To continue as usual

Some numbers
This blog was started in 2010.

By the end of 2011, 100,000 blog pages were opened by 55,000 readers. 1,100 people downloaded Comay’s scientific article showing that the Higgs cannot exist; most of them are plausibly physicists.

The blog demonstrates 20 phenomena that are incompatible with QCD, which is the currently accepted theory of strong interactions.

These phenomena can be explained by 1 physical theory.

To date, there were 0 scientific attempts to refute either the claims or the theory.

“This is the stuff we’re made of, and it’s showing that maybe we don’t understand it as well as we thought.” Francis E. Close, Science News 1989
“We have this elegant theory of quantum chromodynamics, which is supposed to describe the binding of the fundamental constituents of all matter, but we don’t know how to make it work. We can’t even do something as basic as building protons out of quarks.” Robert L. Jaffe, Science News 1989
“Even now, two decades after QCD was formulated, little is known from first principles about the structure of the nucleons and other hadrons.” Robert L. Jaffe, Physics today, 1995

The invisibly obvious
Let’s recall the phenomena which are incompatible with QCD. These phenomena show that it is nearly obvious that the structure of the proton is similar to the structure of an atom with two or more electronic shells. In the proton the quarks play the role of the atomic electrons, and the three valence quarks belong to the outer quark shell.

An illustration of the nucleons according to Comay’s model. In analogy to a noble gas atom, each quark has one negative strong charge unit, the nucleon’s core (blue) has positive strong charge and it attracts the quarks which repel each other. The total strong charge of each nucleon is 0.

The force inside the atomic nucleus

“Ironically, from the perspective of QCD, the foundations of nuclear physics appear distinctly unsound.” Frank Wilczek, about QCD vs. the strong nuclear force, Hard-core revelations, NATURE, Vol. 445 156 (2007)

The main features of the strong nuclear force which stabilizes the atomic nucleus, are known for seven decades, but are not explained by QCD. This force behaves very similarly to the force between atoms of noble gas (van der Waals force). According to QCD, it is not clear why nucleons stop attracting each other at a certain distance (unexplained phenomenon #1), it is not clear why they strongly repel each other in shorter distance (#2), and it is not clear why the graph of nuclear potential vs the distance looks like the graph of the van der Waals potential (#3).

“Currently, the color van der Waals force does not seem to be a correct model for nuclear interaction without modifications.” S.S.M. Wong, about QCD vs. the strong nuclear force, Introductory Nuclear Physics, (Wiley, New York, 1998). p.102

Furthermore, the first EMC effect which was found in 1983 is not understood: it is not clear why the volume of nucleons’ quarks is larger inside large atomic nuclei (#4). The analogous effect in the liquid state of a noble gas and molecules is well known.

“The results are in complete disagreement with the calculations… We are not aware of any published detailed prediction presently available which can explain the behaviour of these data.” J.J. Aubert et al., about the 1st EMC effect, J.J. Phys. Lett. 123B, 275 (1983)

Furthermore, the nuclear tensor force acts between nucleons similarly to the force that acts between atoms with spin. This force is known since the early days of nuclear physics and is not explained by QCD (#5).

The similarity of the force between quarks and the force between electrons
In the proton, the antiquark is pushed towards the outer region, like in the analogous case in which a positron is pushed away from the atomic nucleus. This phenomenon is unexplained by QCD (#6). The phenomenon where the mean square charge radius of the neutron is negative has the same underlying theoretical basis. This phenomenon is unexplained by QCD as well (#7).

An analysis of the proton form factor shows that the quarks distribution inside the proton is similar to the electrons distribution inside atoms (they have higher probability to be located near the center). In the analogous case, in atoms, this is explained in quantum mechanics by the fact that the attraction force between the nuclear positive charge and the electrons is stronger when the electrons are close to the center. This seems to contradict QCD whose asymptotic freedom implies that the quark-quark attractive force becomes weaker when the quarks are closer to each other (#8).

An analysis of the proton-proton cross section curve shows that the forces between components of one proton and components of another proton are stronger when they are closer. This too is incompatible with QCD (#9).

Furthermore, it was found that the strong force, like the electromagnetic force, conserves charge conjugation and parity. These phenomena, lead to the Strong CP Problem, are not compatible with the Standard Model (#10).

