Exploring Microscopics by Computation

Modern physics appeared after a long success story initiated by the scientific revolution culminating at the end of the 19th century in a combination of Newton's mechanics and Maxwell's electromagnetics in full harmony appearing to capture macroscopic physics. 

Of course there were open problems asking for resolution including the ultra-violet catastrophe of black-body radiation viewed to be of particular importance. The start was the Rayleigh-Jeans radiation law stating that radiation intensity scales quadratically with frequency $\nu$, which asks for an upper bound $\nu_{max}$ on frequency to avoid infinite intensity by summation over frequencies. Such a bound was available as Wien's displacement law stating that $\nu_{max}$ scales linearly with temperature $T$. 

The theoretical challenge was to explain the bound $\nu <\nu_{max}$ with $\nu_{max}\sim T$. Planck as leading physicist of the German Empire took on the challenge but was unable to find an answer within classical physics and so resorted to a form of statistical physics inspired by Boltzmann's statistical  thermodynamics. Under much agony Planck thereby took a step out of classical physics into a new form of statistical physics, which then evolved in the quantum mechanics as the essence of modern physics.

The fundamental step away from classical physics as deterministic physics about existing realities, was the introduction of statistical physics about probabilities of possibilities. From specific existing realities to infinite possibilities.  

In the new digital world the distinction between existing unique reality and virtual realities is blurred which means that difference between classical deterministic reality and modern probabilistic possibility is also blurred. 

It is thus of interest to seek to pin down the difference between (i) classical physics as existing realities and (ii) modern physics as probabilities of possibilities. A striking aspect is that (i) does not require any human minds/observers (the Moon is there even when nobody looks at it), while (ii) requires some form of mind to carry/represent thinkable possibilities.  

Quantum Mechanics QM emerged before the computer and so computational aspects were not in the minds of the pioneers Bohr-Born-Heisenberg, who came to develop the Copenhagen Interpretation CI formed in the 1920s based on a multi-dimensional wave function $\Psi (x,t)$ depending on a spatial coordinate $x$ with $3N$ dimensions for an atomic system with $N$ electrons satisfying a linear Schrödinger Equation SE (and $t$ is a time coordinate), with $\vert\Psi (x,t)\vert^2$ interpreted as a probability density over configuration space with coordinate $x$. This is still the text book version as Standard QM StdQM.

The many dimensions makes the wave function $\Psi (x,t)$ uncomputable and so has existence only in the mind of a CI physicist with unlimited fantasy. The grand project of StdQM can thus be put in question from computational point of view, and also from realistic point of view if we think that the evolution of the World from one time instant to a next is the result of some form of analog computational process performed by real atoms.

The World is thus equipped with (analog) computational power allowing evolution in time of the existing reality, but it is hard to believe that it has capacity for exploration of all possibilities to form probabilities of possibilities, unless you are believer in the Many-Worlds Interpretation as an (unthinkable) alternative to CI.

From computational point of view StdQM as all possibilities is thus hopeless. The evolution of the multi-dimensional wave function $\Psi (x,t)$ in time is an impossible project. What is today possible is exploration of thinkable realities as long as they are computable.

The exploration can be done starting from RealQM as a computable alternative to StdQM. To see that it is not necessary to take the full step into the the impossibility of StdQM, we need explanations of in particular (1) Wien's Displacement Law and (2) Photoelectric effect, in terms of classical deterministic physics. This is offered on Computational Blackbody Radiation in the form of classical threshold effects.

It thus appears possible to stay within a framework of deterministic classical computable physics and so open to exploration of thinkable worlds of microscopics by computation, which is not possible starting from StdQM.  

Summary: There is a distinction between (a) specific computable (thinkable) realities, and (b) probabilities of uncomputable possibilities. Your choice! As Schrödinger put it: There is a difference between a specific blurred picture and a precise picture of a fog bank.

 

Quantum Restart 2026 from Hydrogen Atom 1926

This year has been designated as the International Year of Quantum Science and Technology (IYQ2025) by the United Nations as the 100th anniversary of the development of Quantum Mechanics. 

