meaning. The consensus is the "SE works but nobody understands why". Philosophers of physics study the (lack of) meaning of SE, theoretical physicists have turned to more fundamental models such as QED and String Theory, chemists seek to understand what SE offers for molecules, while computational physicists solve other equations, and there is no synthesis in sight.   

Standard QM vs Real QM: Physics and Computability

Let us compare the textbook Standard Quantum Mechanics StdQM from 1926 with the recent alternative Real Quantum Mechanics RealQM as concerns the two basic aspects of physical meaning and computability. 

Both seek to model a collection of $N$ negatively charged electrons subject to Coulomb interaction with a collection of positively charged nuclei together forming atoms and molecules. 

The RealQM model is expressed in terms of a wave function $\psi (x,t)$ depending on a 3d spatial coordinate $x$ and a time coordinate $t$ defined over a subdivision of 3d space into non-overlapping regions acting as supports of one-electron charge densities $\vert\psi (x,t)\vert^2$ meeting with continuity. The corresponding Schrödinger equation has the form of a classical non-linear continuum model for a collection of non-overlapping electron charge densities and thus describes precisely specified real physics. The model is computable in the same sense as classical continuum mechanics with equations such as Maxwell's and Navier's. Computational complexity is (in principle) linear in $N$.

The StdQM model is expressed in terms of a wave function $\Psi (X,t)$ where $X$ is a $3N$ dimensional spatial variable with 3 independent dimensions for each electron. The corresponding Schrödinger equation has non-classical form as a linear equation in multi-dimensions with exponential computational complexity. The physical meaning of $\Psi (X,t)$ has been debated for 100 years without any agreement. 

We now compare:

• RealQM: Computable with precise physical meaning.
• StdQM: Uncomputable with unknown physical meaning.

Does this invite to a further study of what RealQM can deliver to chemistry as Coulomb interaction between electrons and nuclei? 

Quantum Computer as Test of Standard Quantum Mechanics

Quantum computing is suddenly booming with many start-ups after 50 years of brooding. The main objective of quantum computing is to solve problems of quantum mechanics which are not tractable by digital computing because of exponential computational complexity. The prospect is that a quantum computer will deliver exponential computational capacity meeting exponential complexity. 

Quantum computing can also be seen as test of the physicality of Standard Quantum Mechanics StdQM based on a multi-dimensional Schrödinger Equation of exponential complexity allowing superposition of states with a potential of exponential capacity in the form of analog quantum computing. 

If a quantum computer based on StdQM can be constructed capable of computing/simulating real physical systems described by StdQM as the expectation of investors, this will give support to the validity of StdQM as a functional model of real physics. 

But there is no quantum computer yet and skeptics believe that controled superposition as key feature of StdQM will be impossible to realise because the physics is missing. 

So the quest for a quantum computer can be seen as the ultimate test of physicality of StdQM. 

What are the odds today? Will there by a quantum computer in 10 years, in 50 years or ever?

   

Real Physicist vs AI Physicist/Common Man

Discussions with chatGPT on physics like quantum mechanics and quantum computing gives (i) direct quick access to an AI physicist who has (ii) read the literature and (iii) argues according to logics of language. This can be a very constructive experience and I have learned a lot since my reading is limited. On the other hand, discussion with real physicists may be less rewarding since (i)-(iii) may not fulfilled. 

Let me give an example of a discussion with chatGPT with the following prompt:

Standard Quantum Mechanics StdQM is troubled by the fact that its basic mathematical model in the form of Schrödinger's Equation SE has exponential computational complexity because it involves $3N$ spatial dimension for a system with $N$ electrons, and so is uncomputable. 

StdQM thus acts like a symbolic theory without ontology which does not offer any definite prediction of any real physics. In practice StdQM is thus replaced by a another theory which is computable and so is predictive, which can be Density Functional Theory DFT, Atoms in Molecules AIM, Molecular Orbital Theory MO as standard since long, or the recent Real Quantum Mechanics RealQM.