Using QCD laws scientists predicted the existence of several particles and matter states that systematically failed to show up in experiments, like glueballs (#11), di-baryons (#12), strange quark matter (#13) and pentaquarks (#14).

“The whole story – the discoveries themselves, the tidal wave of papers by theorists and phenomenologists that followed, and the eventual “undiscovery” – is a curious episode in the history of science.” C.G. Wohl (LBNL), a review about the search after the Pentaquarks, 2008

QCD cannot provide explanations to the proton spin crisis, which was discovered in 1987 (#15). This phenomenon is explained easily by applying the same laws existing in atomic electrons.

“In 1988, however, physicists were shocked to find experimental evidence suggesting that very little–perhaps none–of the proton’s spin comes from the spin of the quarks…” Ivars Peterson, Science News 1997
“The proton is complicated, but it is a very, very important object in our lives. It is unsatisfying intellectually that we cannot understand how the inside of the proton behaves.” Emlyn W. Hughes, Science News 1997

The interaction with light
Photons interact with electric charges, as every physicist knows for more than 100 years. More than 50 years ago it was discovered that hard photons interact strongly with quarks. This phenomenon is unexplained by QCD (#16). Furthermore, QCD does not explain why the interaction of a hard photon with a proton is similar to its interaction with a neutron, in spite of the different electric charge of their quark constituents (#17).

“No direct translation between the Standard Model and VMD has yet been made.” H.B. O’Connell, B.C. Pearce, A.W. Thomas and A.G. Williams, About the hadronic properties of the photon, Prog. Nucl. Part. Phys. 39 (1997)

Proofs of the existence of massive objects inside the nucleons
The discovery by SLAC during the 1970s that the quarks carry only part of the proton mass caught QCD supporters by surprise. They quickly recovered by invoking the idea that the gluons carry the other part of the mass. However, there are many other phenomena that show beyond any doubt that nucleons contain inner massive objects (gluons are not massive objects).

The rise in the high energy proton-proton total cross section shows that the proton contains other massive objects. This phenomenon is known for 10 years now and cannot be explained by QCD (#18). Furthermore, the rise in the elastic cross section shows that there is a massive object that can be hit and it acts like a solid billiard ball without creating new hadrons. This cannot be explained by QCD (#19) because QCD doesn’t allow any massive objects inside the proton, besides the three valence quarks (and the quark-antiquark pairs). In nearly all collision events, these quarks create new hadrons when hit by highly energetic projectiles.

“The observed excess may indicate that quarks contain something smaller, representing a new level in the composition of matter.” Ivars Peterson, Science News, 1996 (in 1996 there weren’t enough data to confirm this phenomenon which was established only in the beginning of 2000s)

QCD provides weak or no explanation why a meson, which is a quark-antiquark bound state, is not confined inside baryons (#20).

Let’s stop counting here. Twenty unsolved fundamental questions are more than enough for doubting any theory, including QCD.

The sociological question
Why such obvious failures of one of the most important parts of the standard model are ignored by scientists? Why scientists do not even discuss the most obvious explanation to these failures? Why these failures are known for many decades and still many scientific journals do not publish any theory which is not inline with QCD? Why despite spending billions of Euros every year, basic QCD predictions are not substantiated by experimental discoveries for so many years?

The answer, I believe, is inside the question itself. Particle physicists do not discuss this issue because this explanation is obvious, and because they failed to see it for so many years, and because many of them blocked scientific articles which were against the standard model, and maybe also because they are happy to spend billions of Euros every year.

If you have any idea how to change this reality – I will be happy to listen.

Physicists who wish to read a scientific review about this subject – can read it here: EJTP 9, No. 26 (2012) 93–118.


34 thoughts on “To continue as usual

  1. I answered: “Well, the increase within the curve is small, but compared to what one would expect it is not small. If one interprets “asymptotic freedom” as “vanishing interaction at high energy” then a decrease like in the coulomb range should be expected. So we have something here what QCD can’t explain?”

    And got: “What you would expect from the model “the proton has a finite size which determines the cross-section” is a flat line. What you would expect from the model “we have PDFs as function of x and Q^2, and integrate the cross-sections starting from to some minimal momentum exchange” is not far away from a flat line if you take care of multi-parton interactions (otherwise it is rising with energy). It is hard to get the exact shape with QCD without any experimental input, but it is easy to get a reasonable approximation, and the remaining difference is probably just our lack of knowledge about nonperturbative QCD. Relevant concept: Pomerons”

    What’s your opinion?

