Trump Orders US Physicists to "Manipulate Space and Time"

Michael Kratsios appointed by Trump to be Director of the White House Office of Science and Technology to "make US physics great again", promptly delivered during a major science and technology conference the following message:

• The US now possesses technology that can “manipulate time and space” and “leave distance annihilated.”

No doubt that would bring US physics back to the leading position of the Manhattan Project producing "Little Boy" and "Fat Man" dropped on Japan on August 6-9 1945, followed by the Apollo Moon Project as "Big Step for Humanity", which was then lost as US physicists left real space and time to go into many-worlds quantum mechanics and string theory in 11 space dimensions.

This sends a message to the World that the US is now back to the lead with powers to create "Hell never seen before". 

But what is then the new physics of "bending/manipulating space and time" and "annihilating distance"?

Is it simply the 100 year old theory of relativity with its "space contraction" and "time dilation" all just appearances without substance, or the 50 year old string theory on its way out?

Or does "annihilate distance" mean that Einstein's light speed limit can now be overcome by a nuclear powered Musk space ship which can accelerate to any speed and so will be able to reach the nearest star Proxima Centauri in less than 50 minutes and the Andromeda Galaxy in under a year?

The Tragedy of Modern Physics 2015-2025

Ten years ago I posted 2 blog posts 

1. Tragedy of Modern Physics  
2. Tragedy of Modern Physics  

explaining the tragedy to have been caused by a dictate to physicists to confess to the Bohr-Heisenberg-Born so called Copenhagen Interpretation of Quantum Mechanics here referred to Standard Quantum Mechanics StdQM. Today on Good Friday it is time to reflect on repression of heretics.

The above posts tell the story how Schrödinger, the creator of the Schrödinger equation for the Hydrogen atom as the corner stone to the modern physics of atoms, was overpowered by Bohr assisted by Heisenberg and Born to accept that the microscopic mechanics of atoms is fundamentally different from the macroscopic mechanics of classical physics. In short, the dictate was to give up determinism in physical three space dimensions for non-determinism in high-dimensional abstract space. Schrödinger heavily objected but Bohr was mentally stronger and so Schrödinger was eliminated from the quantum mechanics taking power of modern physics into our days. Einstein joined with Schrödinger in critique of non-determinism, but was declared to be an old fool unable to grasp the subtleties of quantum mechanics.

Today is 100 years since Schrödinger formulated his equation for the Hydrogen atom with one electron with inspiration from Hamilton-Jacobi wave mechanics, which however did not lend itself in a natural way to atoms with many electrons. The generalisation was instead performed formally by adding a new 3d space dimension for each new electron into a Schrödinger equation in $3N$ space dimensions for an atom with $N$ electrons, an uncomputable equation without 3d physical meaning  It was here Born stepped in to give it a statistical meaning which was adopted by Bohr with support of Heisenberg into StdQM as the dictate of modern physics. 

A different generalisation of the Schrödinger equation for the Hydrogen atom is given by Real Quantum Mechanics RealQM as a form of classical continuum mechanics of elastic bodies in 3d. Electrons of RealQM occupy different regions of 3d space and carry like elastic bodies a form of strain energy measured by the gradient of electronic wave function/charge density, also referred as "kinetic energy" although no motion in space is involved. But Schrödinger missed this option maybe because he was not familiar with elasticity theory, and so modern physics was doomed to StdQM with all its complications.

Summary:

1. Is StdQM a tragic mistake?
2. Can RealQM replace StdQM as a realistic Schrödinger equation?

 

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.

This is where today RealQM comes in as an alternative to StdQM as a form of small scale classical continuum mechanics unifying physics from macro to micro-scales, described in this lecture:

• Structural Mechanics of the Atom

Russell describes how StdQM twisted chemistry away from a classical paradigm of meaningful realism, which could be visualised even if did not tell the whole story, into a new modern paradigm of abstractions beyond visualisation and human understanding. This is a strange story from Enlightenment to Mysticism. How could this happen? What role did Niels Bohr play?

