Physics of the Covalent Bond Still Debated!

The article The Basics of the Covalent Bond in Terms of Energy and Dynamics by Nordholm and Bacskay from 2020 opens with the following surprising revelation as Abstract:

• We address the paradoxical fact that the concept of a covalent bond, a cornerstone of chemistry which is well resolved computationally by the methods of quantum chemistry, is still the subject of debate, disagreement, and ignorance with respect to its physical origin. 
• Our aim here is to unify two seemingly different explanations: one in terms of energy, the other dynamics. 
• We summarize the mechanistic bonding models and the debate over the last 100 years, with specific applications to the simplest molecules: H2+ and H2.
• In particular, we focus on the bonding analysis of Hellmann (1933) that was brought into modern form by Ruedenberg (from 1962 on). 
• We and many others have helped verify the validity of the Hellmann–Ruedenberg proposal that a decrease in kinetic energy associated with interatomic delocalization of electron motion is the key to covalent bonding but contrary views, confusion or lack of understanding still abound. 
• In order to resolve this impasse we show that quantum mechanics affords us a complementary dynamical perspective on the bonding mechanism, which agrees with that of Hellmann and Ruedenberg, while providing a direct and unifying view of atomic reactivity, molecule formation and the basic role of the kinetic energy, as well as the important but secondary role of electrostatics, in covalent bonding.

We learn that that the most basic of all of chemistry, the covalent bond of the H2 molecule, is still under debate, disagreement and ignorance within the accepted form of quantum mechanics. What to say about that?

We compare with RealQM as a new form of quantum mechanics, which captures the physics of the covalent bond in a very clear and easily understandable parameter-free mathematical form as described in this blog post and this computer code with more chemistry in these posts. What to say about that?

Hint: The key to the direct success without any manipulation of RealQM for H2 (connecting to the decrease of kinetic energy above), is that the two electron densities are localised to two half-spaces and meet at a plane perpendicular to the axis midway between the two proton kernels with continuity and zero normal derivative, and so do not have to decay to zero requiring kinetic energy. The electron density for H2 thus is roughly the double of that for H2+ with one electron, with corresponding roughly double binding energy in agreement with observation. RealQM thus has a clear direct physical meaning, which is not the case using standard methods for computing binding energies.  See output from RealQM code:

 

Important Historical Point 1926: Schrödinger Tragedy

This is a comment to the previous post concerning the basic new problem confronting physicists in 1926 of generalising Schrödinger's equation for the Hydrogen atom with one electron, to atoms with $N>1$ electrons. Let us recall the account of this moment in the book The Stability of Matter in Quantum Mechanics by Lieb and Seiringer (2010): 

• An important historical point is to be noted here. 
• It might have been thought that the correct generalization for $N$ particles is to use 
• $N$ functions of one variable         (1) 
• instead of 
• one function of $N$ variables         (2). 
• Such a "wrong turn" did not happen historically, which is, after all, remarkable.

All the experience from the amazingly successful continuum mechanics of matter and electromagnetics in 3 space dimension (3-d) of classical physics, would point to the option (1) as $N$ one-electron (complex-valued) functions $\psi_1(x)$, $\psi_2(x)$,...$\psi_N(x)$ depending on a common 3-d variable $x$. This is the Ansatz of Real Quantum Mechanics RealQM as the "wrong turn", which was explored only recently. RealQM is a non-linear system in 3-d which is parameter-free in the same sense as Schrödinger's  equation for the Hydrogen atom. Computational cost scales polynomially with $N$.  

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But all this experience was thrown overboard in 1926 when physics history instead took a leap into the completely unknown territory of option (2), as one N-electron (complex-valued) function $\psi (x_1, x_2,...,x_N)$ depending on $N$ 3d spatial coordinates $x_1$, $x_2$,...,$x_N$, altogether $3N$ spatial variables, to form the Schrödinger equation of Quantum Mechanics here referred to as Standard QM or StdQM,  as a linear equation in 3N-d. Computational cost scales exponentially with $N$.

