A Challenge to Physicists

Physicists are invited to respond, refute or comment on any issue that was discussed in this web site. In particular, you are invited to take one of the following missions.

Comay model missions
1. Find an experimental result that contradicts or not explained by Comay’s model which is explained by QCD.

2. Find more experimental results that are not explained by QCD and can be explained by Comay’s model.

Other topics
Here you are invited to read a few lines and refute at least one of 3 arguments demonstrating the existence of fundamental errors in the textbooks, on which you may have successfully passed exams in the past. These errors have repercussions which cast doubts on other central topics.

3. You can see here www.tau.ac.il/~elicomay/dpp_new.pdf a proof showing that the argument for QCD construction is incorrect. The proof is written on about one half of a page containing a double spaced text.

4. The following link contains a short proof showing an inherent contradiction of the electroweak theory. See http://www.tau.ac.il/~elicomay/EL_WEAK.pdf

5. We show here in 10 lines that textbooks are wrong when they claim that the real wave function of the Klein- Gordon equation has a Hamiltonian.

www.tau.ac.il/~elicomay/Appetizer.pdf

If you can devote a little more time to it, then you are invited to read the following article and try to contest at least some of its conclusions. Among other things, this article proves that the Higgs particle is also based on an error, it has no Hamiltonian, and therefore it cannot exist.

www.tau.ac.il/~elicomay/MathPhys.pdf

6. Here is a brief demonstration (less than one page) that within the framework of Quantum Theory, there are unsolved problems in the common use of the electromagnetic gauge.

www.tau.ac.il/~elicomay/Problem.pdf

Your comments will be welcome. Prefer to send an email? Send it to Eliyahu Comay.

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55 thoughts on “A Challenge to Physicists

  1. Is there somebody able to calculate the binding energy of the simplest bound nucleus, the deuteron allias 2H? Of course only with fundamental laws

    • The fundamental problem in nuclear physics is to calculate the binding energy of nuclei from fundamental laws. For example, the simplest bound nucleus, the deuteron 2H can be calculated by a simple formula. Unfortunately, it seems that there is no possibility to write equations or post figures here. You may see my theory, the only theory able to calculate the binding energy of a nucleus without fitting by simply applying electric and magnetic Coulomb-Poisson laws, two centuries old.
      Therefore the strong force doesn’t exist: its fundamental laws are unknown.
      You may see one of my papers here:
      http://www.scirp.org/journal/PaperInformation.aspx?PaperID=24389#.U-X8_Eh3U84

      Sincerely

      Bernard

  2. A Reply to Bernard Schaeffer’s Comment of December 31, 2012 at 10:29 AM

    Dear Bernard,

    It is clear that you ignore well established data and well established physical theories. Let me put one proof for each of these claims.

    The data show that the electric polarizability of the neutron is about 0.001 (in fm^3) (see http://pdg.lbl.gov/2012/listings/rpp2012-list-n.pdf ). The deuteron radius is about 2 fm (see [1], p. 58). Using these values, one finds that the order of magnitude of the interaction of the proton’s charge with the induced electric dipole of the neutron is 4 orders of magnitude smaller than the deuteron’s binding energy. This result completely disproves your claims.

    Effects like alpha disintegration prove that nucleons are quantum mechanical objects. You carry out a classical calculation which means that you either ignore or deny quantum mechanics.

    Please see at the upper right hand side of this blog a request not to use this blog for discussing such ideas.

    References:
    [1] S. S. M. Wong, “Introductory Nuclear Physics”, (Wiley, New York, 1998).

    Sincerely, Eli

    • Dear Eli,

      It seems that you don’t know the difference between a permanent dipole and an induced dipole. A proton near to a neutron induces a dipole in the neutron by separating the electric charges of the neutron. Perhaps you don’t know that the neutron has electric charges of no net charge. The proton induced dipole in the neutron is the frozen in the deuteron in its quadrupole.

      Quantum mechanics are falsely applied to the atomic nucleus where there is no orbital movement possible because the nucleus “contains no massive central body which can act as a force center” (see “The Atomic Nucleus” by Evans, p 359, uploadable here
      http://ist-socrates.berkeley.edu/~phylabs/adv/ReprintsPDF/MUO%20Reprints/05%20-%20The%20Atomic%20Nucleus.pdf

      Sincerely, Bernard

      • A Reply to Bernard Schaeffer’s Comment of January 1, 2013 at 12:39 PM

        Dear Bernard,

        Please note the following points:

        1. The existence of a massive body at the center is not a necessary condition for a state whose angular momentum is greater than 0. Take for example the states of the positronium which has no massive body at the center (see [1], p. 177, where a P-wave of the positronium is presented). This example invalidates your claim against the applicability of quantum mechanics to nuclear states.
        2. Beside angular momentum, there are many other quantum properties in nuclear physics. For example, interference effects, tunneling effects, spin states etc.
        3. The estimate of the energy associated with the neutron’s polarizability that is presented in my previous Reply is correct, because it relies on measured quantities whose sources are given. It shows that you are wrong by 4 orders of magnitude and therefore, it totally disproves your claims.
        4. I feel that our dialog is not fruitful, and I don’t think we share the same ground. I have chosen not to discuss any idea which contradicts quantum mechanics, special relativity or general relativity. This is a personal decision, and I do not wish to spend my time on such ideas.

        Sincerely, Eli

        References:
        [1] D. H. Perkins, “Introduction to High Energy Physics” (Addison-Wesley, Menlo Park CA, 1987).

    • The electric polarizability is measured in a uniform electric field and therefore invalid between nearby proton and neutron. The only solution is the electric and magnetic Coulomb’s laws the only existing method able to calculate with success the binding energy of the simplest nucleon, the deuteron. All the self called “modern” theories fail to do it.

  3. A Reply to VoxPop’s Comment of December 29, 2012 at 8:03 PM

    Dear VoxPop,

    1. I insist on the details of my Reply of December 17, 2012 at 9:06 AM. It is my opinion that by pointing out your errors I help you doing better.
    2. I still insist on my statement that you do not understand the difference between eigenvalue & initial value problems of differential equations.
    3. This site is not the right place for academic lectures. Issues pointed out in my Responses to you can be found in textbooks.
    4. In my opinion, I’ve devoted enough time for answering your Comments. I regard your last Comment as impolite and for this reason I decide not to answer you any more.

    Eli

    • Your error is that you don’t know the difference between induced and permanent dipole. The neutron polarizability is small only because the electric field is small. The electric field due to a proton near to a neutron is much higher than that a macroscopic apparatus can create. The polarizability is not a constant, according to Coulomb’s laws.

      Any way you are unable to calculate the binding energy of even the simplest nucleus from fundamental laws and constants.