It appears that today all physicists claim and most chemists accept that chemistry in principle is reducible to quantum mechanics, including Peter Atkins stating that there is no chemistry, only quantum mechanics and David Deutsch, Klaus Ruedenberg and Martin Head-Gordon, but there are also a few chemists doubting this idea including Robin Hendry and Hans Primas.   

The New Clothes of Quantum Mechanics

 

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 

• $E_{tot}=E_{kin} + E_{pot}$

as sum of kinetic energy 

• $E_{kin}=\frac{1}{2}\int\vert\nabla\Psi (x)\vert^2dx$ 

and Coulomb potential energy 

1. $E_{pot}=-\int\frac{\Psi (x)^2}{\vert x\vert}dx$

under the side condition of unit electronic charge 

• $\int\Psi (x)^2dx = 1$. 

We see that kinetic energy is an integral measure of the spatial variation of $\Psi (x)$,  and that potential energy is an integral measure of charge density $\Psi (x)^2$ weighted by the kernel potential $-\frac{1}{\vert x\vert}$ representing the proton placed at the origin $x=0$. The minimum represents best compromise of being close to the kernel while being spread out.

The solution $\Psi (x)$ is referred to as a wave function and as such represents a standing wave in $x$ independent of time, and has the simple analytical form (in atomic units):

• $\Psi (x)=\frac{1}{\sqrt{\pi}}\exp(-\vert x\vert )$.                    

We now take a step back and note:

1. The potential energy is classical Coulomb potential energy for a negative charge density around a positive unit point charge. 
2. The kinetic energy has the form of elastic strain energy in classical continuum mechanics. 

We can thus read the blue-print for the ground state of a Hydrogen atom as a charge density $\Psi (x)$ with minimal total energy in classical continuum mechanical terms. This is the full story displayed in full detail to us in very familiar terms from classical continuum mechanics without any mystery. 

We have now read Nature's book for the ground state of the Hydrogen atom. RealQM takes you further to atoms and molecules in the same spirit. Go to read!

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.

But what would such a generalisation look like for the Helium atom with two electrons? Schrödinger hesitated, but ended up taking the easy ride resorting to formal mathematics just adding a new 3d variable for the second electron, thus ending up with a differential equation in six spatial dimensions with unclear physical realistic meaning. 

This was the critical point in 1926 when Max Born stepped in to shape modern physics until our days by giving the six-dimensional wave function for Helium a probabilistic meaning thus leaving deterministic reality, which all leading modern physicists have described as weird, and Schrödinger refused to teach from 1928 to essentially give up quantum mechanics in despair.  

Today 100 years later there is a generalisation of Schrödinger's equation for the Hydrogen atom to atoms and molecules with many electrons in the original spirit of Schrödinger in the form of Real Quantum Mechanics RealQM. 

Why did not Schrödinger take this route, which is very natural,  and instead let himself be overpowered by Born (boosted by Bohr and Heisenberg)? 

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 $i=1,2,...,N$,                                           

where each $x_i$ is a 3d coordinate for a copy of $R^3$ and $\Delta_i$ the Laplacian differential operator with respect to $x_i$. The Hamiltonian $H_{std}$ 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.

Compared to classical mechanics in physical 3d space, this is a new (strange) construction with $N$ versions of $R^3$ so to speak stacked upon each other into a product space $R^{3N}$ of $N$ versions of $R^3$, which are separated but yet share the same $R^3$ in the electronic repulsion potential $\frac{1}{\vert x_i-x_j\vert}$. The result is that $H_{std}$ has no interpretation in real physical space $R^3$, only a statistical invented by Born under protests from Schrödinger who never accepted $H_{std}$ as physics.