The natural option (1) of deterministic continuum physics as ontology as real physics, was thus discarded in favour of option (2) as a new form of physics as epistemology without physical meaning.

Remarkable, or maybe not at all remarkable because (2) was very easy as a purely formal mathematical generalisation, which could be done with a stroke of the pen. As easy as formally generalising from one spatial dimension to many dimensions in a Calculus course. To realise (1) was less obvious and so the ease of a formal mathematical generalisation as StdQM took over the whole scene into our days.

Today RealQM offers an alternative to StdQM. RealQM is a computable model as real physics, while StdQM is an uncomputable model without real physical meaning. 

Over the years reduced versions StdQM have been attempted with wave functions restricted to be sums of  products of one-electron charge densities $\psi_i(x_i)$ with global support as Hartree-Fock models.

Density Functional Theory DFT is a further reduction into a single charge density $\psi (x)$ representing the collective charge density of all electrons. Hartree-Fock and DFT have delivered results for atoms, but less so for dynamics of molecules. 

RealQM takes the form of a free boundary problem for a system of one-electron wave functions with non-overlapping supports, each satisfying a homogeneous Neumann condition on the boundary of its support, and meeting on a free boundary with continuity of charge density. RealQM can be used for complex molecules in dynamics of molecules as chemistry. Ready to give RealQM a try?

Here is what ChatGPT has to say when asked about the idea underlying RealQM.

Tragedy of Schrödinger and His Equation

ChatGPT informs (see also previous post) us that the common view of modern physicists is that the physics of quantum mechanics is weird, which can be seen as the desperation underlying the crisis of fundamental physics commonly recognised. See also previous post.

Let us seek the origin of the idea that the accepted form of fundamental physics, referred below to as Standard Quantum Mechanics stdQM, is weird and as such may not qualify as rational science. 

StdQM was born in early 1926 when Erwin Schrödinger during a happy vacation in the Alps with his girlfriend formulated a mathematical model of the Hydrogen atom consisting of a positive kernel surrounded by negative charge distribution $\psi (x)$ expressing balance between two forms of energy:

• $E_C = -\int\frac{\psi^2(x)}{\vert x\vert}dx$                  Coulomb potential energy 
• $E_K =\frac{1}{2}\int \vert\nabla\psi (x)\vert^2dx$   charge distribution energy ("kinetic energy")

where $x$ is a Euclidean space coordinate with the kernel positioned at $x=0$. Schrödinger also formulated a version of the model depending on a time coordinate, named the Schrödinger equation forming the basis quantum mechanics. The ground state of the Hydrogen atom corresponds to a minimum of the total energy $E_C+E_K$, with the charge distribution as close as possible to the kernel at a gradient cost. This model has the form of classical continuum mechanics as a model of an elastic body in a potential well, very well understood.

Schrödinger's model exactly captured the spectrum of the Hydrogen atom and so was an amazing success only comparable to Newton's law of gravitation, which propelled Schrödinger to fame. 

Schrödinger then faced the challenge to generalise to atoms with more than one electron, starting with Helium with two electrons. A formal generalisation presented itself in terms of a wave function $\psi (x,y)$ depending on two Euclidean space coordinates $x$ and $y$ thus on altogether 6 spatial dimensions, which was first rejected by Schrödinger, because such a function can only describe something beyond real physical space in 3 dimensions. In any case, the easy catch of a formal generalisation was irresistible and so the Schrödinger equation for an atom with $N>1$ electrons of stdQM was formulated as a linear equation for a wave function depending on $3N$ spatial dimensions. 

Combined with a statistical interpretation of the multi-d wave function supplied by Born, this model serves as the foundation of stdQM according to the Copenhagen Interpretation.  

