Schrödinger vs Real Quantum Mechanics

Erwin Schrödinger created quantum wave mechanics in 1925 and summarises his view on the subsequent development into the Copenhagen Interpretation CI in Chapter 1 of Thee Interpretation of Quantum Mechanics (Dublin Seminars 1949-1955):

• 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.
• 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. 

Schrödinger goes on to outline his basic idea that atom physics can be seen as a form wave mechanics similar to that of classical mathematical physics/continuum mechanics. This is the view adopted in my books Real Quantum Mechanics RealQM and Mathematical Physics of BlackBody Radiation BBR.

In particular, Schrödinger points to the basic role of wave resonance, which is a central theme in both RealQM and BBR (see earlier posts).   

Schrödinger strongly opposes to view atom physics as particle physics, also expressed in RealQM:

• Hence the idea of point-electrons, whatever it may mean elsewhere, becomes absolutely inadequate ....within the body of an atom. 
• To my mind it is patently absurd to call anything the probability of finding an electron near a particular point ... with respect to the nucleus.  
• Nobody has ever tried to look for one, nobody ever will; in fact nobody has ever experienced or will ever experiment in this fashion on a single atom of hydrogen or whatnot. 
• What astonishes me most is, that this kind of consideration is adopted as the basis of their theory (CI).

In particular, there is in Schrödinger's quantum mechanics no place for Bohmian Mechanics, since it gives particles an essential role. 

Altogether, RealQM can be seen as a concrete realisation of the ideas put forward by Schrödinger from his kick start in 1925 to maturity in later years. 

In RealQM there is no Measurement Problem from "collapse of the wave function" as a main mystery of CI. The spectrum of an atom is measured in resonance with a measuring device. In RealQM there is no reason to seek to measure the position of an electron as particle in an atom. 

New Year's Question:

• Did Schrödinger contemplate RealQM and dismissed it, or did he simply miss it? 

Maybe something for you to rethink?

PS Schrödinger on atomism, particles, quantum jumps/discontinuities and resonance:

• Hence there can be no shadow of a doubt, that the elementary particles themselves are Planckian ''energy parcels". This is fine. 
• But if we now dismiss the idea as too naive, the idea that energy is always exchanged in whole parcels (quanta), if we replace it by resonance view, does this not mean that atomism will go by the board? 
• Well no, not atomism, only the corpuscles, the atoms and the molecules, but not atomism. I believe the discrete scheme of proper frequencies/resonances... to be powerful enough to embrace all the actually observed discontinuities in nature for which atomism stood, without our having to enhance them by fictitious discontinuities that are not observed.

On philosophy of quantum mechanics:

• Philosophical considerations about quantum mechanics have gone out of fashion. There is a widespread belief that they have become gratuitous, that everything is all right in this respect for we have been given the marvellously soothing word of complementarity, that it is only the detailed mathematical or physical theory which is still at fault.
• I cannot share this view. In the 20 years of its existence, serious objections have again and again been raised against the current interpretation. Some of them have not been solved but shelved.
• No lesser person than Einstein still withholds his assent. In a letter to Max Born, he formulated his opinion in one marvellously poised sentence: 
• "Of this I am firmly convinced that we shall eventually land at a theory in which the things that are linked by laws are not probabilities but imaged facts, as was taken for granted until lately.''

Schrödinger’s Equation vs Heisenberg’s Uncertainty Principle

Schrödingers wave equation in a wave function $\Psi (x,t)$  serves as the foundation of quantum mechanics. For an atomic system with $N$ electrons, $x$ is a $3N$-dimensional space variable and $t$ is a time variable. The physical meaning of $\Psi$ has been hotly debated for close to hundred years without ever any agreement being reached, the reason being that the equation for $N>1$ came out as a purely formal generalisation without physical basis of the equation Schrödinger formulated in 1925 for the case $N=1$ from an model of an electron as a form of negatively charged cloud with charge density $\vert\Psi (x,t)\vert^2$. A form of consensus named Copenhagen Interpretation CI to give $\Psi$ a probabilistic meaning has emerged including an agreement to not ask any further questions.  

A different generalisation to $N>1$ into a system of non-overlapping electronic charge density clouds is presented as RealQM. 

The Heisenberg Uncertainty Principle HUP is viewed as a corner stone of quantum mechanics stating that there is limit to the precision of measurements of the position and velocity of a particle. 

It is natural to ask what role HUP serves in either CI or RealQM? HUP concerns particles while CI and RealQM concern waves and there is no clear connection between particles and waves, in particular not between HUP and RealQM. 

It is also a question of what measurements can be performed on atoms. Atomic spectra can be observed as total electronic energies and there is no limit to measurement precision, while local electronic charge densities cannot be observed at all. 

Thus HUP does not seem to say anything about the wave mechanics of RealQM. It is natural to ask if it does say anything about CI?  

The Quantum Kabbalah

Kabbalah picture of the noble gas Oganesson with 118 electrons structured into shells.

The foundation of the quantum mechanics of atom physics is the Schrödinger equation 

• $i\frac{\partial\Psi}{\partial t} =H\Psi$   (S) 

in a wave function $\Psi$, with $H$ a Hamiltonian linear operator. (S) can be seen as the sign of a Kabbalah, which is a school of thought of Jewish mysticism or more generally an esoteric method within Western mystery tradition. For a system with $N$ electrons the wave function $\Psi$ depends on $3N$ space variables and evolves over time $t$ from one time instant to the next. 

The Kabbalah connection is natural because physicists have made it very clear that (S) is a true mystery, which cannot be understood as physics, but nevertheless has to be accepted as a perfect model of physics with predictions always in exact agreement with observed reality. 

In a conversation/dispute you can always bring in the wave function $\Psi$ as a complete description of the subject at hand, ultimately "the wave function of the World" which will give you an advantage in the discussion. 

The reason that (S) cannot be understood as physics, is that it is derived by a purely formal mathematical generalisation without physical basis of a model for the Hydrogen atom with $N=1$ with physical basis, to all the atoms in the periodic table with $N=2, 3,...,118$. The $3N$-dimensionality of $\Psi$ asks for $100^{3N}$ mesh points in computational resolution, which makes $\Psi$ uncomputable already for $N=4$. 

This makes (S) into a symbol carrying a secret which cannot be revealed, thus into a modern physics version the Ein Sof (Endless One) of Kabbalah with connection in the above picture.

The fact that $\Psi$ cannot be computed has split the physics community into chemical physicists at chemistry departments using electronic "orbitals" to reduce dimensions in practical computations filling supercomputers, and philosophers at philosophy departments seeking to understand the mystery of (S) as foundational quantum mechanics without computation, while physicists at physics departments since long have left (S) for deeper theories of quantum field theory and string theory deeper into a mystery far beyond any form of computability. This is the crisis of modern physics witnessed by many.                

PS Erwin Schrödinger formulated the Schrödinger equation for Hydrogen (with physical basis) in 1925, but could not accept the generalisation to $N>1$ because it was not physical, and sought for help in Indian Philosophy from his standpoint expressed in the opening of The Interpretation of Quantum Mechanics (Dublin Seminars 1949-1955):

• 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.
• 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 every thing 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 (Many Worlds Theory)
• 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. 

