Friday, January 29, 2021

String Theory Is Still Vaporware

String Theory has many problems. 

It has six (or in some accounts seven) space-time dimensions too many. It predicts lots of new supersymmetric particles and forces (even without adding in gravity) that we haven't observed (experimental exclusions for such particles were reviewed at this post). It needs to explain why we don't observe proton decay. It predicts a scalar-tensor theory of gravity that isn't observed. It is happiest in an "anti-deSitter" universe which is roughly equivalent to a negative cosmological constant when the measured value of the cosmological constant of General Relativity is positive. The physics journalist for Forbes magazine recaps these issues.

Ethan Siegel has an excellent piece on the basic problem with string theory (to the extent it’s well-defined, it has too large a (super)symmetry group and too many dimensions, no explanation for how to recover 4 space-time dimensions and observed symmetry groups).
Here’s why the hope of String Theory, when you get right down to it, is nothing more than a broken box of dreams.

From Not Even Wrong

[T]here are a lot of symmetries that you could imagine would be respected, but simply aren’t. You could imagine that the three forces of the Standard Model would unify into a single one at high energies in some sort of grand unification. You could imagine that for every fermion, there would be a corresponding boson, as in supersymmetry. And you can imagine that, at the highest energies of all, that even gravity gets unified with the other forces in a so-called “theory of everything.”

That’s the brilliant, beautiful, and compelling idea at the core of String Theory. It’s also has absolutely no experimental or observational evidence in favor of it at all. . . .  
Many ideas — such as grand unification and supersymmetry — would involve adding new particles and interactions, but would also lead to experimental consequences like proton decay or the presence of additional particles or decay pathways not seen at colliders. The fact that these predictions haven’t panned out helps us place constraints on both of these ideas. 

String theory, though, goes many steps farther than either grand unification or what we know as supersymmetry does.

For grand unification, the idea is to take the three forces in the Standard Model and embed them into a larger, more symmetric structure. Instead of the particles we know with the interactions we know — with multiple disjoint frameworks corresponding to each of the forces — grand unification tries to fit the Standard Model inside a larger structure.

This might just sound like words to you, but the group theory representation of the Standard Model is SU(3) × SU(2) × U(1), where the SU(3) is the color (strong force) part, the SU(2) is the weak (left-handed) part, and the U(1) is the electromagnetic part. If you want to unify these forces into a larger framework, you’ll need a bigger group.

You can take the route of Georgi-Glashow [SU(5)] unification, which predicts new, super-heavy bosons that couple to both quarks and leptons simultaneously. You can take the route of Pati-Salam [SU(4) × SU(2) × SU(2)] unification, which adds in the right-handed particles, making the Universe left-right symmetric instead of preferring a left-handed neutrino. Or you can go even larger: to SU(6), SO(10), or still larger groups, so long as they contain the Standard Model within them.

The problem, of course, is that the larger you go, the more stuff there is to get rid of, and the more explaining there is to do if we want to understand why these extra components to reality don’t show themselves, either directly or indirectly, in our experiments, measurements, and observations of the Universe. The proton doesn’t decay, so either the simplest model of grand unification is wrong, or you have to pick a more complicated model and find a way to evade the constraints that rule out the simpler models.

If you want to talk about unification and group theory in the context of String Theory, however, your group suddenly has to become enormous! You can fit it into one of the SO groups, but only if you go all the way up to SO(32). You can fit it into two of the exceptional groups crossed together — E(8) × E(8) — but that’s enormous, as each E(8) contains and is larger than SU(8), mathematically. This isn’t to say it’s impossible that String Theory is correct, but that these large groups are enormous, like a block of uncut marble, and we want to get just a tiny, perfect statuette (our Standard Model, and nothing else) out of it.

Similarly, there’s an analogous problem that arises with supersymmetry. Typically, the supersymmetry you hear about involves superpartner particles for every particle in existence in the Standard Model, which is an example of a supersymmetric Yang-Mills field theory where N=1. The biggest problem is that there should be additional particles that show up at the energy scales that reveal the heaviest Standard Model particles. There should be a second Higgs, at least, below 1,000 GeV. There should be a light, stable particle, but we haven’t observed it yet. Even without String Theory, there are many strikes against N=1 supersymmetry.

