Acknowledgment:
This blog has profited from on-going discussions with many friends, some of them having been theoretical physics students at the Universté Quebec, and Université Sherbrooke.
Contents.
(1) Background (2) Two-slit experiment (3) Quantum reality (4) Janaka Wansapura's article in the Lanka web and de Silva's preprint (5)Conclusion.
1. Background.
As I teach science, and also give popular science talks to small adult audiences, I find that the demand is high for a number of topics. They are topics like (a) evolution and man (b) mind and consciousness (c) Rebirth, Buddhism etc., as well as topics from modern physics. These are (i) Wave-particle duality, Schrödinger's cat, Wheeler's delayed-choice thought experiments, many-world interpretations etc., associated with quantum phenomena (ii) Space-time and relativity paradoxes.
I have already discussed the topics of Rebirth, Buddhism and modern science in a previous blog (see this-life-buddhism.blogspot.com/) .
Here I am going to give a brief summary of my usual presentations about wave-particle duality in a scientific manner. This topic has been abused much and shrouded in weirdness by many popularization writers. This is perhaps because people like to hear weird fantasies!!!!
2. Two-slit experiment.
Suppose you are in a room that has two windows and when you look out all you see is a blank wall a few meters beyond the windows A and B. You have a gun and you shoot bullets. The bullets can hit the blank wall if the shot goes through one window or the other. So the bullets that pass through stick on the blank wall in two piles. These are: pile a opposite window A, and pile b opposite window B. There are no shot marks on the blank wall between A and B because that area is blocked by the room wall (see Fig. 1).
In physics you do experiments on "reduced systems". That is, in a controlled enclosure which doesn't let the outside to mess up things (this messing up is called decoherence). So instead of a room we have everything contained in a small box, and instead of two windows we have two tiny slits on a barrier wall, and the blank wall becomes a screen coated with fluorescent paint which lights up at any spot hit by an electron. Instead of a gun we have a hot wire which emits electrons. If we lower the temperature of the wire we can lower the number of electrons shot out towards the slits. We can also close one or both slits. This is the two slit experimental set up.
If a very tiny particle (a quantum particle), e.g., an electron, a photon, or a hydrogen atom rather than a shot is hurled randomly at the two windows, it turns out that the blank wall now gets marked not only near the pile a opposite window A, and near pile b at window B, but also at other places, EVEN IN BETWEEN THE TWO WINDOWS, i.e., in the blocked area marked m of the blank wall.
How did an electron get to the blocked area m? Weird?
Experiments revealed that electrons arrive on the screen and produce luminous spots. These spots are more numerous in some places, and sparse in other places. The distribution seems to be as in an interference pattern (IP) arising from two ripples starting from the two slits. So it is as if waves guided the electrons to come to the screen, with the waves themselves NOT manifesting themself directly.
Even the great Richard Feynman had said that how a photon or electron goes through two slits and ends up at some point X on the screen, to give an IP is something that you should not waste time trying to picture, since it is not intuitive. If you follow your intuition, i.e., cultural and innate prejudices, then you end up getting the wrong results. You don't try to say that the "electron came through both slits", or one slit, or by a given path. Amazingly, if you try to look for (single-valued) paths are found to be taken by the electron, as in the Feynman path-Integral method!
So, don't ask which 'path' was taken by the electron! In German this is called the "Welcher-Weg frage" (which-way question). That was Feynman's advise.
But we know how to calculate any final result of an experiment with perfect accuracy using the Schrodinger wave equation.
Does the "welcher-Weg Frage" sound like one of the "unanswerable questions posited by the Buddha? Or by the positivists of the first half of the 20th century"?
However, the work of David Bohm, John Bell, and the rise of quantum field theory as well as quantum information theory have led to a very clear concept of what wave-particle duality is about. We can for instance state the two-slit experiment in a clean, non-ambiguous way so that puzzles like "how can a particle be in two places at the same time", or paradoxes like the "Schrodinger's cat" do not arise to plague our thinking.
