Weak Reactivity of Gold by RealQM

 Here is a new article to the series about RealQM as an alternative to StdQM:

• Real Quantum Mechanics: Weak Reactivity of Gold

RealQM explains why Au with electron shell configuration 2+8+18+32+18+1 with 1 valence electron in a last shell outside a sphere of radius R containing all other shells, does not form a molecule Au2 by covalent bonding as a geometric effect of large R preventing electron accumulation between kernels.

RealQM explains covalent bonding of H into H2 and non-bonding of He2 in this earlier article in the series:

• Real Quantum Mechanics: Covalent Bonding. 

Download files and open in Acrobat to get active hyperlinks.

Origin of CMBR?

Here is an interesting video about the possible origin of the Cosmic Microwave Background Radiation CMBR other than an "afterglow" of a Big Bang proving the Big Bang hypothesis to be correct, as the currently most popular cosmological theory:  

The video recalls early theories about a static Universe filled with some form of interstellar dust radiating a Planck spectrum of around 2-5 Kelvin. Such a thing was detected in 1967 at 2.7 K and was then  connected to Big Bang deleting the old theories from the map. In particular the Big Bang theory claimed to resolve the mystery of the observed red-shift of galaxies increasing with distance suggesting an accelerated expansion of the Universe. 

One of the old theories was the "tired light" hypothesis presented by Zwicki in 1929 suggesting that the red-shift could be the result of a loss of energy of light passing through interstellar dust over long distance with energy scaling with frequency.  

The idea of an active interstellar dust actively radiating at 2.7 K seems more natural than that of a Big Bang "afterglow" still hanging on after 13.8 billion years. 

Zwicki's "tired light" hypothesis can be connected to some form of dark matter as source of gravitation which shows up as CMBR resulting from sucking up energy from passing light.  I have discussed dark matter in posts on Neo-Newtonian Gravitation.   

Computational vs Theoretical Mathematics in Physics

The mathematical models of physics take the form of partial differential equations like Euler's Equations for incompressible inviscid fluid flow EE, corresponding Navier-Stokes equation for viscous flow NSE and Schrödinger's equations for atoms and molecules SE. 

The task of a theoretical mathematician has been to prove by symbolic analytical techniques (i) existence, (ii) uniqueness and (ii) regularity of solutions to a given equation with data given in some large class of possible data with data including initial data, forcing and parameters like viscosity in NSE. 

The task of a computational mathematician has been to compute solutions for specific choices of data which in each specific case can answer (i)-(iii) by inspection of the computed solution. 

It has been argued that computation is not enough, even if for each specific choice of data (i)-(iii) can be answered, because only a limited number of specific choices can be inspected. The possibly very large class of data can thus never be exhausted by computation, which gives analytical symbolic mathematics a role to play by covering a large class of data.

It is natural to ask if there are examples of equations for which the class of relevant data is so small that it can be exhausted by computation. This means first that the equation cannot contain any parameter like viscosity. Are there any models of interest which are parameter free? Inspection of EE and SE shows that they are both parameter free, and so meet the requirement of Einstein of an ideal mathematical model opening to say something about the world without measuring anything. This is like learning the area of a circular disc by computation with unit radius as only input.

Solving EE computationally thus delivers the drag of a body moving through a slightly viscous fluid such as air and water at a subsonic speed with the only data being the shape of the body and not any viscosity as parameter. This limits the class of data to shapes of bodies with a limited range of shapes of interest to be covered by computation. This is all described here.

The case of SE is in its traditional form of Standard Quantum Mechanics StdQM troubled by the fact SE by its multi-dimension nature is uncomputable and so needs dimensional compression which introduces parameters. 

RealQM is different realisation of the same parameter-free Hamiltonian as StdQM into computable form without introduction of any parameter. RealQM thus expresses SE in parameter-free computable form and so opens the possibility of saying something about the atomic world without experimental input. RealQM thus computes the ground state of an atom with the only input being the number of electrons and so can exhaust the Periodic Table.      