    • Dear Gabor,

      There is no doubt that the calculation of a strongly interacting process is a very difficult assignment. However, even without doing such calculations one can apply fundamental laws of physics and derive conclusion pertaining to hadronic structure. Below I write few points that are relevant to the proton-proton scattering data depicted on p. 11 of Hereafter, these data are called “the p-p data”.

      1. The data of electron-proton scattering prove that for high energy the process is described as a collision of the electron with a single quark. This property holds even for the energy which was available nearly 50 years ago. The term Deep Inelastic Scattering describes this process. See e.g.
      2. The electron-proton high energy scattering data show that the total cross-section decreases with increasing energy (see e.g. the Rosenbluth formula) and that for a heavy collision, the portion of elastic cross-section decreases even faster. Therefore, the data of electron-proton scattering is completely different from that of the p-p data, where, at very high energy, both the elastic and the total cross-sections increase.
      3. Fundamental wave properties indicate that as the projectile’s energy increases and its associated wave-length decreases, the effective scattering region decreases. (Indeed, divide a thin spherical shell around the scattering center into a sum of thin circular rings and examine a pair of such rings at (r,+-\theta). Consider a scattering in a given direction D where its angle \theta’ is different from zero. For different points at the rings, there is a path difference for the wave scattered at direction D. As the wave-length decreases a destructive interference builds up and the contribution of this spherical shell fades away. It means that the effective scattering region becomes smaller. This effect holds for every direction which is defined like D. This is the reason for the decrease of the electromagnetic electron-proton cross-section. Therefore, unless new dynamical factors arise or the interaction near the origin grows much faster than 1/r, the total cross-section should decrease with an increasing scattering energy.) This is a general scattering property of every quantum particle. On top of that, one should also note that QCD’s “asymptotic freedom” means that the quark-quark interaction practically vanishes at small distance. It follows that if QCD is right then the proton-proton scattering cross-section should decrease much faster than the electron-proton cross-section. This QCD result is completely inconsistent with the p-p data.
      4. QCD says that the proton comprises three quarks, additional quark-antiquark pair(s) whose probability is about 1/2 and gluons. All these ingredients participate in every case of a high energy interaction and this theory does not show how new dynamical factors can arise. On the other hand, the p-p data are explained by the Regular Charge Monopole Theory (RCMT). See for example section 7 of the following article and the corresponding chapters of the book As a matter of fact, beside the QCD problem with the p-p data, these references describe many other different kinds of QCD experimental failures.
      5. It is interesting to note that theoretical QCD problems concerning the rise of hadronic cross-section with energy have also been pointed out by A. A. Arkhipov (see e.g. Unfortunately, the community has ignored his attempts and an appropriate debate did not follow his work.

      Cheers, Eli Comay

      • You said: “The electron-proton high energy scattering data show that the total cross-section decreases with increasing energy (see e.g. the Rosenbluth formula)”

        This is a formula for elastic scattering, and with electron/proton collisions instead of proton/proton collisions so you would not expect the same result. Also, where did you integrate it over all phase space?

        You said: “Fundamental wave properties indicate that as the projectile’s energy increases and its associated wave-length decreases, the effective scattering region decreases. This is the reason for the decrease of the electromagnetic electron-proton cross-section”

        This argument is faulty as it ignores the proton PDFs and the minimal momentum exchange to be considered a collision. At high energies you have more particles in the proton that can contribute to a collision.

        You said: “On top of that, one should also note that QCD’s “asymptotic freedom” means that the quark-quark interaction practically vanishes at small distance.”

        The coupling goes down for higher energies, but that just means the cross-section for jets with 1/4 the proton energy (random example) goes down. So what, that’s not the total cross-section.

        And now?