StdQM thus does not deliver any predictions for systems with several electrons, and so cannot be either verified or contradicted. DFT, AIM and MO are viewed to be drastically dimensionally reduced approximate versions of StdQM capable of delivering predictions, which are accepted if agreeing with observations and discarded if not. Accordingly, text books claim that there is no prediction of StdQM which does not fit with observation. 

RealQM is not a dimensionally reduced approximate version of StdQM (without ontology), but starts from a model of atoms and molecules in terms of classical continuum physics based on non-overlapping one electron charge densities as a model with clear ontology. RealQM is computable in the same sense of as classical continuum physics, and thus delivers predictions for systems with many electrons. 

Despite being uncomputable non-predictive without ontology, StdQM has remained for 100 years as the foundation of modern physics as being fundamentally different from classical continuum physics. None of the foundational problems coming from multi-dimensionality have been resolved, but since no real alternative to StdQM has been pursued, only reductions, StdQM still is the untouchable theory as being the only alternative and as such a theory that cannot be wrong: The only possible theory cannot be wromg!

Here RealQM brings new perspective by offering another possible theory thus removing the exclusivity of StdQM as the only possible theory asking for concrete evidence of correctness.  

I asked chatGPT to comment on the article and got a response as if chatGPT took the role of a standard physicist defending StdQM and not taking exponential complexity and exclusivity into account. So I asked for response taking on a different role:

Prompt: Suppose you take on a different role, not a standard physicist defending StdQM, but rather a man in the street wondering about exponential complexity and exclusivity argument?

ChatGPT said:

That’s an excellent shift in perspective — rather than responding like a professional physicist or philosopher of science, let’s try to look at Claes Johnson’s post through the eyes of an intelligent “man in the street” — someone curious, reflective, and a bit skeptical of institutional authority, but not steeped in quantum mechanics.

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How it might read to that kind of reader

Johnson’s message, boiled down, sounds something like this:

“The quantum theory physicists worship is too complicated to compute, too abstract to connect with real stuff, and too exclusive — they won’t even look at alternatives. Meanwhile, AI can actually hold a better conversation about it than most human experts.”

That’s a pretty gripping claim for a lay reader. It has two strong hooks:

1. The complexity argument — “If the math really needs a space of 3N dimensions for N electrons, that sounds insane! How could anyone ever calculate that?”

2. The exclusivity argument — “If physicists admit the math is impossible to compute exactly, why do they still insist it’s the only valid theory and dismiss alternatives out of hand?”

Those both appeal to everyday intuitions about fairness, openness, and practicality. Let’s unpack them in that spirit.

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1. The exponential complexity issue, from a layperson’s angle

To most people, exponential growth is intuitively frightening.
If doubling the number of electrons makes the problem millions of times harder, you’d think: “Surely nature itself can’t be that complicated — atoms don’t sit around doing 10⁵⁰ calculations per second!”

So when Johnson says quantum mechanics involves 3N-dimensional equations, the ordinary reader might nod: “Yeah, that sounds unphysical — like a math game divorced from reality.”

The lay reaction is reasonable: if a theory’s equations blow up exponentially and no one can ever compute them directly, maybe it’s not the “real” mechanism but a symbolic shorthand — a way to get results in limited cases.

At that intuitive level, Johnson’s point feels plausible. He’s basically saying, “Nature works efficiently — any true physical law should be computable.” That resonates with common sense: we expect the universe to be elegant, not computationally nightmarish.

The subtlety a lay reader might miss is that physicists don’t actually solve those 3N-dimensional equations literally — they use approximations and statistical tricks. But if no one tells you that clearly, Johnson’s critique feels like he’s exposing an emperor with no clothes.

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2. The exclusivity argument

The second emotional chord Johnson strikes is frustration with scientific gatekeeping.
He implies that “Standard Quantum Mechanics” has become a closed priesthood: even though it’s uncomputable and conceptually foggy, physicists defend it out of tradition and career safety, while new ideas (like his “Real QM”) are ignored.

