Feyman Doubling Down by QED

Feyman diagrams revealing the deepest secrets of Nature.

This is a continuation of the previous post on the evolution of theoretical physics during the 20th century in a sequence of doubling downs to a new more complex theory when facing difficulties with an old theory instead of resolving the difficulties. Let us take a look at the step from the Quantum Mechanics QM of atoms of the 1920s to the Quantum Electro Dynamics QED of the 1950s including light preparing for Quantum Field Theory QFT as the ultimate quantum theory of modern physics underlying the Standard Model of elementary particles.   

QED was presented to a general public by its leading proponent Richard Feynman in 4 lectures later collected into the book QED The Strange Theory of Light and Matter. 

Newton's primitive idea of light as a stream of light particles was in the late 19th century replaced by Maxwell's equations, where in particular light appears as a wave carried by oscillating electromagnetic fields. Maxwell's equations concisely captures all of electromagnetics as the top jewel of classical mathematical physics. 

Einstein refuted Newton in 1916 and Feynman refuted Maxwell in 1948 and so returned to Newton: Light is a stream of particles named photons. In the book Feynman's argues: 

• The theory of QED describes Nature as absurd from the point of view of common sense. 
• We have so far, found nothing wrong with QED. It is therefore the jewel of physics- our proudest possession.
• It is very important to understand that light behaves as particles, especially for those of you who have gone to school, where you were probably told something about light behaving like waves.
• We were talking about light. The first important feature about light is that it appears to be particles: when very weak monochromatic light (light of one color) hits a detector, the detector makes equally loud clicks less and less often as the light gets dimmer
• Newton thought that light was made up of particles- he called them "corpuscles"—and he was right (but the reasoning that he used to come to that decision was erroneous). We know that light is made of particles because we can take a very sensitive instrument that makes clicks when light shines on it, and if the light gets dimmer, the clicks remain just as loud-there are just fewer of them. Thus light is something like raindrops-each little lump of light is called a photon—and if the light is all one color, all the "rain- drops" are the same size.
• So now, I present to you the three basic actions, from which all the phenomena of light and electrons arise. ACTION #1: A photon goes from place to place. ACTION #2: An electron goes from place to place. ACTION #3: An electron emits or absorbs a photon.
• The problem is, when we try to calculate all the way down to zero distance, the equation blows up in our face and gives meaningless answers-things like infinity. This caused a lot of trouble when the theory of quantum electrodynamics first came out. 
• People were getting infinity for every problem they tried to calculate!

We see here typical ingredients of doubling down raising the bid so that it cannot be called as in poker: 

1. The theory is absurd beyond comprehension. 
2. The theory is perfect with perfect agreement with observation. 
3. The theory appears to give meaningless results. 
4. The theory is primitive as being reduced to Action #1-3.   

Since the theory is incomprehensible it cannot be questioned or called. That the theory shows perfect agreement with observation is impossible to check, since direct application of the theory by a non-expert gives meaningless infinities.

The reason QED produces infinities is Action #3 which opens to self-interaction: An electron emits a photon and then absorbs the photon, as discussed in this post showing the danger of self-feed back. 

Feynman like Einstein propelled himself to be the golden boy of modern physics as expressed in the book Genius: The Life and Science of Richard Feynman. In later years his geniality has been questioned by e g Freeman Dyson in particular the mystery of self-interaction.

The argument that light is shown to be a stream of particles because light can give rise to "clicks" of an instrument, is as silly as saying that a good joke is a particle because it can give rise to a laugh.  

PS The Standard Model divides particles into matter (fermions) and force carriers (bosons) with photon the massless carrier of the electromagnetic force. The trouble with this double set of particles with matter particles interacting by forces transmitted by force carrying particles, in the above setting electrons interacting by emitting and absorbing photon particles, is that it opens to self-interaction going wild into infinities. In the setting of gravitation this would require some form of graviton particles, which have not been found. Instead, gravitational force appears to come from a gravitational potential field present everywhere. The trauma of modern physics is that the Standard Model is incompatible with gravitation. The trouble comes from the role of bosons as force carrying particles. If there are no gravitons, maybe there are no bosons either? And then what about QED and QFT?   