        Cheers, Gabor

      • Dear Gabor,

        1. A deep inelastic e-p process begins as an elastic electron-quark scattering. Furthermore, the scattering amplitude of the different quarks is added incoherently. An inelastic effect results from the strong interaction of the knocked quark with the rest of the system. The latter effect does not alter the meaning that a scattering event takes place. Hence, this final state interaction does not change the cross section. Therefore, the general feature of the energy dependence of electromagnetic elastic formulas holds.
        2. If the angular dependence of the differential cross section decreases then also its integral decreases.
        3. Referring to your paragraph that begins with “This argument is faulty…”. The electron interacts electromagnetically with charge carrying proton constituents. According to QCD the proton’s charge carrying constituents are the 3 valence quarks, the additional quark-antiquark pairs (whose probability is about 1/2) and nothing else. This structure (plus gluons) also holds for the scattering that results from proton-proton strong interaction. Therefore, your statement “At high energies you have more particles in the proton that can contribute to a collision”, means that QCD is wrong. If we really agree on this point then we have made a meaningful step forward.
        4. Referring to the paragraph that stands before “and now?”. As stated above, one should recognize that a scattering process begins as an elastic event of the energetic electron with a parton. Inelastic events in general and jets in particular are results of the interaction of the knocked parton with other proton constituents. The later processes do not change the fact that a scattering event has occurred. Therefore, they do not affect the cross section. The data show that at high energy the proton-proton cross section goes up. This feature is dramatically different from the e-p data. The rise of the cross section is also inconsistent with theoretical expectation from an interaction which is “asymptotically free”. Fundamental wave properties prove that the cross section of this kind of interaction should decrease even faster than electromagnetic scattering.

        Cheers, Eli

  2. With respect to (#9), I have asked within a particle physics Forum about an explanation for the flat pp total cross section increse and got this answer:

    “Protons have a substructure and a finite size. The roughly flat cross-section over a large energy range is just something like the geometric size of the protons. The cross-section for events like “half the collision energy ends up as transverse energy” goes down, but you get more and more collisions with small momentum exchange relative to the collision energy – and the PDFs rise quickly if you go to smaller x. The small rise is not well understood, and there are multiple ideas, but that is a small effect.”

    Regarding this effect as “small” where it should fall rapidly. It this a valid view?

    Gabor Törö

  3. Dear Eli

    Is it possible that fundamental particles has a connection (symmetry) between magnetic
    and coulomb properties? I’m thinking of a electron “twin” with one magnetic
    charge and no coulomb charge (magnetic monopole). And if a particle has both
    magnetic and coulomb charge they are limited to a fraction 1/3 + 1/3 or maybe 1/3 + 2/3 of both (quarks). Is quarks with two different magnetic charges consistent with your theory?

    • Dear Lars,

      The relations between electricity and magnetism can be obtained from duality transformations. This is just an example of a rotation by pi/2 in the charge-monopole plane. Other kinds of rotations may be used. Hence, it means that the pure electric charge of the electron is just a (very) useful convention.

      After defining the electron’s charge as a pure electric charge, we find in experiments that monopole carrying particles (namely quarks) come in 3 generations and each generation contains two quarks, one with an electric charge 2e/3 and the other with an electric charge –e/3. This is what experiments tell, and for this reason any theory must use it in a description of hadronic states. Experiments also tell us that the elementary monopole unit is much larger than its electronic counterpart.

      It turns out that all quarks have the same monopole unit. The reason is that all mesons are unstable and the final outgoing particles are electrons, neutrinos (and their antiparticles) and photons. All these particles have no monopole charge. It means that the sum of the monopole charge of the quark-antiquark meson constituents is zero.

      The foregoing discussion indicates that for an actual description of hadrons one must use the known data. However, as an exercise of the mathematical aspect, one may play (cautiously!) with particles that have a different charge-monopole ratio.

      Cheers, Eli

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    in mind of. I say to you, I definitely get annoyed whilst people consider concerns that they plainly do not recognize about.
    You managed to hit the nail upon the top and defined out the whole thing with no need side-effects , folks can take a signal.
    Will likely be again to get more. Thank you

    • Dear Lars,

      A profound interpretation of the outcome of a collision of a heavy ion requires a solution that is obtained from a very difficult calculation. I’m not sure that this problem will be the first one to be explained. Here I rely on the history of Quantum Mechanics (QM). One hundred years ago people already knew experimental data of simple atomic energy levels and also the many body quantum effects of ferromagnetism and superconductivity. QM has been constructed on the basis of the data of simple atomic states. Only later it has been recognized that it explains many body effects. Using this analogy, it is my opinion that the simpler hadronic states will be the first cases to be explained.

