Why We Still Don’t Have Quantum Nucleodynamics by Norman D. Cook

Your paper is pretty interesting, though rather removed from my experience beyond an undergraduate elective course in nuclear physics. At the risk of showing how ignorant I am of nuclear physics, or what might be called classical or pre-QCD nuclear physics, I am going to bounce an idea here. It seems to me that the LDM and the IPM might represent different phases of a nucleus. The two approaches seem to reflect different scales with which the isospin nuclear force acts.

Some years ago emergent supersymmetry was discovered in the physics of the nucleus. It has been my speculation there is some sort of phase transition in the nucleus. This phase transition might be similar to BCS superconductivity, but with a twist. The conductivity of a medium is

σ(ω) = j(ω)E(ω).

The conductivity σ(ω) = Re[σ(ω)] iIm[σ(ω)] for BCS conductivity the Re[σ(ω)] determines how well a superconductor absorbs photons of frequency σ(ω) for ω > ω_c = 2Δ the photon can demolish a Cooper pair into two uncorrelated electrons. The critical frequency or Δ is determined by a Bogoliubov coefficient. This connects with a phase structure for black holes, or for collective systems that have properties analogous to black holes. The photon entering a black hole has a relationship to a photon exiting the black hole by Bogoliubov coefficients. The black hole may possess a charge, or BPS gauge index, and the incoming photon will interact with the charges on the stretched horizon. For ω > ω_c the photon penetrates the stretched horizon with charged fermions in a correlated or Cooper pair type of state. The wave equation for the vector potential is

(∇^2 - ∂_t^2 m^2)A^μ = 0,

where the mass is an effective mass m^2 = q|ψ|^2 from the coupling with the fermions ψ. This results in a dispersion relations and a frequency dependent σ(ω), where for ∇^2A^μ = k^2A^μ, where as k --- > 0 the conductivity is

σ(ω) ~ lim_{z--->0}E(ω,z) B(ω,z)

This is analogous to computing the effective the impedance of free space on the boundary of an anti-de Sitter spacetime in the AdS/CFT correspondence. The conductivity is independent of the interchange E < --- > B, where the conductivity is constant for ω = ω(k) < ω_c. The current is the proportional to the potential, from σ(ω) = j(ω)E(ω) constant, the .current

j(ω,k) = const A(ω,k) ~ const ωE(ω,k)

where the current is divergent at ω = 0. This is then a superconducting phase

For AdS_2/CFT_1, the CFT is SL(2, R) or under Euclideanization a representation of an SU(2) isospin gauge theory. This is the nucleon force in a nucleus. The inherent supersymmetry in this correspondence may then be the source for the emergence of supersymmetry in some nuclear states.

Cheers LC

Hi Lawrence,

Thanks for the comments. The topic of the "phase" of nuclear matter is complex (the gas-to-liquid transition has been studied mainly in the framework of high-energy multifragmentation, see "Statistical Models for Nuclear Decay" A.J. Cole, IOP, Bristol, 2000, for discussion). Although the identity of the solid-phase and gaseous-phase IPM description of nuclei has motivated by own research, whichever "phase" is assumed, the surprising finding from the 1990s is that nuclei exist in well-defined IPM states only 75-80% of the time (Pandharipandhe, Rev. Mod. Phys. 69, 981, 1997), with the remaining percentage being "transition" states. John Wheeler and Niels Bohr both commented that the LARGE nuclei have many characteristics of solids, but, from the perspective of the lattice representation of the IPM, it appears that the 20%-25% of non-IPM states might be due to the fluid movement of nucleons between lattice sites on the nuclear surface... a liquid-like "skin" around a lattice core. The emergence of "supersymmetry" might be more evident in the lattice than in the liquid....

Cheers

Norman

The AdS/CFT analogues appear to hold for some solid state physics systems with heavy metals. This leads to superconductor behaviors and is thought to be a case of how high temperature superconductivity physics occurs. I would tend to agree that if this happens with nuclei this happens in the lattice phase. If I understand properly the liquid drop model pertains to highly excited nuclei, which is a case where the nucleus has been excited into a "melt." At much higher energy I presume one could say the nucleus is vaporized into a scattering of protons and neutrons. There was some work at the tevatron along those lines. There are though some heavy ion work and experiments with HRIC and now the heavy ion work at the LHC which is searching for black hole.AdS like behavior in quark-gluon plasmas. This would then represent a more extreme case; a case where the nucleus is replaced with a QCD-lattice of quark-gluon physics.

I will comment more after I read your references.