  4. A Reply to VoxPop’s Comment of December 29, 2012 at 7:40 PM

    Dear VoxPop,

    I must say again that I really wonder about your approach. Indeed, all engineers would tell you that physics is a very reliable science and that if they use physical laws correctly then the devices that they design and produce work. Now, some physical effects have been found accidentally (like superconductivity). On the other hand, there are other effects that have been predicted on the basis of physical theories. Within the domain of electrodynamics, I wish to point out three effects: electromagnetic radiation, transistor and laser. These effects are an important part (I would say a crucial part) of modern industry. This success indicates that the principles of electrodynamics and quantum mechanics are correct (or at least very useful). It means that your statement: “I was trying to demonstrate the repeated error of physicists jumping to the next level of problems before understanding the current level” is not completely justified. The assumption stating that you are right (which is an incorrect assumption) means that physicists should not give us the basic information concerning the physical laws required for modern industry.

    My paper mentioned in one of my previous Replies, solves the relativistic problem where one charge has an infinite mass. (Following your request about a link to this paper, I’ll try to put it in my site. See later the section entitled: “Nevertheless, I Adhere to Foundations of Theoretical Physics.”)

    In the rest of this Reply I refer to some aspects of your statement: “I also deliberately said CLASSICAL EM interaction (Lorentz FORCE, not Lorentz transformation) as this should be easier than the relativistic situation (a la Dirac).”

    1. In this statement you use an inadequate terminology, which shows again that you have not finished successfully your studies in physics. For your info: in physics the notion “classical” refers to phenomena that can be described without the need of quantum mechanics. Classical physics contains Newtonian mechanics and relativistic mechanics (see e.g. the title of [1], where relativistic mechanics is discussed).
    2. Here I take advantage to your present restriction of non-relativistic motion. An examination of the Darwin Lagrangian (see [1], pp. 179-182) shows that in this case the problem is reduced to a form which is analogous to the Newtonian gravitation law. These problems are solved adequately. Thus, for an example of eclipse calculations see http://en.wikipedia.org/wiki/Battle_of_Halys . Here people have solved a many body problem of the sun, earth, moon, Jupiter, Mars, Saturn and probably other bodies.

    I conclude that your total attack on physics is unjustified and that you still have no adequate background for doing that.

    References:

    [1] L. D. Landau and E. M. Lifshitz, {\em The Classical Theory of Fields} (Elsevier, Amsterdam, 2005).

    Cheers, Eli

  5. A Reply to Bernard Schaeffer’s Comment put on December 15, 2012 at 8:57 AM

    Dear Bernard,

    It is true that QCD is unable to explain nuclear interactions. Evidently, nuclear interactions, like any other physical data, should be explained by a theory that has a self-consistent structure and its results fit experimental measurements. It turns out that your idea is inconsistent with these requirements. Let me show briefly few examples that support this conclusion.
    1. Unlike the statement in your article, the shape of the nuclear force differs from the inverse square law. The radial dependence of this force is obtained from scattering experiments and its shape is very similar to the van der Waals force. See the discussion in the item ‘An invitation to solve a mystery’ at the right hand side near the top of this page. You can see there two figures taken from textbooks that demonstrate this similarity.
    2. The neutron is an electrically neutral particle and its electric dipole moment is practically zero. An induced electric dipole moment of the proton by the neutron violates parity. Strong interactions are known to conserve parity.
    3. If you are right then the spin-1 deuteron must have an ordinary electric dipole moment. This is another violation of parity. Such a deuteron should also affect electronic states. This phenomenon has not been detected. The difference between the electronic states of the hydrogen isotopes is shown in the hyperfine structure and is understood by conventional physics.
    4. The strength of interactions related to the nuclear charge distribution is a well known phenomenon, called nuclear Coulomb interaction. In light and medium nuclei, the size of this interaction is smaller than the nuclear interaction. Hence, ordinary electric interactions can explain neither the deuteron state nor that of the alpha particle.
    5. An induced polarization of the proton’s charge means an excitation of the proton’s ground state. Particle physics data show that in order to do that, you must “pay” an energy amount of several hundreds of MeV. Hence, this effect cannot explain the relatively very small size of the deuteron’s binding energy which is about 2.2 MeV.

    These points show that you do not take the right course. For an explanation of strong interaction phenomena you may see http://www.ejtp.com/articles/ejtpv9i26p93.pdf and references therein. The ideas presented in these works rely on the Regular Charge-Monopole Theory. It has indeed an electromagnetic like structure and it conserves parity.

    Cheers, Eli

    • The problem is that the Coulomb force is only a large-scale statistical summary. It does not describe how two charged electrons behave.
      No-one has ever calculated the dynamics of 2 classical point charges moving only under their mutual Maxwell effects, never mind including any quantized effects. Physicists love to move on to ‘deeper’ challenges before they have solved the current problems (e.g. start of universe).
      So nuclear theories constructed around a Coulomb force are bound to fail (pun intended).

      • Dear VoxPop,

        I really wonder about your statement: “No-one has ever calculated the dynamics of 2 classical point charges moving only under their mutual Maxwell effects”. I’m sure that this statement is wrong, because I’ve done it myself before you have written the above mentioned statement on this blog (see: E. Comay: Solutions of the Lorentz-Dirac Equation in the Ultrarelativistic Domain, J. Phys. A29, 2111 (1996)). You can see there that, contrary to your statements, numerically stable solutions of this initial value problem are obtained if it is solved backwards in time.

        Cheers, Eli

      • Sorry, Eli but your response is again inadequate.
        Your paper did not calculate the mutual dynamics of 2 Dirac electrons on each other but only the effect of a ‘field’ on ONE electron – this is just the standard ‘many-body’ approximation that has been used for 300 years.
        I also deliberately said CLASSICAL EM interaction (Lorentz FORCE, not Lorentz transformation) as this should be easier than the relativistic situation (a la Dirac).
        I was trying to demonstrate the repeated error of physicists jumping to the next level of problems before understanding the current level.
        PS When you reply to a response it would be helpful to add an explicit link for a further response – or do you just want to have the last word?
        PPS Please post a copy of your paper, some of us can’t afford the $33 ripoff fee charged by journals to independent researchers.

      • Dear Eli,


        1 see that you agree that the nuclear force is similar to the Van de Waals force which is electric. Diffusion experiments have a maximum of two digits precision.

        2 The neutron has electric charges of no net charge. I agree that it has no dipole moment but, when a proton approaches to a neutron the electric charges are separated by electric induction, giving a permanent quadrupole in the deuteron whose value is 0.2860 fm^2. Conservation of parity is a very vague theory. The physical laws of the hypothetical “strong” force are unknown.