Quantum Computing Swindle

The previous post gave expression of a Quantum Hype Bubble About to Burst. We may compare with the hype of the 2022 Nobel Prize in Physics:

• The ineffable effects of quantum mechanics are starting to find applications. There is now a large field of research that includes quantum computers, quantum networks and secure quantum encrypted communication.
• It has become increasingly clear that a new kind of quantum technology is emerging.
• The fundamentals of quantum mechanics are not just a theoretical or philosophical issue. Intense research and development are underway to utilise the special properties of individual particle systems to construct quantum computers, improve measurements, build quantum networks and establish secure quantum encrypted communication.
• This year’s laureates have explored these entangled quantum states, and their experiments laid the foundation of the revolution currently underway in quantum technology.
• Being able to manipulate and manage quantum states and all their layers of properties gives us access to tools with unexpected potential. This is the basis for quantum computation, the transfer and storage of quantum information, and algorithms for quantum encryption.

We note that "ineffable" means too great or extreme to be expressed or described in words!!

The Physics Nobel Prize Committee is joined by Knut and Alice Wallenberg Foundation as the major Swedish private funding agency of research with a $100 million donation to Wallenberg Centre for Quantum Technology at Chalmers (my Alma Mater) based on the following hype:

• Through an extensive research programme, we aim at developing and securing Swedish expertise within the main areas of quantum technology: quantum computing and simulation, quantum communications and quantum sensing. Our main project is to develop a high-end quantum computer that can solve problems far beyond the reach of the best conventional supercomputers.

We see that Sweden has been totally carried away by the hype into seeking to take a leading role in finally liberating the ineffable potential of quantum mechanics after 100 years of hibernation. But a hype is a hype is a hype... 

Knut Wallenberg (1853-1938) was a clever Swedish banker who earned a fortune, which he locked into a fund for science to secure that it was not going be swindled away by less clever inheritors, apparently under the impression that science in his time could not be swindle. 

More on swindle (for investors): 

• Dyakonov The Case Against Quantum Computing
• Hoofnagel and Garfinkel Law and Policy for the Quantum Age
• Galitsky Quantum Computing Hype is Bad for Science

Is Quantum Computing Possible?

The possibility of quantum computing was suggested by the famous physicist Richard Feynman some 50 years ago to meet the need of excessive computing power supposed to required to simulate atomic quantum systems on a conventional digital computer. Today much effort is spent on seeking to build a quantum computer operating with qubits instead of the bits of a digital computer. 

The basic idea is that a qubit can represent a superposition of two states (both 0 and 1) instead of the single state of either 0 or 1 of a bit. For a system with $N$ qubits/bits this increases the number of logical states from $N$ with bits to $2^N$ with qubits, thus from linear to exponential. 

IBM claims to have built the most powerful quantum processor in the world – the Osprey, which boasts a massive 433 quantum bits (qubits). The physical type of qubit used by IBM is described as:

• a superconducting transmon qubit, which is made from superconducting materials such as niobium and aluminum, patterned on a silicon substrate. 
• Such systems are not natural qubits, but are instead formed by isolating two energy levels out of many to form our approximate qubit.
• For a superconducting qubit to behave as the abstract notion of the qubit, we must have the device at drastically low temperatures to minimize ambient noise or heat that could excite the superconducting qubit and increase the error probability. 
• Once a system has cooled to the target temperature, which takes several days, the qubit reaches equilibrium at the ground state 0.

Quantum computing boils down to transforming qubits from one state to another by logical gates. It is a tricky subject with standard measurement and randomness playing a central role. The Hadamard gate creates a superposition of 0 and 1 by starting in either the state 0 or 1,  which followed by standard measurement gives 0 or 1 with a probability of 0.5. Altogether this looks like flipping a coin, but the creation of superposition of 0 and 1 prior to measurement is a unique qubit feature.  

Let us compare with the discussion in the previous post on a radiating atom in superposition of a ground state 0 and an excited state 1 under certain exterior forcing with frequency matching the difference of excited and ground state energies. In this case it is the exterior forcing which creates a superposition of the ground state and matching excited state. By varying the frequency of the exterior forcing, the atomic spectrum can be determined, which can be seen as a form of deterministic spectrum measurement. In this setting the spectrum of the atom is observable, but not the underlying electronic structure.  

A bit can be realised as an atom with value 0 in non-radiating ground state and value 1 in radiating superposition of ground state and excited state, both deterministically observable/measurable.  A bit is in direct contact with exterior forcing determining its value to be 0 or 1. 

As a qubit a radiating atom would allow superposition of ground and excited state and thereby offer a richer playground of states for processing by certain logical gates performed with zero exterior forcing. But measuring the result would amount to exterior forcing destroying superposition to randomely deliver either ground or excited state. The richer processing would thus come with randomness and a net gain would seem to be possible only for very special problems including randomness.      

Summary so far: A bit is in direct contact with exterior forcing allowing deterministic processing and reading without destruction of the state. A qubit must be insulated from exterior forcing during processing, while reading destroys the state and delivers a random result. 

Main question to answer: Is superposition possible without radiation/exterior forcing? If No, quantum computing may be impossible.

Christmas Gift: Radiating Atom

Bohr atom model as a planetary system with fixed orbits

Here is a small gift to the quantum mechanics community in search for mathematical models of reality with the basic question: Why is the minimal energy ground eigenstate of an atom stable without radiation, while excited eigenstates with larger energies radiate and give rise to a spectrum? 

The common answer is that the ground state of minimal energy does not radiate because if it did it would not be stable and so not exist over time. But this is a form of circular reasoning expressing that an atom is stable because if was not stable,  then it would not exist. Not so illuminating. 

This answer connects to the collapse of classical atomic models with electrons in swirling motion around the kernel which radiate, because electrons in accelerated motion do generate varying electrical fields and so radiate. In particular, the ground state would be radiating but it does not and so electrons cannot be swirling around the kernel as in the classical Bohr atom model with a planetary type system of electrons. 

A different more precise answer is given by RealQM: The ground state does not radiate because its electron charge density does not vary in time and so does not accelerate and give rise to radiation. On the other hand the charge density of a superposition of the ground state with minimal energy $E_1$ and eigenstate of higher energy $E_j>E_1$ is time dependent with frequency $E_j-E_1$ and so does radiate.

To see some details consider the following 1d Schrödinger equation, which is analysed in detail at Computational Blackbody Radiation:      

• $i\frac{d\Psi}{dt} = H\Psi$    (*)

where the Hamiltonian $H$ is given by

• $Hu = -\frac{d^2u}{dx^2} - \gamma \frac{d^3u}{dt^3}$

acting on functions $u(x,t)$ defined for $0<x<\pi$ and $t>0$ satisfying the boundary condition $u (0,t)=u (\pi,t)=0$ for $t>0$, and $\gamma\ge 0$ is a small constant. The $\gamma$-term with $\gamma >0$ corresponds to outgoing radiation of intensity 

• $\gamma (\frac{d^2u}{dt^2})^2$

including the acceleration $\frac{d^2u}{dt^2}$.