Cheers LC

Dr. Cook:

Your excellent essay presents a clear example of the fallacy of non-unique explanations, where a conventional picture is assumed to explain a set of results, even though an alternative picture may reproduce the same results with greater logical consistency. Unfortunately, this fallacy is quite prevalent through science, and indeed all human endeavors. You might also be interested in my own essay (The Rise and Fall of Wave-Particle Duality), where I point out that neutron diffraction from a crystal does NOT uniquely prove that the neutron is a de Broglie wave. The same diffraction results follow for a small-particle neutron scattering from a lattice with quantized momentum transfer.

Alan Kadin, Princeton Junction, NJ, USA

Hi Alan,

Thanks for the comments. I will respond to your essay elsewhere, but want to follow up on our common concerns here.

In connecting the dots to form a picture (whether ink dots on paper or data points in our minds), everyone is guided by tacit assumptions about what the final picture should look like. Once the picture has been drawn and made explicit, however, it is hard "not to see" the final product in the mind's eye - and nearly every new data point will act only to reinforce that view. The "bias for the familiar" is a plague on all scientific endeavor and means that, especially for those of us trying to rethink fundamental physics, we need to offer more than "alternative" views. Alternatives are necessarily less familiar... and consequently suspect! Fair or unfair, we need to do two more things: (1) show how our alternatives are indeed improvements, and (2) show how the historical context led earlier researchers to their (we believe, mistaken) views. The first is simply the development of the new idea itself (and is fun and creative work), but the second is the more arduous task of understanding the ideas of others.

Cheers

Norman

Congratulations Norman - your many years of hard and original work on the problem of nuclear structure are gradually bearing fruit as more and more people read and respond to your approach. I am particularly grateful to you for stressing the FCC (face-centered-cubic) lattice as the one Nature prefers. As you know I have adopted it in my own theory (of everything - or nothing - i.e. in the vacuum ;). There is something exquisitely beautiful about the diamond-like arrangements of nucleons - shown in the illustrations of your essay. Dirac would have admired your work - he was moved by beauty in physics as this 1970's interview shows.

It is a very interesting essay. I reproduce the text from abstract that interests me.

"The core problem has been the assumption of a central nuclear potential-well to bind nucleons together, in analogy with the Coulomb force that binds electrons to the nucleus. "

I believe the problem is still more fundamental and originates from concept of conservation as applied to energy (with neutralization) while no negative mass or energy particles have been found till to-date. If neutralization is extracted out of conservation, Konservation is left behind. (See upcoming essay on 5-Dimensional Universe)With this, potential well cease to have meaning for confinement.

Elsewhere, I have commented with particle model from PicoPhysics describing particle as a collective set of photons. It is bound together by difference in relaxation time characteristic of particle with affected space surrounding the particle.

Picophysics view of stability has two predominant affect;

1. Space surrounding the particle has an affect on particle stability. This results in different cross-sections for interaction with other particles.

2. Result in specific energy level of emitted radiations

3. Nuclear Magic numbers

However, the nuclear dimension of PicoPhysics will be presented at level -4. Only level-1 is publicly available www.picophysics.org

Dear Norman Cook,

I think you have another winning essay. You clearly state the issue: "The core problem has been the assumption of a central nuclear potential well to bind nucleons together..."

Since Quantum Chromodynamics is unable to calculate spin and other form factors for the nucleons, and predicted a 'quark gas' instead of the 'perfect fluid' found when heavy ions collide, it is probably not too surprising that the 'nucleon gas' perspective also fails.

What is surprising is that gaseous independent particle model (IPM) mimics the symmetries of the lattice such that "to know the quantum mechanical structure of the nucleus... is to know its lattice structure and vice versa." I was somewhat confused about the meaning of angular momentum quantum number until I found that it's based on the distance from the nuclear spin axis (as I had guessed it must be).

You may recall from my earlier essay and "Chromodynamics War" that my model of nucleons is based on a self-sustained flux tube that provides a pseudo-lattice structure based on nearest-neighbor interactions (at least through the alpha particle and potentially higher). My current essay The Nature of the Wave Function is based on the same field but is focused on the quantum mechanical wave function of free particles and atomic electrons. I have not applied it to the nucleus. As you mention the "many debates concerning the interpretation of quantum mechanics", I hope that you find the opportunity to read my essay, and I very much look forward to your comments.

I also found it helpful to read your 2010 monograph and suggest other interested readers do so. Finally, this essay and monograph and your previous essay have inspired me to buy your book on "Models of the Atomic Nucleus". In short, you have convinced me.

Congratulations again on an excellent essay which seems to unarguably challenge a key assumption of the last century.

