- The US now possesses technology that can “manipulate time and space” and “leave distance annihilated.”
fredag 18 april 2025
Trump Orders US Physicists to "Manipulate Space and Time"
torsdag 17 april 2025
The Tragedy of Modern Physics 2015-2025
Ten years ago I posted 2 blog posts
- Is StdQM a tragic mistake?
- Can RealQM replace StdQM as a realistic Schrödinger equation?
onsdag 16 april 2025
Modern Chemistry Beyond Human Understanding
The book The History of Valency by C. A. Russell from 1971 tells the story how the revolution of modern physics in its canonical form of Standard Quantum Mechanics StdQM clashed with classical chemistry in particular concerning the nature of chemical bonding:
- The Schrödinger wave-equation is now accepted as one of the foundations of modern theoretical chemistry. Yet its immediate impact upon chemistry was small, mainly because of the enormous difficulties in solving it.
- With the discoveries that followed in mathematical physics the pictures of the atom that emerged looked progressively less and less like mechanical models.
- In its turn valency moved steadily away from the position in which it could be happily imagined in terms of spring-like “bonds”.
- The analogies changed to the unmechanical ones of “‘clouds’’. Even electrons, after a short-lived existence as “‘particles’’, are now often “delocalized” in a way that no mechanical model could possibly permit.
- And this is only half the story, because the ionic “‘bond’’ has now been stripped of all mechanical accretions, and is now no longer visualized but accepted as another case of action-at-a-distance.
- It is eminently amenable to mathematical treatment but quite incapable of being represented pictorially.
- C. A. Coulson observed: I described a bond, a normal simple chemical bond; and I gave many details of its character (and could have given many more). Sometimes it seems to me that a bond between two atoms has become so real, so tangible, so friendly that I can almost see it. And then I awake with a little shock: for a chemical bond is not a real thing: it does not exist: no one has ever seen it, no one ever can. It is a figment of my own imagination.”
- Thus the wheel has turned full circle. From a hesitantly produced metaphor the concept emerged as an intricate mechanical model. Thence it has been sublimed into a solution to an equation in mathematics, and with this has come, hesitantly, no doubt, the conviction that all visualizations must be incomplete.
- What we once suspected we now know: the limitations of our understanding of the external world.
måndag 14 april 2025
Reading Nature's Book of Atom Physics
The Schrödinger equation is supposed to describe all of (non-relativistic) atom physics. It should thus be possible to read the blue-print or genom of atoms and molecules from Schrödinger's equation if everything is there, right?
Let us then take a look at Schrödinger's equation for the ground state of the Hydrogen atom with one negative electron around a positive proton, for which the solution can be identified as the function $\Psi (x)$ with $\Psi (x)^2$ representing electron charge density in 3d space with coordinate $x$ with minimal total energy
- $E_{tot}=E_{kin} + E_{pot}$
- $E_{kin}=\frac{1}{2}\int\vert\nabla\Psi (x)\vert^2dx$
- $E_{pot}=-\int\frac{\Psi (x)^2}{\vert x\vert}dx$
- $\int\Psi (x)^2dx = 1$.
- $\Psi (x)=\frac{1}{\sqrt{\pi}}\exp(-\vert x\vert )$.
- The potential energy is classical Coulomb potential energy for a negative charge density around a positive unit point charge.
- The kinetic energy has the form of elastic strain energy in classical continuum mechanics.
Where Quantum Mechanics Went Wrong in 1926
The physics of atoms and molecules as the essence of modern physics was born from Schrödinger's wave equation for the Hydrogen atom in 1926. Let me cite from Epistemology and Probability, Bohr, Heisenberg, Schrödinger and the Nature of Quantum Theoretical Thinking by A Plotnitsky:
- Schrödinger’s wave mechanics aimed at offering, and initially appeared to be able to offer, a theory that would be realist and causal and thus would conform to the "classical ideal".
- It was expected to be able, just as classical mechanics did, both to describe the physical processes at a subatomic level (as wave-like processes) and to predict, on the basis of this description, the outcomes of the experiments involving these processes.
- While Schrödinger’s hopes concerning the descriptive capacity of his theory did not materialize, on the predictive side the theory was spectacularly successful.
- Schrödinger’s equation does not describe any physical waves, as Schrödinger initially hoped it would. Instead, quantum probabilistic predictions—enabled by Born’s rules for deriving probabilities from quantum amplitudes.
Schrödinger did not change his philosophy. Instead, he came to doubt and even to repudiate quantum mechanics, at least as a desirable way of doing physics, although he acknowledged that the theory and even understanding it in ‘‘the spirit of Copenhagen’’ (which remained philosophically deplorable to him) may have been imposed on us by nature itself.
We understand that Schrödinger from start was searching for mathematical model within classical continuum mechanics as a wave equation describing the mechanics of an atom, including radiation spectrum. The Schrödinger equation for a Hydrogen atom with one electron has this form. Schrödinger never gave up his hope that his model somehow could be generalised to atoms with many electrons within the same frame of classical physics, with thus atom mechanics as a form of macroscopic mechanics just on a smaller scale.
söndag 13 april 2025
Sabine Asks for Breakthrough in Foundations of Quantum Mechanics
Sabine Hossenfelder describes herself as Particle Physicists' Enemy #1 the reason being criticism of the plan to build the Future Circular Collider FCC with a circumference of 90 km at the same site as the Large Hadron Collider with circumference 27 km through the rocks under Geneva in Switzerland.
Sabine claims that building FCC will not help modern physics forward from its present period of stagnation bogged down in a fruitless search after esoteric new particles in large particle colliders. Sabine says that it would be better to spend efforts to get out of the stalemate in the search for the foundations of quantum mechanics, which has troubled quantum physics since its formation 100 years ago.