For $\gamma =0$ the eigenfunctions of $H$ are given by $\sin(jx)$ for $j=1,2,3...$ with corresponding eigenvalues $j^2$, and so the solution of (*) in this case can be expressed as 

• $\Psi (x,t) =\sum_{j=1}^\infty c_j\exp(-ij^2t)\sin(jx)$,

where the $c_j$ are real coefficients. The ground state with $c_j=0$ for $j>1$ is given by 

• $\exp( -it)\sin(x)$

with modulus squared as charge density independent of time. On the other hand a superposition 

• $\exp(-it)\sin(x)+\exp(-ij^2t)\sin(jx)$
• $= \exp(-it)(sin(x)+\exp(-ij^2t+ it)\sin(jx))$

does have a time dependent charge density for $j>1$ and so does radiate. Merry Christmas!

PS1 To get perspective, try to Google the following question:

• Why do not atoms in ground state radiate?

See that you do not get a meaningful answer. Ask yourself why?

PS2 Pure eigenstates do not radiate, but it is not clear how to excite a higher eigenstate for an atom. For a vibrating string this is possible suppressing the ground state with a light left finger touch on the middle of the string, thus exciting (mainly) the second harmonic (flageolet). In RealQM a superposition of ground state and higher energy eigenstate involves a mean-value Hamiltonian and so is a true "complex mixed state" which needs exterior forcing to sustain over time. In standard QM with a linear Schrödinger equations exact superposition of eigenstates is formally possible without radiation and forcing which formally would sustain over time. But again it is most unclear how to excite higher eigenstates, which puts quantum computing building on such superpositions in doubt as clarified in upcoming post.

Tim Maudlin on What Quantum Theory Tells about The World

In the above interview Tim Maudlin as expert on the Philosophy of Physics reveals the following truths about Quantum Theory:  

• In Quantum Theory if you ask what that theory is telling me about the world, the physicists don't have a clue. 
• That theory is not on a solid conceptual foundation. It is much more the case that from the philosophical side you are trying to understand the theory in a way that the physicists cannot exposit it. 
• It is odd to call that philosophy, why is that not just physics? The answer is that it is physics, a part of physics that has largely been abandoned by physics departments. 
• Physicists interested in the basic questions for example, what does quantum theory tell you about the world, which sounds like a question of physics, they get exiled from the physics departments.
• Almost all physical behaviour that we understand, we understand though quantum mechanics.
• We know how to get predictions out of it, and the predictions are tremendously accurate.
• Quantum mechanics is the most important foundational theory of physics.
• On the other hand it is the least understood. 
• There is zero agreement about what quantum mechanics is telling us about the world.
• Quantum mechanics is the most conceptually dark part of physics, at the same time being the most foundational part. 

So we learn that physicists do not have a clue about what quantum theory tells about the world and that  they are not interested in finding out. We learn that quantum mechanics is the most foundational part of physics but least understood, yet capable of tremendously accurate predictions! This is the situation 100 years after quantum mechanics was formed. 

That sounds pretty serious, but is in line with the impression I have accumulated in preparation of RealQM. 

I have invited Tim to comment.

Superposition as the Collapse of Quantum Mechanics

Today Quantum Mechanics is still viewed to be as weird and strange as at its formation 100 years ago, evidenced in a large number of books like this undergraduate text by Travis Norsen:

• Foundations of Quantum Mechanics An Exploration of the Physical Meaning of Quantum Theory  

The book presents three basic problems:

1. Measurement Problem 
2. Locality Problem
3. Ontology Problem 

along with “solutions” in the form 

• Copenhagen Interpretation 
• Pilot Wave Theory
• Many Worlds Theory
• Collapse Theory

none of which is considered to be satisfactory. The net result for the undergraduate student is frustration from confusion, at least this is my reaction. 

All Problems 1-3 connect to the the fundamental postulate of QM as 

• Multi-d linear Schrödinger equation in non-physical configuration space.  (S)

This is an ad hoc model derived from formal mathematics without real physics in physical 3d space. Solutions to (S) are referred to as wave/state functions typically denoted by $\Psi$. A consequence of the linearity of (S) is superposition: If $\Psi_1$ and $\Psi_2$ solve (S), so does the linear combination

• $\Psi = c_1\Psi_1 + c_2\Psi_2$,

for any coefficients $c_1$ and $c_2$. Typically, $\Psi_1$ and $\Psi_2$ are eigenstates with different energies. This is the Schrödinger Cat in the Box, which can be in superposition of eigenstates of being alive and dead. Strange QM Cat. 

The Measurement Problem concerns the collapse of the wave function $\Psi =  c_1\Psi_1 + c_2\Psi_2$ by observation/measurement into one of the eigenstates $\Psi_1$ and $\Psi_2$ with probability given by the cofficients $c_1^2$ and $c_2^2$, that is upon opening the box discovery of an alive or dead cat with a certain probability.

But the Measurement Problem is unresolved despite 100 years of massive efforts by the sharpest brains. It is reasonable to suspect that this problem is not well formulated. The suspicion goes the the idea of superposition build into (S) as a formal equation in configuration space without physics. 

What forces us to insist that (S) is the foundation of atomistic mechanics? The standard answer is that this is the best we have, even if it leads into an abyss of contradictions. Here RealQM offers an alternative. 

To give perspective on superposition in a linear equation, let is consider the simple case of a vibrating string with the vibration as a linear combination of a ground state and higher harmonics as eigenstates with larger eigenfrequencies, resulting from plucking the string thus exciting all harmonics. But as we listen to a vibrating string the higher frequencies fade away and what remains is only the basic harmonic. This is because the vibrating string equation is not fully linear and so carries some damping increasing with frequency (see above picture).

In the setting of an atom the basic harmonic corresponds to the ground state with minimal energy, which is not radiating and thus can sustain over time, while the eigenstates with higher energies are all radiating and thus can only sustain under exterior forcing. This is how the spectrum is generated. An atom without exterior forcing will thus remain in its ground without collapse.  

The atom in ground state is thus fully deterministic, just as the basic harmonic of a vibrating string.  Higher harmonics have to be excited by exterior forcing, like plucking the string in some specific way, and

the resulting state is then deterministically determined by the forcing. Every time you pluck the same way,

the same sound is produced. The spectrum of an atom always comes out the same way fully deterministic.

The spectrum shows itself under exterior forcing, not by stochastic collapse of wave functions.  

We understand the idea of a linear Schrödinger wave equation (S) allowing sustained superposition over time and only collapsing into an eigenstate under observation, brings a whole battery of problems which have shown to be unresolvable. We are forced to seek to replace (S) with a physical model, possibly in the spirit of RealQM.

We note that computational techniques to find solutions to (S) like Density Theory or Hartree-Fock Slater Determinants effectively reduce (S) to a non-linear deterministic system in 3d like RealQM. 

I have asked Travis Norsen for a comment on this post. 

A Dissenting Nobel Laureate in Physics

Gerhard 't Hooft received the 1999 Nobel Prize in Physics for 

• elucidating the quantum structure of electroweak interactions in physics.

On Wikipedia he is presented as a Quantum Mechanics QM theory dissident:

• 't Hooft has "deviating views on the physical interpretation of quantum theory".
• He believes that there could be a deterministic explanation underlying quantum mechanics.
• Using a speculative model he has argued that such a theory could avoid the usual Bell inequality arguments that would disallow such a local hidden-variable theory.
•  In 2016 he published a book length exposition of his ideas which, according to 't Hooft, has encountered mixed reactions.