Edwin Eugene Klingman

Hi Edwin,

I too am a fan of your work (and will comment under your essay later) - and especially your book, The Chromodynamics War. The only reason it didn't make the New York Times best-seller list is that it is relentlessly high-brow, but I think you have identified - and spun an interesting story about - a hugely important conceptual divide between those who value causal coherency versus those who seem to value Standard Model categorization (even when causal coherency is uncertain). In the context of nuclear structure theory, the various nuclear models can account separately for different data sets, but the necessity of jumping from one model to another is jarring for anyone who values coherency... and makes me think there are different understandings of what "understanding" means.

Hi Vladimir,

I think we share a sense of what is beautiful, but I am repeatedly reminded of the truth that beauty is in the eye of the beholder. So, you and I see beauty in lattice symmetries, while others see greater beauty in the act of experimental verification. The Higgs boson is a good example, but I would say that the collective effort that led to that result is more beautiful than the result itself. In any case, the FQXi essays are good examples of different levels of conceptualization, where we stake out our individual claims of "local" beauty. (Meanwhile, we await your essay...)

Hi Vijay,

Thanks for the comments. The "central" nuclear potential well has been a source of problems in nuclear structure theory for many decades, so it will be of interest to see if your picophysics can account for experimental facts without that fiction. The magic numbers are important, but their empirical identification is a particularly slippery issue because the "magicness" of proton magic numbers is influenced by the number of neutrons, and vice versa. That is why the textbooks sometimes include 6, 14, 28, 40 and 70 as magic or "semi-magic," and modern studies on exotic nuclei with huge excesses of protons or neutrons sometimes report the "disappearance" of other magic numbers. The QM "texture" of nuclei is certain (e.g., my Table 2), but the evaluation of "closed" shells is trickier than the evaluation of the inertness of the inert gases in atomic theory.

Hi Norman Indeed we are blessed to have this openness to beauty in general,and to enjoy Japanese gardens and sense of design and harmony. But the sort of beauty in physics goes beyond just the lovely illustrations - it is in the knowledge of the logic, economy and sheer intelligence in the workings of nature. Of course some may object and say that we impose this sense of order on nature with our theories and ideas, but I think we as natural organisms have evolved in much the same way as atoms and molecules did - and share the same logic!

I just submitted my colorful FQXI essay today it was harder to pare it down to the required length than just writing it!

Cheers!

I guess your references are not on the arXiv. I will try to look them up in library copies. I have been a bit slow, for one of my brothers died recently and I have been involved with that.

Cheers LC

Dr. Cook,

I have gone through your thought-provoking paper dealing with "the core problem has been the assumption of a central nuclear potential-well to bind nucleons together, in analogy with the Coulomb force that binds electrons to the nucleus."

It is true that the central attractive nuclear Coulomb force compels the atomic electrons to orbit around the nucleus, but this is not the case for the nucleons in the nucleus. Here, the nuclear interactions are represented by a single-particle potential that has to provide a depth of around 40 MeV to take care of the Fermi kinetic energy of 32 MeV of the nucleons in the nucleus and the nucleon binding energy per nucleon of about 8 MeV, which represents less than 1 % of the nucleon mass keeping the system nonrelativistic. The mean nucleon density of 0.17/ fm ^3, in the nucleus gives a mean distance of around 2fm between the nucleons and the short-range nuclear forces are most effective at this distance with a repulsive core at r = 0.5 fm. These nucleons move around in this self-generated Nuclear Potential aided by the Pauli Exclusion Principle (PEP) and the presence of the hard core, because inside the nucleus all the available states are occupied excluding the possibility of any collision. In this context, the QED cannot be considered worthier than QND, if this is nature's way.

Over the years, there has been a sharp theoretical-controversy over the water-tight validity of the PEP, but this discussion per se cannot be considered as the last word on this Principle that controls the behavior of Fermions and hence, so much of the universe as we know. Thus, in spite of the nucleon density of 0.17n/fm^3, these fermions with precise momentum and energy values, should have unhindered orbits to move around.

Moreover, the strongly interacting Liquid Drop Model and the Shell Model have been wrongly pitted against each other. The LDP cannot be more liquid than the SM or the other way around, because in both the cases, the same Fermions determine their structure and the interaction-energy content. One has to remember, that the LDM and the LDM-based mass formula of Weiszäker and others, was set up many years before the setting up of the SM.

