Discrepancies in the Electroweak Theory

Comments on ‘tHooft’s Advices on

How to Become a Bad Theoretical Physicist

Written by: Eliyahu Comay

G. ‘tHooft has launch a quite original effort aiming to provide a list of advices on how to become a bad theoretical physicist. (See here)

Let us examine the third paragraph of the present version (July 21, 2014) of ‘tHooft’s work. This paragraph says:

Good theorists as well as bad ones all make mistakes. Science advances in spite of people making mistakes. We produce theories, even ones which cannot be entirely correct, and test them in every odd way we can imagine. Eventually, we manage to remove the errors and obtain marvelous new insights. The difference between a good theorist and a bad one is that good theorists are usually the first to detect the shortcomings of their own theories. They are never afraid of discarding a theory if it appears to be beyond repair. While learning about physics as a student, we all have the ambition of making great discoveries, so we soon start constructing our own theories. They are usually wrong, but never mind, we learn from our mistakes.

(I’ve cast two words in bold italic, in order to facilitate the following discussion. E. C.)

The word “usually” means that ‘tHooft agrees that there are some cases where a good theoretical physicists is not the first one who detects his own errors. The word “eventually” means that an undetermined amount of time elapses between the publication of a theoretical error and its correction. Considering these matters, one infers that at every instant some errors still may exist in theoretical physics and that an examination of the correctness of physical theories is an important task. In my opinion, everybody should agree on this conclusion. The rest of this page is dedicated to some issues that pertain to the electroweak theory.

Background

Maxwellian electrodynamics is a theory of two physical entities, electric charge and electromagnetic fields. Here the electric charge takes the form of a 4-vector jμ (the standard notation is used). This 4-vector, which is called 4-current, must satisfy the continuity equation jμ = 0. It is very well known that this requirement is satisfied in the classical theory (see [1], p. 77) and in the quantum theory of a spin-1/2 Dirac electron (see [2], p. 24). In the latter case the 4-current takes the form jμ = eψ̄γμψ. This expression can be derived from the Noether Theorem (see [3], p. 20).

Discrepancies in the Electroweak Theory

The electroweak theory has been constructed more than four decades ago. This theory uses two electrically charged particles denoted W+, W, respectively. The following discrepancies are related to these particles:

1. Unlike the case of the Dirac electron, textbooks presenting the electroweak theory do not show an explicit expression for the 4-current of the W+, W particles.

2. Probably for this reason, people working with modern colliders like the Tevatron and the LHC, use an “effective Lagrangian” as a basis for calculating the Ws electromagnetic interactions (see [4], eq. (1) and [5], eq. (3)). Here the Noether theorem is not used.

3. Charge density is the 0-component of the 4-current. The lack of a consistent expression for the Ws 4-current also means that there is no consistent expression for the density of the Ws. Hence, as far as the Ws are concerned, one can construct neither a Hilbert space nor its associated Fock space.

4. Regarding the lack of these spaces, one wonders how expectation values in general and transition amplitudes in particular can be calculated for a process which involves one of the Ws. Similarly, what is the meaning of operators if there is no vector space to operate upon?

5. And yet another discrepancy shows up. The product of the density and the mass is the T00 component of the energy-momentum tensor of a free motionless particle. This tensor is a factor of the term that stands on the right hand side of the Einstein equation of General Relativity. Therefore, the absence of an acceptable expression for the density of the electroweak W boson means that this theory is inconsistent with General Relativity. For reading another aspect of this issue, click here.

Physicists in general and electroweak experts in particular are kindly invited to comment on the above mentioned discrepancies of the electroweak theory and on their possible implications. In the case of a long text or a text not written in HTML, please send a link pointing to your file. In order to maintain an appropriate discussion people are requested to write down their full name.

References:

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

[2] J. D. Bjorken and S.D. Drell, Relativistic Quantum Mechanics (McGraw-Hill, New York, 1964).

[3] J. D. Bjorken and S.D. Drell, Relativistic Quantum Fields (McGraw-Hill, New York, 1965).

[4] V.M. Abazov et al. (D0 collaboration), Phys. Lett. B718, 451 (2012)

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

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One thought on “Discrepancies in the Electroweak Theory

  1. Considering these discrepancies and others, it can be deduced that the Maxwellian electrodynamics is not applicable to subatomic interactions. Interactions might operate at entirely different mode at the subatomic level.

    Oded Bar-On

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