Quantum Physics as HyperReality = Crisis

Modern physics as Quantum Mechanics QM is based on a (complex-valued) wave function $\Psi (X)$ depending on a $3N$-dimensional configuration space coordinate $X$ for an atomic system with $N$ electrons giving each electron a separate 3d Euclidean space. 

Configuration space is a mathematical construct which does not have any physical representation for $N>1$. The wave function as a function defined on configuration space shares the same lack of physical representation. The wave function evolves in time as a mathematical construct satisfying a Schrödinger equation. 

To give QM a meaning beyond a mathematical game it is necessary to give the wave function a physical meaning, which has drawn much attention without any common view ever being formed. The credibility of modern physics has suffered from this failure and can be seen as the main reason for its present commonly witnessed crisis, which can be summarised as follows: 

• classical physics = mathematical model with physical origin.   
• quantum physics = mathematical model without physical origin.     

To handle the lack of physical origin in quantum physics, the logic has been twisted by turning the mathematical model into a new form of reality, which then perfectly fits the model. This connects to the French philosopher Baudrillard's concept of hyperreality as imagined reality formed from a model without origin, when the model is turned into real. 

That this is what de facto happened in quantum physics, is evidenced by the fact that quantum model predictions always perfectly match (imagined) reality.  

We can summarise (see also this post and this post):

• classical physics: reality is turned into mathematical model
• quantum physics: mathematical model is turned into hyperreality.

There is a further complication coming from the lack of physical origin/representation of the wave function, namely the conceptual understanding of a mathematical model without origin in some physics connecting to our experience as human beings. In short, how can be capture in our minds a wave-function defined over a $3N$-dimensional configuration space, when our experience is 3d?

The modern quantum physicist thus has to struggle with an imagined reality represented by a mathematical model without real origin as support for imagination. How to imagine a reality when the imagination has nothing relevant to feed from?

There is a way out of this dilemma: Start with RealQM as a quantum model with real origin. 

Recall that we can understand forms of virtual reality without origin but only so far the virtual reality is based on concepts of reality. If the virtual reality displays 6 space dimensions, then we will not be able to properly understand (but possibly pretend to).

Baudrillard uses Disney World as a form of hyperreality as a model of an American society which has never existed, thus without true origin, but yet in familiar terms we can understand.   

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.

    

No Nobel Prizes to Theoretical Quantum Mechanics and General Relativity!

Here is a perspective on the previous post:

Let us consider how the Nobel Committee has awarded work of major theoretical nature on Quantum Mechanics as the foundation of modern physics: 

1932 Werner Heisenberg: Matrix mechanics, 1933 Erwin Schrödinger: Schrödinger wave equation, 1933 Paul Dirac: Dirac equation = Relativistic wave equation, 1954 Max Born: Statistical interpretation of wave function, which can be complemented with very preliminary  1918 Max Planck: Quantum of energy/action $h\nu$ 1921 Albert Einstein: Quantum of light $h\nu$ = photon. There are several Prizes to experimental work connecting to "quantum",  but none to any of the fundamentally different interpretations seeking to specify the physical meaning of Schrödinger/Dirac wave equation and wave functions including: Copenhagen Bohr-Born-Heisenberg 1927, Bohmian mechanics 1952, Many-Worlds 1957, Collapse Models 1990-2000. This means that through the 100 years history of QM as the foundation of modern physics, the physical meaning of the theory is still completely open. The common agreement is that "QM works" exceedingly well, so amazingly well that there not a single experiment not in full agreement with QM, while it is also agreed that "nobody knows why". None of the above interpretations has shown to be worthy of a prize, indicating that they are all wrong.  So the last time a Prize was awarded to QM including theory, was to Born in 1954 for his statistical interpretation in 1927, while this was the reason he was left out in 1932-33.  Modern physics is based on the theories of QM + General Relativity GR. It is very remarkable that no Prize has been given to a discovery of the physical meaning of either the "quantum" of QM or the "curved space-time" of GR.  It is natural to connect the present crisis of theoretical physics to a growing feeling of lack credibility coming from lack of Prize to theory over a very long time.  Recall also that an experiment without theory is blind. An experiment must be interpreted to have a meaning. A number or blip on a screen says nothing in itself.  Recall that all trouble comes from the generalisation of Schrödinger's equation for the Hydrogen atom with is wave function representing its one electron charge density in concrete physical terms, to atoms with more than one electron in terms of a multi-dimensional wave function without physical representation. Real Quantum Mechanics offers a different generalisation with concrete charge density representation. A Prize to RealQM is not unthinkable...

Nobel Prize in Physics 2025 vs Ukulele Vibrating Strings

The 2025 Nobel Prize in Physics was awarded to John Clarke, Michel H. Devoret, and John M. Martinis 

• for experiments that revealed quantum physics in action,
• particularly their pioneering work in demonstrating that quantum mechanical effects can manifest at a macroscopic (larger-than-atomic) scale.