Quantum Mechanics was kick-started fin 1926 with formulation Schrödinger's Equation SE for the Hydrogen atom with one electron,  followed by a swift generalisation to many electrons by Born-Heisenberg-Dirac to form the text book Copenhagen Interpretation CI of Standard QM of today.

StdQM is generally viewed as a formidable success underlying all of modern technology of microscopics, but none of the foundational problems behind the CI have been resolved. StdQM is viewed to "always work perfectly well" but "nobody understands why". 

The previous post recalled the critical moment in 1926 when SE was generalised to many electrons by Born-Heisenberg-Dirac into StdQM under heavy protests from Schrödinger, who took the first step with a SE in a wave function $\Psi (x)$ depending on a 3d space coordinated $x$ with $\rho (x)=\Psi^2 (x)$ representing charge density in a classical sense. 

Recall that RealQM is a generalisation to many electrons different from StdQM by staying within a framework of classical continuum mechanics in the spirit of Schrödinger. The basic assumption is that an atom with $N$ electrons is represented by a nucleus surrounded by a collection of electrons as    

• non-overlapping unit charge densities $\rho_i(x)$ for $i=1,....,N$, 
• free of self-interaction,
• indivisible in space. 

Let us now compare RealQM and StdQM in the case of Hydrogen. For stationary ground states and excited states so called eigenstates, they share formally the same SE but with different interpretations of the wave function:

1. $\rho (x)$ is charge density in classical sense. (RealQM)
2. $\rho (x)$ is probability density in StdQM sense. (StdQM) 

Recall that QM was formed from a perceived difficulty of capturing the spectrum of Hydrogen within classical physics with the spectrum arising from interaction of the atom with an exterior forcing electromagnetic field in so called stimulated radiation. 

Schrödinger resolved this problem by extending SE to a time-dependent form where the frequencies of the spectrum appeared as differences of stationary energy levels, thus with a linear relation between atomic energy levels and resonance frequencies in stimulated radiation. The discrete frequencies appeared as 

• beat frequencies of wave functions in superposition. 

This became the mantra of StdQM which has ruled for 100 years, with superposition signifying the break with classical physics, where superposition in spatial sense is impossible.

If we stay within RealQM, then superposition is impossible because charge densities do not overlap. We now ask the key question:

• Is it possible to capture the spectrum of Hydrogen within RealQM thus without superposition? 

The discrete stationary eigenstates are the same, and so we ask about the time-dependent form of RealQM? Is it the same as that of StdQM? Not in general because RealQM is non-linear and StdQM linear. For Hydrogen RealQM is linear so in this case the same time-dependence as in StdQM is possible.

But this may not be most natural from a classical point of view without superposition in mind. Instead it is natural to think of the radiating electron oscillating back and forth between two energy levels with different charge densities as a classical oscillating dipole. We can thus extend RealQM to a classical dynamical system swinging back and forth between energy levels with different charge distributions. This would describe the radiating Hydrogen atom in terms of classical physics with a continuous transition between different configurations. This would answer Schrödinger's basic question without answer in STdQM about "electron jumps": The electron does not jump but changes charge density continuously in space and time. 

The only thing to explain in this scenario is the linear relation between (difference of) energy and frequency, not from beat frequency and superposition, but from the basic relation between energy and frequency appearing in Planck's Law discussed in this post. 

Summary: It seems possible to capture atomic radiation by RealQM within a classical continuum mechanics framework and so avoid taking the step out of classical physics along the dream of Schrödinger. In particular, superposition is not required and probably not present. Quantum computers built on superposition will not work. Superposition may be superstition rather than reality.  

