Editing Renormalization (section)

== Attitudes and interpretation ==
The early formulators of QED and other quantum field theories were, as a rule, dissatisfied with this state of affairs. It seemed illegitimate to do something tantamount to subtracting infinities from infinities to get finite answers.

Dyson argued that these infinities are of a basic nature and cannot be eliminated by any formal mathematical procedures, such as the renormalization method.<ref>{{cite journal | last=Dyson | first=F. J. | title=Divergence of Perturbation Theory in Quantum Electrodynamics | journal=Physical Review | publisher=American Physical Society (APS) | volume=85 | issue=4 | date=1952-02-15 | issn=0031-899X | doi=10.1103/physrev.85.631 | pages=631–632| bibcode=1952PhRv...85..631D }}</ref><ref>{{cite journal | last=Stern | first=A. W. | title=Space, Field, and Ether in Contemporary Physics | journal=Science | publisher=American Association for the Advancement of Science (AAAS) | volume=116 | issue=3019 | date=1952-11-07 | issn=0036-8075 | doi=10.1126/science.116.3019.493 | pages=493–496| pmid=17801299 | bibcode=1952Sci...116..493S }}</ref>

Dirac's criticism was the most persistent.<ref>P.A.M. Dirac, "The Evolution of the Physicist's Picture of Nature", in Scientific American, May 1963, p.&nbsp;53.</ref> As late as 1975, he was saying:<ref>Kragh, Helge; ''Dirac: A scientific biography'', CUP 1990, p.&nbsp;184</ref>
{{bq|text=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 so-called 'good theory' does involve neglecting infinities which appear in its equations, ignoring them in an arbitrary way. This is just not sensible mathematics. Sensible mathematics involves disregarding a quantity when it is small – not neglecting it just because it is infinitely great and you do not want it!}}

Another important critic was Feynman. Despite his crucial role in the development of quantum electrodynamics, he wrote the following in 1985:<ref>Feynman, Richard P. ''[[QED: The Strange Theory of Light and Matter]]''.  Princeton: Princeton University Press, 1985, p.&nbsp;128. The quoted passage is [https://books.google.com/books?id=2o2JfTDiA40C&pg=PA128 available here] through [[Google Books]] (2014 electronic version of 2006 reprint of 1985 first printing).</ref>
{{bq|text=The shell game that we play to find ''n'' and ''j'' is technically called 'renormalization'. But no matter how clever the word, 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.}}

Feynman was concerned that all field theories known in the 1960s had the property that the interactions become infinitely strong at short enough distance scales. This property called a [[Landau pole]], made it plausible that quantum field theories were all inconsistent. In 1974, [[David Gross]], [[Hugh David Politzer]] and [[Frank Wilczek]] showed that another quantum field theory, quantum chromodynamics, does not have a Landau pole. Feynman, along with most others, accepted that quantum chromodynamics was a fully consistent theory.{{Citation needed|date=December 2009}}

The general unease was almost universal in texts up to the 1970s and 1980s. Beginning in the 1970s, however, inspired by work on the renormalization group and effective field theory, and despite the fact that Dirac and various others—all of whom belonged to the older generation—never withdrew their criticisms, attitudes began to change, especially among younger theorists. [[Kenneth G. Wilson]] and others demonstrated that the renormalization group is useful in [[statistical mechanics|statistical]] field theory applied to [[condensed matter physics]], where it provides important insights into the behavior of [[phase transition]]s. In condensed matter physics, a ''physical'' short-distance regulator exists: [[matter]] ceases to be continuous on the scale of [[atom]]s. Short-distance divergences in condensed matter physics do not present a philosophical problem since the field theory is only an effective, smoothed-out representation of the behavior of matter anyway; there are no infinities since the cutoff is always finite, and it makes perfect sense that the bare quantities are cutoff-dependent.

If quantum field theory holds all the way down past the [[Planck length]] (where it might yield to [[string theory]], [[causal set theory]] or something different), then there may be no real problem with short-distance divergences in [[particle physics]] either; ''all'' field theories could simply be effective field theories. In a sense, this approach echoes the older attitude that the divergences in quantum field theory speak of human ignorance about the workings of nature, but also acknowledges that this ignorance can be quantified and that the resulting effective theories remain useful.

Be that as it may, [[Abdus Salam]]'s remark<ref>{{cite journal | last1=Isham | first1=C. J. | last2=Salam | first2=Abdus | last3=Strathdee | first3=J. | title=Infinity Suppression in Gravity-Modified Electrodynamics. II | journal=Physical Review D | publisher=American Physical Society (APS) | volume=5 | issue=10 | date=1972-05-15 | issn=0556-2821 | doi=10.1103/physrevd.5.2548 | pages=2548–2565| bibcode=1972PhRvD...5.2548I }}</ref> in 1972 seems still relevant
{{bq|text=Field-theoretic infinities – first encountered in Lorentz's computation of electron self-mass – have persisted in classical electrodynamics for seventy and in quantum electrodynamics for some thirty-five years. These long years of frustration have left in the subject a curious affection for the infinities and a passionate belief that they are an inevitable part of nature; so much so that even the suggestion of a hope that they may, after all, be circumvented — and finite values for the renormalization constants computed – is considered irrational. Compare [[Bertrand Russell|Russell]]'s postscript to the third volume of his autobiography  ''The Final Years, 1944–1969'' (George Allen and Unwin, Ltd., London 1969),<ref>Russell, Bertrand. ''[https://books.google.com/books?id=6XmrPgAACAAJ The Autobiography of Bertrand Russell: The Final Years, 1944-1969]'' (Bantam Books, 1970)</ref> p.&nbsp;221: {{bq|style=font-size:inherit;|text=In the modern world, if communities are unhappy, it is often because they have ignorances, habits, beliefs, and passions, which are dearer to them than happiness or even life. I find many men in our dangerous age who seem to be in love with misery and death, and who grow angry when hopes are suggested to them. They think hope is irrational and that, in sitting down to lazy despair, they are merely facing facts.}}}}

In quantum field theory, the value of a physical constant, in general, depends on the scale that one chooses as the renormalization point, and it becomes very interesting to examine the renormalization group running of physical constants under changes in the energy scale.  The coupling constants in the Standard Model of particle physics vary in different ways with increasing energy scale: the coupling of quantum chromodynamics and the weak isospin coupling of the [[electroweak force]] tend to decrease, and the weak hypercharge coupling of the electroweak force tends to increase.  At the colossal energy scale of 10<sup>15</sup> [[GeV]] (far beyond the reach of our current [[particle accelerator]]s), they all become approximately the same size (Grotz and Klapdor 1990, p.&nbsp;254), a major motivation for speculations about [[grand unified theory]].  Instead of being only a worrisome problem, renormalization has become an important theoretical tool for studying the behavior of field theories in different regimes.

If a theory featuring renormalization (e.g. QED) can only be sensibly interpreted as an effective field theory, i.e. as an approximation reflecting human ignorance about the workings of nature, then the problem remains of discovering a more accurate theory that does not have these renormalization problems.  As [[Lewis Ryder]] has put it, "In the Quantum Theory, these [classical] divergences do not disappear; on the contrary, they appear to get worse.  And despite the comparative success of renormalisation theory, the feeling remains that there ought to be a more satisfactory way of doing things."<ref>Ryder, Lewis. ''[https://books.google.com/books?id=L9YhYS7gcXAC&dq=%22Quantum+Field+Theory%22+and+Ryder&pg=PA390 Quantum Field Theory]'', page 390 (Cambridge University Press 1996).</ref>