The general idea is that the microscopic world of quantum mechanics contains wonderful subtle small-scale phenomena of superposition and entanglement not present in the macroscopic world where averaging destroys small scales. 

The idea of quantum computing is to use quantum states in superposition to perform computations in parallel and so reach entirely new levels of computational power. 

The idea of the Nobel Prize is to upscale quantum capacities for parallel computing to larger scales allowing more efficient error control and input/output.  

Upscaling of microscopics to macroscopics is opposite to the downscaling of mechanical calculators to microprocessor of computers behind the digital revolution.  

There is a clear connection to recent blog posts asking to what extent the microscopic quantum world is different from the macroscopic world, with the conclusion that the difference is not so big after all. 

If so, it should be possible to find the wonderful quantum effects like superposition directly on familiar macro-scales like a vibrating string. This opens to use e g an ukulele as efficient computing device in room temperature, instead of super-conduction at very low temperatures. 

Mystery of Planck's Constant Revealed

This is a clarification of this post on the physical meaning of Planck's constant $h$ and so of Quantum Mechanics QM as a whole. The basic message is that the numerical value of $h=6.62607015\times 10^{-34}$ Jouleseconds is chosen to make Planck's Law fit with observation and that this value is then inserted into Schrödinger's equation to preserve the linear relation between energy and frequency established in Planck's Law. 

Quantum Mechanics is based on a mysterious smallest quantum of energy/action $h$ named Planck's constant, which was introduced by Planck in 1900 as a "mathematical trick" to make Planck's Law of blackbody radiation fit with observations of radiation energy from glowing bodies of different temperatures. 

The mysterious Planck's constant  $h$ appears in Planck's Law in the combination $\frac{h\nu}{kT}$ where $\nu$ is frequency, $k$ is Boltzmann's constant and $T$ temperature with $kT$ a measure of energy (per degree of freedom) from thermodynamics. In particular  

•  $\nu_{max}=2.821\frac{kT}{h}$                   (*)

shows the frequency of maximal radiation intensity referred to as Wien's Displacement Law, which also serves as a cut-off frequency with quick decay of radiation intensity for frequencies $\nu >\nu_{max}$.  

If we translate (*) to wave length we get a corresponding smallest wave length 

• $\lambda_{min}= 0.2015\frac{hc}{kT}=\frac{0.0029}{T}$ meter
• $\lambda_{min} \approx 10^{-5}$m for $T=300$ K 
• $\lambda_{min} \approx 5\times 10^{-7}$m for $T=5778$ K (Sun)

We see that smallest wave length is orders of magnitude bigger that atomic size of $10^{-10}$ m, which tells that blackbody radiation is a collective wave phenomenon involving many atoms per radiated wave length.

Summary: 

• Planck's constant $h$ serves the role of setting a peak frequency scaling with temperature $T$ with corresponding smallest wave length scaling with $\frac{1}{T}$.
• The smallest wave length is many orders of magnitude bigger than atomic size showing blackbody radiation to be a collective wave phenomenon involving coordinated motion of many atoms. 
• Planck's constant $h$ thus has a physical meaning of setting a smallest spatial resolution size scaling with $\frac{1}{T}$ required for coordinated collective wave motion supporting radiation. 
• Higher temperature means more active atomic motion allowing smaller coordination length. 
• The standard interpretation of $h$ as smallest quanta of energy lacks physical representation.
• Connecting $h$ to coordination length is natural and gives $h$ a physical meaning without mystery. 
• Formally h = energy x time = momentum x length representing Heisenbergs Uncertainty Relation with h connecting to spatial resolution. Formally $E=h\nu=pc$ and so $h=p\lambda$.   

PS Recall that Schrödinger's equation for atoms and Maxwell's equations for light covers a very wide range of phenomena in what is referred to as a semi-classical model as half-quantum + half classical. In this model light is not quantised and there are no photons to worry about. The above meaning of $h$ from Planck's Law is understandable. The mystery is restored in Quantum Electro Dynamics QED where Maxwell's equations are replaced by the relativistic Dirac's equations and particles/photons appear as quantised excitations of fields. QED is way too complicated to be used for the wide range covered by QM and so is reserved for very special geometrically simplified situations. 

The Physical Meaning of Planck's Constant $h$

Planck's constant $h$ appears in several different contexts in quantum physics including 

1. Planck's Law of blackbody radiation.
2. Schrödinger's Equation SE describing the spectrum of the Hydrogen atom. 

Here 1. involves collective behaviour of atoms, while 2. concerns one atom. The standard view is that the double appearance of $h$ in two fundamentally different contexts is an expression of a deep connection in a mysterious quantum world, which cannot be understood.  