Much of the confusion arose because the popular press, and even pre-print archives like arXive are full of discussions starting from the old debates at the 1930s Solvay conferences involving Niels Bohr, Einstein, Heisenberg, Schrödinger and others. Worse than that, philosophers attempt to foist their cultural or theistic prejudices and "interpret" the quantum theory to suit their whims, and they still continue to debate wave-particle duality in journals on the "philosophy of science". There are some who claim that with out God acting as the observer, there can be no "reality". But such "interpretations do not produce new predictions different from standard quantum theory, nor do they clarify the physical picture as was done brilliantly by David Bohm.
David Bohm transformed the Schrodinger wave equation in to a form enabling him to have particles with definite position and momentum that move under the action of quantum potentials that have special properties. The uncertainty principle is not violated because the indeterminacy is included in the initial conditions of the differential equation.
All that philosophical hog wash about Gods and deities can be dispelled by using a modern statement of the issues involved. In any case, practicing scientist have an unsurpassed theory which works in every known case and hence now-a-days they do not spend time on the 'wave-particle duality problem".
3. Quantum reality.
The best way to understand the issue is to follow the most modern approach. Indeed, it is nothing but a scandal in the popularization of science, as well as in the foundation of science, that the public, and some philosophers, are still misled into believing that the fundamental question of the wave-particle duality of non-relativistic electrons is not settle and not yet clear.
It is very clear today and there is really no mystery when you get used to the enhanced, richer world of quantum phenomena.
This scandalous continued obfuscation about "wave-particle duality" has been denounced by the well-know physicist in two articles that should be read by every serious student of physics. The first van Kampan article is the best one:
van Kampen, N. G., : Physica A 153, 97 (1988)
In discussing the two-slit experiment for an electron we only need to consider the non-relativistic quantum theory embodied in the Schrödinger equation. We are all familiar with the classical field concept. We know of the electromagnetic field of an antenna carrying waves to radios and TVs in the neighborhood. So the "field" concept is well grounded in physics.
The surface of a tank of water can be considered as a "field". The excitations of this field can be seen as waves, or as solitons (solitary waves) etc. Such fields are generated by classical elastic forces. The membrane of a drum is also like a field, limited by boundaries of the drum, and these set up boundary conditions on the elastic field associate with the membrane. The square of the amplitude of the field of the membrane at some point on the drum gives the intensity of the sound emitted by that part of the drum.
It is experimentally found that nature populates the detector screen with electrons in a random fashion, but with a distribution that satisfies the intensity formula for an interference pattern of a wave. This interference happens even with just one electron, with the blip most likely to appear in the high-intensity region of the interference pattern which acts like some hidden hand guiding the electron. So it is natural to ask if there is some field indirectly guiding the electrons to reach the screen. After all, we don't see a magnetic field, but if we place a paper on top of the magnet and put iron filings at random, then the field rearranges the filings to fit with the pattern of intensity of the field.
Louie de Broglie thus came up with the idea of a pilot wave directing the electrons, and remaining in the background as some invisible field.
However, such ad hoc models based on physical intuition became unnecessary when Schrodinger introduced his wave equation. According to Schrodinger, whether it be one electron or many electrons, there exists a field ψ which is a function of all the coordinates of all the electrons and time. The energy (i.e., sum of kinetic plus potential energy) of the system, re-written as as operator is the Hamiltonian operator of the system. The ψ function is an eigenfunction of this operator. The probability of finding an electron at some point X=(x,y,z) is simply the squared modulus of ψ at X, i.e., |ψ(x,y,z,t) |2.
The Schrödinger equation also defines the field, or pilot wave, that Louie de Broglie was proposing, but without the need for any intuitive fiddling. The Schrodinger equation is a natural extension of Hamiltonian mechanics familiar to physicists from the 19th century itself. Heisenberg produced an equivalent formulation, where the ψ-function is expanded in a basis set of other functions, and so ψ becomes a vector in this function space. The time evolution of the tip of this vector in the function space is precisely the Schrodinger equation in a different garb, and is known as Heisenberg's equations of motion. The function space used by Heisenberg was well known to mathematicians as "Hilbert space".