      Putting a long story short, I have no comment on this issue.

      Cheers, Eli

  5. Dear Eli

    I can’t stop wondering about the nucleon core. Do you have any idea what’s
    inside? If it has several positive magnetic charges doesn’t that imply that it
    is composed of several particles? And if so don’t we need a new force to
    hold them together? Or maybe some hard to understand relativistic effects.

    Anyway i think we need something better than QCD. I tried to do some
    calculations long ago then i studied physics at LiTH (Sweden) and i think QCD is so complex that you can adapt it to give any result you want but it will never predict anything new.

    • Dear Lars,

      In my opinion two sets of questions may be asked about the baryonic core. Baryons have an atomic-like structure where quarks are bound by the magnetic monopole strength. Here quarks carry a negative unit of monopole strength and play a role which is analogous to that of atomic electrons. The core is defined as all other baryonic components that are not the three valence quarks and the additional quark-antiquark pairs. By the atomic analogy, one can see that one set of questions may be asked about the additional quarks of inner closed shells and a second set of questions may be asked about the nature of the positive-monopole object of the “true core”.

      I think that the first set of questions is relevant to present day technology. There is a strong evidence indicating that baryons have inner closed shells made (mainly or only) of the lightest u,d quarks. I hope that the actual structure of these shells will be investigated in the future by using scattering data.

      On the other hand, questions about the inner positive magnetic monopole component of the core looks to me like questions about an unmeasurable quantity. We do not know whether or not it is an elementary object and we do not know how many closed shells of quarks exist. For this reason, we do not know the amount of magnetic charge that it carries. Therefore, the structure of the “true core” is irrelevant to contemporary physics.

      Cheers, Eli

  6. Is quarks (with magnetic charge) spin and orbital motion generating an electric (coulomb) dipole in a similar way that an electron in a atom generates a magnetic dipole momentum?
    If so does that affect how protons and neutrons are organised in the nucleus?

    • Dear Lars,
      Yes, the proton and the neutron are isospin doublet particles. Hence, their three u,d quarks are organized in an analogous spin-1/2 state. The duality of electricity and magnetism means that both should carry (nearly) the same axial electric dipole moment that stems from their monopoles. (Note that like the axial magnetic dipole moment also the axial electric dipole moment is consistent with parity conservation.) In the nuclear physics terminology this dipole-dipole interaction is called the nuclear tensor force. See p. 101 of this link:

  7. The concepts of point particle & 3D waves are completely opposed to one another. One implies that an object, such as an electron, occupies only a single point in 3D space at any time while the other indicates that the object spans ALL of 3D space at one instant of time. I emphasize time because QM advocates love to drop time from their formulations, in so-called ‘time-independent’ equations. However, time is the very essence of reality.
    This is just a preamble to indicate that mathematicians who play at physics make the most fundamental error: they confuse their representation with reality – a philosophical mistake known as reification. Philosophers have spent a lot of time distinguishing ontology with epistemology – it would pay mathematicians rich rewards to study philosophy before they attempt to solve the problems of reality i.e. physics.

  8. Hi Mario – this is the answer to your March 6 comment.
    Quantum mechanical particle has both pointlike and wave attributes. For this reason pointlike electrons are distributed inside atomic volume and pointlike quarks are distributed inside hadronic volume.
    In this site, this inherent quantum mechanical duality is accepted as a correct element of physics which is beyond discussion. Without accepting that, I think that any discussion is groundless.