Doubling Down in Theoretical Physics and Geopolitics

Physical scales range from $10^{-18}$ to $10^{22}$ meter about 40 orders of magnitude. 

The US Empire is now collapsing in front of our eyes along with the rest of the West, while the East/South is taking over supported by 90% of the world population. Doubling down by printing more dollar does not seem to work any more. No even the entry of Sweden into NATO will help out.

Geopolitical power is exercised through economical and military power resting on technology based on mathematics and physics.  

The rise of West came with the scientific revolution initiated by Galileo, Descartes, Leibniz, Newton, Euler from a new idea of God as mathematician or theoretical physicist creating a Universe governed by natural laws of mathematical form, like the inverse square law of gravitation. This propelled the West to World domination with the power shifting from Europe to US after WW2. 

The development of the atomic bomb by scientists gathered in US from Europe during WW2 boosted the self-confidence of US theoretical physicists of the 1950-70s into exploration of ever smaller atomic scales in search for a Theory of Everything uncovering God's ultimate mathematical trick. But God showed to be too smart and unsurmountable problems had to be met by doubling down. Here is a time line for physics on ever smaller scales in each new step leaving the old problems unsolved: 

• Faced with difficulties of extending classical deterministic physics to the microscopics of atoms,  theoretical physicists doubled down in the 1920s by presenting Quantum Mechanics as a new form of probabilistic physics on scales of size $10^{-10}$ meter.
• Faced with seemingly unsolvable foundational problems of Quantum Mechanics, theoretical physicists doubled down in the 1950s by presenting Quantum Field Theory as a new form of physics on sub-atomic scales of size $10^{-18}$ meter. 
• Faced with seemingly unsolvable foundational problems of Quantum Field Theory,  theoretical physicist doubled down in the 1970s by developing String Theory as a new form of physics on sub-sub-atomic scales of size $10^{-32}$ meter.

Here is corresponding time line for relativity theory on ever larger scales: 

• Faced with an apparent absence of an aether as a physical medium for the propagation of light, Einstein seeking to get an academic position as physicist in 1905,  decided to change the classical Euclidean/Newtonian concepts of space and time into a new concept of space-time in a new Special Theory of Relativity.
• Faced with questions from leading physicists, which he could not answer, Einstein doubled down by extending to a new General Theory of Relativity.  
• Faced with new questions, Einstein doubled down restricting his theories to the whole Universe making experimental falsification impossible.    

Today the doubling down has come to an end in a theoretical physics troubled by seemingly unsolvable problems. It is not possible to double down to smaller scales nor to larger scales. Theoretical physics of the West has come to a dead end. 

Or can AI help by doubling and redoubling human intelligence? See also this post.

Is it possible that this is the true reason that the geopolitical power of the West is now collapsing?

PS Doubling down in mathematics can take the form of higher level of abstraction. The problem that the square root of two is not a rational number, which destroyed the Pythagorean mathematical school, could eventually be handled in the 19th century by introducing a new more abstract concept of real number, which was then repeatedly doubled down into vast Hilbert spaces capable of housing the quantum mechanical wave function for the whole Universe. 

Newton or Einstein or Newton?

Recall this post.

A physics student of today will to pass exams have to say that Einstein's theory of gravitation is more precise than Newton's theory of gravitation, not less precise. 

The evidence supplied by the book is that the elliptic orbit of Mercury around the Sun shows a slow turn of main axis (precession) of 5600 seconds of arc per century, while Newton predicts 5557 taking in the influence of all other planets and celestial objects, and the missing 43 is predicted by Einstein as a small correction to Newton.  

In Einstein's theory the speed of gravity is equal to the speed of light in vacuum, while in Newton's theory the speed appears as being infinite. 

In a two-body problem of one small planet and a big Sun, the planet will according to Newton follow an elliptic orbit without precession, because the gravitational force on the planet acts in the direction of the Sun without delay from finite speed of gravity. With a finite speed of gravity there would be a delay which would make the planet slowly orbit away from the Sun. Massive observations of elliptic planet orbits show perfect agreement with Newton's theory. Here Einstein's theory can only be less precise.  

