Wednesday, September 30, 2015

Trouble with The Core Theory

A sweet New England reader has sent me a copy of Frank Wilczek's new "beautiful" book (thanks so much, Ann!) and I will discuss many ideas from that book when I finish reading it, which won't be too soon.

But I want to spend a few minutes with one isolated proposal of Wilczek's, one that was also endorsed by Sean Carroll. Frank wants to rename "The Standard Model" – a term that was coined by Steven Weinberg who also wrote the final version of its "weak" part – as "The Core Theory". And he wants to "include" the Einstein-Hilbert action to it, too.

Would I agree with that?

The short answer is No. Just to be sure, this is no "radical No". Clearly, if Wilczek had been faster than Weinberg and he had managed to spread the term "The Core Theory" all over the physics community and textbooks, I would have learned that just like all other students and embraced the term in pretty much the same way in which I and we embrace "The Standard Model".

However, right now, we have two proposed names (and organizations of the theories) and we may compare. Even if I forget that I am a conservative and to conserve the existing name may be easier, cheaper, or safer, I still tend to think that "The Standard Model" is a better name than "The Core Theory". The main reasons behind this conclusion are the following five:
  1. Excessive appearance of the word "theory" in our lectures
  2. Inappropriate "universality" of the word "theory"
  3. The misleading impression from the word "core" that we have found the essence unequivocally dictating the structure of the model that makes sense
  4. The impression from both words, "core" and "theory", that the model is complete, canonical, and here to stay – that it's the "core" independently of the random sociological and historical facts; in other words, the pressure of "The Core Theory" to abandon the search for Beyond the Standard Model physics
  5. Incompatibility of the Standard Model with GR that "The Core Theory" – which is a non-renormalizable theory – tries to completely hide
We study theories, a theory, and theories of theories related to theories with theories

First, I love theories – a sentiment that shouldn't be surprising for a theoretical physicist. Theories are cool and smart and wise. They're the right way to organize the important truths. Nevertheless, I do think that we use the word "theory" way too often.

Have you ever given a talk about the relationships between important ideas in the 20th century physics? And if you have, have you counted how many times you were forced to use the word "theory"? Quantum field theory has to be reconciled with the general theory of relativity while the latter has arisen from the special theory of relativity. And the only consistent reconciliation is string theory. But Einstein also found the theory of the Brownian motion and the photoelectric effect.

The word "theory" is and sounds pretty technical and we may improve the prose. "Special relativity" and "general relativity" are sometimes considered "officially incorrect" terms. But they're great sequences of words helping you to reduce the repetition of the word "theory" in your talks, to shorten them. It's great that the quantum theory – something that perhaps Max Planck initiated in 1900 when he explained the black-body curve by the light quanta – morphed into quantum mechanics. Quantum mechanics is also a "theory" ("mechanics" stands either for "men repairing machines" or "mechanical theory" or "the umbrella organization that represents all the shared interests of the ### mechanical theories") but it has this cool name that avoids the word "theory".

Also, you may replace "theories of particular things" by "coherent explanations of particular things", and do similar things. When you're finished, the repetition of the word "theory" decreases to tolerable levels. "The Standard Model" is an important part of this beneficial process. It's an important set of equations that was named "The Standard Model". That's why the discussion of the last 50 years in theoretical physics keeps the repetition of the word "theory" at levels that people don't find too awkward.

The word "model" suggests that some choices of "fashion" have been made, and it's right for the Standard Model

My second point is concerned with the universality of the word "theory" or its tendency to be an "umbrella term" that may cover many particular versions of the ideas. The word "model" is a particular version of the idea.

Now, quantum field theory is a "theory" in this sense because it contains some general concepts, methods, and insights. But they may be used in various ways – you may construct different "particular" quantum field theories. If you want to focus on those, you may call them "models". The models differ from each other just like particular female models or supermodels do. All of them are basically the same (humans with breasts) and performing the same tasks (to dress, undress, smile, and walk) but if you look carefully, they just differ – by the hair color, size of breasts, IQ (you're rarely exposed to that unnecessary and unusual feature), and other things.

Needless to say, the usage of the word "theory" and "model" isn't a rigorous science. They overlap, the fuzzy boundaries depend on one's habits, taste, and background, among other things. But there is this "general difference" between the structures we imagine lurking behind the words "theory" and "model". A "model" is more specific.

Sometimes, when we want to emphasize the non-specific character of a "theory", we call it a "framework" instead. So quantum field theory in the general sense, in the sense of a subject or course, may be said to be a theory; but you may also say it is a "framework". The word "framework" is supposed to cover even an greater collection and diversity of cases, to be even less specific, and to require an even greater amount of "detailed information" before you use the framework to derive something about a particular observation. The details are so "unspecified" when you talk about a framework that you may even claim that a "framework" is close to the sociological category of "training" or "occupation". One learns certain skills to work on a "framework" but he may quickly learn some details and apply her skills in many different ways. (For example, the supermodel may walk to the right but she may also walk to the left.)