        3 I am not interested to the exciting excited electronic states, only the fundamental one. I cannot solve all the problems simultaneously with a magic stick. All the information is in the mass tables with a precision up to 10^-8, which is not the case for diffusion experiments. I guess you are unable to calculate even the simplest nucleus with your strange violation of parity.

        4 The Coulomb interaction is used only to calculate the decrease of the binding energy of the heavy nuclides. It is very approximate because it is averaged over the entire nucleus. How can you average the deuteron with only one proton?

        You say “electric interactions can explain neither the deuteron state nor that of the alpha particle”. I don’t “explain”, I calculate and obtain the right result. No other theory is able to do it. Do the calculation yourself you will see. The usual theory can calculate only one part of the ratio alpha particle over deuteron binding energy.

        5 The deuteron binding energy is not very small and the largest binding energies per nucleon are less than 5 times larger. You speak of hundreds of MeV but this is the total binding energy.

        The so called “right course” is simply completely irrealistic because based on wrong assumption such as the believe of orbiting nucleons as in the atom. The nucleus is not like an atom because it has no force center as the atom. My theory uses classical physics, no strange forces.

        An imaginary strong interaction cannot be explained : it needs to be proved.

        Cheers

        Bernard

    • Your reply is based only on vague ideas and qualitative arguments. My theory in in accord numerically with the experimental results for the lightest nuclei. it uses a theory established since two centuries and experimental data known since more than half a century (the neutron containing electric charges and the magnetic moments of the nucleons). There is no fiction, no mysterious strong force, no hypothetical orbiting nucleons, no fitting, no centrifugal force, only static Coulomb’s laws.

      Nobody else is able to calculate even a simple nucleus.

      • Dear Bernard,

        On December 16, 2012 I put a Reply to your Comment. This Reply describes briefly five different reasons why your idea is wrong. (BTW, more arguments also yield this conclusion.) You describe these points as “vague ideas and qualitative arguments”. Please note that everybody who has finished successfully MSc studies in physics knows for sure that each of these arguments has a solid experimental support. Your description of these points as “vague ideas and qualitative arguments” indicates that you have not yet finished successfully your studies in physics. Obviously, a person who has finished his studies is more likely not to be trapped in pitfalls. Therefore, I kindly advise you to finish successfully your studies in physics before beginning to propose new physical theories.

        Sincerely, Eli

    • Dear Eli,
      1 How do you know that “the shape of the nuclear force differs from the inverse square law.”? In fact you do not know the strong force law.

      2 The neutron has electrical charges with no net charge.

      3 the deuteron has a quadrupole moment

      4 The nuclear Coulomb interaction is the electric repulsion between protons. Strangely enough it is of the same order of magnitude as the binding energy, at least in the deuteron.

      5 “Hence, ordinary electric interactions can explain neither the deuteron state nor that of the alpha particle.” How do you explain that it explains it?
      In fact, a strong interaction was imagined because of the belief that the atomic nucleus is like an atom. Unfortunately, the nucleus has no nucleus; thus the nucleons cannot orbit around nothing. As a consequence, there is no centrifugal force and no strong force needed to equilibrate it.

      6 I speak about the fundamental state; do not mix the problems. The binding energy of the deuteron may be given by the simple Coulomb formula B = e^2/(4πε0R)= 1.44 MeV where R= 1 fm, the approximate radius of a nucleon. You can easily check it. The binding energy of the deuteron is 6 times smaller than that of the α particle but nobody has yet explained it (I don’t understand your explanation). I explain it by the fact that there are 4 times more neutron-proton interactions in 4He, each proton induces two neutrons, thus multiplying by 2 the electric attraction. The magnetic moments of the nucleons, being inclined by 60°, their repulsion energy is divided by 2. Therefore we have 4x2x2x2,2=35 MeV not far from the experimental value 28 MeV. This is too large because, in this simplified calculation I have neglected the magnetic repulsion between neutrons and between protons.

      Cheers, Bernard

      • My explanation is very simple, at least for the deuteron. It needs only to know the electric and magnetic Coulomb laws respectively in 1/r and 1/r³. There is a static equilibrium between the electrostatic attraction and the magnetic repulsion. There is no centrifugal force, thus no need of a hypothetical strong force.
        There is no need of knowing the radius of a nucleon, the electric charges being assumed to be point charges. Without any other hypothesis, it explains quantitatively the binding energy of the deuteron. See my paper here, explaining it in detail “Electric and Magnetic Coulomb Potentials in the Deuteron”
        http://www.aemjournal.org/index.php/AEM/article/view/218
        It is of course more complicated for 4He but I obtain, with still some approximations, 6.2 MeV for 7.1 experimental.

        The strong force will disappear as the geocentrism by Copernicus and Galileo, the phlogiston by Lavoisier and the ether by Einstein.

        Cheers

      • Dear Bernard,

        I see that you have ignored my advice of December 17, 2012 and you have studied nothing in physics. You should realize that many technologies that work perfectly are based on good physical theories. Your attempts to throw away everything are ridiculous and a waste of your time and your readers’ time as well.

        Your work is full of errors and this site is certainly not the right place for discussing them in detail. Therefore I refer here only to one point. In the article mentioned in your post of December 18, 2013 you say that the deuteron state is a balance of the coulomb attraction between the proton’s electric charge and the charge of the neutron’s constituents on one hand and the proton-neutron magnetic repulsion on the other hand. If you are right then there must be a lower energy state for the deuteron where this magnetic force disappears (it is called an S-state). This state does not exist and this fact disproves your idea.

        Please respect my request and do not post new comments on this site before you finish successfully your studies in physics.

        Cheers, Eli

  6. A Reply to VoxPop’s Comment (of December 13, 2012 at 3:35 AM).

    Dear VoxPop,

    The many body problem (where the 3-body problem is just one example) is solved by approximate mathematical algorithms. Today computers are used as the work horse. This is a problem of applied mathematics. For the atomic case where the number of electrons is greater than 1, physicists use a truncated Hilbert space whose functions are terms where each of which belongs to a configuration. The goodness of a solution is obtained from a comparison of two solutions where the second solution has more terms. If the difference is smaller than the required accuracy then the solution is accepted. Otherwise, the number of terms is increased and the procedure is repeated (see, e.g. A. W. Weiss, Phys. Rev. 122, 1826 (1961)).

    This site shows many different kinds of experimental examples that disprove QCD. It is also shown that QCD has been constructed on the basis of a misunderstanding of physical laws (see http://www.tau.ac.il/~elicomay/dpp_new.pdf ). Therefore, I see no reason why one will try to enter into details of the work of people who try to solve an erroneous problem.