Thus the Schrödinger equation also defines the field for just one quantum particle or many quantum particles. If the experiment is done in a container with impenetrable walls, then the field extends everywhere inside the container, and goes to zero at the hard walls. The Schrödinger quantum filed ψ(x,y,z,t), specifies the amplitude of the field at the point x,y,z, at the time t. If there were two particles, we need a ψ(x1, y1, z1, x2, y2, z2, t). Here we consider just one particle for convenience.The square of the amplitude gives the intensity. It is the strength of the field. This Intensity at X is just the number-density of excitations (i.e., electrons) at that point.
Hence an electron is simply an excitation of the Schrödinger field.
The |ψ(x,y,z,t) |2 tells us the probability of finding an electron at that point x,y.z, at the time t.
This function has to satisfy the boundary conditions imposed by the walls, screens, slits, collimaters and others components of the apparatus enclosed in the container (the "reductionist" object of study). The moment a slit is closed or opened, or a wire mesh is place or removed, the ψ(x,y,z,t) will change to take account of the new configuration. This is exactly as in a classical field, where the whole field changes when new charges, conductors or dielectrics are added to the experimental set up.
Most things in nature are described by differential equations and they are sensitive to the boundary conditions. Even the sound of a drum depends on the boundary conditions imposed on the shape and edges of the drum membrane. This fact that the wavefunction ψ(x,y,z,t) i.e., the Schrödinger field is sensitive to all the boundary conditions is hence nothing mysterious. However, some people now begin to use words like "the quantum field knows" what is going on. It has some "intelligence" etc., and that this is an example of "pan-psychism". All that is hog wash, and mere semantics.
The sensitivity to boundary conditions is brilliantly included in Bohm's quantum theory where the effect of the boundary conditions are included in the effective potentials known as "quantum potentials" arising naturally in Bohm's method. So, the quantum field ψ(x,y,z,t) pervades the whole space of the experiment. It is everywhere up to its boundaries. If there are slits it passes through all of them, and like a jelly pervades everything. Since Bohm's form of the Schrodinger equation is a classical Hamilton-Jacobi equation containing quantum potentials, one can calculate particle trajectories, and it is found that in all cases, the particle passes through only one or the other of the slits, but NOT both, while the quantum potentials involve both slits.
Where is the electron if the electron gun emits just one electron. The electron modifies the amplitude of the field, to conform to an occupation number of just one electron. Where is the electron? The electron is an excitation of the field, and since the field is everywhere, it can manifest itself anywhere. We can say that the electron is averged out and distributed every where, but it is not a useful picture. It has simply become energy in the field. We only see the electron if an excitation occurs and if a phosphorescent screen or some such particle detector is at the right place to detect the excitation.
That is, we need to set up the experimental configuration to observe the electron. This setting up changes the boundary conditions, and the wave function modifies to the new conditions. This process is part of the so-called collaspe of the wavefunction (that misleading language can be avoided if Bohm's approach is used, where the Schrodinger equation is transformed exactly into a classical Hamilton-Jacobi equation).
If there were two slits, the field would have formed with the interference from the two slits built into ψ(x,y,z,t) via the need to satisfy the boundary conditions of Schrodinger's differential equation. An approximate way of doing this is to write this as a linear combination of two wavefunctions, one of which represents the region for slit A, and the other for the region of slit B. But that is an approximate procedure, and it is better to solve the Schrodinger equation in detail, say on a mesh of points, using a differential-equation solver, to obtain ψ(x,y,z,t) .
A phosphorescent blip could occur any where on the screen, and then we say that we have detected an electron at some X1= (x1, y1, z1). The probability of that happening is |ψ(x1, y1, z1,t) |2. That is, whether just one electron, or two electrons, or more had been sent out by the electron gun, the interference exists if there are two slits, and an intensity may be seen at a, b, m or any where X1 on the screen depending on the square of the field amplitude.
If there were only one slit, the field-amplitude function ψ(x,y,z,t) ("wavefunction") of the system changes to fit the existence of just one slit. The intensity is still given by the square of the new no-slit wavefunction and now there is no interference.
The whole ambiguity comes when people talk of the "wavefunction of the electron". In fact, the wavefunction is a property of the whole experimental set up.
The electron is just a possible excitation state of this set up.
A wave is also an excitation in the Schrodinger field.
Bohr's complementarity principle says that waves and particles are the basic excitations of quatum physics (the wave-particle duality), but they never occur AT THE SAME TIME. They are complementary realities.
