Quantum electrodynamics (QED) was invented during the 40’s and 50’s of the previous century, and it is considered as the jewel of particle physics. However, QED is not error free, as several Nobel prize laureates mentioned several times in the past.
Fixing these errors is probably one of the most important missions in particle physics, but it seems that very few (or maybe none) of today’s scientists spend time on these problems. Recently, a new article by Eliyahu Comay was published and it shows new problems in the structure of QED.
One chapter in the book “Science or Fiction?” discusses some of the problems in QED. The chapter title is “What Carries the Electric Force?”, and its text is below. One remark before you read it: the terms “spin” and “parity” were discussed in previous chapters, and you should know that spin (or, more accurately, angular momentum) and parity are conserved in the electromagnetic interactions as well as in the strong interactions.
And now, the chapter from the book:
In the next series of chapters we will discuss the particle, the discovery of which was instrumental in establishing the foundations of quantum theory—namely, the photon. Before we can understand the role of this important particle in nature, and particularly its role in the function of strong forces operating inside nucleons, we will first examine the validity of several preconceptions.
One minor note before we delve into the details: the entire discussion presented in this chapter is not trying to show any flaws in QCD theory. It will, however, enable us in coming chapters to better understand the role of the photon in the strong forces that operate inside neutrons and protons.
The photon is defined by numerous textbooks and websites, like the Hebrew version of Wikipedia (2013), as “an elementary particle, the quantum of light, and all other forms of electromagnetic radiation, and the force carrier for the electromagnetic force….”
The English version is slightly different and I will discuss it later.
This statement, that the photon is the “force carrier for the electromagnetic force,” is actually quite new. Until the mid-twentieth century, the photon and the “electromagnetic field” were two clearly distinct concepts. The photon interacted with electric charges, but no one argued that it was the photon that “carries” the electric force.
We will begin by showing that one cannot simply accept the idea that photons are indeed the force carriers for the electromagnetic force.
Because of Its Spin
The positive charge inside atoms is located in protons that attract electrons in the atomic shell. If photons do carry the electromagnetic force, then the positive center would emit photons that are absorbed by electrons.
Figure 48. The proton and electron inside the hydrogen atom. Were the proton to emit a photon in order to hold the electron, and were the electron to absorb it, the electron’s parity would change concurrently with that of the proton inside the nucleus. This, however, fails to occur.
However, photons are odd, spin 1 particles. When an electron absorbs a photon, it needs to comply with the law of conservation of angular momentum, as the entire atom reverses its parity (this topic is discussed in earlier chapters on spin). When an even atom with even parity electrons absorbs a photon, its parity becomes odd and vice versa. It therefore follows that if the positive center truly emits photons to the electrons in the atomic shell, it means that the parity of those electrons ought to change almost constantly. Instead, we know that parity is a stable property that is maintained by the atom so long as there is no external interaction.
A hydrogen atom in its ground state, for example, has an even-parity electron. The hydrogen atom will remain in this state so long as it is not affected by external factors.
An examination of the nucleus reveals an even greater flaw. I will demonstrate it by analyzing a helium ion whose nucleus holds one electron. If the helium nucleus emits a real photon, then it must change its parity and its angular momentum as well. Moreover, since the ordinary helium nucleus has a zero angular momentum, it must shift to a state where it has an angular momentum of 1.
Each of these changes forces the nucleus to shift into an energetic state much higher than its ground state, as nuclear energy is several orders of magnitude greater than that of electrons inside the atom. This effect rules out the possibility that real photons are involved in the operation of the force that keeps electrons bound to the nucleus.
Therefore, atomic nuclei cannot attract electrons by emitting real photons.
There are other contradictions to the simplistic acceptance of the idea that photons carry electric force that do not necessitate in-depth understanding. For example, let’s examine a free electron at rest. The electron has a charge, and it exerts force on any other charge in the universe. How does it do this? When at rest, it can not send photons in any direction because of the law of conservation of energy. Furthermore, because a free electron does not disappear within a short amount of time, and because it conserves its energy so long as it does not enter an electromagnetic field, it is unclear how it might be able to emit photons capable of wandering freely until they find an electric charge to harass. Some scientists attempt to solve this much more obvious problem by positing a “virtual” photon that is distinguishable from a “real” one.
The English Wikipedia “Photon” article is slightly different from the Hebrew article, as it addresses the concept of “virtual” photons. The thing is, virtual photons are not real photons, and the question of whether virtual particles exist is more philosophical than scientific.
The Feynman Diagrams
Whence, then, comes the idea that photons carry electromagnetic force?
In the 1940s and 1950s something known as field theory was developed. A significant part of that theory was called quantum electrodynamics, or QED. Field theory provided computational tools that afforded unprecedented accuracy when it came to electric forces.
The principal computational tool provided by field theory is called the Feynman diagrams, named after Richard Feynman, who developed them. Some Feynman diagrams include a photon that carries the electric force.
Do the Feynman diagrams imply that the photon indeed carries the electric force? Not exactly. But Feynman used the photon equations to develop his diagrams. At some point as he developed his equations Feynman arrived at unphysical, infinite quantities. He “removed” these infinite quantities, without mathematical justification, in order to arrive at finite quantities. The finite quantities obtained were spectacularly commensurate with experimental findings.
The removal of infinite quantities is known as “renormalization.” Dirac criticized the concept of renormalization by sarcastically arguing that we’re allowed to remove miniscule quantities, but we shouldn’t remove infinite quantities just because we find them uncomfortable. Feynman himself noted in his book that he finds the whole process of renormalization uncomfortable particularly because it succeeded, because it is not mathematically justified, and because the scientific community prefers to be content with this unmathematical process rather than look for a suitably consistent theory.
The transformation of field theory into a consistent theory is perhaps the most important problem in the field of particle physics, despite, as Dirac and Feynman feared, the fact that every scientist is happy with its current formulation and prefers to disregard this inconsistency. What we can say in the meantime is that as long as there isn’t a consistent theory whereby photons carry electric force, arguing that they do would be unjustified, especially when we find serious contradictions to this idea, as mentioned in the beginning of this chapter.
Today we can see what scientists think about the subject, since the rather irksome question of how photons are able to carry electric force is occasionally presented. It is not easy to find two scientists who give the same answer to that question. One can try dividing them into several groups: the first group is composed of physicists who actually believe that a real photon literally carries electromagnetic force; another group includes physicists who endorse the concept of virtual photons; the third group consists of those who do not clearly differentiate between virtual and real particles; and the fourth group considers the wording of “virtual” photon an unfortunate mistake, as the carrying of electromagnetic force shouldn’t be ascribed to particles at all.
Let’s end the discussion here, and agree that a real photon is not a particle that carries electromagnetic force.
 http://profmattstrassler.com/articles-and-posts/particle-physics-basics/virtual-particles-what-are-they/. “The Feynman diagram is actually a calculational tool, not a picture of the physical phenomenon.”
 Helge Kragh, Dirac: A scientific biography, Cambridge University Press 1990, p. 184. “Most physicists are very satisfied with the situation. They say: ‘Quantum electrodynamics is a good theory and we do not have to worry about it anymore.’ I must say that I am very dissatisfied with the situation, because this so-called ‘good theory’ does involve neglecting infinities which appear in its equations, neglecting them in an arbitrary way. This is just not sensible mathematics. Sensible mathematics involves neglecting a quantity when it is small—not neglecting it just because it is infinitely great and you do not want it!”
 Richard P. Feynman, QED, The Strange Theory of Light and Matter, Penguin 1985, p. 128. “But no matter how clever the word [renormalization], it is still what I would call a dippy process! Having to resort to such hocus-pocus has prevented us from proving that the theory of quantum electrodynamics is mathematically self-consistent. It’s surprising that the theory still hasn’t been proved self-consistent one way or the other by now; I suspect that renormalization is not mathematically legitimate.”
 Scientific American, October 9, 2006, Ask the Experts. “Are virtual particles really constantly popping in and out of existence? Or are they merely a mathematical bookkeeping device for quantum mechanics? Gordon Kane, director of the Michigan Center for Theoretical Physics at the University of Michigan at Ann Arbor, provides this answer. Virtual particles are indeed real particles…”
 http://profmattstrassler.com/articles-and-posts/particle-physics-basics/virtual-particles-what-are-they/. “Perhaps unfortunately, this type of disturbance, whose details can vary widely, was given the name ‘virtual particle’ for historical reasons, which makes it sound both more mysterious, and more particle-like, than is necessary…”