    BTW. Any theory that is used for solving the proton’s state must cope not only with the 3-body problem of three quarks because it must contain terms where additional quark-antiquark pairs are included. The reason is that antiquarks are detected explicitly in the proton (see D. H. Perkins, “Introduction to High Energy Physics”, (Addison-Wesley, Menlo Park CA, 1987), p. 282). On top of that, quarks carry only about one half of the proton’s mass. The object that carries the rest of the mass certainly interacts with quarks (because it does not leave freely the proton). This is another reason explaining why the proton’s problem is much more complicated than a 3-body problem.

    Cheers, Eli

    • Hi Eli:
      Thanks for your reply. I raised this issue because I know that computer calculations are the current evaluation technique. What I was hoping to hear was: a) How do outsiders check on these calculations? b) How are initial conditions determined? c) How are chaos solutions avoided? – Poincare showed over 100 years ago that the 3-body techniques are unstable – adding another digit to a starting variable parameter can create wildly varying trajectories.
      Secondly, how can massless field theories compute masses for multi-body aggregates (like nucleons) where internal interactions are not instantaneous?
      Thirdly, the helium calculation is a fraud. It uses hydrogen wave functions as a mathematical sum whose weights are varied until the ‘correct’ answer is found. This has 3 problems: a) it uses 3D spherical harmonics which are known to be a complete set so they can be used to match ANY space-time variation (just like 1D Fourier series) b) this provides no analytic perspectives so we learn nothing c) this technique has never been extended to more complex atoms, probably because of 2.
      What’s your response, Eli to these criticisms?

      • Dear VoxPop,

        1. Outsiders can check the correctness of a numerical calculation reported in the literature by writing an appropriate computer code and running it.
        2. Instability of the initial value problem is discussed in the literature. This issue is completely irrelevant to the calculations of quantum states in general and of atomic states in particular. Indeed, here one has to solve the appropriate eigenvalue and eigenvector problem of a Hermitian matrix obtained from a truncated Hilbert space. This problem is stable and chaos does not appear.
        3. A problem where all fields are massless is irrelevant to this site.
        4. Instantaneous expressions are obtained from an expansion of the retarded interaction in a power series. The Darwin Lagrangian is obtained for classical problems and the Breit Interaction is obtained for quantum mechanical problems.
        5. Point (a) of your last paragraph is nearly correct. It contains a flaw because a quantum state is calculated as a time-independent problem.
        6. Your point (b) is unacceptable because it represents a complete misunderstanding of the meaning and the usefulness of numerical solutions to differential equations. You must attend a relevant university course before making statements of this kind.
        7. If you write in google the following 3 words – lithium atom state – then you obtain links to many Articles that solve states of the 3-electron lithium atom. Some of these Articles have been published about half a century ago. Hence, the statement in your point (c) is completely incorrect.

        I conclude that you need to study the problem before you make up your mind. This is the right chronological order of doing a good work. Your impolite word ‘fraud’ which is made by a person who does not understand the problem is certainly unacceptable. It also violates an explicit request to refrain from using an offensive language (see the right hand side at the top of this page).

        Cheers, Eli

    • Sorry, Eli I’m not buying your ‘standard’ answer. You have not responded enough with detailed info but only with arm-waving generalities. The 3-body problem is critically dependent on initial conditions when ‘solved’ numerically. This is hidden in computer solutions because computers use finite representations of ‘real’ numbers that actually need an infinite number of digits.
      Using jargon like ‘truncated Hilbert space’ is just more math smoke. As I said, the Hylleras style approach uses the wave mechanics of 3 electrons (nothing fancy) but fakes the answer by ‘form-fitting’ to the known results by using a truncated 3D complete set. Please do better with your next reply – you are not dealing here with green students trying to get a degree in general physics – show some respect.

      • Dear VoxPop,

        I really try to treat people with respect. I also strongly believe that telling a person that he makes an error is an excellent advice because it helps him doing better.

        Your series of comments prove beyond any doubt that you do not understand the difference between ‘an initial value problem of differential equations’ and ‘an eigenvalue problem of differential equations’. I kindly ask you to understand thoroughly the difference between these notions before continuing to make further Comments on these topics.

        Cheers, Eli

      • Eli:
        You continue to pontificate instead of giving detailed answers.
        Of course, I know the difference between eigenvalue & initial value problems. You are not the only one to have studied undergraduate physics. Telling someone they have made an error is a poor response – if you are so convinced you are right in responding, give some details to justify your position. This approach reflects the arrogance of power manifest by too many poor teachers.
        Please show some respect, if you wish to have a dialogue here – or do you just want to have a pulpit to spout off your own ideas?

    • I agree that math is NOT physics. The many theories of nuclear physics are pure fantasy because the fundamental laws and constants of the mysterious “strong force” is unknown. It is not the strange Higgs boson that will solve the problem.

      In fact the electromagnetic Coulombs’ laws work fine to predict the nuclear interaction as I have shown it in my paper
      “Electromagnetic Theory of the Binding Energy of the Hydrogen Isotopes”

      The big error of the nuclear physicists was to believe that the Bohr model of the atom may be applied to the nucleus. The problem is that, in contrast with the atom, a nucleus has no nucleus and, therefore no massive central body that can act as a force center.

      • Worse, fields have no mass (they are only mathematical fictions, defined EVERYWHERE & EVERYWHEN) so how can another field (the ‘Higgs’) solve this mathematical paradox?
        But then, these guys are now all mathematicians so they are never bothered by physical issues or philosophical contradictions.
        Philosophy has gone full circle & returned back to the pre-Newtonian theologians.

  7. You will not find such a paper, because there is no need for such explicitations. If there was, refereees would have asked Sakurai et al to provide them.

    A. The interaction is presented in the form of contractions of four-vector currents, so it is by construction covariant without the need for a formal proof. Once the interaction is thus expressed you can use it in whatever frame you want (for instance, the target hadron rest frame) at no risk.

    B. The mathematical language of four-vectors is widely accepted, there is no need for saying what it means in words and editors do not like redundancy.

    C. Wigner’s theorem does not apply because (i will say it again) the vector meson is a virtual state, not a real state. Field theorists knew perfectly that in the 60’s, so there is no need for clarification in a paper.

    And, again, all of this thread was not about VMD but about the standard model and the Higgs.

    • Hello Daniel. I think that QFT must be connected to Relativistic Quantum Mechanics (RQM), which, by its classical limit, is known to be connected to Relativistic Classical Physics (RCP). Indeed, QFT is used for describing interaction processes. However, evidence and analysis of such an interaction are derived from detectors that mesure physical properties of particles that come out of the interaction region. These particles travel a very long distance (if length is measured in fm) and their behavior along their paths is derived from RCP and Classical Electrodynamics. You deny this and claim that QFT is a stand-alone theory which is completely independent of theories like RQM.