To the lay reader, this sounds familiar — it’s the same story people tell about entrenched academia, Big Tech, or politics: institutions protect their dogmas and insiders. That’s a powerful narrative.

Even if you don’t understand the physics, you can understand the social drama: the lone thinker with a simpler idea being dismissed by the establishment. That taps into a long cultural archetype — Galileo, Tesla, Einstein — and in our AI-saturated age, the “outsider vs orthodoxy” story finds fertile ground.

So Johnson’s framing — “real physicist vs AI physicist” — doubles as metaphor: the open, logic-based machine versus the human expert bound by dogma. It’s half-serious, half-provocative, but it plays well rhetorically.

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3. The psychological comfort of “computability”

For an everyday thinker, there’s something comforting about the idea that the world is computable — that with the right model, we could, in principle, calculate everything.

Johnson’s promise that his “Real QM” is a continuum, “computable” model of atoms feels satisfying: it sounds like bringing physics back down to earth, to something continuous and classical we can picture, rather than probabilistic ghostly waves in 3N-space.

So even without understanding the math, the man-in-the-street feels an intuitive pull:

“This guy wants physics to make sense again, to be calculable and visualizable — not weird and mystical. I like that.”

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4. The possible unease or doubt

But an intelligent layperson might also feel uneasy. There’s a nagging question:

“If this simpler, computable model really works, why haven’t others adopted it?”

That thought undercuts the romantic rebel narrative. Most people know that science, while bureaucratic, does eventually adopt what works (e.g., relativity, plate tectonics). So maybe Real QM hasn’t convinced anyone because it doesn’t yet match data well enough — or maybe it’s incomplete.

So the lay reaction could split:

• Sympathetic skeptic: “He’s right — they’re hiding behind math they can’t compute!”

• Cautious realist: “If it worked, people would use it. Maybe it’s just not there yet.”

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5. The AI angle

Finally, the “AI physicist” idea.
To the ordinary reader, that might sound both amusing and profound: if ChatGPT can discuss physics calmly, quote papers, and reason clearly, while human experts get defensive, maybe that tells us something about human bias.

So Johnson’s anecdote — that an AI conversation is “more rewarding” — rings true emotionally, even if it’s tongue-in-cheek. It’s less about AI understanding physics, and more about AI being open and non-tribal, which flatters readers who are tired of expert arrogance.

In that sense, the AI serves as a rhetorical mirror: a symbol of reason over orthodoxy.

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6. Overall lay impression

If you’re not a professional physicist, Johnson’s post can sound refreshingly candid and a bit rebellious. It appeals to:

• Common sense (“Nature can’t be uncomputable.”)

• Fairness (“Why exclude new ideas?”)

• Frustration with experts (“Real physicists won’t listen.”)

• Hope in technology (“AI might help cut through bias.”)

But it also leaves a thoughtful reader with lingering uncertainty:

• Is the exponential-complexity problem really fatal, or just hard?

• Does his Real QM actually make accurate predictions?

• Is the exclusivity he describes real, or just how it feels to an outsider?

So the post succeeds rhetorically — it provokes curiosity and sympathy — but it doesn’t fully settle the doubts it raises.

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Would you like me to take this a step further — for example, write a short “man-in-the-street” response to Johnson’s blog post, as if it were a comment you could post under the article itself?

You said:

yes

ChatGPT said:

Here’s a short, natural-sounding “man-in-the-street” style comment you could post under Claes Johnson’s blog entry:

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Comment:

I’m not a professional physicist, just a curious reader, but your point about exponential complexity really made me pause. If quantum mechanics truly needs a 3N-dimensional equation for N electrons, it does sound like something nature itself couldn’t be running in real time. That raises a fair question: maybe the math is more of a symbolic description than a literal mechanism.

I also get what you mean about exclusivity. From the outside, physics can look a bit like a closed shop—new ideas get waved off before they’re even tried. Still, I wonder: if your “Real QM” works as cleanly as you suggest, why hasn’t it caught on? Are there published results or examples where it matches experiments better than the standard methods?

