Speakable and Unspeakable in Contemporary Physics :Physics Without Sweeping Infinities Under the Rug

It is a wide-spread rumor among the Frontiers of physics, that some time “sweeping under the rug” practice has been quite the norm rather than exception. In other words, the leading paradigms have strong tendency to be hailed as the only game in town. For example, renormalization group theory was hailed as cure in order to solve infinity problem in QED theory. A quote from Richard Feynman goes as follows: “What the three Nobel Prize winners did, in the words of Feynman, was "to get rid of the infinities in the calculations. The infinities are still there, but now they can be skirted around . . . We have designed a method for sweeping them under the rug."[1] And Paul Dirac himself also wrote with similar tune: “Hence 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 any more." I must say that I am very dissatisfied with the situation, because this socalled "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 turns out to be small—not neglecting it just because it is infinitely great and you do not want it!”[2] Similarly, dark matter and dark energy were elevated as plausible way to solve the crisis in prevalent Big Bang cosmology. That is why we choose a theme here: Speakable and Unspeakable in Contemporary Physics, analogous to J.S. Bell’s book.[3] Similarly we observe similar sweeping under the rug practice in the electromagnetic theory development, in particular what is termed as "longitudinal wave."