String theory is a single unified theory – just like a particular quantum field theory, including the Standard Model. But on the other hand, it is a single theory that has so many solutions – and so many descriptions or methods to approach them – that whenever we talk about its consequences for experiments, it's as non-specific as the quantum field theory framework. So we sometimes say that even string theory is a "framework" even though it is a single well-defined robust theory.

I have made it clear that I do consider The Standard Model to be very specific – thanks to its detailed and seemingly arbitrary choice of the gauge group, representations for the fermions, three generations etc. That's why the word "model" sounds more appropriate than the word "theory" to me.

The Standard Model is a rather messy beast and the name "The Standard Model" conveys this point well. The messiness is also the reason why the T-shirts don't look particular beautiful or inspiring. (And the formula for the effective action on the T-shirt is still just a rough schematic sketch, anyway.)

The contrived features of the Standard Model haven't been "explained" yet

My third point is almost the same but it is focused on the word "core" rather than the word "theory". The problem is that the word "core" sounds too unique, too. When you get to the core of the things, you should better know why you made the choices that you have made and why you didn't choose the structure differently. The Earth has a core. It's some ball at the center. Using arguments involving either gravity or linguistics combined with tautologies, we may explain why the most central part of the Earth – the "core" – is located near the center of the planet. ;-)

It is not really the case of the Standard Model. We don't really know why the gauge group has to be what it is, why the matter comes in the Standard Model-prescribed representations of the gauge group, why there are three generations of fermions, and why all the parameters are what they are. The Standard Model is an effective theory approximating something deeper – it is not really the "core", the ultimate explanation that answers the "Why" questions, yet. If we were supposed to pick a quantum field theory that seems to be at the "core", it would probably be a simpler one.

Search for new physics and explanations shouldn't be discouraged

I clumped these points – the criticism of the word "core" and the word "theory" that look too complete – as my fourth point which has a new concern, too. The concern is that a too "definitive" name such as "The Core Theory" discourages one from asking questions about physics beyond the model. Also, it makes some people unprepared for the possibility that the model will have to be expanded. "The Core Theory" is some final thing that can't be adjusted, can it?

But the Standard Model may very well need to be extended or adjusted. Maybe very soon, we will discover the W'-bosons coupled to the right-handed quarks and we will have to replace the chiral Standard Model with the left-right-symmetric models where the difference between the left-handed and right-handed fermions basically emerges as some spontaneous symmetry breaking.

If that happens, or if supersymmetry is discovered, or if any need for BSM physics is established, are we supposed to modify our definition of "The Core Theory"? That would be bad because the definition of scientific terms would evolve with time – and you would always need some "date of publication" or "date of the talk" to understand what someone is actually saying. Or are we supposed to admit that the model we have been using wasn't the complete "core theory" and must be superseded by "The Even More Core Theory"? And then by "The Super Duper Hardcore Theory"? And so on? Has Frank Wilczek prepared the new names or is he simply assuming that nothing like that will ever be needed?

Something like that will almost certainly be needed, for example because there probably exist new particles that manifest themselves as the dark matter. They may be axions, they may be WIMPs, but it's more likely than not that they're manifestations of BSM (beyond the Standard Model) physics. Even if you don't agree that it's "more likely than not", physicists think that the probability that the empirical data from cosmology force us to believe in some BSM physics is substantial. So the terminology shouldn't be built in a way that seems to assume that this extension of the Standard Model can't ever occur.

Frank would actually have to overcome a much greater ensemble of specific terminological hurdles for his proposal to be viable. The problem is that "The Standard Model" is a term that already has generalizations in the phenomenological literature such as the MSSM, "The Minimum Supersymmetric Standard Model". Would he ban the research of it? Or NMSSM and many others? Or would he rename them as "The Minimum Supersymmetric Core Theory"? Any variation of this sort sounds doubly contrived because "The Core Theory" implicitly indicates some uniqueness. But when you look at the models that people study, "The Standard Model" isn't really unique. And I stress that both "The Standard Model" and the MSSM may be right, and so can many other models (in each model, the SM, MSSM, or NMSSM etc., only a small part of the parameter space remains compatible with the experiments). The non-uniqueness of the "right QFT-based explanation" of the available experimental data is a fact. So any term for a particular model – however minimal – that sounds too unique is counterproductive.