Finite speed of gravity thus appears to disagree with observations, at least in a Newtonian setting. To save Einstein's theory it is necessary to show that it contains some form of non-Newtonian effect which exactly cancels the delay effect of a finite speed of gravity. It is doubtful that this is possible. 

Newton's theory appears to be perfect (except for Mercury). Einstein's theory thus appears as a less precise version of Newton's theory (except for Mercury), in contradiction to the above book answer: Newton is more precise than Einstein. 

Concerning the precession of Mercury it is natural to ask: 

• What is the accuracy of Newton's prediction of 5557? Is everything taken into account?
• What is the accuracy of Einstein's prediction of 43 as a correction to Newton? 
• In order to match the observation of 5600, it is necessary that both 5557 and 43 are correct. Possible?   

If Einstein is less precise than Newton, what does that say about modern physics vs classical physics?

What did Einstein mean by saying "Newton, forgive me?" What what so wrong that an excuse was needed? 

To correct Newton requires a full understanding of all aspects of Newton's gravitation, and then a full understanding of Einstein's gravitation as a correction. Is there any living physicist with this intellectual capacity?

The Nobel Prize in Physics 2017 was awarded "for decisive contributions to the LIGO detector and the observation of gravitational waves" in the form of an extremely weak signal from an extremely massive collision of two black holes at an extremely large distance 1.3 Billion light years away from the detector. This was viewed as extremely strong evidence that Einstein is correct.  

Max Born on Copenhagen Interpretation

Max Born played an important role in forming the new quantum mechanics based on Schrödinger's wave equation presented in 1925, by giving its wave function solution a statistical interpretation as electron configuration probability instead of actuality as in classical deterministic mechanics.

It was the multidimensional form of the wave function with $3N$ space dimensions for a system with $N$ electrons without meaning in classical deterministic mechanics in 3 space dimensions, which required a non-classical interpretation and it was Max Born who in 1926 came up with the idea of letting the multi-dimensional wave function represent an immensely rich world of possibilities rather than a real world of actualities in a step from determinism to new quantum world ruled by games of roulette. 

Schrödinger received the Nobel Prize in Physics in 1933 for "the discovery of new productive forms of atomic theory", while it Born had to wait until 1954 to be awarded for "the statistical interpretation of the wave function". 

In his Nobel Lecture Born describes his mixed feeling about quantum mechanics in general and his work in particular: 

• It contains no discovery of a fresh natural phenomenon.
• It contributed to the solution of an intellectual crisis into which our science had fallen as a result of Planck’s discovery of the quantum of action in 1900. 
• Today, physics finds itself in a similar crisis. 
• Planck, himself, belonged to the sceptics until he died. Einstein, De Broglie, and Schrödinger have unceasingly stressed the unsatisfactory features of quantum mechanics and called for a return to the concepts of classical, Newtonian physics while proposing ways in which this could be done without contradicting experimental facts. Such weighty views cannot be ignored. 
• Niels Bohr has gone to a great deal of trouble to refute the objections. I, too, have ruminated upon them and believe I can make some contribution to the clarification of the position. 
• The matter concerns the borderland between physics and philosophy.
• What is the reality which our theory has been invented to describe?
• The answer to this is no longer physics, but philosophy.
• The lesson to be learned from what I have told of the origin of quantum mechanics is that probable refinements of mathematical methods will not suffice to produce a satisfactory theory, but that somewhere in our doctrine is hidden a concept, unjustified by experience, which we must eliminate to open up the road.

In short, Born was not very happy with the state of quantum mechanics 30 years after it was invented. Physics was in a state of crisis in 1900, 1925, 1954 and still is. The cure of statistics has not worked. RealQM presents an alternative without statistics. 

From Statistical Mechanics to Quantum Statistics

Boltzmann was not easy to argue with.

The development of modern physics follows a path from statistical mechanics (Boltzmann 1866) over statistics of energy quanta of blackbody radiation (Planck 1900) to quantum mechanics statistics (Born 1926). In each case there was a pressing demand from empire power politics on theoretical physicists to assist in advancement of new technologies, from steam engines to atomic energy:

1. Boltzmann took on the challenge to give the 2nd Law of Thermodynamics a rational mathematical physical meaning as the outstanding problem of the mid 19th century.  
2. Planck took on the challenge to give blackbody radiation a rational mathematical physical analysis, as the outstanding problem of classical physics at the end of the 19th century. 
3. Born took on the challenge to give the wave function of the new quantum physics a scientific meaning.       