      Wigner’s analysis of the irreducible representations of the Poincare group applies to systems that are stable for appropriately long period of time. A real photon certainly belongs to this category. Now, VMD writes the state of a real photon as a linear combination of a pure electromagnetic photon and a vector meson:

      |Gamma> = c_0 |Gamma_b> + c_h |h> (1)

      Here the sum of the absolute value of the coefficients is unity and each of them does not vanish. I call (1) a supperposition of two different states, each of which has a probability greater than zero. On the other hand, you argue that the second term of (1) is virtual. I think that you just try to evade a problem by playing with words. Moreover, (1) is a mixture of a massless state (characterized by helicity) and a massive state (characterized by spin). I rely on Wigner’s work and conclude that VMD is a clear violation of Special Relativity. On the other hand, you are quite happy with VMD and claim that (just in order to avoid redundancy…) there is even no need for proving its consistency with covariance.

      In your comment of March 28, 2010, you say: “(I emphasize again: VMD is not a part of the standard model).” Now a photon belongs to electrodynamics and a nucleon belongs to QCD. Both theories belong to the Standard Model (SM). It follows that the photon-nucleon interaction is included within the validity domain of the SM. Therefore, relying on your emphasized statement quoted above, I claim that the SM is unable to explain the hard photon-nucleon interaction. I also think that this inability is a very serious problem. On the other hand, you are quite happy with the situation and think that this inability does not cast any doubt on the SM validity.

      For these reasons (and for some others that I skip mentioning here) I think that our exchange of ideas becomes unfruitful. Therefore I suggest to wait for new experimental results.

      • Please explain how Newton’s 3-body problem (that caused him to give up mathematical physics & take up theology) has been overcome in the case of QCD where 3 quarks strongly interact continuously.

      • QCD is unable to calculate any nuclear binding energy. Classical electrodynamics is able to calculate hydrogen and helium isotopes, more precisely the electric and magnetic Coulomb’s laws as I have shown in my paper for 2H and 4He:
        http://www.scirp.org/journal/PaperInformation.aspx?paperID=24389

        Indeed, in contrast with the atom, the nucleus has no nucleus e.g. no massive central body which can act as a force center. Therefore there is no need of a mysterious “strong force”.

  8. I’m afraid that we have arrived to a misunderstanding.

    In your comment of March 28, 2010 , you say about VMD: “The theory has a math formulation, of course, which is explicitly covariant.” You also say that it was done in the 60s. In my comment of April 2, 2010 I asked you: ” Can you show me an explicit reference from the 60s, proving covariance of VMD?” In your comment of April 2, 2010 you respond with a list of publications, the first of which is ” Vector Meson Exchange Model for Isobar Production, Leo Stodolsky and J. J. Sakurai, Phys. Rev. Lett. 11, 90–93 (1963).”

    I’ve read this paper and did not find a PROOF OF VMD’S COVARIANCE in it.

    Therefore I repeat my request in the most explicit form: In order to substantiate your statement of item 1 above, you must show me the following:

    A. A reference to one article from the 60s AND the page number and the line number where the VMD covariance proof begins. This must also be done for the last line of the proof.
    B. The proof must contain an explicit statement indicating that a proof of VMD’s covariance is presented.
    C. The paper must explain why Wigner’s analysis of the irreducible representations of the Poincare group does not negate the proof.

    The merits of the above mentioned work of Wigner has been described as follows: “It is difficult to overestimate the importance of this paper, which will certainly stand as one of the great intellectual achievements of our century” [1]. Just compare this statement with the obvious theoretical values of your “phenomenological theory”.

    [1] S. Sternberg, Group Theory and Physics (Cambridge University Press, Cambridge, 1994). See p. 149.

  9. A few of the many 60’s production on vector meson physics (Sakurai is the creator of the model)

    Vector Meson Exchange Model for Isobar Production, Leo Stodolsky and J. J. Sakurai, Phys. Rev. Lett. 11, 90–93 (1963)

    Vector-Meson Dominance and Current Algebra in the Parity-Violating Nonleptonic Decays of K Mesons and Hyperons, J. J. Sakurai, Phys. Rev. 156, 1508–1510 (1967)

    Finite-Width Corrections to the Vector-Meson-Dominance Prediction for e+ e-, G. J. Gounaris and J. J. Sakurai, Phys. Rev. Lett. 21, 244–247 (1968)

    Vector-Meson Dominance and High-Energy Electron-Proton Inelastic Scattering, J. J. Sakurai, Phys. Rev. Lett. 22, 981–984 (1969)

    Sakurai has writen a textbook on quantum mechanics and the volume two is devoted to field theory; for sure he explains a little of his theory there.

    Bauer et al, more than 10 years after the model was put forward, didn’t have the need to check the covariance, and made a description in the hadron rest frame (once you choose a frame you loose explicit covariance). In that expression (2.1), the left hand side is a real photon, but the right hand side is a superposition of VIRTUAL (not real) states.

    And, please, check that vector meson physics is by far not the only way to
    describe photon-hadron interactions. Try searching photon+hadron+interaction at scholar.google.com and you will see.

    But, above all, all this is history, and does not have anything to do with the consistency of the Standard Model not with the Higgs particle. The point here is your use of RQM to prove the SM inconsistent, which is untenable.

  10. In your last remark you state:” No serious physicist would claim ever that a real photon is a linear combination of real particles, one of which is a vector meson.” Well, on page 271 of [1], the state of a physical photon is defined as follows

    |Gamma> = c_0 |Gamma_b> + c_h |h> (2.1)

    where c_i are normalization coefficients, |Gamma_b> is the pure electromagnetic (“bare”) component of the photon and |h> is its hadronic component, which is made of a chargeless meson, like the rho_0, omega and phi. (Here I use different symbols for the numerical coefficients of (2.1).)

    Eq. (2.1) exactly agrees with (10.104) which can be seen on p. 298 of [2]. These quotations from the literature prove that the above mentioned citation from your last remark does not hold water.

    Another statement made in your last remark supposedly relies on work from the 60’s says about VMD: “The theory has a math formulation, of course, which is explicitly covariant.” Well, note please that [1,2] have been written in a later period. The Authors of [1] and [2] use a contradictory terminology. Indeed, just below (2.1) of [1] it is claimed that: “all states in Eq. (2.1) have the same 3-momentum k.” This is certainly a violation of covariance, because, in order to represent a meson, the 0-component of the photon’s 4-momentum is altered, whereas covariance must conserve the invariant E^2 – k^2. An analogous violation of covariance can be found on p. 299 of [2] which says: “the ratio of c_h/c_0 increases with increasing energy.”