Because of the $3N$ spatial dimensions, the Schrödinger equation built on the Hamiltonian $H_{std}$ of StdQM, is uncomputable if $N$ is not very small, and so $H_{std}$ must be dimensionally compressed to computable form. Density Functional Theory performs the most drastic compression into a Hamiltonian $H_{DFT}$ acting on a joint electron density $\rho (x)$ depending on a single 3d $x$ spatial coordinate obtained by integrating $\Psi (x_1,...,x_N)\vert^2$ over all coordinates $x_i$ but one. But the corresponding integration of $H_{std}$ does not compress the electron repulsion potential $\frac{1}{\vert x_i-x_j\vert}$ to a potential acting on $\rho (x)$ and $H_{DFT}$ cannot be derived from $H_{std}$ and so has to be invented, which has shown to be very difficult. The result is that the use of DFT has shown to require a lot of expert knowledge.  

The Hamiltonian $H_{real}$ of RealQM takes the form 

• $H_{real}= \sum_{i}(-\frac{1}{2}\Delta_i -\frac{Z}{\vert x_i\vert}) +\sum_{j<i}\frac{1}{\vert x_i-x_j\vert}$ for $i=1,2,...,N$,     

which is identical to that for StdQM above, but with a different meaning of the $x_i$ given as follows: Physical space $R^3$ is partitioned into non-overlapping domains $\Omega_i$ with $x_i$ being the coordinate $x$ in $R^3$ restricted to $\Omega_i$. The Hamiltonian $H_{real}$ acts on a wave function $\psi (x)$ appearing as a sum of one-electron wave functions $\psi_i(x)$ with $x\in\Omega_i$ thus with non-overlapping supports, all depending on the same space coordinate $x$. 

We thus see that both $H_{std}$ and $H_{real}$ start from formally the same abstract Hamiltonian but employ different concrete realisations, with the principle differences being: 

• 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.

The Schrödinger equation of RealQM is a system of partial differential equations for non-overlapping electron charge densities depending on a 3d space coordinate, with computational complexity scaling linearly with $N$ opening to simulation of large molecules. RealQM can be seen as a refined form of DFT with the original electron repulsion potential of StdQM, thus avoiding the main difficulty of DFT of inventing such a thing.

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.

Could Wittgenstein Speak about the Wave Function $\Psi$ of Quantum Mechanics?

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)

We are led to ask: 

• 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?

Maybe a theoretical physicist would say yes without hesitation, but maybe a chemist would like to speak about something more concrete like chemical bonding between atoms into molecules. It is here RealQM comes in as something which definitely is the case, and so something to speak of?

To clarify the meaning of "what is the case", Wittgenstein continues from (1):

• The world is the totality of facts, not of things. (1.1)

This opens to a world that is not only materialistic consisting of things like atoms, but also contains facts about atoms in play when atoms form molecules.

The famous quantum physicist Anton Zeilinger claims in Einstein's Schleier. Die Neue Welt der Quantenphysik (2003) that Wittgenstein had little understanding of modern physics in particular quantum mechanics in its StandardQM form, and that (1) should better read:

• The world is everything that is the case, and all that can be the case. (2)

But is (2) really better than (1)? Of course the purpose of adding "all that can be the case" is to cover up the main weakness of quantum mechanics as a science about physics, namely the probabilistic interpretation of the wave function as a description of "what can be the case" rather the "what is the case".

Which world view is most profound, that of Wittgenstein or Zeilinger?  Certainly, speculations about "what can be the case" is what all planning is about, which takes up a major part of the day as more or less constructive day-dreaming, but if you do not make a distinction between dream/fiction and reality/case then you will end up in deep trouble. 

RealQM gives a new form to quantum mechanics in the sense of classical physics, which has a meaning within Wittgenstein's perspective, and does not need Zeilinger's extension. 

PS The idea of proposition (6.57) above is to avoid confusion, resulting from too much speaking. Both mathematicians and physicists have a habit of doing so, which has led to a lot of confusion. For example, mathematicians speak about the infinitely large and infinitely small often without clear qualification which has caused lots of confusion for students. And quantum mechanics is filled with words like duality, complementarity, identity, entanglement, probability, exchange, correlation all creating lots of confusion. The idea of RealQM is to reduce the confusion by showing that it is not necessary to speak about all theses things when speaking about atoms and molecules.