Let us see if we can uncover some the mystery. We recall from this post  that $h$ was introduced by Planck in 1900 to make Planck's Law fit with observation, specifically in a high frequency cut-off factor $C(\alpha )$ with $\alpha =\frac{h\nu}{kT}$ where $\nu$ is frequency, and $k$ as Boltzmann's constant combined with temperature $T$ into $kT$ serves as an energy per degree of freedom in thermodynamics.  For $h\nu << kT$ then $C(\alpha ) =1$ and for $h\nu >kT$, $C(\alpha )$ decays to zero. The quantity $h\nu$ is thus compared to the elementary energy $kT$ and so $h\nu$ is referred to as a basic quantum of energy $E=h\nu$ connected to the frequency $\nu$. This is a linear relation and $h$ is the constant of proportionality between energy and frequency. 

Energy $E$ is thus connected to frequency $\nu$ by $E=h\nu$ with physical meaning of setting the high-frequency cut-off in Planck's Law in relation to $kT$.  This explains the function of $h$ in 1. as serving in high frequency cut-off. High-frequency connects to small-wavelength which connects to spatial resolution. Wien's displacement law takes the form $\nu \approx \frac{k}{h}T$ with linear scaling between frequency and temperature as measure of energy.  We see that $h$ appears in a high-frequency threshold condition scaling with $T$ which gives $h$ a physical meaning but not as measure of physical quantity representing some smallest quantum of energy $h\nu$. Threshold condition and not physical quantity.  

We now turn to 2. recalling Schrödinger's Equation SE with $H$ a Hamiltonian:

• $ih\frac{\partial\psi}{\partial t}+H\psi =0$

with solution $\exp (i\frac{E}{h}t)\Psi$ where $\Psi$ is an eigenfunction satisfying $H\Psi =E\Psi$ with $E$ an eigenvalue as energy. We see frequency $\nu =\frac{E}{h}$ with thus $E=h\nu$. We thus see that SE is constructed to carry a linear relation between energy and frequency, more specifically the relation $E=h\nu$. Notice that temperature $T$ does not appear in SE, only in the context of blackbody radiation as collective behaviour.

We understand the value of $h=6.62607015\times 10^{-34}$ Jouleseconds is chosen to make Planck's Law fit with observation as concerns high frequency cut-off based on $h\nu$ scaling linearly with frequency $\nu$, and with $T$ in Wien's displacement law.. 

Once the value of $h$ was determined to fit 1. with linear scaling of energy vs frequency as $E=h\nu$, that value of $h$ was inserted into SE with the effect of preserving the linear scaling of energy vs frequency as $E=h\nu$. The appearance of $h$ is SE was not due to a miraculous intervention of Nature, but simply the effect of putting it in by the design of SE. 

Summary: 

1. The value of $h$ as conversion factor between energy and frequency as $E=h\nu$ in a linear relation, is set to make Planck's Law fit with observation. 
2. That value of $h$ is then inserted by design into SE to keep the $E=h\nu$ linear relation between energy and frequency. 
3. The design is elaborated by connecting a one electron energy jump $E$ to emission/absorption of one photon of frequency $\nu$ determined by $\nu =\frac{E}{h}$ as the mechanism behind the spectrum of Hydrogen.
4. In short: The appearance of  $h$ is SE is not deep mystery, but simply the design of SE.  
5. Is the fact that SE describes the observed spectrum of Hydrogen a mystery? Not with charge density representation of the wave function solution to SE, in which case SE has classical continuum mechanical form of a vibrating elastic body and as such not a mystery. 
6. Extension to atoms with more than one electron presents new questions to be answered differently by Standard QM and RealQM.

Einstein vs Lorentz, Planck and Bohr: Tragedy

Modern physics as relativity theory + quantum mechanics was born out of two misconceptions formed in the mind of the young Einstein as patent clerk in Bern in 1905 with little scientific training, but strong ambition to contribute to the emerging modern physics of  

1. Blackbody radiation.
2. Photoelectricity. 
3. Apparent absence of a unique aether carrying electromagnetic waves.  

In 1900 Planck had derived Planck's Law of blackbody radiation based on a smallest quantum of energy $h\nu$ connected to radiation/light of frequency $\nu$ with $h=6.55\times 10^{-34}$ Jouleseconds named Planck's constant. Planck did not assign any physical meaning to the smallest quantum $h\nu$ and viewed it simply as a "mathematical trick" used to derive Planck 's Law. 

In one of Einstein's 5 articles from the "miraculous year" 1905, Einstein assigns the quantum $h\nu$ a physical meaning as the energy of a "photon" as a "light particle" in a heuristic explanation of 2. Einstein thus did what Planck had said does not make any sense. In 1926 the mysterious quantum $h\nu$ appeared in Schrödinger's equation for the Hydrogen atom as the basic mathematical model of quantum mechanics.

In another 1905 article Einstein assigned the Lorentz transformation a physical meaning, which Lorentz had said would not make any sense, and so formed his Special Theory of Relativity SR.

Einstein thus contributed to the formation of modern physics in 1905 by attributing physical meanings to both Planck's quantum $h\nu$ and the Lorentz transformation, in direct contradiction to both Planck and Lorentz.  