But Schrödinger was not happy with his equation in this form as he recalled in  in Chapter 1 of Thee Interpretation of Quantum Mechanics (Dublin Seminars 1949-1955):

• Let me say at the outset, that in this discourse, I am opposing not a few special statements of quantum mechanics held today, I am opposing as it were the whole of it, I am opposing its basic views that have been shaped 25 years ago, when Max Born put forward his probability interpretation, which was accepted by almost everybody.
• The view I am opposing is so widely accepted, without ever being questioned, that I would have some difficulties in making you believe that I really, really consider it inadequate and wish to abandon it.

In short, Schrödinger could not survive within stdQM and so gradually drifted away into other forms of physics. From inside to outside. A tragedy. Einstein shared the same fate when questioning quantum mechanics as statistics. There are critics still alive such as Penrose but discussion can only take place outside physics departments. Physics is settled, in crisis.

Suppose we do not fall for the temptation of an easy catch in terms of a wave function for the Helium atom $\psi (x,y)$ depending on two 3-d spatial variables $x$ and $y$, and instead seek a wave function as a sum of two one-electron wave functions

• $\psi_1(x) + \psi_2(x)$ 

depending on a common 3-d variable $x$, with $\psi_1(x)$ representing the charge density of one of the electrons of Helium and $\psi_2(x)$ the other, assuming the densities do not overlap. This is a very natural Ansatz, and it would be very interesting to know if Schrödinger ever tried this. 

In any case, if you do try then you come with a different form of Schrödinger equations described as RealQM.  I am sure Schrödinger would have been very happy with this model, since it has a direct deterministic physical interpretation in terms of classical continuum mechanics and gives very good agreement with observations. 

It is possible that with RealQM instead of stdQM much of the crisis of fundamental physics from being weird, will disappear. Ready to try?

If a physical theory still after 100 years of conception, appears as being very strange and incomprehensible, then something must be wrong... 

ChatGPT: The World Itself Is Weird

After a long conversation with ChatGPT o1 about quantum mechanics, ChatGPT comes to the following conclusion by collecting the collected wisdom of all the great physicists of the 20th century:

• The reason quantum mechanics is weird is that the world itself is weird—but only from the perspective of our classical minds. At the quantum level, the universe simply operates by different rules, ones that are no less valid than those of classical physics. This weirdness is a feature of the universe’s richness and complexity, and it pushes us to continually rethink our understanding of reality. Instead of resisting the weird, we should celebrate it as part of the incredible mystery of existence!

The conclusion that quantum mechanics is weird comes from the fact that the basic mathematical model of Quantum Mechanics QM in the form of the standard linear Schrödinger equation in multidimensional configuration space stdQM, does not describe any form of possible/thinkable physical reality. 

In other words, the stdQM Model of the World is Weird. Does it follow that the World Itself is Weird? 

Only educated physicists like Feynman would be pretentious or brave enough to say: Yes! 

An ordinary intellect/mind would say without hesitation that it is not sure that the World Itself is Weird just because a Model of the World is Weird. That there is a difference between a Model of the World and the World Itself. Ok?

An ordinary intellect/mind would probably also say that the World Itself cannot be Weird, because if is, then it would not exist. Really weird things can exist only as Fantasy not in reality. Something which is both wave and particle at the same time cannot really exist. Something which is both square and circular at the same time cannot exist. 

Ok, so the World Itself cannot really be Weird. What then to do with a Model of the World which is Weird? Can a Weird Model work? Yes, it is possible if the weirdness somehow is cancelled out. 

And Yes, it is possible to get something reasonable out of the standard Schrödinger equation stdQM, if only what is weird is cancelled out and this is what Real Quantum Mechanics RealQM does. 

RealQM is not weird since it has the form of a classical continuum mechanical model in 3d space, which is conceptually well understood. 

The nice thing with ChatGPT is that it makes it possible (for me) to have a conversation with an AI physicist in a situation where all my attempts to have a conversation with a real physicist have turned out in a weird way. Try ChatGPT yourself. It is educating and fun!