The Tragedy of Schrödinger (and QM)

The atomic world was opened to theoretical exploration in 1926 when Erwin Schrödinger formulated a mathematical model of the Hydrogen atom with one electron in terms of a wave function $\Psi (x)$ depending on a 3d spatial coordinate $x$ with $\Psi^2 (x)$ representing electron charge density. So could Schrödinger represent the ground state of the Hydrogen atom by the real-valued wave function $\Psi (x)$ minimising the total energy 

• $E(\psi )=E_{kin}(\psi )+E_{pot}(\psi )$

where 

• $E_{kin}(\psi )=\frac{1}{2}\int\vert\nabla\vert^2dx$  is kinetic (electron "compression") energy 
• $E_{pot}(\psi )=-\int\frac{\psi^2(x)}{\vert x\vert}dx$ is Coulomb potential energy

over all functions $\psi (x)$ defined in 3d Euclidean space with $\int\psi^2(x)dx=1$. Using his solid knowledge of Calculus, Schrödinger was very pleased to find the solution in analytical form:

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

In an outburst of creativity in the Alps in the Winter 25-26 together with one of his girlfriends, Schrödinger generalised to a time dependent form capturing the observed spectrum of Hydrogen, and the success was total as a first glimpse into the atomic world to form the new focus of modern physics.

The next step beyond Hydrogen was Helium with two electrons. What could the wave function look like for two electrons?  How to generalise from one to many? Two options presented themselves:

1. Real physics: Add a new non-overlapping charge density for each new electron. 
2. Formal mathematics: Add a new set of 3d spatial coordinates for each new electron. 

Schrödinger contemplated 2. but did not think it was the right way to go because the wave function for Helium would involve 6 spatial dimension and so lack physical representation. For some reason Schrödinger did not pursue 1. either. So right after the big success with Hydrogen Schrödinger hit the wall. 

But other physicists were ready to quickly jump in (1927) following 2. with enthusiasm:

• Born-Oppenheimer: Formal generalisation without Pauli Exclusion Principle PEP. Probabilistic interpretation of wave function.
• Heisenberg-Dirac: Addition of PEP, antisymmetry and Slater determinants.

This forms the basis of Standard QM StdQM also today in its Bohr-Born-Heisenberg text book Copenhagen Interpretation.  

To Schrödinger the take-over of his baby came as a shock:  

• I am not happy with the probability interpretation. In my opinion, it is an ephemeral way to avoid the true problem.
• The whole antisymmetrization seems to me to be a desperate expedient to save the particles’ individuality. Perhaps it is not fundamental but only an approximation.
• The use of Slater determinants in atomic theory seems to obscure the physical picture even more.
• I don’t like it, and I’m sorry I ever had anything to do with it.
• The $\psi$-function as it stands represents not a single system but an ensemble of systems. It does not describe a state of one system in configuration space but rather an ensemble of systems in ordinary space. The $\psi$-function itself, however, does not live in ordinary space, but in the configuration space of the system. And not merely as a mathematical device — it really exists there. That is what is so repugnant about it.

Schrödinger thus quickly became incompatible with StdQM and accordingly was marginalised, along with Einstein sharing similar criticism.

RealQM represents a new initiative to follow 1. as real physics in the spirit of Schrödinger. What would Schrödinger have said about RealQM which lay on the table already in 1927? What would have happened if Schrödinger had been allowed to take care of his own baby and not given it away others? 

From Abstract to Concrete by Computation

The computer changes practice of science and technology. Let us see if the computer also changes the nature and role of theory as expressed in mathematical models. 

A classical Newtonian paradigm is to formulate a model as a set of differential equations describing laws of physics such as Newton's laws of motion, as  a dynamical system with state $U(t)$ depending on time $t$ satisfying (with the dot signifying differentiation with respect to time):

•  $\dot U(t)=F(U(t))$ for $0<t\le T$ with $U(0)$ given and $T$ a given final time,      (N)

where $F(v)$ is a given function of $v$. We call the function $U(t)$ the trajectory of the system.

Calculus was developed to solve (N) using symbolic mathematics of integrals and derivatives, which worked for a limited set of dynamical systems. When symbolic solution failed or was too complicated numerical solution could always be used in the form of time-stepping

•  $U(t+dt) = U(t)+dtF(U(t))$ with $dt>0$ a small time step,               (C)

allowing successive computation of $U(t)$ for $0<t\le t)$, without the use of symbolic Calculus.