An analytical estimate of ground state energy as the result of a longer or shorter sequence of successive bounds, can be seen as a form of symbolic computation, while a numerical computation can be seen as very long arithmetic proof.

Computation with a parameter-free mathematical model can produce a rich set of outputs from very limited structural input, which can serve as data for AI in need of rich data. Computation is then used both to produce data and to learn from data. Symbolic mathematics has an important role to set up computation.

The Clay Institute Millennium Problem on (i)-(iii) for NSE is still open in the form of symbolic mathematics with no progress reported over 25 years. Can computation get the million dollar Prize?

Covalent Bonding by RealQM

Here is the next article in a sequence of articles exhibiting the capabilities of RealQM as an alternative to StdQM as the canon of modern physics: 

• RealQM: Covalent Bonding

with earlier articles in recent posts. Download article and open in Acrobat to get hyperlinks to essential codes to run, inspect and modify.

Shut up and Calculate vs Compute, Learn and Speak

Here is a reflection connecting to the previous post on RealQM as a computable model of atoms and molecules and Mearmin's Shut up and Calculate desperate reaction to the difficulty of making sense of the theory of Standard Quantum Mechanics StdQM. 

Let us recall the following views on the divide between StdQM as the theoretical foundation of chemistry according to physicists and the theoretical chemistry actually used by chemists. 

Eberhardt 2012:

• Chemistry is a discipline of two faces, one applied and the other theoretical. The applied face focuses on the design and synthesis of molecules and solids, while the theoretical face looks for explanations of a molecule or solid’s properties.

Bader 2011:

• ....the divide that exists in chemistry between those who seek their understanding within a universe wherein the laws of physics apply and those who prefer alternative universes wherein the laws are suspended or bent to suit preconceived ideas.

Dirac 1929:

• The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble. It therefore becomes desirable that approximate practical methods of applying quantum mechanics should be developed, which can lead to an explanation of the main features of complex atomic systems without too much computation.

Dirac identifies the root cause of the divide as the impossibility of solving Schrödinger's equation of StdQM for the complex atomic systems of chemistry. If computational solution was possible there would be no divide and the whole of chemistry would be like an open book to read by computation. 

RealQM is an alternative to StdQM which is ab initio computable for the complex atomic systems of chemistry and is also understandable in the same sense as classical continuum mechanics. If RealQM indeed shows to models physics, then there is no longer any reason for a divide between theory and practice. The Shut up and Calculate can then be replaced by Compute, Learn and Speak. 

 

RealQM Article: Stability of Atoms

Here is another article in a series of articles about RealQM to be submitted:

• Real Quantum Mechanics: Stability of Atoms 

Recall the first article in the series:

• Real Quantum Mechanics: Introduction

Download file and open in Acrobat to get active hyperlinks.

RealQM Article to Submit

I am now now preparing to submit a sequence of articles about Real Quantum Mechanics to relevant journals and here is a first test to check out reaction:

• Real Quantum Mechanics

Take a look and give a comment. 

Political Role of Quantum Mechanics

The shift from the old quantum mechanics of Niels Bohr happened with Werner Heisenberg's July 1925  "Reinterpretation" article introducing a new form of matrix mechanics without Bohr's electron trajectories to form the new quantum mechanics.  

Heisenberg was a student of Max Born at the University of Göttingen with the mathematician Hilbert as world authority of mathematical physic acting as Born's mentor. Göttingen mathematical physics was an important part of the "Weimar Renaissance" during the recovery of Germany after the defeat in WWI getting momentum in 1925. 

It is thus possible to give Heisenberg's new quantum mechanics political dimensions stretching into WWII with Heisenberg as leading scientist in Germany's quest for an atomic bomb in the "Uranium Club".  

Planck had a similar role at the height of the German Empire when he in 1900 took on the responsibility to resolve the outstanding open physics problem of black-body radiation, when to avoid failing he resorted to statistics of quanta which resurfaced in Born's interpretation of Heisenbergs new quantum mechanics.