StdQM/DFT and RealQM as Deterministic Theories

Continued conversation with chatGPT in the previous post comparing StdQM with RealQM, makes clear:

• 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.

This may seem surprising since it is commonly believed that stdQM involves elements of roulette, to which both Schrödinger and Einstein heavily objected.

StdQM and RealQM thus both fully deterministically predict the ground state of an atom (or spectrum), only in different ways. StdQM works with overlapping electron densities stacked on top of each other in a non-physical multi-dimensional space, while RealQM works with non-overlapping electron densities in ordinary physical 3d space. The essence of Coulomb interaction and electron kinetic energy, is shared. 

RealQM is to be compared with Density Functional Theory DFT, which is StdQM reduced to a common electron density, while RealQM keeps individual electron densities.

I hope this post will add substance to a discussion about StdQM vs RealQM. In particular, it shows RealQM as a more detailed DFT and less detailed StdQM.

How does then the roulette enter StdQM, if not through SE? The common idea is that this is somehow through measurement but then in a way different from random effects on measurements in a classical deterministic setting. This is the measurement problem of StdQM still open after 100 years. In RealQM there is no measurement problem beyond those of classical physics. 

But wait, what about the Schrödinger wave function $\Psi (x,t)$ as solution to a SE describing the evolution of an atomic system over time $t$ from an initial state at $t=0$ to a final state $t=T$ with $\vert\Psi (x,t)\vert^2$ supposed to signify according to Born/StdQM:

• The probability of finding an electron/particle at the point $x$ at time $t$. 

This is a mantra of StdQM you will hear physicists repeat in unison and which chemists have accepted. But the mantra is empty since to determine $\Psi (x,T)$ requires specification of multi-dimensional initial data $\Psi (x,0)$ and computation of the evolution, both impossible to realise. What remains is the eigenvalue problem as a deterministic energy minimisation problem, which does not need any initial data and is deterministic in the same sense as a classical mechanics problem.  

The evolution problem of StdQM represents an uncomputable fiction, while the eigenvalue problem of StdQM is deterministic in a classical sense, but still uncomputable.  

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?

The initial response by chatGPT is:

• Quantum mechanics explains chemistry, in principle.

Then follows a long conversation when chatGPT gradually retracts from this position to end up with: 

Why It Might Not Be True — Even In Principle:

1. No Clear Ontology in QM

We’ve talked about this:

• If quantum mechanics doesn’t clearly tell us what exists (particles? wavefunctions? information?), then how can it explain the ontology of chemistry?

• 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

• Bonds, hybridization, reactivity, acidity, aromaticity — none of these have straightforward derivations from quantum principles.

• They are empirical and heuristic, developed by chemists to explain observable patterns.

• If QM were explanatory “in principle,” we would expect these to emerge naturally. They don’t.

3. QM Is About Probabilities, Not Causal Mechanisms

• Chemistry is about how and why things happen — mechanisms, pathways, intermediates.

• QM gives us probabilistic outcomes, not clear causal stories.

• 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

• 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.

• Chemistry might require non-reducible, emergent principles to be fully intelligible.

My Summary of the conversation

We agree that QM is not a physical theory about the ontology (what exists) of atoms and molecules, because QM only says something about probabilities of outcomes (of experiments) without revealing the real physics behind the outcomes. This is Dirac's Shut up and Calculate (and do not ask for any explanations). But science is about explaining things, not just watching or calculating.

QM is like telling that many tosses of a perfect coin will give about half heads up, without saying anything about the real physics of tossing non-perfect real coins. It is an a priori statement without any ambition to explain anything about the ontology of coin tossing. 

Now, explanation requires elements of ontology and if QM is void of ontology, then QM cannot explain chemistry. This is the conclusion of chatGPT and also of most chemists, since it gives room for a science of explaining chemistry, which is not simply applied QM physics. Most physicists would say the reverse. 

ChatGPT tells this story and it is interesting to find that chatGPT has learned to practice the logic of language better than many human scientists. Try yourself and get surprised.

RealQM is a new form of quantum mechanics with ontology, which may explain chemistry.