ChatGPT as AI does not suffer from the same protective prestige as a real physicist, because it has not been so programmed I guess.

Trauma of Modern Physics: The Wave Function

The root of the present crisis of modern physics can be traced back to Schrödinger's equation for a system of $N$ electrons formulated nearly 100 years ago in terms of a wave function 

• $\Psi (x,t)$ with $x=(x_1,x_2,...x_N)$ 

as a complex number depending on $N$ three dimensional (3d) coordinates $x_i$ for $i=1,..,N$ plus a time coordinate $t$, in total $3N$ spatial coordinates plus time. The Schrödinger equation specifies how $\Psi (x,t)$ changes over time starting from some given initial configuration $\Psi (x,0)$. 

This may look harmless from purely notational point of view, but the wave function is a monster from both conceptual and computational point of view, since it depends on so many spatial coordinates.  

The conceptual difficulty is to give the wave function a physical (ontic) meaning in 3d physical space, and there is no resolution in sight. Physicists have simply given up resorting to "Shut up and calculate".

The computational difficulty is that even a coarse discretisation of each coordinate into say 10 different positions makes $\Psi$ to depend on $10^{3N}$ numbers, which already for $N=10$ is beyond the capacity of any thinkable computer. In particular, the specification of the initial configuration $\Psi (x,0)$ is a daunting task. 

Since modern physics is based on Schrödinger's equation (+ relativity theory), the above difficulties have remained as the deep trauma behind the present crisis, witnessed in many books including:

• The Wave Function (eds Ney and Albert).
• Philosophy of Physics: Quantum Mechanics (Tim Maudlin)  

To get perspective on the nature of $\Psi (x,t)$ let us compare with the Monadology of Leibniz with the world seen as a collection of monads or simple substances each one with its own mind capable of forming its own (blurred) conception of the world in interaction with all other monads. 

The simple particles without mind of early atomism are here given minds capable of perception and so connect to the wave-function. The trouble with such a many-mind theory is that there is no common 3d space as basis for some ontology, only a collection of separate individual views impossible for an external observer to make sense of. 

To make progress, the standard Schrödinger equation with its hopeless wave-function must be replaced by another atomistic model which has an ontic meaning and is computable. Real Quantum Mechanics offers such a model. It may be the model Schrödinger was searching for when realising that his equation did not make sense and so in despair giving up and leaving quantum mechanics to Bohr and Heisenberg.  

Invisible Foot Prints of Giant Creatures

                                 The Mountain laboured and produced a rat. 

In the Theories of Everything podcast Humans Create the Quantum World? Julian Barbour recalls that quantum mechanics as one of the two pillars of modern physics, is a non-classical mechanics theory for which the experimental evidence has classical mechanics form such as tracks in a cloud chamber or dots on a photographic plate, since this is what we can experience. 

It is possible sometimes to understand classical mechanics, since our experience has such form, but we cannot understand quantum mechanics in the same way since it has a fundamentally different form. More precisely, as expressed by Nobel Laureate Richard Feynman: Nobody understands quantum mechanics. 

Barbour then turns to Eddington's 1919 photo of solar eclipse observation with a little dot being shifted, which has come to serve as main confirmation of Einstein's general theory relativity as the other pillar, despite Eddington's own critical view: 

• We have found a strange foot print on the shores of the unknown. 
• We have devised profound theories one after another to account for the origins. 
• At last we have succeed in reconstructing the creature that made the footprint. 
• And Loh, it is our own. 

Eddington would probably say the same thing about CMBR as footprint of Big Bang, and LIGO as footprint of gravitational wave from merger of black holes. In both cases the footprint is extremely weak, while the creature is extremely big, which does makes little sense, see this post.

Even more mysterious, the giant creatures of dark matter and dark energy coming with giant effects appear to leave no foot prints at all.  

