Striking Standard Model Discrepancies

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This page proves inherent discrepancies of the weak and the strong interaction sectors of the Standard Model. It follows that physics truly needs coherent theories of these interactions.

A remark for readers: This page describes a few striking Standard Model discrepancies. If you can refute any of them, please send me an email (elicomay@post.tau.ac.il) describing your opinion in a scientifically acceptable form. I will be happy to include your scientific reasoning with or without your full name.

Here is a list of some specific Standard Model discrepancies that deserve better attention.
  1. Problems with equations of motion.
    1. Every (or nearly every) QFT textbook explicitly presents the Maxwell equations.
    2. Every (or nearly every) QFT textbook explicitly presents the Dirac equation.
    3. In contrast, no QFT textbook presents an explicit form of the partial differential equations of the W± and of the Z particles (see e.g. the exercise at the end of this page).
    4. Furthermore, no QFT textbook explains why this vital element is omitted.
    5. Result: No QFT textbook shows that solutions of these partial differential equations appropriately describe relevant experimental data.
    6. Conclusion: Unlike Maxwellian electrodynamics and the Dirac theory of the electron, the electroweak theory lacks coherent theoretical basis.

  2. Standard Model supporters do not really understand the notion of isospin. For reading a short proof of this apparently unbelievable claim, click here.

  3. Standard Model supporters violate the continuity equation of an electrically charged particle.
    1. The validity of the continuity equation of an electrically charged particle is a primary requirement of Maxwellian electrodynamics.
    2. Every (or nearly every) QFT textbook proves that solutions of the Dirac equation satisfy the continuity equation.
    3. In contrast, a proof that the functions of the electrically charged W± particles of the electroweak theory satisfy the continuity equation requirements is nowhere to be found in any QFT textbook.
    4. No QFT textbook explains or even discusses the reason for this omission and its implications.
    5. The following evidence confirms the previous claim. Several decades after the birth of the electroweak theory, the CERN LHC ATLAS collaboration still uses a phenomenological expression for the electromagnetic interaction of the W± particles [see [1], p. 293, eq. (3)].
    6. A straightforward test proves that this expression is inconsistent with the continuity equation. Indeed, their interaction term depends on derivatives of the W± functions. Here the Noether theorem proves that if a derivative of the quantum function exists then a new term is appended to the conserved 4-current. This new term is not included in the original expression.
    7. Conclusion: This is another proof showing that the electroweak theory lacks coherent theoretical basis.

  4. Standard Model supporters violate an elementary physical requirement: They ignore the balance of dimension of one of their expressions.
    1. Let us examine again eq. (3) of [1]. The first term on its second line represents an electromagnetic interaction. It can be written like this

      ℒ' = -eWμWνμν , (1)

      where e denotes the electric charge, WμWν denote the W 's quantum functions, and μν denotes the electromagnetic fields tensor.
    2. It is well known that the electromagnetic fields tensor μν does not carry an electric charge.
    3. In units where ℏ = c = 1, the dimension of a Lagrangian density is [L-4]. Hence, the dimension of each of the electroweak W± functions is [L-1], and that of the product of the two Ws of (1) is [L-2].
    4. This is inconsistent with electric charge density, whose dimension is [L-3].
    5. Thousands of people are Authors of [1], and it has been cited by more than one hundred articles. Apparently, none of the persons involved has noticed this terrible error.

  5. Standard Model supporters ignore the interaction of a hard photon with nucleons.
    1. The interaction of a hard photon with a proton is very similar to its interaction with a neutron, and the strength of this interaction is stronger than the expected electromagnetic interaction (see [3] or here ). The present form of QED cannot explain these experimental data. The same is true with QCD because it is a non-electromagnetic interaction.
    2. An idea called Vector Meson Dominance (VMD) and related ideas aim to explain these data. The primary element of these ideas says that the state of a physical photon is a superposition of a pure electromagnetic state and a state of a massive meson (see [3] or here ).
    3. These explanations are theoretically unacceptable, because they violate the Wigner analysis of the unitary representations of the inhomogeneous Lorentz group. Wigner's work proves that a massive quantum particle (such as a meson) and a massless quantum particle (such as a photon) are completely different objects [4]. (For example, the helicity of a photon has 2 degrees of freedom, whereas the spin=1 of a massive vector meson has 3 degrees of freedom.) Other serious VMD problems are mentioned here.
    4. The present status of the effect of hard photon interaction with nucleons is very unfortunate. Although the photon is a very well-known quantum particle and the nucleons are the best known hadrons, most (if not all) Standard Model textbooks that have been published in recent decades simply ignore the existence of the effect as well as the Standard Model inability to provide a scientifically acceptable explanation for it.
    5. Conclusion: The Standard Model has no explanation for the data of a hard photon interaction with nucleons despite the fact that the pehnomenon is known for more than half a century and it is well inside its domain of validity.

    Exercise: (see item #1 of this text)
    1. Examine the electroweak Lagrangian density that is written in the present (July 31, 2020) Wikipedia item on the electroweak theory here. Due to its complexity, it is written as a sum of 8 sub-Lagrangian densities, where each of which comprises several explicit terms.
    2. Apply the Euler-Lagrange equation (see [2], p. 16) to every quantum function of the Lagrangian density of the previous item and derive the required equations of motion.
    3. Solve these equations for simple cases.
    4. Compare the results with the Dirac equation of the electron.
    5. Consulting the Okham razor principle (see here ), what are your conclusions with respect to the validity and soundness of the relevant theories?

    Remark: This page describes just the tip of the iceberg...

    References:

    [1] G. Aad et al. (ATLAS Collaboration), Phys. Lett., B712, 289 (2012).

    [2] M. E. Peskin and D. V. Schroeder, An Introduction to Quantum Field Theory (Addison-Wesley, Reading Mass, 1995).

    [3] T. H. Bauer, R. D. Spital, D. R. Yennie and F. M. Pipkin, Rev. Mod. Phys., 50, 261 (1978). (See pp. 269, 293).

    [4] S. S. Schweber, An Introduction to Relativistic Quantum Field Theory, (Harper & Row, New York, 1964). (See pp. 44-53.)