Here RealQM may show a way out of from the artificial difficulties created (without proper reason) by replacing the determinism in real 3d space of classical physics by probabilities in abstract phase space of modern physics. Track record shows that progress in physics may lead into dead ends, and that restart with classics may be needed to go forward. Maybe this is what Sabine says.
From StdQM to DFT and to RealQM
RealQM is a new version of quantum mechanics, which we now compare with the text-book version StandardQM or StdQM and Density Functional Theory DFT as a compressed form of StdQM, all based on versions of Schrödinger's equation based on different Hamiltonian operators starting from this post.
The Hamiltonian $H_{std}$ for StdQM takes 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:
- $H_{std}= \sum_{i}(-\frac{1}{2}\Delta_i -\frac{Z}{\vert x_i\vert}) +\sum_{j<i}\frac{1}{\vert x_i-x_j\vert}$ for $i=1,2,...,N$,
- $H_{real}= \sum_{i}(-\frac{1}{2}\Delta_i -\frac{Z}{\vert x_i\vert}) +\sum_{j<i}\frac{1}{\vert x_i-x_j\vert}$ for $i=1,2,...,N$,
- StdQM uses electronic wave functions with global support in multi-dimensional space.
- RealQM uses electronic wave functions with non-overlapping local support in 3d space.
We see that RealQM neatly fits in between StdQM and DFT as (i) being computable with (ii) the electron Coulomb electronic repulsion of StdQM, thus keeping the main advantages of both. This is the conclusion of a long journey to be completed in a revision of the RealQM book including a lot of chemsitry.
lördag 12 april 2025
Could Wittgenstein Speak about the Wave Function $\Psi$ of Quantum Mechanics?
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I cannot speak about $\Psi$ because it is not something which is the case. |
Physicists generally like to speak about the time-dependent Schrödinger wave function $\Psi (x,t)$ as a solution to the initial value problem with $t$a time variable and $x$ a multidimensional spatial variable:
- $i\dot\Psi = H\Psi$ for $t>0$ and all $x$
- $\Psi (x,t) =\Psi_0(x)$ for $t=0$ and all $x$,
where $\dot\Psi =\frac{\partial\Psi}{\partial t}$ is the time derivative of $\Psi$, $H$ is a Hamiltonian differential operator acting in space and $\Psi_0(x)$ is a given initial value. The existence of $\Psi (x,t)$ is said to be solidly guaranteed by mathematical analysis because the Hamiltonian is a linear.
But determining a specific $\Psi (x,T)$ at some specific time $T$ requires (i) specification of $\Psi_0(x)$ for all $x$, and (ii) time stepping of the equation $i\dot\Psi =H\Psi$.
Since $x$ has $3N$ dimensions for a system with $N$ electrons, both (i) and (ii) represent daunting tasks. In fact both appear to be impossible as soon as $N$ is not small, certainly impossible for a system with more than $10$ electrons.
This means that speaking about a wave function $\Psi (x,t)$ for an atomic system with many electrons such as a big molecule, is like speaking about something with features which are forever hidden to inspection.
What would Wittgenstein have said about such a situation? Let us recall the first and last sentence of his Tractatus:
- The world is everything that is the case. (1)
- Whereof one cannot speak, thereof one must be silent. (6.57)
- Is $\Psi$ something that is the case even if $\Psi$ cannot be computed/determined?
- Can we speak of $\Psi$ if $\Psi$ cannot ever be computed/determined?
- The world is the totality of facts, not of things. (1.1)
- The world is everything that is the case, and all that can be the case. (2)
fredag 11 april 2025
StdQM/DFT and RealQM as Deterministic Theories
- The StdQM Schrödinger Equation SE for an atom is a deterministic differential equation.
- The eigenvalues of SE as typical deterministic output, represent the spectrum of the atom, with smallest eigenvalue equal to the energy of the ground state of the atom.
- There is no probabilistic element in this picture. SE deterministically predicts the ground state energy of an atom. No game of roulette is involved.
- The probability of finding an electron/particle at the point $x$ at time $t$.
Summary:
- RealQM is a classical deterministic computable theory with potential of predicting both atomic spectra and atomic dynamics since initial data remain 3d.
- DFT is a drastically reduced StdQM theory with potential of predicting atomic spectra, but the reduction carries unresolved problems.
Does QM Explain Chemistry?
Here is an illuminating conversation with chatGPT starting from my question also posed in this post:
- Does Quantum Mechanics QM explain chemistry?
- Quantum mechanics explains chemistry, in principle.
Why It Might Not Be True — Even In Principle:
1. No Clear Ontology in QM
We’ve talked about this:
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If quantum mechanics doesn’t clearly tell us what exists (particles? wavefunctions? information?), then how can it explain the ontology of chemistry?
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You can't derive a theory of molecules and bonds from a framework that can't decide what “an electron” even is.
2. Chemical Concepts Don’t Emerge from QM
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Bonds, hybridization, reactivity, acidity, aromaticity — none of these have straightforward derivations from quantum principles.
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They are empirical and heuristic, developed by chemists to explain observable patterns.
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If QM were explanatory “in principle,” we would expect these to emerge naturally. They don’t.
3. QM Is About Probabilities, Not Causal Mechanisms
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Chemistry is about how and why things happen — mechanisms, pathways, intermediates.
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QM gives us probabilistic outcomes, not clear causal stories.
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So even in principle, it may not be the right kind of theory to explain chemical behavior.
4. Computational Intractability Is Not Just Practical — It’s Theoretical
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Some philosophers argue that the complexity of real chemical systems isn't just a matter of brute computational power — it’s a sign that QM is the wrong level of description.
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Chemistry might require non-reducible, emergent principles to be fully intelligible.