The field can have other excitation states, with two electrons, or three electrons etc., when the field intensity increases. Mathematically one can describe the "action" of the electron gun to "create electrons", i.e., excitations in the field using operators that act on the wavefunction. These are called creation field operators A+f and adjoint operators annihilation field operators Af. they create and destroy these excitations at the location f or momentum state f. These operators obey anti-commutation rules if they are for electrons, and their time evolution is governed by the Schrödinger equation. This is a sophisticated but fool-proof way of saying that electrons obey the Schrödinger equation.
So, what do we mean by a particle? Exactly as in classical physics, a particle is a localized entity at or around some location X1 and we indicate this by a delta function. δ(X-X1). A field is some thing that pervades every where, and is somehow the antithesis of the particle which is localized. In quantum physics particles are excitations of fields. The effects of fields dominate the behaviour of particles and hence boundary conditions on the wavefunction become important. In classical physics many such excitations have collected together to form macroscopic bodies, and the associated fields have shrunk. Thus the effect of the boundary conditions is negligible.
If an electron is created at time t0 at the electron emitter located at X0, we describe this process by the operator A+0. Let the electron propagate to the slit S1 at time t1. Then its presence can be sampled using the operator As1. The mean-value of the Wick product of operators, denoted by G=<T A+0As1 >, where T is the Wick-time ordering operator is known as the propagator of the electron. It is shown in books on quantum field theory that that this propagator is simply the Green's function of the Schrödinger equation. It can be shown that the Green's function is single valued, and hence the electron cannot be in two places at the same time. Thus the electron must pass through just one slit, and we need the quantum field as well, to bring in the interference effect. We cannot do without the field. This is a mathematical consequence of the nature of the Schrodinger equation.
Thus the quantum wave-particle duality states that the description of quantum phenomena requires underlying Schrödinger quantum field, and its excitations that manifest either as particles or as waves, but not both at the same time .
Its mathematical character can be noted by looking at the Fourier transform of the delta function where is expressed in terms of plane waves (1/√V)exp(ik.x) where V is the volume of the reduced-system under study and k is a momentum state. A momentum state has a definite momentum but no position. A delta-function has a definite position but no definite momentum as it is made up of a complete set of plane waves in the Fourier sum. Thus we see that the complementarity between position and momentum is buried in the Fourier expansion property.
And yet, people don't like this rather counter intuitive wave-particle duality. Even Einstein didn't like it because whether a particle will appear or not has become probabilistic. Strict cause-and-effect has been dethroned. Einstein wanted strict cause and effect rather than probabilistic uncertainty in nature. That is why he said "God doesn't play dice". Note that for Einstein, "God" stood for the orderly, causal nature of reality and not a God that you pray to.
So people try to get rid of wave-particle duality by inventing other models, usually even more weird. Just as there is no end of people trying to "disprove relativity", there are thousands of people trying to challenge wave-particle duality. In the next section we discuss an attempt to discard the wave picture and explain the two-slit experiment "using a purely particle model". Studying such attempts are interesting in some what the same way as studying proposed models of perpetual machines in sharpening our understanding of physics.
4. Nalin de Silva's articles.
I saw a recent example in a Sri Lankan e-journal that I often read as I am originally from Sri Lanka. The article by Janaka Wansapura (JW), a medical physicist, had the title "Wave-particle duality of nature challenged at Kelaniya University". Subsequently, an article by prof. Nalin de Silva's was posted.
The account in the JW article smacked strongly of Afshar's experiment (http://arxiv.org/abs/quant-ph/0701027) , but made no mention of it. I posted a comments wondering if the authors had missed Afshar;'s experiment or worse. Then JW posted a link to an article by Dr. Nalin de Silva (NdeS) at http://arxiv.org/pdf/1006.4712v1.pdf clarifying matters. The Afshar experiment was also an attempt to discredit wave-particle duality by trying to claim that he could demonstrate the path of the electron that managed to pass through the two slits.Indeed, Dr. Silva's preprint contained a discussion of the Afshar experiment.