    I stop here and ask you two questions:

    1. Why the Authors of [1,2] ignore the “explicitly covariant” attribute that you ascribe to VMD of the 60s?
    2. Can you show me an explicit reference from the 60s, proving covariance of VMD?

    [1] T. H. Bauer, R. D. Spital, D. R. Yennie and F. M. Pipkin, Rev. Mod. Phys., 50, 261 (1978).
    [2] H. Frauenfelder and E. M. Henley, Subatomic Physics (Prentice Hall, Englewood Cliffs, 1991).

  11. I will be lengthy in my response thinking in visitors, for which this page could operate as a divulgation one.

    I will start with a little epistemology. Saying that a theory does not provide an explanation to some phenomenon is not the same as saying it is wrong; a theory is wrong if it predicts phenomena in contradiction with observations.

    The Standard Model is not a theory of everything, and it is no secret that it cannot be applied strightfowardly to hadron physics because it provides us with a perturbative expansion around quark and gluon vacuum, and hadrons are supposed to be bound states. Supposed to be, I say, because we do not know certainly that QCD leads to confination (that is a Millenium Problem, worth one millon dollars). All we have to do is to use insight from standard model to construct or refine “phenomenological theories” (more about this “oxymoron” below) like pomeron exchange, fragmentation, microjets, VMD and so on.

    The expression “phenomenological theory” is not my invention, it is a term used in the high energy community to refer to some theory with no claims of fundamentality. Hadron interactions provide good examples: as far as we know, the most fundamental theory we know on strong interactions is QCD (an “ingredient” of the standard model), but in situations in which, for whatever reason, it is too difficult to use QCD, one uses some theory that works well enough, allways checking for compatibility. QCD imposes restrictions on phenomenological theories. If a QCD-constrained theory does not fit data, and you can assure that the QCD constraint is the cause, that would be evidence against QCD. Of course, “phenomenological” theories are full-fledged theories, one calls them like that only because one believes that there is a better theory regarded as more fundamental. VMD, dual models, sigma models, nuclear democracy, maximal analicity and so on were proposed in its day as candidates of fundamental theories for hadron interactions.

    Now, let us discuss VMD’s covariance (I emphasize again: VMD is not a part of the standard model). You are tricked again here by your usage of quantum mechanical thinking. No serious physicist would claim ever that a real photon is a linear combination of real particles, one of which is a vector meson. What one is thinking here is that a single particle state in a quantum field can be thought, in very short periods of time, as a combination of virtual states of any set of particles with which the photon can interact. It is not right to say that a photon “has an hadron component” which depends on energy, but if the photon is probed by some hadron that hadron will “see” the virtual hadrons in the photon. This is a description in the frame of reference where the hadron is at rest. If you change the frame to render the photon as “soft”, then you will be boosting the hadron. You can see an application of this for UHE cosmic rays: they cannot come from too far away because high energy protons would see photons from the microwave background as hard photons in its rest reference frame, thus occurring photopion production.

    The former paragraph was not the VMD model but just a caricature of it. I mean, it is not this “cloud of virtual particles” what one uses in the calculations. The theory has a math formulation, of course, which is explicitly covariant. The theory comes from a period of amazing production in high energy physics: the 60s (other examples: V-A currents, dual models, maximal analicity, bootstrap…). They are highly sophisticated theories, not all of them QFTs, again from a hughe comunity of clever and ambitious guys. Relativity was then a firmly established half century old theory, and they knew their theory would have been hopeless if not formulated consistent with it. Check the original works: you will find that the very first thing they did is establishing explicitly covariant expressions.

    And, finally, another bit of epistemology. Most, if not all of your criticism to modern particle physics, lies in your confidence that QFT and RQM forms a kind of popperian hierarchy. What I have been showing from the beggining is that it is not the case: QFT and RQM are incommensurably distinct paradigms in the sense of Kuhn. RQM is simply the wrong way to take quantum physics to the relativistic domain and the problem is thinking in single-particle quantum states. QFT is a solution to that because the quantum states belongs to the whole field, and single particle states are just particular field states. trying to point out errors in the standard model using RQM is like trying to prove Newton’s gravitation law wrong using aristotelian mechanics (something that indeed happened in Newton’s days).
    In order to put your findings before the high energy physics comunity with hope of being taken seriously you should state them in the language of quantum field theory.

  12. I hope I still have the right to use and quote textbooks. On pp. 298, 299 of [1] it is stated that, due to VMD, the relative amount of hadronic components of the photon “increases with increasing energy” (of the photon). It means that not myself but VMD supporters “switch off” the assumed photon’s hadronic component for low energy photons.

    A more fundamental point. Wigner’s analysis of the irreducible representations of the Poincare group [2,3] proves that massive and massless particles belong to different categories of representations. Therefore, VMD’s main idea, which regards the state of a real photon as a linear combination of a massless particle and a massive particle, is inconsistent with Wigner’s work. Since the Poincare group belongs to the core of Special Relativity, I conclude that VMD violates Special Relativity.

    You state: “On the other hand, vector dominance is a phenomenological theory”. Why do you use this kind of oxymoron? Is VMD a theory (which can be disproved by mathematical arguments) or a phenomenological idea (which is evaluated just by the usefulness of its formulas)? In the first case, VMD has been disproved in the previous points. In the second case, the Standard Model has no theoretical explanation for the hard photon-nucleon interaction.

    Therefore, I believe that the arguments included in the second paragraph of your last response are irrelevant to the discussion.

    [1] H. Frauenfelder and E. M. Henley, Subatomic Physics (Prentice Hall,
    Englewood Cliffs, 1991).
    [2] E. P. Wigner, Annals of Math., 40, 149 (1939).
    [3] S. S. Schweber, An Introduction to Relativistic Quantum Field Theory, (Harper & Row, New York, 1964). Pp. 44-53.

  13. You cannot switch off non-electromagnetic interactions by changing your reference frame! There is not reference frame in which you get only an “electromagnetic photon”. On the other hand, vector dominance is a phenomenological theory which predates standard model and which is subsumed by it, and which is based on observed data.

    Thousands of physicists have been using the standard model for calculations in accelerator phenomena and contrasting them to experiments (tons of data) for the last 30 years. Each of them has been anxiously looking for discrepances between the standard model and experiment; finding such discrepancies would be the key to new physics and a very significant achievement for he who pinpoints the discrepancy. I am talking of thousands of clever and ambitious guys all over the world. They have pointed out several theoretical difficulties of the theory, they have created dozens of alternatives (SUSY, technicolor, strings, GUTs…) but the few claims about minimum discrepancies between theory and observations have proven statistical fluctuations which dissapeared as more data has been collected. You don’t think there is a “Standard Model Conspiration”, do you?