Before the computer (C) could be too time consuming, and so the symbolic Calculus was developed by reformulating (N) into a new paradigm of Lagrangian mechanics, where a specific dynamical system solution $U(t)$ was not described by (N) but instead by a Variational Principle VP  stating that the integral

• $\int_0^TL(u(t))dt$                               (VP)

with Lagrangian $L(v)$ (determined by $f(v)$) depending on an arbitrary trajectory $u(t)$, has a vanishing small variation under small variations of $u(t)=U(t)$. 

The differential equation (N) with one specific solution $U(t)$ was thus replaced by a VP including variation over many trajectories $u(t)$. The generality of VP formulation turned the 18th century into Lagrangian mechanics, thus from (N) to (VP). This was a step towards abstraction from concrete Newtonian mechanics to Lagrangian mechanics based on abstract VP.

We have seen that (N) has a natural computational form as (C), while the computational form of a VP is not direct since comparison over a rich variation is not efficient.

With the computer there is thus today a shift from VP back to (N). From abstract to concrete, because computation is concrete like taking yet another time step forward.

This has important implications because the generalisation to classical mechanics to quantum mechanics has followed the path of Lagrangian abstraction put to an extreme in the Quantum Field Theory by Feynman as "sum over all paths".

In particular the generalisation of Schrödinger's equation from one electron to many electrons took an abstract path into multi-dimensional wave functions, which has haunted Quantum Mechanics from start. 

RealQM offers a concrete generalisation which directly lends itself to computation.

Summary: Computation takes concrete form and so naturally connects to concrete differential equations formulation rather than to some abstract variational principle. 

PS1 Recall the light can be viewed to propagate following a principle of least time (without direct computational realisation), as an alternative to wave propagation (with direct computational form).

PS2 Certain configurations can be characterised as minimising energy, which can be resolved computationally by gradient method as a form of time-stepping.

  

How Computation Changes Theoretical Physics of TD and QM

The physical theories of Thermo Dynamics TD and Quantum Mechanics QM were both formed before the computer, and so do not include the aspect of computation, computability and computational work. Both theories focus on separate equilibrium states rather than dynamical evolution between different states. Rather statics than dynamics, because dynamics is more demanding by including evolution in time.  

The computer changes the game by offering computational power allowing computational simulation of evolution in time of dynamical systems and so opens to a better understanding of the World as it evolves from one instant of time to a next in a process of time-stepping. 

The change is fundamental and opens entirely new possibilities and also resolution of fundamental unresolved problems in TD and QM connected to the static nature of these theories in standard form. 

So can the 2nd Law of TD be given an explanation based on finite precision computation confronting instability as explained in Computational Thermodynamics. 

So can the basic unresolved foundational problems troubling QM since 100 years, be circumvented by a reformulation into Real Quantum Mechanics RealQM which can be explored in dynamical form by computation. 

Let us here focus on the dynamical aspects of RealQM, which come in two forms (i) time-periodic and (ii) dynamical evolution between equilibrium states. 

RealQM takes the following form for an atomic system consisting of $N$ electrons as non-overlapping unit charge densities and a set of atomic nuclei for simplicity as particles at fixed positions, interacting by Coulomb forces, which can be described by a complex-valued wave function $\psi (x,t)$ depending on 3d spatial coordinate $x$ and time $t$ satisfying a Schrödinger Equation SE of the form 

• $i\dot\psi (t)+ H\psi (t) = f(t)$       (SE)

where the dot denotes differentiation with respect to time, $H$ is a Hamiltonian acting on $\psi$ and $f(t)$ is an exterior driving force. Here $\vert\psi (x,t)\vert^2$ has a direct physical meaning in 3d space as charge density. 

We note that (SE) has the form of a classical dynamical system in a function $\psi (x,t)$ with direct physical meaning depending on a 3d spatial coordinate $x$ and $t$.  Given an initial value $\psi (x,0)$ the value of $\psi (x,t)$ at a later time $t>0$ can be determined by resolving (SE) by time-stepping with computational work scaling linearly with $N$ (in the case of RealQM but exponentially in QM.

A time-periodic solution (with $f(t)=0$) can take the form 

•  $\psi (x,t)=\exp(iEt)\Psi (x)$. 
• $H\Psi =E\Psi$. 
• $\Psi$ eigenstate and $E$ (real) eigenvalue as energy.