The lack of progress to resolve any of these mysteries since long, is expressed as a stagnation of fundamental physics.   

The stagnation of quantum mechanics is well expressed by theoretical philosopher Tim Maudlin in a recent long interview about the difference between classical mechanics and quantum mechanics:

• The Copenhagen Interpretation with its collapse of the wave function, is not a theory, only a set of slogans going in all sorts of directions. Physicists do not understand it. They just nod their heads to criticism.
• Shut up and calculate is not any kind of theory.
• Many Worlds Interpretation says nothing about physics. 
• Bohmian Mechanics is the Schrödinger equation without collapse of the wave function augmented by particles guided by a pilot wave equation (as a hidden variable theory not generally accepted).  

In short: the fundamentals of quantum mechanics are as mysterious in 2024 as in 1924-26 when Schrödinger developed his equation. Schrödinger left quantum mechanics in the 1930s because he could not accept the Copenhagen Interpretation.  

The root of all the trouble is the form of the standard Schrödinger equation as a linear equation in multi-dimensional configuration space without connection to real physical space. To make progress, this equation has to be abandoned for a new type of equation in real physical space, and this is what Real Quantum Mechanics offers. Why not take a look? It makes sense. It is not a rat.

Sabine: Stagnation in Physics 1924-2024

Sabine Hossenfelder has taken up the mission to expose the so called crisis in physics, or rather in her words the stagnation of fundamental physics presented in this long interview starting out

• We haven't really made any progress on the big open questions since they occurred a century ago.
• We still do not understand how Quantum Mechanics QM works.
• QM has a problem of inconsistency.

Here Sabine gives reason for the stagnation of fundamental physics ultimately based on QM as atom physics: 

• If we do not understand QM, how can we understand anything based on QM?
• QM is not understandable, because it does not make sense as a theory of physics. 
• A physical theory which does not make sense as real physics cannot be understood in a real sense. 

In this situation, there are two possibilities: 

1. QM is anyway accepted even if does not make sense. This is the current agreement by the physics community. 
2. QM is discarded (since it does not make sense).  

I have followed 2 by developing a different form of atom physics named Real Quantum Mechanics RealQM, which is fundamentally different from the accepted QM which I refer to as Standard QM or StdQM initiated by Schrödinger in 1924.

RealQM is understandable as a physical deterministic continuum mechanics model in 3 space dimensions. The reason StdQM is not understandable, is that it is a statistical model in many-dimensional configurations space without physical meaning. Compare with John Clauser.

Sabine has emerged as a very successful presenter of science, after giving up a career as fundamental physicist, since quantum gravity did not make sense, with particular mission to expose the stagnation in fundamental physics. This is admirable. What is less admirable (from my point of view) is that Sabine does not show any interest in finding some path to progress away from stagnation, such as RealQM.

Maybe this post can open to some communication.  

"Swedish Brigade" in Ukraine Fights North Korea

                         A soldier tells that tank was hit but it was as if nothing had happened.

Swedish MSM Svenska Dagbladet today happily reports to the Swedish people that:

• Since 2 months the "Swedish Brigade" equipped with Swedish Combat Vehicle 90 and Battle Tank 122 are getting ready near the border in the Kursk/Russia region to fight North Korean Special Forces on the battle field. 
• In another mission a Battle Tank 122 was hit without causing any damage. 
• Denmark together with Sweden buys an additional 205 Combat Vehicles 90 for 10 Billion Euro. 
• Combat Vehicle 90 is produced by Hägglunds in Örnsköldsvik, the main Swedish weapons factory owned by BAE Systems London.    

PS1 The Swedish Embassy was one of the first embassies in North Korea, opening in 1975 and until 2001, Sweden was the only Western country with uninterrupted diplomatic representation in the city. The Swedish embassy serves as the protecting power for the United States and as consular representation for Australia, Canada, Italy, Latvia, Iceland and Finland. What will now happen with the Swedish Embassy in Pyongyan?

