Effective quantum field theories and hierarchial reality
Over the last hundred years, there has been a fruitful cross-fertilisation of concepts and techniques between the theory of condensed matter and the quantum theory of elementary particles and fields. Examples include spontaneous symmetry breaking, renormalisation, and BCS theory. Sometimes, these efforts have occurred in parallel and only later did people realise that two different communities were doing essentially the same thing but using different language. Other times, one community adopted ideas or techniques from the other.
Central to condensed matter theory are ideas of emergence, a hierarchy of scales, and effective theories that are valid at a particular scale. Elementary particle theorists such as Steven Weinberg often distinguish themselves as reductionists with different goals and approaches. I only recently became aware that effective field theories have become a big thing in the elementary particle community, and Weinberg has been one of the leaders of this!
There is a helpful article in the CERN Courier, published just a year ago.
Michèle Levi takes a tour through the past, present and future of Effective Field Theory, with applications ranging from LHC physics to cosmology.
The figure below, taken from the article, shows a hierarchy of energy scales and the corresponding effective field theories (EFTs).
n.b. Energy increases from bottom to top. [This may be confusing for condensed matter physicists, as we tend to put the high-energy theories at the bottom].
The standard model is now considered an effective field theory.
For the associated history and philosophy, I found this article helpful. Effective Field Theories, Reductionism and Scientific Explanation, by Stephan Hartmann
The decoupling theorem, proved by Appelquist and Carazzone in 1975, [cited 2,500 times] is central to EFTs and a hierarchy of scales.
In its simplest case, this theorem demonstrates that for two coupled systems with different energy scales m1 and m2 (with m2 > m1) and described by a renormalisable theory, there is always a renormalisation condition according to which the effects of the physics at scale m2 can be effectively included in the theory with the smaller scale m1 by changing the parameters of the corresponding theory. The decoupling theorem implies the existence of an EFT at scale m1 which will, however, cease to be applicable once the energy gets close to m2.
There are two distinct approaches to finding effective theories at a particular scale, referred to as bottom-up and top-down approaches.
Top-down requires one to have a theory at a higher energy scale and then integrate out the high energy degrees of freedom (fields and particles) to find the effective theory for the lower energy scale. This is what Wilson did in his RG approach to critical phenomena. Another example is how string theorists try to derive GR and the Standard Model starting with strings.
Bottom-up can always be done because one does not need to know the higher energy theory. One can often write down the Lagrangian for the EFT based on symmetry considerations and phenomenology. An example is Fermi's theory of beta decay and the weak interactions.
In a previous post, I considered Bei Lok Hu's discussion of these two different routes to developing a quantum theory of gravity.
A major outstanding challenge in the theory of elementary particles and fields is the hierarchy problem: the measured values of some masses and coupling constants are many orders of magnitude different from the "bare" values used in the Lagrangian.
The articles I have read about the role of effective field theories make no mention of the corresponding issues in condensed matter or how emergence is involved. Emergence occurs in systems where there are many interacting components. Here those components are the quantum fields and their components with different momenta/energy. Hence, I would say that emergence is at the heart of big questions in the theory of elementary particles and fields.
"... emergence is at the heart of big questions is the theory of elementary particles and fields ..." Is there a multiverse-HIggs fields that is essential for understanding emergence?
ReplyDelete"The discovery ... of the Higgs boson will mark a watershed in particle physics. In the future, the calendar of particle physics will surely be divided into BH (before Higgs) and AH (after Higgs), with 2012 being year 0. The discovery of the Higgs will signpost the direction that both theoretical and experimental physics will take in the decades to come."
John Ellis, Mary K. Gaillard, Dimitri V. Nanopoulos, "A Historical Profile of the Higgs Boson", 2012, https://arxiv.org/abs/1201.6045 arXiv:1201.6045v1 pages1–22 (quote on p. 13)
So far, I have been unable to convince any of the string theorists that they should carefully study the empirically successful predictions made by Milgrom's MOND over the past 40 years. Are my opinions about MOND cuckoo? Google "lelli mcgaugh sanders scarpa" and "kroupa milgrom wu zhao".
Consider this possibility: String vibrations are approximately confined to 16 copies of the quaternions. There is a multiverse-Higgs field. In any particular alternate universe in the multiverse, the Higgs field is either right-handed or left-handed depending upon the quaternionic spin of the Higgs field. A right-handed Higgs field has quaternionic spin +(i,j,k) and occurs in a predominantly matter universe. A left-handed Higgs field has quaternionic spin –(i,j,k) and occurs in a predominantly antimatter universe. The quaternionic spin of the Higgs field is the reason that paradoxical MOND inertia exists. The explanation of the dark matter phenomenon is paradoxical MOND inertia. The multiverse-Higgs field is what allows Guth's inflation to occur.