As time went on and the authority of Planck and Lorentz faded, Einstein's ideas about physicality of photons and the Lorentz transformation slowly gained support, but when they became the standard of the new Quantum Mechanics of Bohr-Born-Heisenberg-Dirac in the 1930s, then Einstein said: Stop, QM is no longer real physics!  Only Schrödinger said the same thing, but both were efficiently cancelled by Bohr. 

Einstein thus started out and ended as a tragic figure. First he genuinely misunderstood Planck and

Lorentz about physical reality and so contributed the development of a new form of physics, which he on good grounds criticised for lacking physicality. The irony was that physicists listened when he was wrong but not when he was right.   

The Secret of $E=h\nu$ as Smallest Quanta of Energy/Action

Quantum Mechanics was born from the smallest quantum of energy (or action) $h\nu$, with $h$ Planck's constant and $\nu$ a frequency, appearing in Planck's mathematical analysis of blackbody radiation which captured the dependence on temperature $T$ and $\nu$ of the energy transfer $E$ from a glowing body in the form of Planck's Law 

• $E(\nu, T)=\gamma T\nu^2\times C(\alpha )$ with $\gamma =\frac{2k}{c^2}$,     (1)

where $k$ is Boltzmann's constant and $c$ the speed of light, and 

• $C(\alpha )=\frac{\alpha}{\exp^\alpha-1}$ with $\alpha =\frac{h\nu}{kT}$ 

is a high-frequency cut-off  factor with activation if $h\nu >kT$.   

The analysis concerned a hypothetical blackbody as a cavity with reflecting walls filled with waves of many frequencies brought to a common temperature by the presence of a small piece of sooth.

Planck determined a value of $h=6.55\times 10^{-34}$ Jouleseconds to make his Law fit with observation of the cut-off factor $C(\frac{h\nu}{kT})$ with $\nu$, $k$ and $T$ given.  

The smallest quantum of energy/action $h\nu$ was used as a "mathematical trick" to get a the observed dependence of the high-frequency cut-off factor on $\frac{\nu}{T}$ as an expression of Wien's displacement law. No real physics. Not yet any atom.

The next step was Einstein's association of the smallest quantum of energy/action $h\nu$ to exactly one "particle of light" of frequency $\nu$ later named "photon", in his 1905 heuristic analysis of the photo-electric effect as "one electron - one photon". No real physics. Not yet any atom. Einstein formally identified the energy $E$ of one electron through $E=h\nu$, but he did not yet have any model of an electron. 

In 1913 Bohr presented a model of a Hydrogen atom as one electron revolving around a kernel in different possible orbits of with certain specific energies, with differences $E$ of these possible one-electron energies showing to fit with the observed frequencies $\nu$ of the radiation spectrum of Hydrogen if the shift/jump of one electron was assigned an energy $E=h\nu$. Success, but an ad hoc model of an electron without physics with an ad hoc assignment of exactly the energy $E=h\nu$ to the jump of one electron between the two energy levels.   

In 1926 Schrödinger presented a wave equation model of a Hydrogen atom in terms of a wave function representing electron charge density with eigenvalues coinciding with the energy levels of the Bohr model. Again with an ad hoc association of the energy $E=h\nu$ to one electron shifting between energy levels differing by $E$. Great success in the form of a classical continuum model, but the generalisation to atoms with more than one electron carried physics into the new modern world of quantum physics fundamentally different from continuum physics with Planck's constant $h$ setting a form of smallest scale requiring quantisation of physics. We sum up:

The secret of Planck's constant $h$ with $h\nu$ smallest quantum of energy/action.  

1. A value of $h$ is determined to make the high frequency cut-off depending on $\frac{h\nu}{kT}$ in Planck's Law of blackbody radiation, fit with observation.
2. The value of $h$ so determined is connected to Schrödinger's Equation SE for a Hydrogen atom with one electron in the following way. The eigenvalues of SE represent different possible energies of the electron and differences $E$ between energy levels represent shifts of energy $E$ of one electron, which in SE is assigned a frequency $\nu = \frac{E}{h}$ so that $E=h\nu$. 
3. The shift between energy levels of the one electron of the Hydrogen atom $E=h\nu$ is associated with emission/absorption of one photon of frequency $\nu$ carrying an energy of $h\nu$. 

Altogether we understand that Planck's constant $h$ is determined to make the high-frequency cut-off in Planck's Law fit with observation. This value is then used to assign the energy $E=h\nu$ to one photon corresponding to the jump of one electron of a Hydrogen atom between energy levels differing by $E$.

We understand that high-frequency cut-off is related to small-wavelength cut-off as condition on spatial resolution as discussed in detail in Computational Blackbody Radiation. 

To understand that the smallest quantum of energy/action $E=h\nu$ is a definition without physical representation, it helps to recall that $h$ in the 2019 SI specification of units is assigned the exact value $6.62607015\times 10^{-34}$, which differs from Planck's original value $6.55 \times 10^{-34}$. If $h\nu$ really carried some real physics, it would not make sense to assign it a specific value, since it does not make sense to prescribe real physics how to behave. Ok?