Heisenberg worked as Bohr's assistant in 1925 and Bohr invited Born to Copenhagen in 1926, and so they came to form the Bohr-Born-Heisenberg Copenhagen school setting the agenda for quantum mechanics from its beginning into our time. 

Schrödinger entered in 1926 with his equation showing to be equivalent to matrix-mechanics, but Schrödinger did not accept the Copenhagen Interpretation and so left the field to come back only in 1954 to discover that BBH still controlled the scene. 

After WWII the US took over quantum mechanics still in the spirit of BBH.

All physicists of today say that following the idea of the mathematician von Neumann that the wave function of quantum mechanics lives in a Hilbert space of infinite dimension and most physicists will confess to the Copenhagen Interpretation even if its meaning is unclear. Schrödinger's request of physicality is met with "shut up and calculate". 

What do the Chinese say? Is it time for Schrödinger to come back in the form of RealQM in the "China Renaissance" that is now reshaping the world? It is not impossible since the Chinese are very clever, very organised and result oriented towards a clear plan.

ChatGPT: After completing his doctoral work in Budapest and Zurich, von Neumann spent the academic year 1926–27 at Göttingen. There he

• Studied under David Hilbert, attending Hilbert’s lectures on the mathematical foundations of quantum mechanics,

• Sat in on Max Born’s seminar on the new quantum theory, and

• Published his first quantum‐mechanical notes out of Göttingen later that year.

Issues with Standard Quantum Mechanics 1926-2026

There are basic unresolved foundational "issues" with Standard Quantum Mechanics StdQM based on Schrödinger's Equation SE, basically issues with SE: 

1. Unitary deterministic evolution of the wave function.
2. Collapse of the wave function upon observation.
3. Statistics of collapsed wave function by Born's Rule. 

There are many more issues (ontology, correlation, non-locality...) but the all connect to 1-3 in one way or the other. 

Major efforts have been made since the 1926 when Schrödinger formulated SE, to resolve the issues but there is still no resolution in sight accepted by most physicists. There are several very different proposals (Copenhagen, Many-Worlds, Bohmian Pilot Wave...) with the great variety suggesting that they are all wrong. 

The previous post exhibited the "weirdness" of SE in the sense of electrons having both separated existence in different worlds and existence in a common shared world. This is expressed in the multi-dimensional nature of the Hamiltonian $H_{weird}$ underlying SE. 

But there is a different interpretation of $H_{weird}$ named RealQM, which is not weird because the electrons in RealQM have only shared existence with the corresponding Schrödinger equation taking the form of classical continuum mechanics.  

By restricting electrons to share the same 3d world/coordinate system, all the issues troubling StdQM evaporate. RealQM comes out as a form of classical continuum mechanics without issues beyond those of classical physics. RealQM thus offers a unified continuum model including both micro and macro-scopic physics. 

It is a mystery why RealQM was not tried in 1926, since it is the most natural way of generalising Schrödinger's equation from one electron to many electrons, staying within classical continuum mechanics without all the issues of StdQM, which was Schrödinger's approach.

It seems that it was Heisenberg and Born who made history turn in the direction of StdQM and not RealQM. 

The following quotes of Heisenberg shows his ideas rooted in his matrix-mechanics as a new form of physics, which express essence of StdQM:

• What we observe is not nature itself, but nature exposed to our method of questioning.
• Not only is the Universe stranger than we think, it is stranger than we can think.
• The reality we can put into words is never reality itself.
• The atoms or elementary particles themselves are not real; they form a world of potentialities or possibilities rather than one of things or facts.
• The existing scientific concepts cover always only a very limited part of reality, and the other part that has not yet been understood is infinite.
• The ontology of materialism rested upon the illusion that the kind of existence, the direct "actuality" of the world around us, can be extrapolated into the atomic range. This extrapolation is impossible, however. 
• The conception of objective reality ... has thus evaporated ... into the transparent clarity of mathematics that represents no longer the behavior of particles but rather our knowledge of this behavior.