Here we can listen to what how Gerhard explains his position to a general audience: 

with the following key confessions:

• QM is first of all a theory which is correct.
• I am not going to put any doubt to the fundamental correct nature of QM.
• The entire world is controlled by QM.
• But a question was not answered properly: What is reality?
• What is a particle, a field?
• Bohr framed an agreement to not ask such questions.
• I disagree, I am asking these questions.
• Many worlds and pilot waves theories cannot be right.
• QM sounds crazy, QM sounds wrong, but it works.
• There should be a real world.
• This is a dangerous thing to say.
• I you say so you place yourself outside the discussion area. 
• I am convinced we will get the truth about what QM really means, but it may take a long time...

So Gerhard says that QM is correct but at the same time that it cannot be correct. There must be something better yet to discover...

I have suggested Gerhard to take a look at RealQM and will report if I get a reaction. 

The Unfortunate Strangeness of Quantum Mechanics

Quantum Mechanics QM started out in the 1920s from a need to explain the mechanics/physics of the atom perceived to be composed of a $N$ negatively charged electrons attracted by a kernel with a positive charge balancing the electrons into a neutral atom. For the basic case of the Hydrogen atom with $N=1$ Schrödinger formulated in 1925 an eigenvalue problem for a wave function $\Psi (x)$ depending on a 3d space variable $x$ and $\Psi^2(x)$ representing electron charge density, expressing stationarity of a total energy composed of potential energy = $-\frac{\Psi (x)}{\vert x\vert}$ from kernel attraction and kinetic energy measured by $\frac{1}{2}\vert\nabla\Psi (x)\vert^2$ with $\nabla$ the gradient with respect to $x$, both integrated over $x$. 

The ground state of minimal total energy as smallest eigenvalue is given by $\Psi (x)=\exp(-\vert x\vert)$ modulo normalisation, which expresses an electron charge density minimising kernel distance under gradient  penalty. The observed spectrum of Hydrogen fits very precisely with differences of larger eigenvalues. 

This was a formidable success, but the generalisation to atoms with $N>1$ showed to present difficulties which could not be overcome, and as a result QM turned away from the atom into abstractions of multidimensional wave functions representing not actualities of physical reality, but instead statistics of possibilities for more and more contrived experiments not with atoms but with photons of unknown physics.

The atom as the most stable predictable building block of the material world was thus turned into the unpredictable ball of a roulette table. This was a veritable collapse of scientific rationality into strange physics which has led into a permanent crisis of modern physics. Einstein and Schrödinger protested but where annihilated by Bohr using heavy artillery of strangeness and Born statistics. Check out RealQM as antidote.

Crisis of Nobel Prizes in Physics to Quantum Mechanics

The theoretical mathematical foundation of modern physics is commonly is commonly viewed to be Quantum Mechanics QM and Einstein's General Theory of Relativity, although incompatible. Einstein did not get any Nobel Prize for his theories of relativity and the only Prize for related work is that to 

• 2020 Roger Penrose “for the discovery that black hole formation is a robust prediction of the general theory of relativity”.

The Prizes to theoretical QM are:

• 1932 Werner Karl Heisenberg “for the creation of quantum mechanics, the application of which has, inter alia, led to the discovery of the allotropic forms of hydrogen”. 
• 1933 Erwin Schrödinger and Paul Adrien Maurice Dirac “for the discovery of new productive forms of atomic theory”.
• 1945 Wolfgang Pauli “for the discovery of the Exclusion Principle, also called the Pauli Principle”.
• 1954 Max Born “for his fundamental research in quantum mechanics, especially for his statistical interpretation of the wavefunction”.

with continuation into quantum field theory:

• 1965 Sin-Itiro Tomonaga, Julian Schwinger and Richard P. Feynman “for their fundamental work in quantum electrodynamics, with deep-ploughing consequences for the physics of elementary particles”

followed by  

• 2022 Alain Aspect, John F. Clauser and Anton Zeilinger “for experiments with entangled photons, establishing the violation of Bell inequalities and pioneering quantum information science” 

confronting quantum theory with experiments for "entangled photons". There are a few more Prizes to experimental QM, but that's it as concerns theory. 

We read that the major theoretical work on QM was completed in the 1930s (with delayed Prizes to Pauli and Born) with apparently little added since then worthy of a Prize. 

This is remarkable since already from start the theory of QM showed to harbour deep problems, which would have earned Prizes if resolved. 

But that did not happen. This is strange, as a reflection of the "strangeness" of QM. Why has no progress been made for nearly 100 years on theoretical QM worthy of a Nobel Prize? Is this the root of the "crisis of modern physics" witnessed by so many physicists (also here).

Time to make a fresh start with RealQM?

PS Here is how Simon Saunders starts the book Many Worlds? Everett, Quantum Theory and Reality (2010):

• Ask not if quantum mechanics is true, ask rather what the theory implies. 
• What does realism about the quantum state imply? What follows then, when quantum theory is applied without restriction, if need be to the whole universe?
• This is the question that this book addresses. The answers vary widely. According to one view, ‘what follows’ is a detailed and realistic picture of reality that provides a unified description of micro- and macroworlds. 
• But according to another, the result is nonsense — there is no physically meaningful theory at all, or not in the sense of a realist theory, a theory supposed to give an intelligible picture of a reality existing independently of our thoughts and beliefs. 
• According to the latter view, the formalism of quantum mechanics, if applied unrestrictedly, is at best a fragment of such a theory, in need of substantive additional assumptions and equations.
• So sharp a division about what appears to be a reasonably well-defined question is all the more striking given how much agreement there is otherwise, for all parties to the debate in this book are agreed on realism, and on the need, or the aspiration, for a theory that unites micro- and macroworlds, at least in principle. 
• They all see it as legitimate—obligatory even—to ask whether the fundamental equations of quantum mechanics, principally the Schrödinger equation, already constitute such a system. 
• They all agree that such equations, if they are to be truly fundamental, must ultimately apply to the entire universe. And most of the authors also agree that the quantum state should be treated as something physically real. 
• But now disagreements set in.

Ok, so we learn that all parties agree on the need of a theory for the microworld of atoms and molecules as something physically real, but disagree on what such a theory could be. This is as far as theoretical physics has come 2022.  You could call it a crisis.  

The Spell of QM

Experiments spell doom for QM

The Schrödinger equation for the Hydrogen atom solves the eigenvalue problem in the real-valued wave function $\Psi (X)$ depending on a 3d spatial variable $X$:

• $(-\frac{1}{2}\Delta - V)\Psi = E\Psi$   (Q)

where $V(X)=\frac{1}{\vert X\vert}$, with normalisation 

• $\int \Psi^2 (X) dX = 1$.

The equation (Q) is formally derived from a classical one-particle Hamiltonian $H(x,p)$ with $x$ a 1d particle position variable and $p=\dot x =\frac{dx}{dt}$ corresponding momentum, of the form 

• $H(x,p)=\frac{1}{2}p^2 - W(x)$      (C)

where $W(x)$ is a potential depending on position $x$. We see that (Q) corresponds to formally replacing $p$ by $i\nabla\Psi$ and $W(x)$ by $V\Psi$. Really strange!