PS1 A basic difficulty of understanding theoretical physics is that the distinction beween definition and physical fact is often blurred. If you do not understand that the speed of light in vacuum and smallest quantum of energy are assigned certain values rather than being given by the Creator, you miss something very essential.

PS2 The central theme in all the above models is the radiating atom in radiative equilibrium with light of certain frequencies showing up in the emission or absorption spectrum of the atom, as a resonance phenomenon analysed in Computational Blackbody Radiation. The basic mathematical model takes the following form in a wave function $\phi (t)$ depending on time $t$ satisfying

• $\ddot\phi -\nu^2\phi -\gamma\dddot\phi = f$           (2)

where a dot signals differentiation with respect to a time variable, and $f$ is forcing with frequency $\tilde\nu\approx \nu$ in near resonance and $\gamma <<\frac{1}{\nu^2}$. The essence of radiative equilibrium as output = input reads (in terms of time averages)

• $\gamma\ddot\phi^2 =\gamma T \nu^2 = f^2$,          (3)
• $T = \dot\phi^2+\nu^2\phi^2$. 

Here $T$ represents temperature for a macroscopic body, while for a single atom rather $T\sim N$ with $N$ number of electrons. The 

Planck's Law connects the differences of discrete electronic energy levels $E=h\nu$ of an atom in radiative equilibrium with light of frequency $\nu$ appearing in the emission/absorption spectrum of the atom as isolated atom or as part of a macroscopic body, with $h$ acting like a constant connecting energy with frequency.  

Planck's Faustian Deal: The Quantum

Here is a short excerpt from my book Dr Faustus of Modern Physics giving perspective on the birth in 1900 of Quantum Mechanics with Planck's mathematical analysis of blackbody radiation introducing $E=h\nu$ as a smallest quantum of energy. 

To boost his career and the science of the booming German Empire, Max Planck, professor at the University of Berlin with a background from thermodynamics, took on the main open problem of physics at the end of the 19th century, namely to explain why the ultra-violet catastrophe of blackbody radiation predicted by classical theoretical physics cannot be observed. At stake was the credibility of a science of physics (and the German Empire) predicting very intense high-frequency radiation which simply refused to exist. The stakes were thus very high and Planck with ambition stepped in:

• The whole procedure was an act of despair because a theoretical interpretation had to be found at any price, no matter how high that might be... 

The price was to give up his soul as very serious scientist with deep conviction to classical ideals, which paved the way for new quantum physics giving up classical principles of reality, causality and determinism, now in deep crisis.  

1. Nobel Prize to Planck

 The Nobel Prize in Physics 1918 was awarded (in 1919) to Max Planck:

• in recognition of the services he rendered to the advancement of Physics by his discovery of energy quanta.

It took the Nobel Committee more than 10 years to come to this conclusion, because Planck’s new concept of a smallest quantum of energy was so difficult to swallow, described by the Swedish mathematician Ivar Fredholm as “hardly plausible”. In 1918 the Committee gave in under pressure to give the prize to Bohr and Einstein, which required a prize to Planck first. The presentation speech by Ekstrand stated:

• Planck’s radiation theory is, in truth, the most significant lodestar for modern physical research, and it seems that it will be a long time before the treasures will be exhausted which have been unearthed as a result of Planck’s genius.
• Planck constant, proved, as it turned out, to be of still greater significance: The product $h\nu$, where $\nu$ is the frequency of vibration of a radiation, is actually the smallest amount of heat which can be radiated at the vibration frequency $\nu$. This theoretical conclusion stands in very sharp opposition to our earlier concept of the radiation phenomenon.

Planck was thus viewed as having “discovered” a physical phenomenon of “energy quanta”, which in fact was a “theoretical conclusion”. This contradiction has come to form the ideology of modern physics made possible by breaching the classical holy distinction between reality and mathematical model.

2. Planck's Confession

From Planck's self-biography:

• We shall now derive strange properties of heat radiation described by electromagnetic wave theory.
• ..the whole procedure was an act of despair because a theoretical interpretation had to be found at any price, no matter how high that might be... 
• Either the quantum of action was a fictional quantity, then the whole deduction of the radiation law was essentially an illusion representing only an empty play on formulas of no significance, or the derivation of the radiation law was based on sound physical conception. Mechanically, the task seems impossible, and we will just have to get used to it (quanta). 
• My futile attempts to fit the elementary quantum of action into classical theory continued for a number of years and cost me a great deal of effort. Many of my colleagues saw in this something bordering on a tragedy (Planck shortly before his death).
• I tried immediately to weld the elementary quantum of action somehow in the framework of classical theory. But in the face of all such attempts this constant showed itself to be obdurate...
• My futile attempts to put the elementary quantum of action into the classical theory continued for a number of years and they cost me a great deal of effort.
• The assumption of an absolute determinism is the essential foundation of every scientific inquiry.
• All matter originates and exist only by virtue of a force which brings the particle of an atom to vibration and hold this most minute solar system of the atom together. We must assume behind the existence of this force the existence of a conscious and intelligent mind. This mind is the matrix of all matter...
• In order to find the correct resonator entropy S it must be assume that the energy U of a resonator with frequency ν can only take on discrete energy values, to wit, integer multiples of h times ν, in contrast to classical theory where U can be any multiple, integer or not, of ν. We now say that U is quantised.
• My maxim i always this: consider every step carefully in advance, but then, if you believe you can take the responsibility for it, let nothing stop you.
• For by nature I am peaceful and disinclined to questionable adventures...for unfortunately I have not been given the capacity to react quickly to intellectual stimulation.

3. Planck on Politics

Planck lost his son Karl in combat during 1st World War and his son Erwin was executed after a plot against Hitler at the end of the 2nd World War. Planck signed together with 93 German intellectuals the Appeal to the Cultured Peoples of the World on 4 October 1914:

• We declare the leaders of German art and science to be at one with the German army.

Planck reports as Rector of Berlin University in 1914:

• The German people ha found itself again. One thing only we know, that we members of our university...will stand together as one man and hold fast until - despite the slander of our enemies - the entire world comes to recognise the truth and German honor.
• But we shall also see an feel how, in the fearful seriousness of the situation, everything that a country could call its own in physical and moral power came together with the speed of lightning and ignited a flame of holy wrath blazing to the heavens, while so much that had been considered important and desirable fell to the side, unnoticed, as worthless frippery.

Unified Field Theory of Matter + Light Without Quantum

The unfinished revolution of modern physics as quantum physics is unification with classical continuum physics expressed as Newton-Maxwell differential equations in terms of gravitational and electromagnetic fields as functions of 3d space coordinates and a time coordinate as real numbers forming a space-time continuum without smallest scale. 

Classical physics describes a macroscopic world of matter separated from a microscopic world of light as a Newton-Maxwell deterministic Field Theory covering a change of scale of $10^{35}$ from gravitation on billions of light-years down to nanometers of visible light. 

This seemed to be the end of physics, but with the start of the 20th century of modernity a discovered new world of atoms required something new beyond Newton-Maxwell. In 1915 Danish physicist Niels Bohr presented a model of the electron of the Hydrogen atom with energies restricted to the observed discrete spectrum of Hydrogen as a form quantisation, however without convincing physics.    

In 1926 Austrian physicist Erwin Schrödinger presented a model of the Hydrogen atom as an eigenvalue problem of classical form with the eigenvalues representing energies exactly corresponding to the observed spectrum of Hydrogen. This saved classical Field Theory in the case of only one electron, but the world of atoms with more than one electron remained to be modeled to maintain credibility of the new atomic physics.  

This is where history of physics took a turn which became the leading principle of modern physics through the 20th century into our time as a break with classical deterministic physics in 3 space dimensions into a new form of probabilistic physics in $3N$ space dimensions for an atom with $N>1$ electrons without clear physicality. This became the story of Standard Quantum Mechanics StdQM as the fundamental theory of modern physics. It came with the stroke of a pen by a purely formal extension by adding a new set of space variables for each new electron. An easy catch which however came with severe side effects of leaving classical deterministic continuum physics in 3d for a new world of probabilities instead of actualities. 

StdQM thus split physics into classical Newton-Maxwell continuum theory for macroscopic matter and microscopic light into new physics with main objective to describe the interaction between microscopic atoms and light. Physicists claimed to be forced to take this step by a Nature refusing to be described within classical continuum physics, in a heroic or rather desperate act of giving up classical ideals of rationality in the words of Max Planck, who took the first step in his 1900 analysis of blackbody radiation starting from a proclaimed ultra-violet catastrophe. 

To avoid catastrophe Planck introduced a concept of smallest quantum of energy $h\nu$ connected to light of frequency $\nu$ and $h$ a small constant, which was picked up by the young Einstein in 1905 in a "heuristic" explanation of the photoelectric effect returning to Newton's since long abandoned idea of light as a stream of light particles each carrying an energy $h\nu$. From these acts of desperation was then  StdQM born 20 years later as a Schrödinger equation in terms of a multi-d wave-function carrying probabilities of distributions of quanta of energy.   

So was modern physics as StdQM formed by modern physicists under the condition that blackbody radiation and the photoelectric effect cannot be explained within classical continuum physics.

If this condition would show to not be binding, then the premises for modern physics would change. RealQM offers an explanation of both blackbody radiation and the photoelectric effect which is based on a threshold condition on wave frequency $\nu$ as a condition on spatial resolution instead of any quanta of energy. RealQM thus offers a Unified Field Theory within classical continuum mechanics of matter+light over all scales, which was the unfinished dream of both Einstein and Schrödinger,   

PS. I checked with chatGPT what could have happened if blackbody radiation, photoelectric effect and atomic spectra had been resolved within classical continuum mechanics, as suggested by RealQM, and got this counterfactual answer:

• ✅ Yes: Up through ~1920, a clever deterministic continuum model could plausibly have “explained away” choseblackbody, photoelectric, and spectra. Physics might have developed as a wave-resonance continuum theory instead of quantum mechanics.
• ❌ But: Once Compton scattering and single-particle double-slit came in, the cracks would show. The particle-like momentum transfer and the self-interference of single quanta are incompatible with any local classical continuum.
• So your hunch is right: a classical deterministic continuum could have survived if physics stopped before Compton + double-slit. But with those experiments, and later Bell tests, the “classical-only” path would collapse.   

We see that modern physics was not really forced to follow the track chosen by Bohr-Born-Heisenberg under protests from Schrödinger...  

Schrödinger Equation Anniversary 1926-2026

In March 1926 the 39 year old Austrian physicist Erwin Schrödinger published an article entitled Quantisation as Eigenvalue Problem presenting a mathematical model of a Hydrogen atom with one electron in terms of classical continuum mechanics, which kick-started modern physics into the era of Quantum Mechanics, since it exactly captured the observed spectrum of Hydrogen.

The success was complete, and Schrödinger was very happy with his one-electron mathematical model as a wave equation in terms of a wave function representing electron charge density of clear physical nature like any density of classical continuum mechanics. 

But the happiness did not last long, since his one-electron model was quickly generalised to atoms with $N>1$ electrons in the hands of Bohr-Born-Heisenberg BBM in terms of a wave function $\Psi$ depending on $3N$ spatial coordinates, which could only be given a probabilistic meaning and so could not be accepted by Schrödinger with his deep conviction of physics as reality. The effect was that Schrödinger was quickly "cancelled" and had to spend the rest of his life as outsider without any say. The success was turned into its opposite.      

At a Dublin 1952 Colloquium Schrödinger restated his deep conviction carried for 26 lonely years that history took the wrong turn after March 1926 when his Schrödinger equation for Hydrogen was hijacked by Bohr-Born-Heisenberg to form the Copenhagen Interpretation as Standard Quantum Mechanics StdQM, which has filled text books, students and physicists minds for 100 years and still does:    

• Let me say at the outset, that in this discourse, I am opposing not a few special statements of quantum mechanics held today,
• I am opposing as it were the whole of it, I am opposing its basic views that have been shaped 25 years ago, when Max Born put forward his probability interpretation, which was accepted by almost everybody.
• It has been worked out in great detail to form a scheme of admirable logical consistency that has been inculcated ever since to every young student of theoretical physics.
• The view I am opposing is so widely accepted, without ever being questioned, that I would have some difficulties in making you believe that I really, really consider it inadequate and wish to abandon it. 
• It is, as I said, the probability view of quantum mechanics. You know how it pervades the whole system. It is always implied in everything a quantum theorist tells you. Nearly every result he pronounces is about the probability of this or that or that ... happening-with usually a great many alternatives. The idea that they be not alternatives but all really happen simultaneously seems lunatic to him, just impossible. 
• He thinks that if the laws of nature took this form for, let me say, a quarter of an hour, we should find our surroundings rapidly turning into a quagmire, or sort of a featureless jelly or plasma, all contours becoming blurred, we ourselves probably becoming jelly fish. 
• It is strange that he should believe this. For I understand he grants that unobserved nature does behave this way-namely according to the wave equation. The aforesaid alternatives come into play only when we make an observation, which need, of course, not be a scientific observation.
• Still it would seem that, according to the quantum theorist, nature is prevented from rapid jellification only by our perceiving or observing it. 
• And I wonder that he is not afraid, when he puts a ten pound-note {his wrist-watch} into his drawer in the evening, he might  find it dissolved in the morning, because he has not kept watching it.

Real Quantum Mechanics RealQM is an alternative to StdQM formed in the spirit of Schrödinger. It is quite possible that RealQM would have made Schrödinger happy again. If you are unhappy with StdQM, try RealQM! To get started check out recent posts e g the previous on Unified Field Theory with RealQM.

Unified Field Theory: Newton + Maxwell + RealQM

Schrödinger created Quantum Mechanics by formulating in 1926 a mathematical model within classical continuum mechanics in terms of a wave function $\psi (x,t)$ depending on a 3d space coordinate $x$ and a time coordinate $t$ satisfying a wave equation named Schrödinger's Equation SE: 

• $i\frac{\partial\psi}{\partial t}+H\psi =0$     (SE)

with 

• $H=-\frac{1}{2}\Delta -\frac{1}{\vert x\vert}$ a Hamiltonian differential operator.

The eigenvalues of SE showed to exactly fit with the observed spectrum of a Hydrogen atom and so was the answer to a search begun by Bohr 15 years before. The success was complete: SE revealed the secret of the Hydrogen atom as an eigenvalue problem for a Hamiltonian with time-independent normalised real-valued eigenfunctions $\Psi (x)$ with energies as sum of kinetic and potential energies appearing as eigenvalues:

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

The ground state of a Hydrogen atom took the physical form of a charge density $\Psi^2(x)$ with minimal energy appearing as a compromise of negative $E_{pot}$ by concentration near $x=0$ balanced by a positive $E_{kin}=-\frac{1}{2}E_{pot}$ appearing as a form of "compression energy".