  9. Yes, there is something else inside the proton: quarks are composite. Somebody may say now ‘come on, we haven’t seen it’, and the truth is that we have seen several indications of it. The first one was found in 1956 by Hofstadter when he determined the charge distributions of both nucleons. (one can see them around p. 450 (depending on the edition) of the Berkeley Physics Course, vol. 1 (Mechanics)). We clearly see that both nucleons have two layers (shells) of internal constituents. Unfortunately these results were put aside from 1964 on due to the success of the quark model and of QCD later on. From 1985 on we began to see more indications of compositeness, but we were so enthusiastic with the Standard Model that we didn’t pay much attention to them. A partial list of them: 1) in 1983 the European Muon Collaboration (EMC) at CERN found that the quarks of nucleons are slower when the nucleons are inside nuclei; 2) in 1988 the SLAC E143 Collaboration and the Spin Muon Collaboration found that the three quarks of the proton account for only half of its total spin (other subsequent collaborations (EMC in 1989 and Hermes in 2007) have confirmed this result which is called THE PROTON SPIN PUZZLE); 3) in 1995 CDF at Fermilab found hard collisions among quarks indicating that they have constituents (this was not published because CDF didn’t reach a final consensus); 4) Prof. Gerald Miller at Argonne (Phys. Rev. Lett. 99, 112001 (2007)) found that close to its center the neutron has a negative charge equal to -1/3e (inside the positive region with +1/2e); 5) new measurements of the EMC effect have been carried out by J. Arrington et al. at Jefferson Lab and they have shown that the effect is much stronger than was previously observed; 6) the ad hoc Kobayashi-Maskawa matrix elements; 7) the null charge dipole moment of the deuteron and its non-null charge quadrupole moment etc.
    Gerald Miller wrongly attributed to d quarks the -1/3e charge at the neutron center, but as the neutron is a udd system we know (from QCD) that none of the 3 quarks spends much time at the center.
    The relevant paper on this subject is Weak decays of hadrons reveal compositeness of quarks which can be accessed from Google (it is at the top of the lists on the subjects Weak decays of hadrons, Decays of Hadrons and Weak decays).

    Therefore, we should go back and probe further the nucleons in the low energy scale, and carry on Miller’s experiment with the proton.

    • Hi Mario. See below why I think that present experimental data show that quarks are structureless point-like particles.

      I think that an examination of experiments should rely on fundamental principles of physics. Here I refer to the fact that a higher energy means a shorter wave-length. Hence, in order to find finer details of an object’s structure, we need higher collision energies.

      The deep inelastic electron-proton collision (of the late 1960’s) indicates that quarks are point-like [1]. Therefore, I do not believe that lower energy collisions of earlier times can be used for denying this conclusion.

      The so called “dipole formula” ([1], p. 196) is successful for a large energy scale. This fact indicates that for this energy region no new players (like a breakdown of quarks into smaller components) enter the game. BTW, this kind of argument proves that the twists of the proton-proton cross section graphs (see p. 12 here ) prove that the proton has other components beside QCD’s valence quarks, gluons and quark-antiquark pairs. See a discussion of this issue here and elsewhere in this site.

      Your point 1. The first EMC effect does not prove that quarks are composite objects. It shows that quark’s distribution increases with the number of nucleons in a nucleus. See p. 102 here

      Your point 2. The second EMC effect does not prove that quarks are composite objects. It proves that quark states are composed of configurations. See e.g.

      Your point 3 is obscure and I cannot refer to it. Generally I rely on experimental evidence supported by PDG. See .

      Your point 4. The results of Miller’s Letter are inconsistent with the negative value of the neutron’s mean square charge radius published here . Let us wait and see what will come out of Miller’s Letter. Please note also that in the conclusions of his Letter, Miller states that a further analysis is required. Furthermore, Miller’s Letter discusses quark distribution in nucleons and not the issue of quark compositeness.

      Your point 5. Please see the remark on your point 1.

      Your point 6. I do not think that the Kobayashi–Maskawa matrix proves quark compositeness. Please note that a quark, like a lepton, is not an isolated object but it is “dressed” with a probability of particle-antiparticle pairs.

      Your point 7. These effects prove parity conservation by the strong and the electromagnetic interactions. It has nothing to do with quark compositeness.

      In conclusion: duality of quantum mechanics of bound systems shows that a pointlike quantum object has a wave nature and it is distributed inside a finite volume.
      [1] D. H. Perkins, Introduction to High Energy Physics, (Addison-Wesley, Menlo Park CA, 1987).

      • Dear Eliyahu Comay

        Thank you for your commments. But just imagine that quarks constituents are almost massless… Another very important point: why all weak decays are obeyed by a quantum number derived from the assumption of quark compositeness?
        You did no mention the most strong evidence: the charge distributions in both nucleons as found by Hofstadter in the 50s. Three point-like quarks do not reproduce them.
        I still believe I am right.