Here (C) represents a classical problem in a 1d position variable $x(t)$ depending on time $t$, while (Q) is a partial differential equation for a function $\Psi (X)$ of a 3d space variable $X$. The formality takes us from an ordinary differential equation in real-valued function $x(t)$ depending on time $t$ as the equations of motion for (C), to a partial differential equation pde in 3d space for $\Psi (X)$. We see that the point position $x$ is formally expanded to a function $\Psi(X)$ depending on 3d space variable $X$. (Q)  thus can be seen as a formal expansion from point to full 3d space. 

The Schrödinger equation (Q) can be directly formulated as a classical partial differential equation in a function $\Psi (X)$ with $\Psi^2(X)$ representing charge density with the Laplacian $\Delta$ forcing $\Psi(X)$ to spread out away from the kernel at $X=0$. So for the one-electron atom of Hydrogen (Q) is a pde of classical form in 3d. Schrödinger was very happy with this model since the eigenvalues of (Q) perfectly matched with the observed spectrum of Hydrogen. The first step into modern physics was a complete success and expectations quickly mounted. 

But how to generalise (Q) to atoms with with $N>1$ electrons? The classical formulation (C) could directly be extended to $N$ particles simply by letting the position variable represent $N$ different particle positions with corresponding momenta. That would correspond to expanding from one to $N$ position coordinates as the subject of classical Lagrangian mechanics. Doing the same thing in (Q) would bring in a full 3d coordinate system for each electron altogether a pde in $3N$ space dimensions. This was what Schrödinger did and so was QM born from a formal generalisation of classical mechanics with a mysterious replacement of momenta by $i\nabla$ acting in $3N$ space dimensions, and then formed into a canon named Copenhagen Interpretation CI filling text  books. 

But the generalisation of (Q) for the Hydrogen atom was done through a purely formal process without physical meaning and the struggle to give meaning has not been successful. Schrödinger gave up in despair leaving the scene to Bohr.

RealQM offers a different generalisation of (Q) into a model with physical meaning. With the renewed interest into the foundations of QM motivated by the 2022 Nobel Physics Prize, I hope that RealQM can attract some attention. RealQM has a direct deterministic physical meaning free of the statistics of the CI. Why not give it a try?  

It is truely amazing the foundations of QM are still hotly debated 100 years after QM was created by Schrödinger and Heisenberg and then canonised by Bohr and Born into an abstract recipe to make statistical predictions of outcomes of experiments with attempts by Bohm, Bell and Everett to give physical meaning to the abstractions which did not bring clarity. 

The hype today is to build a quantum computer capable of computational simulation of quantum systems by building the quantum computer to mimic the quantum system, that is making the quantum computer simulate itself. This is like thinking of yourself when you are thinking of yourself, in order to figure out what you are thinking about yourself...  

Adam Becker gives in What Is Real?: The Unfinished Quest for the Meaning of Quantum Physics

the following summary as of 2018:

• So what is real? Pilot waves? Many worlds? Spontaneous collapse? 
• Which interpretation of quantum physics is the right one? 
• I don’t know. Every interpretation has its critics (though the proponents of basically every non-Copenhagen interpretation are usually agreed that Copenhagen is the worst of the lot). 
• Somehow, something is going on in the world that is related to the mathematics of quantum physics.
• There is a correct interpretation, though it may not be any of the ones that we have yet. 
• Simply dismissing the quantum world as a convenient mathematical fiction means we aren’t taking our best theories of the world seriously enough, and we are hobbling ourselves in the search for a new theory.
• Stating that the conclusions of the Copenhagen interpretation are “inevitable” or “forced upon us by the mathematics of the theory” is simply wrong. 
• It is not true that it’s meaningless to talk about reality existing independently of our perceptions, that we must think of the world solely as the subject of our observations. 
• Solipsism and idealism are not the messages of quantum physics.

This is a disappointing result after 100 years of apparently fruitless quest into the foundations of QM as the show piece of modern physics. But this reality is unacceptable and as a cover-up the Nobel Prize in Physics 2022 is given to "ultimate verification of (foundations of) QM":

• The founding fathers of quantum mechanics were well aware of its potentially revolutionary physical and philosophical implications, and held very different, and sometimes bluntly contradictory, views on the subject. 
• Indeed, the overwhelming empirical evidence in the realms of atomic and optical physics was, to most practitioners, confirmation of the potent predictive power of quantum mechanics. 
• Others saw them as fundamental discoveries about the nature of physical reality, providing an ultimate verification of quantum mechanics in a regime that is far removed from classical laws and reasoning.

PS1 The question What Is Real? directly confronts our daily life: What are the foundations of human society, what is true, what is fake, is Big Brother real and what are His plans, what is freedom of thought, why are we freezing, who will survive, what is information, what is desinformation, what is the value of classical laws and reasoning...?? 

PS2 Travis Norsen gives in Foundations of Quantum Mechanics a critical analysis in Chapter 5 The Ontology Problem of giving a physical meaning to the $3N$-dimensional wave function of CI:

• Perhaps we can thus summarize “the ontology problem” as follows: in quantum mechanics, there simply is nothing in the theory other than the wave function with which to describe the physical state of a microscopic system; but it simply is not clear how the wave function might be understood as describing some material structures in three-dimensional physical space. Put simply, it is just not at all clear, from the mathematical formulation of the theory, what sort of physical things quantum mechanics might be about.

This Ontology Problem (about what is?) was apparent from start to both Lorentz, Einstein and Schrödinger and the problem remains today, despite 100 years of efforts to sweep it under the rug. 

The Unsuccessful Quest for Foundations of Quantum

Let us see what leading physicist/philosopher Tim Maudlin has to say about the foundations of Quantum Mechanics QM as the prime expression of the modern physics behind modern atomic/information society. Tim starts out with the following declaration in Philosophy of Physics: Quantum Theory (2019):

• There is no discussion (in the book) of the most famous "interpretation" of quantum theory of all: The Copenhagen Interpretation CI ascribed to Niels Bohr and his colleague. Why is that? 
• A physical theory should clearly and forthrightly address two fundamental questions: what there is, and what it does. The answer to the first question is provided by the ontology of the theory, and the answer to the second by its dynamics. The ontology should have a sharp mathematical description, and the dynamics should be implemented by precise equations describing how the ontology will, or might, evolve.
• The CI does not. 
• There is little agreement about just what this approach to quantum theory postulates to actually exist or how the dynamics can be unambiguously formulated. Nowadays, the term is often used as shorthand for a general instrumentalism that treats the mathematical apparatus of the theory as merely a predictive device, uncommitted to any ontology or dynamics at all. 
• That predictive device is described under the moniker “the quantum recipe.” Sometimes, accepting the CI is understood as the decision simply to use the quantum recipe without further question: Shut up and calculate. 
• Such an attitude rejects the aspiration to provide a physical theory, as defined above, at all. Hence it is not even in the running for a description of the physical world and what it does. More specific criticisms could be raised against this legacy of Bohr but our time is better spent presenting what is clear than decrying what is obscure.