Here, one often talks about the Mean Free Path (MFP) of nucleons in the nucleus, in the context of the formation of Compound Nucleus. An example, a thermal neutron (zero-kinetic energy) enters the nucleus of, say, 235 U. Once inside the nucleus, its binding energy of 6.5 MeV is freed and it can excite the nucleons of the nucleus only down to 6.5 MeV from the top of the Fermi energy of 32 MeV. These excited nucleons are projected into the unoccupied states of the continuum. Here, understandably, the MFP becomes very short, but this cannot be case, when an occupied state cannot be emptied into the unoccupied continuum states.

One has to conclude that the SM has been and remains the unassailable backbone of low energy nuclear physics with its spherical and deformed shells for the phenomena like spectroscopy, fission, fission-barrier structures and the production of Super Heavy Elements.

The Fcc Lattice Model is a good adventure, but it has to go a long way to root in its value. As an example, in the SM the cold fusion of D+D and the fission of Pd via the heat of the chemical energy, are not conceivable, but it seems that the Lattice Model does not exclude these. If here, the predictive power of this Model is confirmed., it will be its grail.

Professor Asghar,

Many thanks for commenting in such detail (here and elsewhere). Despite obvious differences in perspective, I am not sure how mutually-exclusive our views are. Specifically, I would agree with you that the shell model's description of "independent" nucleon states is "unassailable". But the theoretical contortions that are needed to get to that description in a "nuclear gas" are, I believe, dubious. Moreover, the fact that the final description of nuclear states is precisely replicated in the lattice model suggests an alternative. As most nuclear theorists would admit, the other (liquid-drop, cluster, etc.) models of nuclear structure theory are fundamentally not quantum mechanical (QM) and are, for that reason, widely held to be limited analogies between macroscopic objects and a small set of nuclear properties, but are far from being comprehensive theories of the nuclear world. In that sense, I think the choice for the "one truly comprehensive theory" of the nucleus will necessarily be either the QM lattice or the QM shell model.

There are lots of specialist topics where the two models differ and where a decisive experiment might yet distinguish between them, but let me ask you about the shell model's invocation of the exclusion principle to justify the "orbiting" of nucleons in the dense nuclear interior. Weisskopf (1951) introduced that idea soon after the first publications on the shell model (1949), and stated it frankly as a hypothesis that needed examination: "It remains to be proved whether this [exclusion] effect is sufficient to establish independent orbits in low-lying states of nuclei in spite of the existence of strong interactions" (Blatt and Weisskopf, 1953, p. 778).

But the hypothesis was soon taken by others to be a fundamental "truth," and has since been generalized to the form you mention, where the exclusion "principle" is said to be a "force" of nature! Gravity, EM, weak and strong forces..... and the fifth "force" of one particle excluding another particle from entering its QM space by virtue of "exclusion". I am not the only one who finds that logic a little bit strange. Herzberg (1937, p. 123), Condon and Shortley (1935, p. 167), Yang and Hamilton ("its physical basis remains an open puzzle", 1996, p. 193) and a handful of others over the years have commented that, as true as the exclusion principle is in describing certain fermion phenomena in both atomic and nuclear physics (and even QCD), it still needs to be explained on the basis of underlying physical forces.

The invocation of the exclusion principle in nuclear theory is an example of the kind of domino effect that faulty assumptions produce: If you assume an experimentally unknown central nuclear potential around which nucleons orbit, you then need to explain how the nucleons can squeeze past each other in a substance as dense as nuclei. If the nuclear volume were much larger or the nucleons much smaller, then nucleon collisions might be sufficiently infrequent and their "orbiting" might be justified. But a typical heavy nucleus like Lead has more than 200 nucleons (rms radius, 0.9 fm) inside of a rather small nuclear volume (rms radius, 5.5 fm), making the nuclear interior about one-half filled with nucleons and making the nucleon "mean-free path" extremely short. So, having made the faulty assumption of a central nuclear potential, a nuclear gas is implied, but in order to justify nucleon orbiting, the exclusion principle must then elevated to the level of a "force of nature".

So, I see what the shell model theorists are up to, but a less tortured view of nuclear structure is to accept the short-range nuclear force inherent to the liquid-drop model (and experimentally known!) - and simply forget about the novel use of the exclusion principle as a force of nature. All of the shell model QM states of nucleons are retained in a frozen liquid-drop (the nucleon lattice) - and the lattice shares most of the macroscopic properties already described in the liquid-drop model.

In the end, does the lattice model today accomplish as much as the shell model, independent-particle model, the liquid-drop model and the cluster models have achieved?! The answer is: Not yet. But, if you would be so kind as to send me 10,000 graduate students and a few years of supercomputer time, I think we will leave the shell model in the trash bin of history where Ptolemy hangs out.

