Naturalness Is Dead. Long Alive Naturalness.

I was elated when I saw that Gian Francesco Giudice announced the “Dawn of the Post-Naturalness Era,” every bit the championship of his recent newspaper promises. The craze inward particle physics, I thought, powerfulness finally come upward to an end; information brought argue dorsum to footing afterward all.

But disillusionment followed swiftly when I read the paper.

Gian Francesco Giudice is a theoretical physicist at CERN. He is maybe non the most prominent fellow member of his species, but he has been extremely influential inward establishing “naturalness” every bit a criterion to select worthwhile theories of particle physics. Together amongst Riccardo Barbieri, Giudice wrote i of the pioneering papers on how to quantify naturalness, thereby significantly contributing to the belief that it is a scientific criterion. To engagement the newspaper has been cited to a greater extent than than thou times.

Giudice was also the get-go somebody I interviewed for my upcoming book well-nigh the relevance of arguments from beauty inward particle physics. It became clear to me quickly, however, that he does non remember naturalness is an declaration from beauty. Instead, Giudice, similar many inward the field, believes the criterion is mathematically well-defined. When I saw his novel paper, I hoped he’d come upward some to run across the mistake. But I was overly optimistic.

As Giudice makes pretty clear inward the paper, he silent thinks that “naturalness is a well-defined concept.” I lead maintain previously explained why that is wrong, or rather why, if you lot brand naturalness well-defined, it becomes meaningless. Influenza A virus subtype H5N1 quick walk through the declaration goes every bit follows.

Naturalness inward quantum acre theories – ie, theories of the type of the measure model of particle physics – way that a theory at depression energies does non sensitively depend on the alternative of parameters at high energies. I oft withdraw heed people say this way that “the high-energy physics decouples.” But complaint that changing the parameters of a theory is non a physical process. The parameters are whatever they are.

The processes that are physically possible at high energies decouple whenever effective acre theories work, pretty much past times Definition of what it way to lead maintain an effective theory. But this is non the decoupling that naturalness relies on. To quantify naturalness you lot motion some betwixt theories inward an abstract theory space. This is rattling similar to moving some inward the landscape of the multiverse. Indeed, it is belike non a coincidence that both ideas became pop some the same time, inward the mid 1990s.

If you lot straight off desire to quantify how sensitively a theory at depression issue energy depends on the alternative of parameters at high energies, you lot get-go lead maintain to define the probability for making such choices. This way you lot demand a probability distribution on theory space. Yes, it’s the exact same work you lot also lead maintain for inflation too inward the multiverse.

In most papers on naturalness, however, the probability distribution is left unspecified which implicitly way i chooses a uniform distribution over an interval of well-nigh length 1. The typical justification for this is that in i trial you lot factor out all dimensionful parameters, you lot should solely lead maintain numbers of social club 1 left. It is amongst this supposition that naturalness becomes meaningless because you lot lead maintain straight off simply postulated that numbers of social club 1 are improve than other numbers.

You wanted to avoid arbitrary choices, but inward the destination you lot had to brand an arbitrary choice. This turns the whole thought advert absurdum.

That you lot lead maintain to hand-select a probability distribution to brand naturalness well-defined used to live well-known. One of the early on papers on the theme clearly states

“The “theoretical license” at one’s discretion when making this alternative [for the probability distribution] necessarily introduces an chemical factor of arbitrariness to the construction.” 

Anderson too Castano, Phys. Lett. B 347:300-308 (1995)

Giudice also mentions “statistical comparisons” on theory space, too thence I am sure he is aware of the demand to define the distribution. He also writes, however, that “naturalness is an inescapable resultant of the ingredients by too large used to build effective acre theories.” But of course of pedagogy it is not. If it was, why larn inward an additional requirement?

(At this indicate unremarkably someone starts quoting the decoupling theorem. In illustration you lot are that somebody permit me say that a) no i has used mass-dependent regularization schemes since the 1980s for skilful reasons, too b) non solely is it questionable to assume perturbative renormalizability, nosotros genuinely know that gravity isn’t perturbatively renormalizable. In other words, it’s an irrelevant objection, too thence delight permit me move on.)

In his paper, Giudice farther claims that “naturalness has been a skilful guiding principle” which is a foreign affair to say well-nigh a regulation that has led to simply i successful prediction but at to the lowest degree 3 failed predictions, to a greater extent than if you lot count other numerical coincidences that physicists obsess well-nigh similar the WIMP miracle or estimate coupling unification. The tale of the “good guiding principle” is i of the peculiar myths that gets passed some inward communities until everyone believes it.

Having said that, Giudice’s newspaper also contains some skilful points. He suggests, for example, that the role of symmetry principles inward the foundations of physics powerfulness lead maintain outlasted its use. Symmetries powerfulness just live emergent at depression energies. This is a fairly quondam thought which goes dorsum at to the lowest degree to the 1980s, but it’s silent considered outlandish past times most particle physicists. (I verbalize over it inward my book, too.)

Giudice furthermore points out that inward illustration your high issue energy physics mixes amongst the depression issue energy physics (commonly referred to every bit “UV/IR mixing”) it’s non clear what naturalness fifty-fifty means. Since this mixing is believed to live a mutual characteristic of non-commutative geometries too quite mayhap quantum gravity inward general, I lead maintain picked people’s brains on this for some years. But I solely got shoulder shrugs, too I am none the wiser today. Giudice inward his newspaper also doesn’t lead maintain much to say well-nigh the consequences other than that it is “a large source of confusion,” on which I totally agree.

But the determination that Giudice comes to at the destination of his newspaper seems to live the exact contrary of mine.

I believe what is needed for progress inward the foundations of physics is to a greater extent than mathematical rigor. Obsessing well-nigh ill-defined criteria similar naturalness that don’t fifty-fifty brand skilful working hypotheses isn’t helpful. And it would serve particle physicists good to position their previous mistakes inward social club to avoid repeating them. I dearly hope they volition non just supplant i beauty-criterion past times another.

Giudice on the other mitt thinks that “we demand pure unbridled speculation, driven past times imagination too vision.” Which sounds great, except that theoretical particle physics has non just suffered from a dearth of speculation. Instead, it has suffered from a lack of audio logic.

Be that every bit it may, I found the newspaper insightful inward many regards. I sure concur that this is a fourth dimension of crisis but that this is also an chance for alter to the better. Giudice’s newspaper is rattling timely. It is also simply moderately technical, too thence I encourage you lot to give it a read yourself.