Tim thus discards the commonly accepted (obscure) CI and so turns instead to Collapse Theories, Bohm's Pilot Wave Theory and Everett's Many Worlds Theory, all of which however directly connect to the CI without better answers to the fundamental questions (in my view).  

I have asked Tim about a reaction on my attempt to answer the fundamental questions in the form of Real QM.

Bohm and the Nobel Prize in Physics 2022

David Bohm struggles in Causality and Chance in Modern Physics to give a meaning to Quantum Mechanics in its probabilistic Copenhagen Interpretation CI based on Schrödinger's equation advocated by Bohr/Born/Heisenberg. Bohm expresses his main hang-up, which he shares with Schrödinger and Einstein (and myself), as follows:

• The Schrödinger wave equation does not describe a wave in ordinary 3d space, but instead a wave in an abstract $3N$-dimensional space with $N$ the number of particles.
• This is not really acceptable in a physical theory, and should at least be regarded as an artifice that one uses provisionally until one obtains a better theory in which everything is expressed once more in ordinary 3d space. 

The wave function $\Psi (x1,x2,...,xN;t)$ as (complex/real-valued) solution to Schrödinger's equation thus depends on $N$ 3d particle position variables/coordinates $x1$ to $xN$ thus on $3N$ spatial variables (plus time $t$), which for $N>1$ do not represent any reality of physical 3d space. 

100 years ago Born came up with the idea of letting the 3N-dimensional coordinates $(x1,...,xN)$ represent possibility of particle positions rather than actuality of reality, with $\vert\Psi (x1,x2,...,xN;t)\vert^2$ the probability of a particle configuration at time $t$ with particle $i$ at position $xi$ for $i=1,...,N$. 

This is still today the doctrine of the physics community serving as background to the Physics Prize 2022, and the protests from Bohm, Schrödinger and Einstein are no longer voiced. The Prize 2022 is meant to give final blow to Einstein's "God does not play dice" still haunting modern physics with the question: How is it possible that atoms always show exactly the same spectrum if their electrons are simply gambling?  How come that the periodic table appears to be written in stone, when electrons are jumping around playing roulette?   

But CI is filled with unresolved questions and contradictions:

1. By multidimensionality the wave function is uncomputable on any foreseeable computer. Claims that CI always agrees with observation cannot be verified. 
2. Atoms have fully deterministic excited states/energies with stable ground state/energy. No role for probabilities here.
3. The generalisation of Schrödinger's equation to $N>1$ from the physical model for the Hydrogen atom with $N=1$ is performed with a stroke of a pen as a mathematical formality without physical reality. Real Quantum Mechanics presents a different generalisations with physical meaning. Real QM is computable and so elevates simulation and not observation as in CI to focal interest.
4. Bohm tried to give a physical meaning to CI in the form of a pilot wave theory, but retained the uncomputable multidimensional wave function. Wheeler tried the idea of giving possibility the same reality as actuality in his Many-Worlds version of QM. The physics community could not embrace Bohm nor Wheeler although both tried (but without success) to give meaning to CI.
5. The Nobel Physics Prize 2022 sells the idea of a 2nd quantum revolution into quantum information/computing based on multidimensional wave functions of immense richness/power, but reality may be lacking. Will it be a quantum jump into the void? Who will call the bet?   

Here is Sabine Hossenfelder's explanation of Bohmian Mechanics:

  

Instant Action at Distance vs Pre-Established Harmony

Pre-Established Order of Fighter Airplanes.

The 2022 Nobel Prize in Physics puts the light on the the apparent instant action at distance in Newtonian gravitation, which Leibniz brought up but Newton did not want to discuss: The gravitational force between two bodies at a given common time $t$ is supposed to depend on the position of the bodies at time $t$ without any time delay. 

But instant action at distance appears to violate principles of locality and finite speed of propagation of physical effects as principles held holy by Einstein, but being under fire by the 2022 Prize. Can something enlightening be said? 

We see the same phenomenon in the basic model of the harmonic oscillator in the form of a body attached to one end of a linear elastic spring fixed at its other end, which in 1d takes the form:

• $\frac{dv}{dt} = - x(t)$,
• $\frac{dx}{dt} = v(t)$,  

with $x(t)$ is position, $v(t)$ velocity and $-x(t)$ spring force at time $t$ and the solution is $x(t)=sin(t)$ and $v(t)=cos(t)$ if started at $t=0$ with the body at $x=0$ with $v=1$ (with the spring fixed at $x=0$). 

Here the restoring body force $-x(t)$ and acceleration $\frac{dv}{dt}$ appears to instantly react to the present length of the spring $x(t)$ as a global quantity. It appears that the body and spring act in perfect harmony without time delay as an expression of pre-established order in the words of Leibniz. 

The harmonic oscillator can be seen as a model of a Sun-Earth system with the gravitational pull from the Sun as a spring force with instant action and the resulting elliptical orbit as pre-established order from instant action at distance. With time delay the planet system would spin out of order (as well as the harmonic oscillator).

To give perspective, let us imagine the the fixed end of the spring in the harmonic oscillator is subject to a perturbation at a certain time. We expect the perturbation to trigger a wave in the elastic spring, which will reach the body with some time delay and alter its motion, and so we move away from instant action at distance under perturbations. We may expect the same effect if the Sun suddenly would take a leap. 

So we have a harmonic oscillator which appears to move under instant action at distance from an elastic spring as long as the fixed end of the spring is not moved, but with delayed action if the fixed end is suddenly perturbed. So we see a form of pre-established order of motion under instant action at distance if the system is not subjected to sudden perturbations. We do not expect the Sun to take a sudden leap.

This is like two fighter jets acting in perfect coordination seeming under instant action at distance as long as no pilot makes a sudden move. Does this resolve the apparent mystery of instant action at distance of the gravitational pull from the Sun? Is this an illusion which does not hold under perturbations? Can pre-established harmony rule the World as long as there are no sudden perturbations? Maybe. 

PS We can make a connection to group think, with all Swedes in unison politically moving in the same direction (e g NATO and FossilFree Society) as under a pre-established order, where there is no place for perturbations of view.  See also:

 

Back to Foundations of Quantum Mechanics

Ground state wave function of Hydrogen (surface plot of 2d section) as minimizer of energy.

Quantum Mechanics QM was formed in the 1920s in a search for a mathematical model of an atom understood to consist of a positively charged kernel surrounded by negatively charged electrons. Attempts by in particular Niels Bohr to form a classical "planetary" model with electrons as particles orbiting a kernel under Coulomb attraction, had miserably failed because orbiting electrons radiate energy and so lose energy in contradiction to observations of stable atoms. 

Schrödinger took on the challenge and in a moment of heavenly inspiration during a vacation trip to the Alps with a companion, came up with a model for the most basic case of the Hydrogen atom with one electron, with the electron being represented by a real-valued wave function $\Psi (x)$ depending on a 3d position variable $x$ with $\Psi ^2(x)$ representing charge density with normalisation 

• $\int \Psi^2 (x) dx = 1$.