INalin de Silva's gave details of a variant of that experiment done at Kaelaniya, Sri Lanka. Furthermore NdeS claims that he does not need "wave-particle duality" and proposes to discuss everything with just particles. In fact, the paper is still a pre-print, and it is indeed the scientific tradition of transparency to post a pre-publication so that people can comment on it even before publication, so that the authors can deal with any lacunae and criticisms.
In my view, the discussion reveals many misunderstandings in physics, and a failure to grasp how Bohr's principle of complementarity applies. I don't see in it any challenge to the ``wave-particle duality" observed in quantum physics. The authors claim that their cultural beliefs enable them to believe that the electron passes through both slits at the same time. This belief can be shown to be incorrect using mathematics.
The preprint claims that the particle passes through both slits at the same time!
The probability of finding a particle at the slit A is
<ψ*(xA)ψ*(xA)>
where the mean value is taken over the volume region VA of slit A.
A similar result holds for finding the electron at xB, where the volume region is VB'
However, the probability for find the same particle passing through BOTH slits is the mean-value of
<ψ*(xA)ψ(xA)ψ*(xB)ψ(xB)>
where the mean value is evaluated by integrating over both volumes, using the product-volume element: dVAdVB. The total wavefunction ψ(x) for any x for the region of interest may be taken as a linear combination of a basis function centered on A, and another centered on B and orthogonal to that at A. Then it is easily shown that the joint probability of an electron passing through both slits at once is zero.
Critical discussion of the de Silva preprint:
http://arxiv.org/pdf/1006.4712v1.pdf
This preprint addresses the two-slit experiment for non-relativistic electrons. In section 2 itself NdeS makes a number of puzzling statements.
The double-slit experiment has been carried out with only one electron passing through the slits one at a time. ....In the case of several electrons passing through the slits simultaneously it could be explained using the wave properties of the particles, in other words resorting to the wave picture. Unfortunately in
the case of electrons being shot one at a time this explanation was not possible
as what was observed on the screen was not a faint interference pattern corresponding to one electron but an electron striking the screen at a single point
on the screen (P 2).
Thus it seems, as far as I can understand his statement, that according to NdeS, a single electron in a two-slit system does not show interference? This is simply NOT correct. A single electron in a two-slit system is observed precisely according to the probability density associated with an interfering quantum field.
NdeS further says, repeatedly:
However, what the Physicists failed to recognize was that in the case of one electron shot at a time there was no weak interference pattern observed on the screen for each electron thus illustrating that a single electron did not exhibit any wave properties (P 3).
Thus NdeSilva expects to see a faint interference pattern accompanying the blip from the electron! He seems to have forgotten the Bohr complementarity principle where wave- and particle- properties do NOT occur together!
It is clear that the explanation given by the Physicists for the formation of interference patterns on the basis of the particle picture is not satisfactory. We saw earlier that the explanation given in the wave picture is also not satisfactory as a single electron fired from the source does not form a faint interference pattern on the screen. If the particles behave like waves then even a single particle should behave like a wave and produce a faint interference pattern, having interfered with itself (P 4-5)
As we have argued a single electron emitted from the source would
not exhibit a faint interference pattern on the screen but a spot or an image
having passed beyond the slits. The Physicists are interested in the wave pic-
ture to explain the interference patterns as they find it difficult to believe that
a particle would pass through both slits simultaneously. Thus they mention of
particle properties when they are interested in “capturing” particles and of wave
properties in explaining phenomena such as the interference pattern (P 8)
Could he possibly mean that a single electron does NOT interfere, does NOT obey a Schrodinger equation? That a single electron does not have a wavefunction? This is simply NOT correct. It obeys the one-electron Schrodinger equation for the two-slit system. A single electron, or two, or many electrons are all excitations of the underlying Schrodinger quantum field. There is no difference in the formalism for one electrons or many electrons, unless we begin to take electron-electron exchange-correlation effects into account. But NdeS is dealing with non-interacting non-relativistic electrons.
The fundamental error of NdeS seems to be his belief that wave-particle duality implies that every electron has a manifestly observable wave associated with it, and so when a single electron comes through the slit, the wave should have interfered, and a faint interference pattern should be seen! That belief is unwarranted by complementarity and that is not what is promised by the Schrodinger equation or the Heisenberg equations of motion, or even by Louie de Broglie's pilot-wave theory. The Schrodinger equation predicts exactly what is seen.