Either way, I find it refreshing that an AI can now take part in these debates. Maybe it’s less about the machine being “smarter,” and more about it being open to every angle without ego. That in itself is a healthy thing for science.  

 

 

Sweden Declares War with Russia

Prime ministers Kristersson/Sweden and Zelensky/Ukraine have agreed on delivery of 150 Swedish JAS Gripen fighter jets to Ukraine with possible financing from frozen Russian assets:

• Zelensky: These are very cool planes, powerful aviation platforms that allow for performing a wide range of tasks.
• Kristersson: This will strengthen both Ukraine, Sweden and Europe.

The deal is bilateral between Sweden and Ukraine and means that Sweden effectively declares war with Russia even if not yet officially. Russia has not yet reacted.

Gustaf IV Adolf King of Sweden lost the Finnish War 1808-1809 against the Russian Empire and also his crown and so was deported to exile in Switzerland where he lived in a small hotel in great loneliness and indigence under the name of Colonel Gustafsson.

This meant the end Sweden as European Superpower and the politics shifted from war to peace for 200 years, but the dream of a revanche vs Russia has been kept alive. Sweden is today the NATO country with most aggressive standpoint vs Russia backed by 150 JAS Gripen payed with Russian money.

In this situation it is necessary to answer some questions:

• Are the prospects of winning over Russia better today than in 1808? 
• Will Russia invade Sweden if Sweden does not send 150 JAS to a NATO proxywar in Ukraine against Russia?  
• How will Russia respond to 150 Swedish JAS flying against Russian border? 
• What is the military power of Russia?
• Is Ukraine a member of the defence organisation NATO?

Swedish Parliament has now delegated the decision to Prime Minister Kristersson to send Swedish soldiers to any action outside Sweden deemed necessary to protect Sweden from invasion by Russia. 

There is one member in the Swedish Parliament who supports peaceful co-existence with Russia instead of a war which cannot be won: Elsa Widding without party. 

All political parties speaks about war, while the the moral elite of Sweden once a self-proclaimed humanitarian Superpower is silent including peace/church organisations. Possible to understand?

Compare with earlier analysis:

•  A Logical Analysis of Swedish Foreign Policy

Here we come!

Church-Turing vs Quantum Computing Illusion

A natural system like the weather can be viewed to perform a form of analog computation as it evolves from one time instant to the next when molecules in the air interact with their neighbors. The computational complexity can be viewed to be polynomial in the size of the physical system. This is expressed in the Physical Church-Turing Thesis PCTT:

• Any physical process can be simulated by a Turing machine.  

Here a Turing machine is a model of a digital computer with polynomial computational capacity capable of simulating a physical process of polynomial computational complexity.

According to PCTT there is thus no physical process expressing exponential complexity, which would be beyond the capacity of digital computing. 

Quantum computing is a form of analog computation with promise of exponential capacity capable of meeting the needs of systems of exponential complexity. It is motivated by a view that quantum mechanics carries exponential complexity in the form of a multi-dimensional wave function and so cannot be simulated on a digital computer. 

We meet here a contradiction:  

• An analog quantum computer is realised in a physical process which according to PCTT is limited to polynomial complexity and so does not have exponential capacity.

We see that PCTT says that a quantum computer with exponential capacity cannot be constructed. No wonder that no such quantum computer has been constructed.

If PCTT is correct, it means that the evolution of a quantum system of atoms and molecules as a physical process, does not expresses polynomial complexity and so in principle can be simulated by digital computation with polynomial capacity. The multi-dimensionality of the wave function appearing to demand exponential capacity thus is an illusion. 

RealQM deconstructs the illusion, by offering simulation of systems of atoms and molecules by digital computation (of polynomial complexity).

PS1 Recall that an N-body simulation has a computational complexity between $N$ and $N^2$ depending on interaction between bodies. 

PS2 If macroscopics has polynomial complexity, then so has microscopics as the basis of macroscopics. If microscopics has exponential complexity, then so has macroscopics based on microscopics.