  14. In your last response you state: “Arguing here that “standard models contains errors” is circular reasoning.”

    Well. Let us take just one specific example. VMD is an item in the PACS scheme :
    12.40.Vv Vector-meson dominance
    Without VMD you have no explanation for the interaction of a hard photon with a nucleon [1]. Here the photon-proton interaction is about the same as the photon-neutron interaction. Now VMD is a sheer violation of Special Relativity. Indeed, it assumes that the state of an energetic photon is a linear combination of a pure electromagnetic photon and a vector meson. The supposed vector meson interacts strongly and exchanges energy-momentum with a nucleon at the target. Now examine the process in a reference frame where the photon is just an optical photon and, therefore, it is a pure electromagnetic photon. In the later frame strong interactions do not participate in the process and the pure electromagnetic interaction distinguishes between a proton and a neutron. This is a contradiction. See also [2].

    Furthermore, you can find a quite long list of QCD experimental failures on this site’s page, “The Standard Model vs Reality”, which has been mentioned in my previous response.

    [1] T. H. Bauer, R. D. Spital, D. R. Yennie and F. M. Pipkin, Rev. Mod. Phys. 50, 261 (1978).
    [2] E. Comay, Apeiron 10, 87 (2003).

  15. 1- In fact, I don’t. There is not “experimental proof” that any particle is point-like. In fact, even fundamental particles show spatial structure due to renormalization. What we can say is that, to our knowledge, electrons, neutrinos, quarks and all gauge particles (that includes photons) have spatial structure well described by “fundamental” fields, while others, like protons, pions, etc are supposed to be bound states.
    2- Here we are talking about a supposed error of the standard model. Arguing here that “standard models contains errors” is circular reasoning.
    3- What you call “errors” in the standard model I think is missunderstanding, and you know most physisists don’t think as you on this respect, so you should not use such “errors” as a settled matter.
    4- And some people do not support the esfericity of the Earth; that proves nothing.
    5- QFT does not rely at all on RQM for experiments. The connection goes through the S-matrix and cross sections.
    6- You are talking here outside any framework. That something does not make sense in RQM does not mean that it doesn’t. If you discuss interactions in a field theory you have to discuss it in the frame of that theory; you cannot avoid it by just saying that “the theory has mistakes”. And, again, there is no any mass term in the standard model.
    7- So does Higgs field, which IS MASSLESS. The so called “massive” Higgs particle is an effective (and unstable) excitation in the physical gauge.
    8- I still didn’t read it in any detail; I see you use again this argument about the hierarchies of theories, thus I guess you use RQM somehow. In that case it is possible I will have simmilar complaints as I read it in detail.

  16. Hi Daniel
    1. I understand that you agree to our reasoning of the list of massive pointlike particles.
    2. Please note that the Standard Model contains many errors, some of which are listed on this site, just after the middle of the page “The Standard Model vs Reality”.
    3. As of today these errors are not explained by Standard Model supporters. Personally, I think that ignoring errors is not the best scientific policy.
    4. Considering the previous points, you should realize that there are people who do not follow the Standard Model.
    5. As stated in my previous reply to you, experimental particle physicists rely heavily on Relativistic Mechanics and Classical Electrodynamics. These theories yield the particles’ trajectories from the interaction point to the detectors. My usage of the hierarchy scheme for theories, shows how a Dirac particle is connected to classical physics. In your last text you do not show how a particle belonging to the KG family is connected to Classical Physics. For example, how a particle whose energy density depends quadratically on mass disintegrates into particles whose energy density depends linearly on mass?
    6. In my previous reply to you, I argue that energy density of a boson depends quadratically on mass. This kind of mass is yet unknown. You do not address the problem of how this kind of mass is incorporated in physics in general and in Einstein’s equation in particular.
    7. Wigner’s analysis of the irreducible representations of the Poincare group proves that massless particles belong to a different category. Therefore, one should not be surprised to find that photons require a different mathematical treatment.
    8. Apropos gauge. Item 2 at the top of this page presents a link to a short text describing a serious problem with the gauge idea. As of today, nobody has tried to explain it. I’ll be happy to read an analysis of this problem and of its consequences.

  17. All particles in the Standard Model are massless, that’s the point for a Higgs mechanism. Photons, Ws, Zs and higses are massless interacting bosonic fields. Electrons, neutrinos and quarks are massless fermion fields. What we call “mass” in the standard model is a dynamic effect, distinct from “mass terms”. Else, gauge symmetry would be violated.

    The key point is here: you say
    “For the present case, RQMT (Relativistic Quantum Mechanics Theory) is good for cases where the number of particles can be regarded as a constant of the motion”.
    There is not such limit for boson fields if you want localized states.

    As an exercize, try to construct a Hamiltonian for a single photon. You will be unable to find it, for simmilar reasons that for KG particles. Would you then render impossible the existence of photons?

  18. What can be seen is that it is not possible to construct a consistent theory with nontrivial interactions in the frame of relativistic quantum mechanics: interactions “creates” and “destroys” particles. You cannot obtain relativistic quantum theory as any limit of quantum field theory, so you cannot place constraints on QFT based on results on RQM. I mean, KG QFT is a qualitatively different theory than “relativistic KG particle”. In particular, what is a Schrodinger-like equation in the latter (and thus subject to probabilistic interpretation) is a classical field equation in the former. There is a Hamiltonian of the field, and the condition of positivity on field Hamiltonians leads to the spin-statistic theorem (you cannot get anything simmilar in the context of RQM). Recall that the Standard Model is indeed a field theory.

    And in regard to point particles, you are forgetting in your list all gauge particles, which as far as we know are “point-like”. They are not KG, but RQM cannot accomodate spin-one either. There is a good chance that Gravity acts trough a spin 2 particle (also a RQM impossibility).

    Of course, QFT has lots of formal troubles. But any theory does, that keeps research interesting. And certainly RQM have far worst problems, that’s why it has been left behind in favour of the first, which in spite of its faults it proved very usefull.

    • This answer would be long…

      The notion of a physical theory and the interrelations between theories is explained in the first 6 pages of [1]. I urge everybody who reads this page to study these pages. I’ll put forward few relevant points for the sake of the discussion.

      One should not expect that a physical theory be able to explain everything. For example, mechanics cannot predict the motion of an eagle flying in the sky. For this reason, a domain of validity is defined for any theory. The goodness of a theory should be evaluated only for cases belonging to its domain of validity. Thus, Newtonian mechanics is good for velocities where v<<c and the classical limit of quantum mechanics holds, etc. For this reason, a theory should have a well defined domain of validity.