In discussing the complexity of the nuclear version of the Schrodinger wave equation, you say "The first is that the nucleus contains two types of nucleon, protons and neutrons, that are distinguished in terms of the so-called isospin quantum number i. The second is the notion of the coupling of orbital angular momentum (l) with intrinsic angular momentum (s) - giving each nucleon a total angular momentum qunatum value (j=l+s)."

Using these ideas and "a strong and short-range nuclear force that acted only among nearest-neighbor nucleons" you show an FCC structure describes a "shell model descriptions of nuclear spins, magnetic moments, shells, subshells and parity states.."

Unfortunately, you also point out "The nuclear lattice does not of course address issues of nucleon substructure or the interpretation of quantum theory itself, and many aspects of quantum 'weirdness' remain enigmas in the lattice."

I liked your essay and learned a lot, especially the clarity the two tables bring to the subject.

There are other models that match the results of these two tables. Consider big thin shells layered on top of each other. Intrinsic angular momentum (s), is modelled as the spin of that shell and orbital angular momentum (l) is modelled as the spin around the axis of the particles precession, which is independent of the intrinsic spin. Animations showing the Larmor frequency of this style of particle can be seen here. Hope you may be so inclined to comment on this.

Thank you for the contribution, a great read.

Dear Professors Cook and Ashgar,

I hesitate to enter a discussion between two such highly qualified nuclear physicists, but as you note,there are unresolved quantum issues involved.

It is my opinion that the exclusion principle is neither a principle nor a 'force', but a consequence of the physical wave function discussed in my essay, to the effect that the physical wave function of fermions will interfere in such a manner as to preclude their occupying the identically same state.

This model of the nucleon wave function predicts (at the same particle velocity) a physical wave six orders of magnitude weaker than that of the electron, based strictly on mass density. This should be significant from the perspective of de Broglie 'steering' of the particles. Additionally, the associated nuclear model tends to support a lattice structure, or at the very least lattice-based alpha particles.

The model is very new and has no establishment support at the current stage of development, yet at the informal level of FQXi blog comments I feel safe in saying the model supports Dr. Cook's lattice model.

Edwin Eugene Klingman

Dr. Cook.

Thank you for the reaction to my comment on your article. This allows me once more to clarify a few points:

1. The SM potential is not central like for the QED but it is the self-generated single-particle potential due to all the nucleons of the nucleus in which they are supposed to move freely. If it is shown beyond reasonable doubt that the PEP and hard core cannot ensure this unhindered movement, one has to find another reason to understand the validity of this fundamental Model. Since more than 60 years, this SM has been the unassailable source - nay, the raison d'être, with an immense predictive power, for the vast enterprise of Low Energy nuclear physics. Its vast and unique heritage cannot be wished away or pushed down just as a trash (even of the future history) simply by condemning it to be artificial in its conception, because the lack of understanding of something should not make it artificial.

2. The Fcc Lattice Model is an elegant enterprise, but its range of validity remains to be shown on the ground in its own right. Of course, you will not get 10000 PhD students and an unlimited computing power to prove the capacity of this Model. However, as I tried to suggest before, one has to find something that the Lattice Model can treat, but the SM cannot deal with. This seems to be case for the chemically induced cold fusion of D+D and the fission of Pd. Of course, there may some other things too. The uniqueness of these phenomena will be a powerful backing and justification for this Model in its own right.

3. Please avoid these caravans of citations that have a tendency to end up as the truth on the point treated and this does not do any good to anybody. Moreover, these comments have to be made without hankering after any applause and panegyrics. Finally, I am grateful for the opportunity for these objective comments (and elsewhere) and wish all the best for the Fcc Lattice Model and its practitioners.

The Pauli exclusion principle is a quantum topology. The PEP states that ψψ = 0, where we may then see this as a form of d^2 = 0, which is the dual of ∂∂ = 0 (the boundary of a boundary = 0) in topology. This becomes generalized in supersymmetric form with generators Q. The state ψ is such that Qψ = 0, but where ψ =/= Qχ. Therefore the state is ψ \in kerQ/imQ = H^1(Q), which is a cohomology ring.

The PEP permits one to write a large Slater determinant for the wave function composed of the wave function of each nucleon. The potential between each nucleon would be the Yukawa potential

V(r) = Ae^{-λr}/r

The space would then in an equilibrium situation assume an "egg carton" potential function, where each pocket would exist at each nucleon. It would then seem possible to write a numerical program to simulate a nucleus and to determine which of these models is most accurate.

LC