Here the eigenstates appear as static states. The eigenstate with smallest energy is the groundstate of the system. It is possible to compute the groundstate by parabolic relaxation in the form of time-stepping of 

• $\dot\Psi + H\Psi =0$ with renormalisation to unit charge. 

which can be seen as a gradient method towards minimum energy as an actual physical process when an atom or molecule finds its minimum energy equilibrium state.

But (SE) opens to computational simulation of genuine dynamical evolution between physical states described by charge density under exterior forcing. 

RealQM thus offers a new capacity of computational  simulation of complex atomic systems in terms of charge density as real physics with clear meaning.

RealQM should be compared with StdQM based on a multi-dimensional Schrödinger Equation StdSE with only probabilistic physical meaning with exponential computational complexity requiring drastic reduction into physics with unclear meaning.

Notice that RealQM stays within the classical world of continuum physics and so does not meet the unresolvable problems of StdQM of (i) meaning of wave function, (ii) role of measurement and (iii) computational complexity. There is no need of any special Philosophy of RealQM as for StdQM. 

Summary: Computation offers a new tool to simulation and understanding of atomic systems when applied to RealQM as a computable model with clear physics. Thus 100 years after conception QM may take a leap into a new era of Computational QM, leaving the unresolved foundational problems of StdQM behind as irrelevant. 

PS The typical reaction to RealQM is not a welcome as possibly something offering new capabilities and relief from old troubles, but rather the opposite as an unwanted disturbance to a status quo in full agreement that "nobody understands QM" as a "soft pillow" in the words of Einstein. 

Physics as Becoming as Computational Process

Recents posts have discussed the role of Planck's constant $h$ in Standard Quantum Mechanics StdQM presented as the smallest quantum of action as one of Nature's deepest secrets. It can thus be of interest to seek to understand the concept of action as formally energy x time or momentum x length in combinations without clear physical meaning.

Let us then ask if in physics concepts which have a more or less direct physical representation, have a special role? We thus compare concepts like mass, position, time, length, velocity, momentum,  and force, which have physical representations, with the concepts of energy and action, which are not carried the same way in physical terms.    

To seek an answer recall that in the age of the computer it is natural to view the World as evolving from one time instant to a next in processes involving exchange of forces, which can be simulated in computations involving exchange of information, as computational dynamical systems where the dynamics of the World is realised/simulated in time stepping algorithms. Stephen Wolfram has presented such a view. It is a computational form of the general idea of a World evolving in time from one time instant to the next.

This is a World of becoming with focus shifting from what the World is to what the World does, from state to process. 

The time-stepping process for the evolution of the state of a system described by $\Psi (t)$ from time $t$ to time $t+dt$ with $dt$ a small time step, takes the form 

• $\Psi (t+dt) =\Psi (t)+dt\times F(t)$   (or $\frac{d\Psi}{dt} = F$)   (P)

where $F(t)$ represents the force acting on the system at time $t$, which may also depend on the present state $\Psi (t)$. We speak here about 

• state $\Psi (t)$
• force $F(t)$ 
• process (P).

We see that the concept of state (what is) is still present, but we can bring forward the process (becoming) to be of main concern including the force $F(t)$. 

We can describe such a world as a Dynamical Newtonian World based on Newton's Law

• $\frac{dv}{dt}=\frac{f}{m}$ or $v(t+dt)=v(t)+dt\times F(t)$,

with $v(t)$ velocity, $m$ mass, $F(t)=\frac{f(t)}{m}$ and $f(t)$ force. 

This is the ever-changing world of Heracleitos based on state and force and process with physical representations. 

But there is also the world of Parmenides as a static world as Einstein's space-time block Universe. 

The idea of a space-time block Universe is present in the minds of theoretical physicists speaking about physics governed by a Principle of Stationary Action as 

• stationarity of $A(\Psi )\equiv\int_0^T L(\Psi (t))dt$      (PSA)

where $A(\Psi )$ is action, $L$ is a Lagrangian depending on $\Psi (t)$ and $t=0$ is an initial time and $T$ a final time for the dynamical system $\Psi (t)$. PSA means that the actual evolution $\bar\Psi$ is characterised by vanishing change of the total action $A(\Psi )$ under small variations of $\Psi$ of $\bar\Psi$. We note that the action $A(\Psi )$ does not have a direct physical representation but requires a counting clerk to take specific value.