      The relation between theories can be examined from the following aspect. Let D_A and D_B denote the domains of validity of theories A and B, respectively. If D_A is a subset of D_B then B's rank is higher than that of A. On the other hand, since A holds for D_A, one finds that B must agree with A for all cases belonging to D_A. Therefore, the lower rank theory A imposes constraints on the corresponding results of the higher rank theory B.

      Generally, a lower rank theory has also the advantage of taking a simpler mathematical form. Indeed, calculating the quite simple problem of a free fall of a massive body in a vacuum chamber is much simpler in Newtonian mechanics than in any other theory. In particular, one wonders whether or not QFT can be used for solving this problem… (The relevance of this kind of examination to QFT is also discussed later.)

      For the present case, RQMT (Relativistic Quantum Mechanics Theory) is good for cases where the number of particles can be regarded as a constant of the motion and effects of pair production are smaller than the experimental uncertainty. (If antisymmetry is imposed on identical Dirac particles of RQMT then it can be used for a system of many particles.) Hence, RQMT is a lower rank theory of QFT. As explained above, QFT must have a limit which does not violate RQMT.

      Near the end of your text, you say: "…certainly RQMT has far worst problems, that’s why it has been left behind in favour of QFT". Here, I believe, you have gone too far. I'm sure Quantum Mechanics and Relavistic Quantum Mechanics courses are studied at your University.

      Moreover, a well known law of physics states that a physical object must be, directly or indirectly, related to measurements. Experimental particle physicists rely heavily on Relativistic Classical Mechanics and Classical Electrodynamics. A Dirac particle obviously fits this scheme, as shown by the following hierarchical chain of theories related to it:

      QFT –> RQMT –> Classical Physics

      The last relation stems from an application of the classical limit to quantum mechanics. Now, you agree that a QFT KG particle is inconsistent with RQMT. Considering this point, can you explain how can a QFT KG particle be related to measurements?

      By the way, the KG (and Higgs) Lagrangian density depends quadratically on mass. Hence, the corresponding energy-momentum tensor and its energy density entry also depend quadratically on mass. Now, how can a Higgs boson disintegrate into 4 Dirac particles, whose respective quantities depend linearly on mass?

      There is another aspect of this point. The Einstein equation of General Relativity (GR) uses the particles’ energy-momentum tensor. For ordinary matter (and for Dirac particles), this quantity depends linearly on mass. Now, the Higgs Boson as well as its original KG particles yield an energy-momentum tensor that depends quadratically on mass. Hence, in GR the Higgs Boson has a new kind of mass which is alien to all known kinds of mass. Thus, how can the (still undetected) Higgs Boson’s disintegration into 4 leptons be consistent with GR?

      Another issue.

      The photon is excluded from the list of massive pointlike particles given in this site, because it is massless. The W and Z bosons are excluded because they have not been experimentally proved to be pointlike. Indeed, a particle’s radius or an upper bound of it, are derived from results of scattering experiments. Here the measured particle collides with another particle. Hence, experiments require that the measured particle be included in a target or in a beam. Short lived particles make a challenge for experimenters. Examining the presently available PDG reports, one finds that among the particles whose size has been measured, the Sigma Minus baryon is the particle having the shortest half life. The half life of the W and Z bosons is shorter by about 14 orders of magnitudes.

      [1] F. Rohrlich, Classical Charged Particles, (Addison-wesley, Reading mass, 1965). See pp. 1-6.

  19. The imposibility of building a single-particle relativistic quantum mechanics is known from the 30’s, not only for Klein-Gordon but also for Dirac particles (see for instance the Klein paradox). The resolution for this is building a many-particle formalism, aka field theory. An early discussion on the subject can be found in Landau’s Relativistic Quantum Mechanics (a book that dates from the 40’s). In Weinberg’s QFT textbook you can find a historic review (first chapter) and a very clear explanation on how fields solves these problems.

    And, if you wish changing ideas with a group of people, it is not a good idea to call them cowards.

    • I do not use terms like “cowards” but there are people who visit this site and feel they need to use such words to express their feelings. My father will answer you soon regarding your physics comments. Thanks.

    • An important aspect of the logics of a physical theory is the notion of its domain of validity [1]. For this reason, the merits of a theory should be evaluated only for cases included within its domain of validity. Thus, a hierarchy of theories is obtained. (For example, relativistic mechanics takes a higher status with respect to Newtonian mechanics). A related property is that the lower rank theory imposes constraints on the respective limit of a higher rank theory.

      The (quite artificial) Klein paradox is just outside the domain of validity of relativistic quantum mechanics theory (RQMT). The same is true for the physical effect called Lamb Shift, etc.

      Therefore, one cannot build a self-consistent relativistic quantum field theory (RQFT) without having a solid RQMT. In particular, one cannot construct a Fock space without having a self-consistent Hilbert space. The Dirac theory has both of them and the Klein-Gordon (KG) theory has neither of them [2].

      It is well known that a comparison between a theory’s predictions and the corresponding experimental results makes a good distinction between good and bad theories. Thus, both Dirac and KG field functions depend on a single set of 4 space-time coordinates of the Minkowski space. Therefore, both describe point-like particles. As of today, all experimentally consistent point-like particles are Dirac particles (leptons and quarks). Hence, one must admit that the KG field theory has failed.

      [1] F. Rohrlich, Classical Charged Particles, (Addison-wesley, Reading mass, 1965). See pp. 1-6.
      [2] http://www.tau.ac.il/~elicomay/MathPhys.pdf

  20. Have you read the above?
    Now do you understand why so many wont question?
    They are cowards, and afraid of “being ridiculed/rejected or commited to psychiatric unit”

  21. Very good!

    I was considered very intelligent untill i had to go to high school (11-16) untill i started telling teachers they were wrong and that the models do not make sence.

    So they put me in a remedials class.
    I do not know if that was as a punishment for questioning dogma or because they are/were convinced by the txt books,and what they were taught; as though it was a pillar of fire by day & cloud by night. And never to question.

    So i did not get education for rest of my life,besides no schooling can teach intelligence only subject.

    I thorised many things in regard to astro physics some of which i have ate stamps of the posts from many years before they were discovered;(i say descovered where i mean understood by someone with a name) Such is the world and life.

    Still my last 2 I.Q. results were both at 154.

    Your father is lucky,he has not been ridiculed or locked up in an asylum for questioning the “standard theory god”.

    Take Care & Best Wishes!

  22. hey Eliyahu,

    i like your style. very clear, understandable, and enjoyable reading.

    we shall ‘see’ if the “new theory” is correct…er, perhaps more rightly stated – we shall shall ‘not see’ if the “new theory” is correct.

    have you ever considered matter to be “thought” consisting via verbal command (directed vibration)?

    shalom,
    __shaul

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