Born came to the help of Heisenberg with the statistical interpretation of the wave function of StdQM:

• If God has made the world a perfect mechanism, He has at least conceded so much to our imperfect intellect that in order to predict little parts of it, we need not solve innumerable differential equations, but can use dice with fair success.
• I am now convinced that theoretical physics is actually philosophy.
• The universe is not a puzzle to be solved, but a mystery to be embraced.

Bohr from his failed attempt to give physics to an atom, also jumped in to help Heisenberg in support of StdQM:

• It is wrong to think that the task of physics is to find out how Nature is. Physics concerns what we say about Nature. 
• Nothing exists until it is measured.
• Opposites are not contradictory but complementary.
• When we measure something we are forcing an undetermined, undefined world to assume an experimental value. We are not measuring the world, we are creating it.
• When it comes to atoms, language can be used only as in poetry.
• There is no quantum world. There is only an abstract quantum physical description. It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about Nature.

Together Bohr-Born-Heisenberg formed a very strong team setting the agenda of modern physics to be  StdQM against the will of Schrödinger who wanted something like RealQM. 

It may be that all the unresolved issues with StdQM having taken toll for 100 years finally will open for a come back of Schrödinger and RealQM.

Why Quantum Mechanics is "Weird"

All leading modern physicists agree that quantum mechanics is so "weird" or "absurd" that it cannot be understood: 

• Quantum mechanics describes nature as absurd from the point of view of common sense. And yet it fully agrees with experiment. So I hope you can accept nature as She is - absurd. (Feynman)
• I think I can safely say that nobody understands Quantum Mechanics. (Feynman)
• If quantum mechanics has not profoundly shocked you, you have not understood it yet. (Bohr)

The "weirdness" of quantum mechanics comes from its foundational principle in the form of Schrödinger's equation based on a Hamiltonian $H_{weird}$ of the following form for an atom with kernel of positive charge $Z$ at the origin of a 3d Euclidean coordinate system $R^3$ surrounded by $N=Z$ electrons labeled $i=1,2,...,N$:

• $H_{weird}= \sum_{i}(-\frac{1}{2}\Delta_i -\frac{Z}{\vert x_i\vert}) +\sum_{j<i}\frac{1}{\vert x_i-x_j\vert}$                                        

where each $x_i$ is a 3d coordinate for a separate copy of $R^3$ and $\Delta_i$ the Laplacian differential operator with respect to $x_i$. The Hamiltonian $H_{weird}$ acts on wave functions $\psi (x_1,x_2,...x_N)$ depending on $N$ 3d spatial variables $x_i$, each $x_i$ serving to represent an electron with presence over the whole of its own copy of $R^3$, thus based on electronic wave functions having global supports.

The weirdness comes from the many dimensions where each electron $i=1,...,N$ is equipped with a separate copy of $R^3$, where it is acted upon by a Laplacian differential operator $\Delta_i$ giving it kinetic energy, yet the electrons interact in a common $R^3$ by the presence of $\vert x_i-x_j\vert$ in the term representing Coulomb electronic repulsion. The electrons thus have both separated individual existence and shared existence. That is weird from classical continuum mechanics point of where a shared single physical 3d space is the only one available. With a travesty of Bohr, one could maybe say

• If from a  knowledge of classical continuum mechanics, you are not shocked by $H_{weird}$, then you have not understood classical continuum mechanics.

Quantum mechanics is thus weird unphysical because it is based on a Hamiltonian $H_{weird}$, which is weird unphysical. Of course, if you are dealing with something which is partly weird, then you have to get rid of the weirdness and keep whatever is not weird and maybe useful.  Efforts to this end e g in the form of Density Functional Theory have been made without however completely getting rid on the weirdness. RealQM is a based on $H_{weird}$ but with a new meaning which is physical and not at all weird, see this post for an intro.