The ground state $\Psi (x)$ of Hydrogen would then be represented as the minimiser of the energy

• $\frac{1}{2}\int \vert\nabla\Psi (x)\vert^2dx - \int V(x)\Psi^2(x)dx$, 

where $V(x)=\frac{1}{\vert x\vert}$, as solution of the eigenvalue problem

• $(-\frac{1}{2}\Delta - V)\Psi = E\Psi$ 

with $E$ minimal eigenvalue/energy. Excited states would then correspond to larger eigenvalues/energies. The energies showed close agreement with the observed spectrum of Hydrogen, which rocked Schrödinger to fame. But it came with expectations of generalisation to atoms with more than one electron. A formal mathematical generalisation just adding a new position variable for each new electron presented itself but Schrödinger was not happy with only a formality, since he was asking the model to be Anschaulich or possible visualisable. 

But the physics community with Bohr and Born jumped the formal generalisation giving the multi-dimensional wave function $\Psi$ a non-physical meaning as a possibility rather than physical actuality (as demanded by Schrödinger), which became the Copenhagen Interpretation CI of QM hotly debated in the 1930s as foundation of QM. 

Then the debate ran out of energy until John Bell revived it in 1964 for a short period before oblivion again, until the Nobel Prize in Physics 2022. So we are back to the foundations and CI. What is the meaning of the multidimensional wave function $\Psi$ of the CI? My take is that this $\Psi$ is uncomputable and as such not carrier of any information. This is because the multidimensional wave function for an atom with $N$ electrons depends on $10^{3N}$ variables with a resolution of 10 in each position variable which already for $N=10$ is beyond any thinkable computational power.

Real Quantum Mechanics presents a different generalisation which has physical meaning in the same sense as Schrödinger's equation for the Hydrogen atom. The number of variables is here $10^3N$ to be compared with $10^{3N}$. Computable compared with uncomputable! Time for a fresh restart on the foundations of QM. 

In Real Quantum Mechanics with 3d electron wave functions having disjoint support, locality is manifest, but not in CI because there wave functions have global support.

Bohr's Measurement Obsession

Bohr predicting to Pauli the outcome of a spinning tippy top experiment. 

• Physics is not about how the world is, it is about what we can say about the world. (Niels Bohr)
• Everything we call real is made of things that cannot be regarded as real. (Bohr)
• If quantum mechanics hasn't profoundly shocked you, you haven't understood it yet. (Bohr)

Bohr as the Grandfather of the Copenhagen Interpretation CI of the theory of Quantum Mechanics QM together with Born and Heisenberg, was obsessed with the role of experimental measurement based on a conviction that the purpose of QM is to predict the outcome of experiments. This may seem a bit strange since what is the point of predicting the outcome of an experiment, when you anyway are going to preform the experiment and so learn the true outcome. Instead of learning anything about the outcome you could of course use the prediction to test the theory. If the prediction is wrong, the theory is wrong (or the experiment is not performed correctly). 

More generally one may say that the role of a theory is to allow prediction of actual events, not only those in the lab. Like the collapse of a bridge under too heavy load performing a finite element simulation of the action of the bridge. Or computational QM simulation of the folding of a protein from a DNA-sequence to find its action in the body by   

But to Bohr that was far into the future and so the focus was a laboratory setting preferably as simple as possible (but often as puzzling as possible), like the double-slit experiment. Then the act of measurement became paramount, and this is where quantum mechanics differed from classical mechanics, since the very act of observation could now influence the outcome by interaction instrument-observed phenomenon. In particular this came to expression by the probabilistic aspect of CI with a state prior to observation (Schrödinger's cat) supposedly being in a superposition of many possible states with the act of observation singling out one into actuality, referred to as "collapse of the wave function".  

So Bohr became obsessed with observation in experimental laboratory settings including interference from the observer, to be compared with computational simulation of a process like protein folding without interference from experimental measurement. Bohr would thus limit the role of QM to prediction of experiment outcomes, while the broader role of QM would be computational simulation of real processes without interference from observation during the simulation. This moves the focus from lab measurements with interference to computational simulation without measurement and interference. 

A main headache of CI is the idea of the state of an object prior to observation (is the cat dead or alive?) as undetermined until the observation, when somehow possibility is made into actuality. How can we be sure that the cat is neither dead nor alive prior to observation and only is decided to be either way at the moment of observation? Is it just like a dice prior to throw has the possibility of 1 to 6. This connects the question of "hidden variables" supposedly answered negatively by the Nobel Prize in Physics 2022. 

All the problems of the CI of QM originate in the multi-dimensionality of the wave function over configuration space arising because of a formal mathematical generalisation of Schrödinger's equation from one electron to many. Nothing says that this is the correct generalisation. Rather the opposite by being a too easy catch.

The Unhappy Nobel Laureate in Physics 2022

John Clauser, Nobel Prize in Physics 2022 joint with Alain Aspect and Anton Zeilinger for experimental work in Quantum Mechanics QM, expressed in his Nobel Lecture that he does not understand the theory of QM. This appears a bit contradictory because his work supposedly says something about the meaning the same theory as expressed in the Prize motivation: 

• for experiments with entangled photons, establishing the violation of Bell inequalities
• and pioneering quantum information science. 

What Clauser cannot understand is the physical meaning in his 3d physical lab space of the QM wave function $\Psi (x1,x2,...,xN;t)$ for an atomic system with $N>1$ electrons satisfying a Schrödinger equation, as a function of $N$ 3d spatial variables $x1,x2,...,xN$ altogether forming a configuration space of dimension $3N$. 

This was the problem which confronted Schrödinger when generalising from the Hydrogen atom with $N=1$ with configuration space = lab space, to Helium with $N=2$ and a 6d configuration space different from lab space. A confrontation which forced Schrödinger to leave QM in despair, leaving Bohr and Born to seek to rescue the situation by giving $\Psi$ a probabilistic interpretation as possibility over configuration space instead of actuality over physical space. Modern atom physics was so born by a heroic sacrifice of actuality or physicality as a most essential aspect of classical physics.

What Clauser expresses is that the step from actuality to possibility created problems, which still after 100 years have not been resolved. 

The root of the problem is that Schrödinger's equation was generalised from $N=1$ to $N>1$ by a purely formal mathematical procedure by simply adding more variables into a $3N$-dimensional configuration space different from lab space. 

Real Quantum Mechanics offers a generalisation retaining actuality in 3d. Other generalisations have been suggested including the Many-Worlds theory by Wheeler and the Pilot Wave theory of Bohm, both with unclear actuality. 

 

 

Nobel Prize 2022 for Proving that Einstein was Wrong?

The Nobel Prize in Physics 2022 was awarded to experimental work supposedly finally closing the fierce debate between Bohr and Einstein on the physical meaning of the Wave Function $\Psi$ of Quantum Mechanics QM, with the sounding conclusion:

• Einstein Was Wrong.   (*)

Bohr represented the Copenhagen Interpretation CI with $\Psi$ representing a probability or possibility of atomic states, while Einstein insisted that fundamental physics as actuality cannot build on playing dice. Bohr said that CI had found its final complete form in the 1920s, while Einstein claimed that something essential named hidden variables was missing. Bohr was younger and more vigorous and won the debate, but Einstein never gave in and his criticism never died. 

A new element was introduced in the 1960s by the young physicist John Bell who showed that outcomes of a CI complemented by any sort of hidden variables must satisfy a certain arithmetic inequality named Bell's Inequality. 