        Mario E. de Souza

  10. You must be lawyer. You did NOT answer my points but went off on a tangent of your own devising. You started with the answer you wanted, namely that the multi-body systems are stable, and then claimed that therefore the math is convergent. Of course, these systems are stable, this is the experimental observation. QM is an eigenvalue equation that can be formulated as a differential equation. The point you are avoiding is that the Schrodinger approach to the dynamics results in a multi-dimensional differential equation in 3n dimensions for n bodies, which has resisted solutions by mathematicians for 300 years when n is 3 or greater.

    Now, if you would like to address my question directly …

    • In my earlier replies I’ve made a reasonable attempt to explain how the Quantum Mechanical equation (Schroedinger or Dirac) can be cast into an eigenfunction problem which is time-independent. This point denies completely your last claim where you refer to time-dependent problems and state: “The point you are avoiding is that the Schrodinger approach to the dynamics results in a multi-dimensional differential equation in 3n dimensions for n bodies, which has resisted solutions by mathematicians for 300 years when n is 3 or greater.”

      This claim is completely inconsistent with what I’ve tried to explain to you. I’m short in time and prefer to put an end to this discussion.

  11. According to the Standard Model, nucleons involve 3 tightly bound quarks. But since Newton, the 3-body problem has defeated all attempts at exact analysis. Please explain how you can have any confidence in this theory since complexity theory demonstrates that small changes in the numerical values of any of the initial conditions (position or momentum) result in massive changes over time i.e. non-stable solutions. All of this theory has involved uncheckable computer programs running on giant computers.

    • You made a good question. However, it turns out that you are not acquainted with the mathematical developments called the Wigner-Racah Algebra (and also angular momentum algebra). Never mind. Particle physicists are also not acquainted with this topic. How do I know this fact? One example is that they are perplexed by the “Proton Spin Crisis” (see e.g.

      A complete answer to your question requires an entire book [1] and this blog is certainly not the right place for this task. For this reason, I’ll make only 2 short remarks.

      1. Your argument also holds for bound states of atomic electrons where the number of electrons > 1. However, calculations of spectroscopic states of atoms have been performed half a century ago and these calculations yield very accurate results [2]. It means that the Wigner-Racah Algebra provides very useful mathematical tools for this kind of problems.

      2. The link shown at the end of the first paragraph of this Reply outlines some details of the calculations that rely on an expansion of the state in an ascending series of configurations.

      [1] A. de-Shalit and I. Talmi, “Nuclear Shell Theory” (Academic Press, New York, 1963).
      [2] A. W. Weiss, Phys. Rev. 122, 1826 (1961).

      • Thank you, Eliyahu for your fast response.
        Yes, I thought it was a good question which is why I was disappointed by your reply.
        You did not address my point about the unsolvable 3-body problem & the wild divergences introduced by computer approaches to this issue. I view the Wigner-Richah algebra as irrelevant to this point: at best these act as a constraint on spin additions but have nothing to do with the detailed dynamics.
        Yes, I know my point applies to the He atom (& higher) and I am equally disappointed that physicists have ignored this major problem in their “pursuit of the new” as they left atomic physics behind for the novelty of nuclear physics. I certainly appreciated your specific reference to the Weiss paper as I continue to look for evidence in the atomic realm. My reading of the abstract would indicate that Weiss only calculated the G/S of He, Li & Be but measured energies require differences – at least, from the first excited states. Even worse, these are just ‘form fitting’ (as he refers to a “19-configuration function”). Since the hydrogen atom uses spherical harmonics which form a complete set then ANY 3D function can be constructed empirically from a sub-set of these functions (3D Fourier analysis). This is not impressive – this was done by Hylleraas in 1930 for He. I was expecting a solution of the dynamics or at least calculation of the wave-functions from the physics, not just ‘fitting the numbers’. The Hartree-Fock method is just a crude approximation of the electro-electron interaction.

      • In your first comment you say: “…complexity theory demonstrates that small changes in the numerical values of any of the initial conditions (position or momentum) result in massive changes over time i.e. non-stable solutions.” You still adhere to this claim in your second comment.

        Let me explain briefly why your comment is wrong:

        1. The fundamental equation of quantum mechanics equates the time-derivative of a given wave function (multiplied by ih-bar) to the result obtained from the operation of the Hamiltonian on this wave function.