"The Standard Model" does convey the fact that it's "the" model that particle physicists have in mind most of the time. At the same time, it is a modest, low-key enough "technocratic" name and that's how things should be. Relatively to the general ideas of quantum field theory, the Standard Model doesn't represent any significant conceptual advance or breakthrough. Relatively to quantum field theory as the framework, the achievements of the Standard Model have been all about the identification of the right fields (including the previously unknown Yang-Mills gauge fields) and the other technical details. Thanks to Nature's generosity, this right combination happened to be spectacularly successful in describing the observed data. But no truly bombshell advance has taken place at the theoretical or conceptual level since the discovery of QFT and its methods which is why it wouldn't be right to use a much more "spectacular" or "explosive" name for the "Standard Model" than the name we have for "quantum field theory".

Inconsistency of QFT and gravity

The final topic is about Wilczek's proposal to include both general relativity and the Standard Model to the concept of "The Core Theory". Again, I am no radical here. If people had been doing that, and they could have, we would get and I would get used to this treatment, too.

But I think that at the end, the separation of the theories seems much more appropriate to me.

Don't get me wrong. General relativity and the Standard Model may be – and constantly are being – "unified" in pragmatic ways that allow us to apply the insights from both "parts" and derive some experimentally verifiable conclusions. There are lots of people who "heavily overestimate" how much incompatible GR and QFT are. There are people who believe that you should doubt the existence of gravitons and other elementary things that follow from the union of GR and QFT.

Well, once you become a competent theorist, you shouldn't have any serious doubts about the existence of the gravitons. Einstein's theory may be added to a large extent. When treated as a perturbative quantum field theory framework to compute Green's functions or scattering amplitudes, the "only" problem of this combination is that the Einstein-Hilbert action has to be supplemented with infinitely many counterterms to subtract the infinitely many types of divergences (infinities). Such a non-renormalizable theory has no predictive power for the phenomena at the characteristic scale of quantum gravity, the Planck scale.

Because of the general relativistic component, "The Core Theory" is a non-renormalizable theory. Before you could use it to make quantitative predictions near the Planck scale, you would need to make infinitely many measurements to find the values of the infinitely many parameters of the theory. At energy scales well beneath the Planck scale, you may want to be ever more accurate but for any finite accuracy, you will only need to measure a finite number of parameters (coefficients of the terms in the action with low enough dimensions). But to have the accuracy to "all orders" or good enough accuracy at the Planck scale, you simply need to find out infinitely many parameters.

This sickness – non-renormalizability – of "The Core Theory" is unfortunate because the theory was free of this sickness – it was healthy – before "someone" added the small final piece, the Einstein-Hilbert action. So Wilczek's addition of the Einstein-Hilbert action made (what used to be) the Standard Model seriously sick. And that's too bad because the renormalizability of the Standard Model – or any other renormalizable theory – is a great virtue of the theory.

It is a virtue that tells us that we should take the "quantum character" of those quantum field theories very seriously. The electron's magnetic moment is being calculated as well as experimentally verified up to five-loop diagrams. The renormalizability of these quantum field theories is a great victory and source of pride about them. Among other things, a proof of the renormalizability of the gauge theories is also what has earned the Nobel prize for Gerard 't Hooft.

So I find it strange, wasteful, and confusing to declare that the renormalizability is no big deal. And by combining the renormalizable parts of the action (The Standard Model) with the non-renormalizable Einstein-Hilbert action (general relativity) on his T-shirt, Frank Wilczek is certainly implicitly saying that the (non-)renormalizability is no big deal. Well, it is one.

When one is careful about the precision one needs to achieve and the different powers of the coupling constant and Newton's constant that are allowed in the terms etc. (and yes, Newton's constant has basically appeared in the leading order only – in all QFT-like perturbative calculations you may imagine), one can use the combination of the Standard Model and general relativity in most of the practical applications. But theoretically and especially pedagogically, we're mixing apples with oranges. A renormalizable quantum field theory is a great achievement of science and to give it up by adding non-renormalizable terms is a great sacrifice. It is wasteful or suicidal. It would make the students' questions about the consistency of "The Core Theory" much more confusing than they are today – and they are already confusing. And yes, quite generally, I think that a linguistic trick designed to make you believe that you may just unify GR and QFT and avoid worries would be just another demagogic recipe to allow the people deny the need for string theory.

That's why it's better if the theories are sold and presented separately and if the student or any physicist is encouraged to realize that by combining these two theories, one enters rather dangerous waters.

These were my reasons why I prefer "The Standard Model" – a term for a specific non-gravitational quantum field theory – over "The Core Theory" – a proposed term for the same theory into which Einstein's general relativity is added while one pretends that everything is fine.

Maybe Frank wanted to produce some T-shirts with the content that would be associated with him. In that case, I would recommend T-shirts with Frank Wilczek himself as a better alternative. And if he wanted to keep the theme of merging both pillars, he could sell T-shirts with both Frank Wilczek and Krusty, a comedian that an ex-colleague of mine claimed to be Frank's lookalike. (I am innocent, of course, and as thousands of TRF readers may testify, I would never promote such a secret funny meme in front of another person LOL.)

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