Boltzmann failed and so invented statistical mechanics based on an idea of macro-states supported by micro-states with probability increasing with number of micro-states. 

Planck failed and inspired by Boltzmann invented a way of computing energy quanta with probability decreasing with increasing frequency. 

Born inspired by Planck resorted to statistics by giving the wave function a meaning as probability of electron configuration. 

 

The use of statistics is fundamentally different in all three cases, but Boltzmann started it all.

This means that modern physics largely is statistical physics. Is this a problem? It means giving up the essence of classical physics as rational deterministic physics based on cause-effect. In statistical physics things happen by chance and rationality is lost. It may be a high price to pay, in particular if it is not really necessary.  

Real Quantum Mechanics offers an new approach to quantum mechanics without statistics.

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.

    

Crisis of Modern Statistical Physics vs Classical Deterministic Physics

This is a further comment on Leibniz Principle of Identity of Indiscernibles seemingly in conflict with the modern physics main-stream idea of electrons all alike like equal probabilities of outcomes of tossing a fair coin. 

That modern physics is in a state of deep crisis is acknowledged by leading physicists and also largely understood by the general public. Buzz words like dark energy, dark matter, inflation, Big Bang, multiversa, entanglement, collapse of the wave function,  particles and quarks, are floating around as elements of relativity theory on cosmological scales and quantum mechanics on atomic scales, both formed 100 years ago but still today harbouring toxic unresolved foundational problems, and on top of that being incompatible. A veritable mess. 

The root of the seemingly unresolvable problems of quantum mechanics can be traced back to the statistical interpretation of the multi-dimensional Schrödinger wave function as solution to the multi-dimensional Schrödinger equation serving as foundation. 

While classical physics is ontology about what reality is, modern physics is epistemology about what can be said. While classical physics is deterministic physics independent of human observer, modern physics in the form of quantum mechanics is statistical physics depending on human observers acting as mathematical statisticians in an insurance company busy computing insurance premiums. 

The departure from classical into modern physics was initiated by Boltzmann in the late 19th century seeking an ontological realistic explanation of the 2nd Law of Thermodynamics as the main unresolved problem of classical physics giving time a direction, which had to be resolved to save physics from disbelief. When Boltzmann understood that he could not reach this main goal of his scientific life, he made a Faustian deal in the form of an explanation based on statistical mechanics. This served to save the life of physics, but not Boltzmann's own life, and opened the door into the heaven of modern physics as quantum mechanics as statistical mechanics, which is now in a state of crisis. 

The step from deterministic physics to statistical physics, was taken in order to save classical physics from credibility collapse in front of the 2nd Law. The medication worked for the moment but the patient as classical physics died and so was replaced by modern physics, which however showed to be quite sick without any cure in sight still today. 

The first step in coming to grips with the crisis of modern physics, is to ask if it is impossible to explain the 2nd Law within classical deterministic physics? If not, then the step to statistics is not necessary and much trouble can be avoided. More precisely, it appears to be possible to replace statistics by a concept of finite precision physics as presented in Computational Thermodynamics and in popular form in The Clock and the Arrow with follow up into a realistic deterministic form of quantum mechanics as Real Quantum Mechanics. 

This means a return to deterministic physics with a new element of finite precision computational physics coming with resolutions of problems of classical physics making it possible to avoid paying the very high price of taking the drug of statistical physics. 

Real physics is what it is and is given to us for free. Statistical physics is man-made physics, which needs massive data and human interference. Real physics seeks to describe the World as it is, while modern physicists have the reduced goal of statistical prediction outcomes of man-made experiments. Schrödinger and Einstein could not accept physics as man-made statistics, but were cancelled. Maybe the present crisis can open to restart following their spirit?  

We may view real physics as a form of engineering or professional soccer game with basic questions: What is the basic mechanism/principle? How to improve it? On the other hand, a statistical physicist simply watches the game on TV and finds meaning in betting.  

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: