QED's Inherent Problems

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Introduction

A well known QED problem is relates to the infinities which are obtained from its calculations. The current resolution of this problem is called renormalization. This procedure looks unacceptable because "it seemed illegitimate to do something tantamount to subtracting infinities from infinities to get finite answers" (see Wikipedia). Two eminent QED figures have objected renormalization. P. A. M. Dirac has described it as a procedure of an "illogical character" [1]. He continued and said: "I am inclined to suspect that the renormalization theory is something that will not survive in the future, and that the remarkable agreement between its results and experiment should be looked on as a fluke". A similar approach has been expressed by R. P. Feynman. He has used a more colorful terminology and called renormalization "a dippy process" [2]. Feynman continued and stated: "I suspect that renormalization is not mathematically legitimate". A similar remark can be found in Ryder's textbook [3]: "...the feeling remains that there ought to be a more satisfactory way of doing things." By contrast, no serious physicist has used such expressions with respect to special relativity. It can be concluded that the final word probably has not yet been said on QED.

The need for a mathematically legitimate procedure indicates that other serious problems may undermine QED's self-consistency and that it deserves a further analysis of its structure. Evidently, any debate where some people play the role of the devil's advocate can only enhance our understanding of the debated issue. Unfortunately, an initiative aiming to organize this kind of debate is not included in the agenda of journals of the present establishment. On the contrary, apparently too many people are quite sure that rejecting "dissident" papers is one of their important duties.

The purpose of this page is to show that besides its renormalization problem, QED suffers from other contradictions.


The QED Lagrangian Density

The Lagrangian density is the cornerstone of any quantum field theory [4,5]. Contrary to the common belief, the QED Lagrangian density contains erroneous elements. A clear and short proof of this claim is shown here . This recently published paper concludes that "the well known infinities of QED show that mathematics screams when stumbling upon something which is inherently wrong."


Gauge Transformations

Gauge transformations are legitimate procedures in a classical theory that takes Maxwell equations and the Lorentz force as its cornerstone. This statement is correct because the 4-potential is not directly used in these equations. However, it can be proved that this is not true for electrodynamics that is derived from the variational principle. Here the 4-potential is explicitly used in the Lagrangian density of the system. (The following expressions are written in units where ħ=c=1 and x denotes the four space-time coordinates.) This issue is clearly seen in a quantum theory where the primary gauge function Λ(x) appears as an exponential factor of the wave function ψ(x) (see [5], p. 78).

ψ(x) → exp(ieΛ(x))ψ(x) (1)

Regarding the power series expansion

exp(ieΛ(x))  =  1 + ieΛ(x) + ... (2)

one finds that the first term is a pure number. Hence, all terms of the expansion must be pure numbers. Now, the imaginary unit i is a pure number and, in the units used herein, the electric charge e is also a pure number where e2 1/137. For this reason one concludes that the gauge function Λ(x) must be a dimensionless Lorentz scalar. This outcome denies the ordinary definition of Λ(x) as an arbitrary function of space-time coordinates. For a further discussion click here .


New Data

Muon dependent measurements of the proton's charge radius show a discrepancy of several percents with respect to the corresponding data that have been obtained from electron dependent measurements (see here ). Thus, the QED amazing precision of seven or more decimal digits has deteriorated into just one decimal digit. This evidence indicates that Dirac was probably right when he said that the remarkable agreement between the results of QED's renormalization and experiment should be looked on as a fluke (see above). This experimental discrepancy provides another good reason for a reexamination of the present QED structure.


References:

[1] P. A. M. Dirac, Scientific American, 208, 45, May 1963. (see here .)

[2] R. P. Feynman, QED, The Strange Theory of Light and Matter (Penguin, London, 1990). (See p. 128.)

[3] L. H. Ryder, Quantum Field Theory (Cambridge University Press, Cambridge, 1997). (See p. 390.)

[4] S. Weinberg, The Quantum Theory of Fields, Vol. I, (Cambridge University Press, Cambridge, 1995).

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