Something Rotten in Copenhagen Interpretation

Modern physics is based on the Copenhagen Interpretation CI of the wave function $\Psi$ as solution to Schrödinger's equation as a full description of all of atom physics. For an atomic system consisting of $N$ electrons labeled $n=1,2,...,N$, the (complex-valued) wave function has the form  

• $\Psi (x,t)$

with each electron $n$ being connected to a 3d Euclidean space $E_n$ with coordinates $x_n$ collected as a $3N$-dimensional coordinate $x=(x_1,x_2,...x_N)$ and a common time coordinate $t$. In CI

• $\vert\Psi (x,t)\vert^2$

represents the the possible appearance of an electronic configuration at time $t$ with electron $n$ appearing as a particle at space coordinate $x_n$ for $n=1,2,...,N$. 

More precisely, $\vert\Psi (x,t)\vert^2dx$ is viewed to be the probability of "finding" an electron configuration within the volume $dx$ around $x$ as an act of an Observer, see PS2 below.   

The very rich $3N$-dimensionality of $\Psi (x,t)$ with a unique 3d Euclidean space $E_n$ reserved for each electron $n$, puts CI outside classical deterministic physics taking place in a common shared 3d Euclidean space $E$, and then outside the rationality of the scientific revolution.  

In CI electrons appear in 3d worlds which are entirely separate but also overlap into a common 3d world. This is not easy to grasp and is the root cause of the never-ending debate about the physical meaning of CI with "shut up and calculate" as desperate dictate.  

Schrödinger's equation contains the following elements with $\nabla_n$ gradient with respect to $x_n$:

• Atomic kernels as point charges with corresponding Coulomb kernel potentials.   ( 1)
• $\vert\nabla_n\Psi\vert^2$ as kinetic energy of electron $n$.                                                                       (2)
• Coulomb potential between each pair of electrons $x_i$ and $x_j$ for $i\neq j$.          (3)     

Here (1) acts in a common space $E$ while(2) acts in each separate $E_n$, which is comprehensible but unphysical. But (3) has a double function which is not comprehensible unless you are a believer in CI.   

The total inter-electronic Coulomb potential energy arising from (3) is given by

• $\sum_{i<j}\int\frac{\vert \Psi (x,t)\vert^2}{\vert x_i-x_j\vert}dx$      (EP)

We see here the presence of all the separate $E_n$ but also the shared presence in $\vert x_i-x_j\vert$.

Each electron in CI thus lives in a separate world, but also appears in the separate worlds of all the other electrons. 

This is not possible in a classical deterministic common world, and so CI presents instead a probabilistic world as a World of Possibilities, instead of a classical world of actualities. 

This is a world so rich that even a system with moderate number of electrons, would span more possibilities than the number of atoms in the whole known Universe. To handle this absurdity CI reduces wave functions to be either symmetric or anti-symmetric, but the number of possibilities is still overwhelming.

A symmetric wave function $\Psi (x_1,x_2,...,x_N,t)$ does not change under permutation of variables which in CI is viewed to signify that electrons lack individuality in space and time, and so that the labelling $n=1,...,N$, has no real physical meaning. Yet each electron has its own 3d space and also appears with individuality in space and time in the shared distance $\vert x_i-x_j\vert$ in (EP). 

There is a general agreement that quantum mechanics in the form CI cannot be understood or visualised in some sense, but still serves as the foundation of all electronic technologies of  modern society. 

The basic difficulty of understanding/visualisation comes from the mix of possibility and actuality carried by the wave function: Electrons interact by actualities in space and time involving individuals within deterministic physics, while electrons also appear as possibilities without individuality outside deterministic physics. Understanding the root of a difficulty is the first step to come to grips with it.

Real Quantum Mechanics presents a form of quantum mechanics within the realm of classical deterministic physics which can be understood, and may well serve electronic technology better than CI. Why not give it a try?

PS1 CI connects to the Monadology of Leibniz with monads as simple substances each one within its own 3d space yet with a window open to interaction with other monads. But Monadology is today not viewed to be science because modern physicists cannot understand it.  

PS2 The world of possibilities of CI is not that of statistical mechanics describing a world of most probable actualities. In CI a possibility becomes an actuality in the act of observation by an Observer causing the wave function to collapse, which is maybe the deepest mystery of CI. The role of an Observer is not crucial in classical mechanics nor in statistical mechanics arising from difficulty of observation in classical mechanics.

Man-Made Confusions about Identity

In the light of quantum theory these elementary particles are no longer real in the same sense as objects of daily life, trees or stones, but appear as abstractions derived from the real material of observation in the true sense. (Werner Heisenberg)

In the Copenhagen Interpretation CI of quantum mechanics as the present standard of modern physics established 100 years ago, quantum particles like electrons do not carry the physical identity of classical particles, which even of the same kind can be identified by their unique trajectories in space and time without jumps. Electrons in CI lack such physicality and appear rather as abstract possibilities than actualities. 

This makes CI into a non-physical theory impossible to visualise, a theory without Anschaulichkeit in the words of Schrödinger. This is the root of the present crisis of modern physics. 