Janaka Wansapura (JW), presumably a colleague of NdeS, also laments that
Physicists have been particularly bothered by the fact that when a single electron, instead of a beam of electron is sent through the double slit what is observed on the screen is not a faint interference pattern but a single dot on the screen depicting an electron striking the screen. If an electron represented a physical wave of some sort Unfortunately, then one would expect a series of bright and dark fringes, however faint it might be on the screen but not a single dot.JanakW does not give any references to any physicist who have been "particularly bothered" by the behaviour of the single electron. The objection that only a spot (and not an interference pattern) should apply not only to one electron, but to two or more electrons. But NdeS et al., seem to see something specially odd in the one-electron experimental result. Basically, the kind of discussion being carried out by JanakaW, and NdeS were done, and done with, in the 1920s and may be found in the writings of Louie de Broglie and others. There is of course no objection to visiting old problems a fresh, but one should not fall into well-trodden, well-known traps.
NdeS seems to suggest that "Western Physicists" have not been able to consider that a particle could be in two places at the same time because of cultural prejudices. He thinks that the electron passes through two slits at the same time, and says that he does not need a wave property. But he brings in the Hilbert space expansion in terms of basis functions, and hence brings back the quantum field by the back door. Or it may be that he has not realized that the Hilbert space expansions (see his sec.5, and sec.7) used by him are equivalent to the use of a quantum field. We already noted that the Green's functions of this quantum filed are single valued and hence the electron cannot be in two places. This it is mathematics, and not cultural or philosophical prejudices that dictate the conclusion that the electron always passes through one of the slits and lands on the screen to be part of a distribution that gives an interference pattern.
The single-valuedness of the Green's function is a result of the linear character of the Schrodinger differential equation. Since Bohm's equation is non-linear, one may wonder if it could support multi-valued propagation as needed for "the electron to be in two places at the same time". However, detailed numerical calculations by Basil Hiley and David iBohm demonstrated that the electron always travelled through just one of the slits.
see: D. Bohm and B. Hiley: The undivided universe: an ontological interpretation of quantum theory
Quantum physicists often speak loosely and say that the electron is in eigenstates of "both wells", or entangled in tow eigentates etc. Here what they mean is that the wavefunction is in a superposition of two states. However, this loose talk is taken over by NdeS to actually mean that the particle named an electron exists simultaneously in two more places. For instance, in a triple quatum well, or in a three-slit system, NdeS would say that the electron is actually in three places at the same time.
Now, NdeS says that although the particles exist in several places simultaneously, they cannot be detected in several places. So we see that we are into metaphysics.
More Metaphysics in NdeS's preprint.
There is actually a lot more metaphysics in NdeS's preprint. He uses these to justify his claim that his interpretation is some how better than any of the standard ones.
In sec. 5, p 9 NdeS says:
We (i.e, NdeSilva and collaborators, added by the blog author ) have no inhibition in believing that the Quantum particles unlike the Newtonian particles could pass through both slits at the “same time”, as the logic of different cultures permits us to do so. Physics and in general Mathematics and sciences are based on Aristotelian two valued twofold logic according to which a proposition and its negation can- not be true at the same time. Thus if a particle is at the slit A, the proposition that the particle is at A is true and its negation that the particle is not at A is not true, and vice versa. Therefore if the particle is at A then it cannot beWe first note basic errors. In the early quarter of the 20th century there were three theories regarding the nature of mathematics.
anywhere else as well, and hence cannot be at B. This is based on what may
be called the Aristotelian- Newtonian - Einsteinian ontology where a particle
can occupy only one position at a given time in any frame of reference of an
observer. However, in fourfold logic (catuskoti) a proposition and its negation
can be both true, and hence in that logic it is not a contradiction to say that a
particle is at the slit A and at somewhere else (say at the slit B) at the “same
instant” or “every instant” Thus according to catuskoti the particle can be at
many places at the same time or at many instants with respect to the observer.