PSA is not realised by computing $A(\Psi )$ for all $\Psi$ and then chosing the true $\bar\Psi$ from stationarity, since the amount of computational work is overwhelming. Instead PSA is realised by time-stepping as a form of (P) with suitable $F$.

Before the computer a problem formulation in terms of PSA was often preferred because the Lagrangian had a given analytical form allowing (P) to be formulated and the $\Psi (t)$ could be determined analytically. But the range of applications was very limited.

With the computer, the focus shifts to (P) allowing unlimited generality. The shift is from PSA where action does not have a physical representation to (P) with physical representation.

Let us now return to $h$ as the smallest quantum of action, with the experience that action is a concept in the head of a counting clerk without direct physical representation and so as the smallest quantum of action. 

This adds to the discussion in recent posts questioning the role of Planck's constant as a fundamental constant of Nature. It does not seem to be so fundamental after all. There is no smallest quantum of action in Nature.

We can compare (P) with a computational gradient method to solve to find an equilibrium state characterised by minimal energy, again with physical representation of (P) but not of energy. 

Doubling Down in Physics

The technique of doubling down in poker when you have a bad hand by raising the bet to avoid being called, sometimes works but is risky. 

The technique can be used in many other settings, for example if you find that your scientific theory meets questions which you cannot answer: Make the theory twice as complicated and hope that the new questions will take time to be formulated. This way you gain time by shifting focus from the old questions without answers to new questions yet to be formulated. 

Einstein used this technique to inflate his Special Theory of Relativity posing many questions he could not answer, to his General Theory of Relativity so complicated that questioning was beyond human capacities. 

Quantum Mechanics QM (1920s) was from start troubled with foundational questions about physical meaning which had no answers, and so was expanded to Quantum Electro Dynamics QED (1940s-) , Quantum Field Theory QFT (1960s-) into String Theory (1980s-) in an ever increasing theoretical abstraction away from physical reality impossible to question. (This is as the root cause of the present crisis of modern physics). 

The result is that today all the foundational questions about QM still remain, all connecting to the basic question of the physical meaning of the (complex-valued) wave function $\Psi (X,t)$ as the subject of QM. The text-book answer to this question takes the form attributed to the Bohr-Born-Heisenberg Copenhagen Interpretation, where $X$ collects all coordinates of all electron positions: 

• $\vert\Psi (X,t)\vert^2$ is the probability density of the electron configuration $X$ at time $t$.

Here an electron is assumed to be a point particle with position identified by a 3d spatial coordinate. The multi-d spatial coordinate $X$ thus contains the positions of all electrons as point particles. The trouble with this definition is that electrons are not physical point particles with positions possible to collect in a multi-d spatial coordinate $X$. This means that the above probabilistic meaning of the wave function, makes as little sense as electron point configuration given by $X$. 

Here a physicist will come in with objective to save the game by confusing the mind of the critic by the following arguments: The wave function 

• encodes possibilities, not realities,
• represents our knowledge or information about a quantum system — not the system itself,
• is a catalog of our expectations, not a real wave.
• guides point particles.
• is real and collapses.

These are all attempts of doubling down by inventing a new language hiding the principal difficulty and then using the new language to meet questioning criticism.

There is an alternative to QM in the form of RealQM with wave function representing a collection of non-overlapping electron densities sharing a 3d spatial coordinate, and as such having a clear physical meaning:

• The wave function of QM has no physical meaning.
• The wave function of RealQM has a direct physical meaning.

A physical science theory without physical meaning will in the long run loose credibility, and this is what today takes the form of a crisis of modern theoretical physics. How will the crisis be resolved?

Wittgenstein on Quantum Mechanics

Wittgenstein starts out in Tractatus (1921):

• The world is the totality of facts, not of things.
• We make to ourselves pictures of facts.
• In order to tell whether a picture is true or false, we must compare it with reality.