Recent posts exhibited the complications arising from the lack of identity of the quantum particles of the CI. These are man-made complication, which do not arise in real physics where identity is not compromised. 

Complications arising from confusion of identity also arise in man-made worlds outside physics. The presence of several copies of a picture or text in the memory of the computer may cause confusion if not all copies are updated the same way. The presence of copies of works of art upsets the art market. The same with branded clothes and bags. The presence of doubles in politics adds to confusion. AI brings further confusion since author identity is missing and intellectual property has no owner. 

Quantum mechanics as man-made physics is full of complications from confusion of identity. All the troubles come from denying an electron physical identity in space and time. It is like denying a person to be citizen of a country, to condemn the person to be stateless or homeless without a passport and bank account, to be a no-person. How to handle electrons or persons without identity? 

Classical physics as real natural physics existing independent of human speculation is not man-made in the same sense and there is no lack of identity. 

Quantum Mechanics vs Crisis of Modern Physics

Schrödinger cancelled by Bohr

The roots of the present crisis of modern physics can be traced 100 years back to the discovery of quantum mechanics based on the Schrödinger's equation in 1925, which directly triggered a fierce controversy concerning its physical meaning. Here Schrödinger/Einstein were outmanoeuvred by Bohr/Born/Heisenberg declaring the Copenhagen Interpretation CI to be the belief all physicists had and still have to confess to. But Schrödinger/Einstein never accepted CI and the unresolved trauma is today manifested in particular in a discussion about Identity, Individuality and Indistinguishability in Physics and Mathematics.

In classical mechanics particles follow continuous trajectories in space-time, which do not overlap, and so can be used to identify particles even of the same type in all other respects.  Particles do not jump from place to place and so can be distinguished. 

This is not so in quantum mechanics: A solution to the Schrödinger equations for a system of $N$ particles (electrons) takes the form of a multi-dimensional wave function $\Psi (t, x_1,...,x_n)$ depending on $N$ three-dimensional coordinates $x_1,x_2,...,x_N,$ and a common time coordinate $t$. In CI the square of the wave function is supposed to represent the probability of a realisation of quantum particle configuration at time $t$, with quantum particle $n$ appearing at position $x_n$ for $n=1,...,N$. Wave functions are either symmetric in the variables $x_n$ representing bosons such as photons, or anti-symmetric representing fermions such as electrons. In CI it is not possible to identify particle trajectories and so quantum particle identity is lost. Yet quantum particles are labeled and have identity in the sense that two quantum particles (electrons with the same spin) cannot share position in space-time. Quantum particles appear as possibilities without identity and continuity in time, to be compared with  classical particles as actualities with identity continuous in time. 

CI is not an ontological model of what is, but something very different still without scientific meaning despite 100 years of brooding by the greatest of human minds. A basic difficulty is that there are so many more possibilities than actualities. Interaction of actualities like collision of classical particles has meaning, while interaction of possibilities appears to be meaningless. Documentation of actualities may be possible, while documentation of all possibilities is impossible. CI is uncomputable.

The nightmare of CI is the idea of collapse of the wave function as the step from possibility to actuality or from anonymity to identity believed to take place upon observation. This is the event of an Observer opening Schrödinger's cat box to find the cat either dead or alive, convinced that before the opening the cat is in a state of all possibilities or superposition of both alive and dead. Schrödinger thus demonstrated the absurdity of CI, but was cancelled by Bohr and there we are today. 

All the questions from 1925 remain about the possible meaning of a physics without identity and continuity in time. In particular the possibility of self-destruction by self-interaction in the absence of individuality and identity discussed in recent posts.   

Real Quantum Mechanics presents a new form of quantum mechanics where identity and continuity in time is restored, a form of physics which is computable.  

Suddenly the Wave Function Collapsed into a Rabbit.

    

Cancellation of Self-Interaction as Renormalisation

The apparent clash between Leibniz Principle of Identity of Indiscernibles PII and the Copenhagen Interpretation of Quantum Mechanics (StdQM) has triggered quite a bit of discussion surveyed in the book Identity in Physics: A Historical, Philosophical and Formal Analysis.

The trouble is rooted in the interpretation of the wave function of stdQM as expressing probabilities of possible electron particle configurations. 

This is to be compared with actual real configurations as in Real Quantum Mechanics RealQM  in a sense of classical physics with non-overlapping charge densities with unique presence in space-time as expression of identity. 

PII is in harmony with classical physics and RealQM, but not with StdQM. 

Schrödinger as inventor of quantum mechanics could not accept the probabilistic interpretation of StdQM, and so was cancelled by the leading Copenhagen school of Bohr, Born and Heisenberg. 

We may ask if PII is of real importance or only of some scholastic philosophical virtual importance?

The previous post brought up the idea that PII connects to self-interaction as a toxic element of Quantum Field Theory QFT as the generalisation of StdQM underlying the Standard Model capturing all of elementary atomic particle physics. It is manifested in the appearance of "infinities" asking for "renormalisation" to be cancelled, like techniques to ignore elephants in the room. 