PS2 Note that the cost of one Combat Vehicle 90 is about 5 million Euro. The total cost of 10 Billion Euro to be compared with a total state budget of about 100 Billion Euro.   

Mystery of Time Resolved?

After millennia of inquiry by most able scientists the concept of time still harbours mystery, which is the theme of these recent podcasts: 

• David Albert: A Masterclass on Time's Arrow
• What is Time? Stephen Wolfram's New Groundbreaking Theory

We all experience that time moves forward from a past over a now to a future, named as the Arrow of Time or 2nd Law of Thermodynamics. Why does our life always move forward to a new day, never rewind to yesterday? Why are our lives irreversible? 

In terms of physics the question can be formulated as follows:

• Why can a macroscopical system based on reversible microscopical physical laws, be irreversible? 

Ludwig Boltzmann took on the challenge in the late 19th century opening the door to modern physics and after much struggle came up with an explanation in terms of statistics as a form of statistical mechanics based on Newtonian mechanics augmented with the throw of a dice. Forward motion of time is here favoured by being more probable than backward motion thus showing an Arrow of Time, as discussed by David Albert.

Stephen Wolfram presents another explanation in terms of computational irreducibility.

My own explanation exposed in detail on this blog, connects to Wolfram's in the sense that physics as computation is given preference, rather than the conventional view based on exact laws of physics. The basic idea is:

1. A physical system changes from one state to a next state through a computational process, which has finite precision and so involves some destruction of information (chopping of decimals).
2. If the complexity of the system increases under repetition of the process, the loss of information will be so big that reversal of is impossible.
3. A prime example is the development of turbulence in laminar fluid flow, which is irreversible. The laminar state cannot be recovered from the turbulent.  

For a popular exposition of this idea see The Clock and the Arrow.

When Will Trump Call Putin? Or Putin Call Trump's Card?

In his presidential campaign Trump promised the American people and the World that he would end the war in Ukraine by directly calling Putin coming to a peace agreement, since he loves peace and is such a good old friend with Putin. 

But after winning the election Trump has not yet called Putin, nor has Putin called Trump, which is a bit strange since they are so good friends always working together to save the world from troubles like nuclear Armageddon. In the mean time before taking office Trump has been silent allowing Biden to continue escalation with the objective of making peace talks impossible. 

Instead of revealing his plans for peace talks with Putin, Trump has leaked through his new appointees an idea to (eventually) call Putin and then tell him that if does not agree to the plan, Ukraine will be flooded with so much more new fresh weapons that Putin simply will have to accept, which aligns very well with Biden's escalation. The idea is that showing strength is the best route to success, even from a weak position.  

But what will happen if it is instead Putin who is the strong man? What will a strong man like Trump do if that is the case? Will he back down and accept Putin's condition for peace: Neutral Ukraine outside NATO? What will Trump do when his trump card is called?

Waiting for Trump's call to Putin, Sweden is happily expressing unfailing continued support to flooding Ukraine with Swedish weapons to allow Trump to approach Putin from a power position. 

Let us hope for a miracle with Trump calling off the escalation before taking office and calling Putin to speak peace as good old friends. Please be reasonable mr Trump and fulfil your promise to the World!

Listen to Alex Krainer:

• A false flag attack takes the people with surprise creating emotion. The media already has the script (recall 9/11 where BBC reported a collapsing 7th World Trade Center 20 min before it happened). 
• Then you start to create mass formation psychosis, where you turn the population from being very very unwilling to engage in a war with Russia, to say: All Right, they struck us, now we will fight them and kill them (now the sentiment in Sweden).
• Trump ran on a promise of peace with Russia but all his new appointees only talk about war. 
• I expect there is extensive coordination between Trump's team and the counterpart on the Russian side...
• Maybe Trump cannot yet talk about being best friends with Putin...maybe there is some hope...