(a) Russell and Whitehead tried to prove their thesis that Mathematics was derivable from Logic (not just Aristotalian, but suitably more extended). This is found in the book "Principia Mathematica". But they failed in their objective as they discovered new paradoxes and problems like Russelll's paradox of sets".
(b) Hilbert, the great German mathematician held that mathematics is just a formal system based on a set of axioms, and that all of mathematics can be generated by formal manipulations on the axiom set. Thus all propositions of mathematics were deducible according to Hilbert.
(c) The Dutch mathematician Brouwer and others believed that mathematics is an intuitive product of the human mind and its foundations cannot be codified.
The discovery of Russell's paradox was followed later by Goedel's theorem, which showed that there were true but non-deducible propositions in any non-trivial calculus. Thus both (a) and (b) are not longer tenable. But Nalin de Silva claims even today that mathematics is derived from Aristotelian logic, and science uses Aristotalian logic ! This is wrong.
NdeS talks of four-valued logics, and seems to believe that two-valued logics are some how incomplete. Already in Boole's work, and from more recent work in computer science we know that all muti-valued logic elements can be constructed from two-valued logics by admitting place values. This is also the basis of binary arithmetic which can represent any number beyond 2. All logic gates can be constructed from binary bits, and that is what computers do. Computers are not restricted to "Aristotalian logic". The Catuskoti that NdeS is taking of can be simulated with just two binary bits.
In any case, Louie de Broglie and others clearly did consider the possibility of an electron being in two places at the same time in their initial musings. Scientists have no inhibitions in regarding that an electron may be in two or many places at once, as they indeed use that parlance in loose talk. In western culture, Santa Claus is entering a whole multitude of chimneys at exactly the same time on christmas eve.!
To communicate effectively words need to have clear meaning in clear discussions. Thus we use the word orange fruit to specify a particular fruit, and do not use the same word to describe an orange flavoured drink. We use the word particle, anshu in Sanskrit and Pali, to specify a localized entity, i.e., the epitome of a delta-function. But, if we want to talk of a particle which is found all over the place, then the correct semantic usage is field. And indeed, the founding fathers like de Broglie, Schrodinger etc., correctly chose that word. Even in eastern cultures, we do not use "anshuva" to denote a distributed entity. The words "tharanga, pravaaha, vaaha, prachaara, ksethra ", etc., are more culturally natural.
In any case, we note that NdeS has NOT removed the wave concept from his formulation. We see in sec. 7, labeled "New interpretation", the use of expressions like |ψ>=Σ|ciψi> as well as the use of the square moduli of amplitudes |c*ici| in his discussions. Such expansions in a function space etc., and use of squared moduli are signatures of the implicitly assumed wavefield. The discussion of the "Kelaniya experiment" also assumes the existence of a wavefield as they say that they placed an aluminum strip along an intensity node, presumably calculated from a wavefunction.
There is just no getting away from the reality of the quantum field and its particle-like excitations.
5. Conclusion
In sections 1 to 3 we discussed how quantum particles (e.g., electrons photons, neutrinos etc) are excitations in quantum fields. The fields proved the wave nature and the excitations provide the particle nature of the quantum world. The fields pervade the full experimental volume of the reduction being studied (a system with boundaries), and hence it is sensitive to the whole space - i.e., it is holistic and non-local. Wave-particle duality does not mean that a wave accompanies a particle, or that an interference pattern occurs faintly for each particle and add up to give a brighter pattern with more particles.
Waves and particles are manifestations of quantum fields, and obey Bohr's complementary principle, i.e., they do NOT occur simultaneously.
In section 4 we discussed an example of attempting to "dethrone" the wave property of quantum particles. Unfortunately, it harks back to the pit falls already cleared up and discussed in the early days of Louie de Borglie. The case discussed in sec. 4, due to Nalin de Silva is particularly interesting as it is presented by that author as an example of an attempt to bring in some cultural concerns to guide the construction of his theory. In fact, we know that the progress of science has always been associated with having to break cultural prejudices and innate beliefs by confronting such cultural beliefs with hard facts.
I think this is a nice contribution to this topic. I appreciate the metaphysics-free presentation where both particles and waves are regarded as simple excitations of an underlying quantum filed that we only know via the wave-function or state vector or what ever.
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