The 2022 Prize is awarded to experiments violating Bell's Inequality, which is taken as evidence that CI cannot be complemented by any hidden variables thus supporting (*). 

But if Einstein was alive today he would still not give in. He could argue: There is a distinction between QM as a general atomistic theory not yet fully formed, and CI as one version of such a theory. Ok, it may be that CI cannot be complemented by hidden variables making it a theory about actuality/reality, but it does not say that this limitation holds for any form of QM. 

The bottom line is that (*) is still open to debate. Get prepared.

You can start listening to Tim Maudlin:

• What Bell Did.
• Corrects the 2022 Nobel Physics Committee About Bell's Inequality

Maudlin points to a misunderstanding by Prize Committee believing that the experiments show (*) in the sense that no "hidden variable" extension of QM is possible, while in fact what the experiments (appear to) show is non-locality or in Einsteins words "spooky action at distance". 

This connects to the earlier discussion about the connection between mass density and gravitational force in Newtonian gravitational theory with last post: Gravitation vs Mass boiling down to view the gravitational potential as primary physical quantity and mass a secondary locally derived quantity.

  

Corruption of Modern Physics 19: $\Psi$ as Elephant

John Clauser will today receive the Nobel Prize in Physics from the hands of Swedish King Carl XVI Gustaf for his experimental verification of a quantum mechanical phenomenon of photon entanglement. In his Nobel Lecture (see previous post) Clauser made it perfectly clear to the perplexed audience and Prize Committee, that he finds it very difficult to understand the theory of Quantum Mechanics QM and so the theoretical significance of his own experiment. Clauser explains his difficulties to results from the presence of a theoretical Elephant in the room in the form of the wave function $\Psi$ as the holy grail of QM. 

Clauser can without loss of scientific credibility admit that he does not understand QM, because this is what most modern physicists do without blushing including Nobel Laureates, but to Clauser this seems to be a real issue, even if not so for the Nobel Committee and the King. What then is the problem with the  wave function $\Psi$? Let's see:

$\Psi (x,t)$ for an atomic system with $N$ electrons is a complex-valued function depending on a $3N$-dimensional variable $x=(x1,x2,...,xN)$ with each $xi$ representing a 3d spatial coordinate for $i=1,...,N$ and $t$ a time variable, which satisfies Schrödinger's equation. The problem with $\Psi (x,t)$ is the many dimensions of the variable $x$ formally representing $N$ different 3d coordinate systems which means that each electron has its own 3d reality while there is no common reality to all electrons. This is the Elephant Clauser is speaking of referring to the $3N$-dimensional space of the $x$-variable as configuration space without common reality, to be compared with the 3d reality of the lab space, where real physical experiments are performed. 

The Clauser Elephant represents the unclear connection between configuration space and lab space, and the Elephant does not want to leave the room.

Different techniques to deal with the Elephant have evolved over time. The most popular advocated by Bohr and Born, is to view the Elephant as only possibility thus admitting giving up reality. The other, advocated by Heisenberg and Dirac admitting nothing, is to shout "Shut Up and Calculate!", effectively resorting to mere formalism. 

So the show goes on: New Nobel Prizes to QM for discoveries nobody can understand, not even Nobel Laureates themselves. Time to listen to Clauser. And maybe take a look at Real QM. 

What is notable is that the Prize is given to experimental support of a special form of theoretical QM which cannot be understood. More precisely for giving experimental support that no other form of theory can be contemplated.

John Clauser Nobel Prize in QM 2022: Does Not Understand QM!

John Clauser shared the 2022 Nobel Prize in Physics with Alain Aspect and Anton Zeilinger for 

• groundbreaking experiments using entangled quantum states, where two particles behave like a single unit even when they are separated. Their results have cleared the way for new technology based upon quantum information.

with further motivation:

• One key factor in this development is how quantum mechanics allows two or more particles to exist in what is called an entangled state. What happens to one of the particles in an entangled pair determines what happens to the other particle, even if they are far apart (supposedly disproving Einstein's requirement of local realism).

In his Nobel Lecture John Clauser is keen to make a confession (last slide at 1.22.30 see above) that he does not understand the physical meaning of Quantum Mechanics QM expressed by Schrödinger's equation for a wave function $\Psi$ over a configuration space of 3N dimensions for an atomic system with N>1 electrons.  

To Clauser as an experimental physicist there is the 3-dimensional lab space, where his experiments are performed, and there is a 3N-dimensional configuration space supporting the wave function,  and he wants to make it very clear that he does not understand their connection. 

This is remarkable because entanglement is a direct reflection of the multidimensional nature of configuration space for $N>1$. Entanglement is built into Schrödinger's equation för any atomic system with more than one electron. But it is a property of a wave function over a configuration space and not lab space. 

Clauser gets the Nobel Prize for an experiment in lab space supposedly giving support to entanglement as an effect in configuration space, while admitting that he does not understand the connection between lab space and configuration space. 

Can you understand this? Clauser is not the first physicist to express that he does not understand QM in configuration space, in fact all do, but it is of particular weight in the context of experimental verification in lab space of an effect in configuration space. Is there a possibility of misinterpretation? 

In particular, Clauser expresses strong frustration with quantum theorists asking him as experimentalist to verify in lab space effects which can only exist in configuration space, and so he finishes by throwing out the following provoking question to his theoretical physics friends, if any left: Can two black holes be entangled?  

Clauser shows his deep belief in real physics as competitive sailor.      

For a version of Schrödinger's equation over lab space see Real Quantum Mechanics.

Corruption of Modern Physics 18: What is a Photon?

This is a continuation of Corruption of Modern Physics 1 as a celebration of the 2022 Nobel Prize in Physics to be delivered on Dec 10 by King Carl XVI Gustaf. 

I read in Electromagnetic fields, size, and copy of a single photon by Shan-Liang Liu:

• Light is almost involved in each field of science anddaily life of everyone, and yet light’s true nature has eluded us for centuries. 
• Albert Einstein successfully explained the photoelectric effect in 1905 by the assumption that light is composed of photons and showed that a photon has constant energy hν and momentum h/λ where h is the Planck constant, ν is the requency, and λ is the wavelength. 
• The theory of relativity tell us that a photon has zero rest mass and always moves at the speed of c=λν in vacuum.
• However, these answers are not satisfactory. Roy J. Glauber once jokingly summarized his theory of photo detection by the sentence: “I don’t know anything about photons, but I know one when I see one”.
• Single photons are essential for the fundamental study of the quantum mechanics and the development of photonic quantum technologies such as optical quantum computing and quantum communication
• However, there is not still a satisfactory answer to the problem what a photon is.
• Experiments have indicated that a single photon can locate in very small space and very short time duration  but how to know the size of a photon is till a puzzling question. 
• The wave-like properties of light or photons are well described by the classical theory of electromagnetic fields. 
• How to properly describe the electromagnetic fields of a single photon is still a fundamental and unresolved question in physics. 

So I get confirmation for my long held suspicion that physicists still today, in particular in the light of the Nobel Prize in Physics this year which was awarded to so called entangled photons, do not know what they are talking about when they are talking about photons. This is yet another example of the strangeness of modern physics.