Wittgenstein followed the development of Quantum Mechanics QM with a critical mind stating that physicists should not occupied be with "interpretations" QM because, as stated in Lectures on the Foundations of Mathematics (1939) and in statements attributed to him:

• Physics is not a theory but the description of facts by means of mathematical symbols.  
• If people did not talk nonsense about quantum theory, there would be nothing remarkable about it.
• Quantum mechanics does not explain anything; it only describes phenomena by means of a calculus.
• When people say that something is "explained" by quantum mechanics, what they mean is that we can calculate it.
• A good model in physics is not one that shows us how nature really is, but one that gives us a clear method of description.

Concerning the probabilistic nature of QM, as opposed to classical physics:

• Physicists say: the laws of quantum mechanics are probabilistic. But probability is not something that exists in nature, like a gas or a liquid. It is a measure we use — a form of description.
• To say "nature behaves probabilistically" is as nonsensical as to say "nature obeys logic".
• We do not describe how nature is — we construct a grammar in which our descriptions make sense.
• The physicists say: at the atomic level there is no causality.
But what are they describing when they say this? A new form of experience?
No. They are proposing a new rule for the use of words like "cause"

W insists that “probability” is a rule of representation — part of the grammar of our scientific language. It tells us how we may speak about phenomena, not what the world is like.

Summary: We read that W like Einstein was critical to an idea that "atoms play dice" which is central to Quantum Mechanics in its main Bohr-Born-Heisenberg Copenhagen "interpretation". W emphasises the role of mathematics as a language/grammar to describe physics rather than to show what physics is. W makes a distinction between classical physics which can be described in a meaningful language rooted in our experience, and QM asking for a new language with new meaning for which the experience is lacking. W would have been happy to meet Real Quantum Mechanics using the same language as classical physics. 

Here is my idea of Wittgenstein's worldview as basically classical physics - rational mechanics to be used as follows:

• Formulate a mathematical model of the World which is meaningful and computable.
• Give input to the model and let it after computation respond by output and compare with reality.
• Use the model as language to speak about/with the World.  

To make QM serve this role is complicated since it has no clear physical meaning nor is computable. 

PS One can make the following distinction as concerns mathematical models/theories:

1. The model is a (more or less complete) representation of the real world.
2. The model is a representation of an imagined world which can be real (more or less).
3. The model is a representation of an imagined world which cannot be real.   

 Here 1. makes the map equal to the territory. while 2. could be W's view, and QM falls into 3. 

Modern Physics: Imagination = Reality: Hyperreality

Modern physics started in 1900 with Planck's mathematical "trick" of imagining a "smallest quantum of energy" to derive Planck's Law of blackbody radiation about an imagined "empty cavity" filled with "degrees of freedom". 

Einstein followed up in 1905 imagining himself riding on a wave of light at the speed of light, or watching a train pass a station with half the speed of light. 

The imagination expanded in 1926 into describing a World filled with "particles" by a complex-valued  "wave function" $\Psi (X,t)$ with "coordinates" $X$ ranging over a "configuration space" with a separate 3d Euclidean space coordinate identifying the position at time $t$ of each "particle" of the World. 

The wave function $\Psi (X,t)$ was viewed to carry "all there is to know" about the World however in a cryptic form which needed unwinding to make sense. 

The evolution in time of $Psi (X,t)$ as function of $X$ was given as solution to a Schrödinger equation. This was the birth of Quantum Mechanics as the foundation of modern physics.

Key question: What is the physical meaning of the wave function $\Psi(X,t)$ with $X$ ranging over configuration space? 

In 1927 Max Born suggested:

• $\vert\Psi (X,t)\vert^2$ is the probability that the particle configuration of World at time $t$ is given by $X$. 
• $\Psi (X,t)$ does not describe an actual configuration $X$ but only a possible configuration. 

This was quickly accepted because it appeared as the only possibility, which decided the path of modern physics to follow. 

The step from actual to possible configuration was a step from firm classical ground into something completely different. A grandiose step worthy a modern physicist. 