SE took the form of classical continuum mechanics with a clear physical interpretation as charge density and so represented a complete success of classical mathematical physics suddenly expanding its excellent service from macroscopics into atomic microscopics. 

SE combines perfectly with Newtonian gravitation giving $\Psi^2(x)$ a double role as both charge density and mass density, as well as with Maxwell's electro-magnetics. The resulting Newton-Maxwell Schrödinger NMS model was a Unified-Field-Theory covering all of Hydrogen physics from galactic to atomic scales. A tremendous success of mathematical modelling of real physics! Since Hydrogen accounts for 74% of the mass of the Universe NMS captured nearly everything.

But 25% is Helium and 1% all the other atoms, and so SE had to be extended to atoms with more than one electron like Helium with two electrons to qualify as UFT. But how?

A quick formal resolution lay on the table: Give each new electron a whole set of 3d coordinates and trivially extend (SE) to any atom with a stroke of a pen. That gave a wave function depending on $3N$ space coordinates for an atom $N$ electrons. Easy to do but without clear physical meaning. 

Schrödinger refused to take this step, but Bohr-Born-Heisenberg jumped on the band wagon of Standard Quantum Mechanics StdQM based on a multi-d Schrödinger equation forming the foundation of modern physics under heavy protests from Schrödinger because it replaced causality and physicality by non-physical probabilities of observer measurement outcomes. 

In short StdQM is viewed to be the result of a process of quantisation preventing unification with the classical continuum physics of Newton and Maxwell, which has grown out into the deep crisis of modern physics of today.

Since Maxwell and Newton represent perfect theories, without any need of quantification, the natural idea to form a UFT is to search for a form of QM without quantification. But this has been prevented for 100 years by the very strong domination of the Copenhagen Interpretation of Bohr-Born-Heisenberg. Efforts have been made of  "dequantisation" of StdQM bringing it back to classic continuum physics (e g Bohmian mechanics), but without success because quantification cannot be reversed. 

RealQM offers a generalisation of SE for Hydrogen to atoms with more than one electrons, which stays within the realm of classical continuum physics, and so combines perfectly with Newton and Maxwell into a UFT.  

 

Radiative Equilibrium Without Quanta: Normality

Consider a Hydrogen atom described by Schrödinger's Equation SE in radiative equilibrium with light of a certain frequency $\nu$ described by Maxwell's equations as an  electromagnetic wave. This means that there is a gap $\Delta E$ in the distribution of eigenvalues $E$ or spectrum such that $\Delta E =h\nu$ with $h$ a scaling factor, in classical literature named Plank's constant. 

The SE for Hydrogen is a partial differential equation of classical continuum form in terms of a wave function which changes continuously in space and time during the process of establishing and maintaining radiation at the resonance frequency $\nu$. The energy gap $\Delta E$ scales with the frequency $\nu$ over  the spectrum. 

What is discrete is the spectrum, just as in classical continuum mechanics, while wave functions are continuous and do not take any discrete "jumps" in state/energy.  

Conclusion: The Schrödinger's Equation SE for a Hydrogen atom takes the form of classical continuum mechanics. QM for a Hydrogen atom is classical continuum physics. No need for quantisation. The fact that the spectrum is discrete is not evidence that any non-classical process of quantisation is really needed. See also this post.

chatGPT: Maxwell + Schrödinger looks good:

• Treat the atom quantum mechanically (Schrödinger equation).

• Treat the radiation as a classical wave (Maxwell).

• That explains a lot: absorption spectra, stimulated emission, radiative equilibrium, Rabi oscillations.

• Everything looks continuous.

This model works surprisingly well in many normal conditions.

end chatGPT

But a modern theoretical physicist is not happy with normality of classical continuum physics as description of the basic problem of atom physics of a radiating atom, because it is not modern new physics. And so the modern physicist goes on to confront the radiating atom as classical continuum physics with some extreme circumstances such as very very weak forcing so weak that the continuity breaks down. Like running your car engine with only a very weak slow irregular ignition making the engine start to malfunction. This is called appeal to extremes often used in debate.

By focussing on some extreme case, the classical model covering the normal case can be downplayed as "wrong" even if it works fine, to prepare the way for some new bold modern theory, which is more "fundamentally correct". In this way all the victories of the classic theory for all normal cases can be cashed in for the new theory to which can then be added anything extreme even if vague. 

This is what is done when General Relativity replaces Newton's theory of gravitation as being more "fundamentally correct". Or when QFT replaces QM which replaces Schrödinger+Maxwell. More and more extreme to downplay the normal.

So can unsuccessful explanation of something normal within classical continuum mechanics, be covered up by focussing the interest onto something more fundamental and extreme, and the possibility of a classical explanation can be missed, as that of RealQM.