In classical physics prevention of self-interaction is possible because it is possible to distinguish each particle from all other particles and so to guarantee in particular that the electric/gravitational field created by a particle only affects other particles but not itself. This is the nature of Newton's Law of gravitation and Coulomb's Law. 

But StdQM describes probabilities of possible particle configurations, which lack particle paths and so lack identity over time. In StdQM bosons (such as photons) can occupy the same position in space-time as well as some fermions (such as electrons with different spin), and particle paths have no meaning. In this setting  self-interaction cannot easily be prevented, and so ask for extra-ordinary techniques for cancellation in the form of "renormalisation".  Nobody is happy with this trick introduced to handle a fundamental difficulty of physics as statistics. 

The possibility that a specific particle occupies some specific position in space-time and the possibility that another particle does the same thing do not appear to be mutually exclusive, which means that particle identity is lost. Probably. Statistics is tricky.

The problem with self-interaction is that it has to steer way from both blow-up to infinity (too much ego) or decay to zero (too much self-criticism) in a very delicate balance threatened by instability.

Recall that the electron of Hydrogen atom is prevented from disappearing into the potential hole of the proton kernel by the presence of the Laplacian in Schrödinger's equation giving the electron an extension in space as a charge density. Likewise the Earth is saved from being swallowed by the Sun by orbiting the Sun as a form of spatial extension.

From the above book:

• It is not clear how collections of non-individual objects can be captured by standard set theory. 
• As the mathematician Yuri Manin put it: “We should consider possibilities of developing a totally new language ...” to deal with collections of entities which do not behave as standard sets (in the sense of obeying the axioms of the usual set theories), since the “new quantum physics has shown us models of entities with quite different behaviour. 
• Even ‘sets’ of photons in a looking-glass box, or of electrons in a nickel piece, are much less Cantorian than the ‘set’ of grains of sand”.
• It is our intention in this book to explore these different issues and, in particular, to go some way towards developing the ‘totally new language’ suggested by Manin.

PS When young men pull on military uniform they lose identity and become soldiers all alike in violation of PII:

Quantum Mechanics as Retreat to (German) Romantic Irrational Ideal

Quantum theory is widely held to resist any realist interpretation and to mark the advent of a ‘postmodern’ science characterised by paradox, uncertainty, and the limits of precise measurement. Keeping his own realist position in check, Christopher Norris provides a remarkably detailed and incisive account of the positions adopted by parties on both sides of this complex debate.

James Cushing gives in Bohmian Mechanics and Quantum Theory (1996): An Appraisal, an account of the rise to domination of the Born-Heisenberg-Bohr Copenhagen Interpretation of quantum mechanics:

• Today it is generally assumed that the success of quantum mechanics demands that we accept a world view in which physical processes at the most fundamental level are seen as being irreducibly and ineliminably indeterministic. 
• That is, one of the great watersheds in twentieth-century scientific thought is the "Copenhagen" insight that empirical evidence and logic are seen as necessarily implying an indeterministic picture of nature. 
• This is in marked contrast to any classical representation of a clockwork universe. 
• A causal program would have been a far less radical departure from the then-accepted framework of classical physics than was the so-called Copenhagen version of quantum mechanics that rapidly gained ascendancy by the late 1920s and has been all-but universally accepted ever since. 
• How could this happen? 
• It has been over twenty years now since the dramatic and controversial "Forman thesis" was advanced that acausality was embraced by German quantum physicists in the Weimar era as a reaction to the hostile intellectual and cultural environment that existed there prior to and during the formulation of modem quantum mechanics. 
• The goal was to establish a causal connection between this social intellectual milieu and the content of science, in this case quantum mechanics. 
• The general structure of this argument is the following. Causality for physicists in the early twentieth century "meant complete lawfulness of Nature, determinism [(i.e., event-by-event causality)]". 
• Such lawfulness was seen by scientists as absolutely essential for science to be a coherent enterprise. A scientific approach was also taken to be necessarily a rational one. 
• When, in the aftermath of the German defeat in World War I, science was held responsible (not only by its failure, but even more because of its spirit) for the sorry state of society, there was a reaction against rationalism and a return to a romantic, "irrational" ideal.

Yes, quantum mechanics (in its Copenhagen Interpretation forcefully advocated by Bohr under influence from the anti-realist positivist philosopher Höffding) was a product of German physics in the Weimar republic of the 1920s, by Heisenberg and Born. 

It seems reasonable to think that if the defeat of Germany in World War I was blamed on a failure of "rationality" and "realism", then a resort to "irrationality" and "anti-realism" would be rational in particular in Germany...and so quantum mechanics in its anti-realist form took over the scene as Germany rebuilt its power...

But maybe today Germany is less idealistic and anti-realistic  (although the Energiewende is romantic anti-realism) and so maybe also a more realistic quantum mechanics can be allowed to develop...without the standard "shut-up and calculate" suppression of discussion...

CONFERENCE: NATURE AND THE PHILOSOPHY OF NATURE IN GERMAN IDEALISM AND ROMANTICISM (SYDNEY, JUNE 15-17, 2015)