Classical physics seeks to describe the actual evolution in time of a physical system from some given initial state typically by time-stepping computational procedure. For each given initial state a final state is computed. But it is out of question to consider all possible initial states because it requires infinite computational work. 

But going from actual to possible as in QM involves all initial values, which means the $\Psi (X,t)$ with $X$ ranging over configuration space is uncomputable. This means that the goal of describing the World by a wave function $\Psi (X,t)$ cannot be reached because the required computational work cannot be created.

How are modern physicists handling the impossible situation they have created? 

The only possibility appears to be to give up the classical physics distinction between a World of specific real configurations evolving in time by some form of computation, and a Mind of an Observer which follows  the evolution but is also free to invent whatever comes to mind. By replacing computable by "thinkable" it is thus possible to let the Mind of an Observer be part of the World and so get around limitations of reality.

Does it work? What happens if we give up the distinction between observer and observed, or painter and model as depicted by Picasso? 

It opens to self-interaction which is a delicate subject. Is imagined reality also reality? A classical physicist would say no, and a modern yes while having to deal with the infinities of QED.

Baudrillard describes imagined reality conceived as reality as hyperreality as an (potentially dangerous)  aspect of modern society. It seems that QM is concerned with hyperreality rather than reality. See next post.

Quantum Mechanics as Thought Experiment as Hyperreality

Modern physics today faces a credibility crisis from lack of realism introduced 100 years ago in the form  of Standard Quantum Mechanics StdQM described by Schrödinger's equation in terms of a multi-dimensional wave function without real ontological physical meaning, only a statistical epistemological meaning in the mind of an Observer. 

This represents a fundamental break with classical physics, where the Observer has no active role to play. 

For 100 years it has been possible to play a double game shifting between ontology (what is in the real world) and epistemology (what is in the mind of an Observer) to cover up the lack of physical meaning of the multi-d wave function. 

To illustrate this state of affairs, consider a Hydrogen atom with one electron surrounding a proton at $x=0$ with the following wave function depending on a 3d Euclidean space coordinate describing the ground state

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

StdQM gives the wave function the following interpretation: 

• $\psi^2 (x)$ is the probability of finding the electron at position $x$. 
• $\psi^2 (x)$ is a probability density.
• Here the meaning "of finding" is crucial?
• Is it possible to experimentally "find" an electron at a particular point $x$?
• No, this is impossible because an electron is not a classical particle.
• There is no real experiment expressing "finding an electron a particular point in space".
• The only possibility is to give "finding" the meaning of a thought experiment. 
•  $\psi^2 (x)$ is the probability density of imagining finding an electron at position $x$.  

RealQM as an alternative to StdQM gives a different meaning in terms of classical deterministic physics:

• $\psi^2 (x)$ is an electron charge density in $x$ as real physics. 
• No probability is involved. No need to give $\psi^2 (x)$ any other meaning than charge density.

The argument extends to atoms with more than one electron. For an atom with $N$ electrons, the StdQM wave function $\psi (x_1, x_2,...,x_N)$ depends on $N$ 3d spatial variable $x_1,...,x_N$ and 

• $\psi^2 (x_1,x_2,...,x_N)$ is the probability of finding electron 1 at $x_1$, electron 2 at $x_2$, electron N at $x_N$. 
• This is again only possible as a thought experiment. 

The electron configuration of RealQM is the result of an energy minimisation over non-overlapping one electron charge densities without need of probability.

In short, StdQM is unphysical in the sense of not connecting theory to real experiments, but instead to imagined thought experiments. 

Thought experiments can be illuminating if thoughts can be transformed to reality. If not thought experiments stay in the head of an Observer and the connection to reality is compromised.  This is the case with StdQM and the result after 100 years is a severe crisis of credibility. Sum up:

• Classic: Independent Reality exists outside Observer. Observer is passive. RealQM
• Modern: Observer active. Reality is what goes on in the mind of the Observer. StdQM 

This connects to the idea of hyperreality used by Baudrillard to capture an important aspect of modern digital society: 

• Mathematical model describes reality which does exist: RealQM: Reality: Classical physics.
• Mathematical model describes a reality which does NOT exist: StdQM: Hyperreality: Modern Physics.