        2. For a (relatively) stable system in its rest frame, the outcome of that time-derivative is the energy of the system in this frame. Hence, for a ground state and for excited states of a quantum system, the Hamiltonian’s differential equation reduces to the form of an eigenfunction and an eigenvalue problem which is time independent.

        3. The Article mentioned by the link at the bottom of the first paragraph of my first Reply to you explains how, for any required accuracy of the solution, one can cast the differential problem to an eigenvector and an eigenvalue matrix problem. Please, read carefully this Article before answering to this Reply.

        4. Since that Article concentrates on angular and spin coordinates, let me add that the radial components of the problem are expanded in the form of a polynomial multiplied by an exponentially decreasing factor. This form ensures the required null value of the wave function at infinity.

        These points complete the proof that your comment is wrong. The problem is certainly not an initial value problem of differential equations but an eigenfunction and eigenvalue problem. Hence, your arguments concerning instability of initial value problems are irrelevant to the issue discussed herein. For eigenfunction and eigenvalue problems one can find a solution that satisfies any required accuracy.

        P.S. I advise you not to use the Hylleraas method. It works neither for relativistic problems nor for atoms having any number of electrons.

  12. I have read through all of your articles as well as the book a number of times and find it extremely interesting and satisfying.

    By analogy to the question of newly-created Mesons being able to escape the nucleon (by virtue of having a neutral magnetic charge), should it not therefore be possible for mesons to spontaneously be generated and emitted at any time, since the 4th quark and associated anti-quark could become a bound pair? Has this been demonstrated experimentally? Is there a flaw in my reasoning?

    As well, I was hoping if you could please clarify the point above with regards to the inability of gluons to provide the “missing mass”. While QCD claims that gluons are massless, I thought that they do still have momentum — and their momentum would add to the total mass of the particle.

    Thanks again for the website, articles and information.

    • Thank you for your nice comments.

      Particle creation processes abide by the energy conservation law. Hence, your idea holds for hadrons that have the required amount of mass. For example, the Delta baryons disintegrate strongly into a nucleon and a pion, and the K-mesons disintegrate weakly into 2,3 pions (the charged K-mesons disintegrate also into the same charged muon and its anti-neutrino). On the other hand, the proton is stable and the neutron is stable against meson emission.

      The rise of the cross-section of energetic proton-proton collision proves that the proton has a core and that gluons cannot explain the effect. See the appropriate discussion in this site and also the following articles:

      • If I understand your comment correctly, the bound state of the 5 quarks is a lower energy state than two separate particles of 3 and 2 quarks, respectively. In my mind, this would be straightforward due to the fact that the core charge attracts the 4th quark far more strongly than the anti-quark would, and similarly, the anti-quark has 4 quarks attracting itself (although partially screened).

        Subject to conservation of energy, would my conjecture hold? You have brought examples of baryon decay, whereby the energy is made of the particles’ mass. What about kinetic energy? If protons are accelerated or their temperature raised, can they not transfer some of their momentum then into a new meson?

        I’ve read that the neutron is less stable than the proton and that it can spontaneously decay into a proton plus anti-neutrino and electron. Is this through a related mechanism?

        Thanks again and all the best

      • The idea of pentaquark has been suggested by QCD supporters that have relied on QCD principles. Hence, a pentaquark is supposed to be a strongly bound state of 4 quarks and an antiquark. The picture is different if the Regular Charge-Monopole theory of hadrons is used (see On the basis of this theory one finds that your idea is incorrect. Here the baryonic core attracts the meson’s quark by the same force as it repels the meson’s antiquark.

        Analogous relations hold for the interaction of the baryon’s valence quarks with the meson. Hence, a baryon-meson interaction is a residual effect. The spin-0 of the pion indicates that this interaction is expected to be smaller than that of the deuteron. This conclusion is supported by experiments which show no evidence of pentaquarks. See

        The idea of kinetic energy conversion into energy used for a particle disintegration is inconsistent with special relativity. Indeed, a disintegration of a massive particle should be seen in every Lorentz frame. Since, it cannot hold in the particle’s rest frame, one concludes that it cannot hold in any frame.

        Temperature is irrelevant to a description of the quantum state of an isolated particle.

        The neutron disintegration is a weak interaction process. Weak interactions and strong interactions are completely different theories.

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