The Standard Model, without supersymmetry, is simply the N=0 case. But if we want String Theory to be correct, we need to make nature even more symmetric than standard supersymmetry predicts: String Theory contains a gauge theory known as N=4 supersymmetric Yang-Mills theory. There’s even more stuff to hand-wave away if we want String Theory to be correct, and it all has to disappear to not conflict with the observations we’ve already made of the Universe we have.

But one of the biggest challenges for String Theory is something that’s often touted as it’s big success: the incorporation of gravity. It’s true that String Theory does, in a sense, allow gravity to be merged with the other three forces into the same framework. But in the framework of String Theory, when you ask, “what is my theory of gravity,” you don’t get the answer that Einstein tells us is correct: a four-dimensional tensor theory of gravity. . . . 

So what does String Theory give you? Unfortunately, it doesn’t give you a four-dimensional tensor theory of gravity, but rather a 10-dimensional scalar-tensor theory of gravity. Somehow, you have to get rid of the scalar part, and also get rid of six extra (spatial) dimensions.

We had, as proposed 60 years ago, an alternative to Einstein’s General Relativity that did incorporate a scalar as well: Brans-Dicke gravity. According to Einstein’s original theory, General Relativity was needed to explain the orbit of Mercury, and why its perihelion (where it came closest to the Sun) precessed at the rate that it did. We observed a total precession of ~5600 arc-seconds per century, where ~5025 were due to the precession of the equinoxes and ~532 were due to the other planets. Einstein’s General Relativity predicted the other ~43, and that was the slam-dunk prediction he finally made in 1915 that catapulted the eclipse expedition into infamy. The 1919 revelation that light bent starlight was the ultimate confirmation of our new theory of gravity.

But by the late 1950s, some observations of the Sun had indicated that it wasn’t spherical, but rather was compressed along its poles into an oblate spheroid. If that were the case, Brans and Dicke argued, then that observed amount of departure from a perfect sphere would create an additional 5 arc-seconds of precession per century that differed from Einstein’s predictions. How to fix it? Add in a scalar component to the theory, and a new parameter: ω, the Brans-Dicke coupling constant. If ω was about 5, everything would still turn out right.

Of course, the Sun actually is a perfect sphere to a much better degree than even the Earth, and those observations were incorrect. Given the modern constraints that we have, we now know that ω must be greater than about 1000, where the limit as ω → ∞ gives you back standard General Relativity. For String Theory to be correct, we have to “break” this 10 dimensional Brans-Dicke theory down to a four dimensional Einsteinian theory, which means getting rid of six dimensions and this pesky scalar term and the coupling, ω, all of which must go away.

What all of this means is that if String Theory is correct, we have to start with a Universe that’s highly symmetric and very unlike the Universe we have today. This Universe, at some early time at very high energies, had 10 dimensions to it, had a scalar gravity component in addition to the tensor component, was unified into some very large group like SO(32) or E(8) × E(8), and was described by a maximally supersymmetric (N = 4) Yang-Mills theory.

If String Theory is correct, then somehow — and nobody knows how — this ultra-symmetric state broke, and it broke incredibly badly. Six of the dimensions disappeared, and the scalar gravity component stopped mattering. The large, unified group broke very badly, leaving only our relatively tiny Standard Model, SU(3) × SU(2) × U(1), behind. And that supersymmetric Yang-Mills Theory broke so badly that we don’t see any evidence for a single supersymmetric particle today: just the regular Standard Model. . . . 

It may be interesting and promising, but until we can solve String Theory in a meaningful way to get the Universe we observe out of it, we have to admit to ourselves what String Theory truly is: a large, unbroken box that must somehow crumble in this particular, intricate fashion, to recover the Universe we observe. Until we understand how this occurs, String Theory will only remain a speculative dream.

There are additional problems that aren't discussed in the article. 

One is the fact that we live in a universe with deSitter rather than anti-deSitter topology. Another is the fact that there are myriad possible versions called vacua, the vast majority of which have an anti-deSitter topology which are called the "swampland" because most of them are starkly incompatible with observed reality.

Another is the fact that experimental evidence has established that supersymmetry, which is a necessary sub-component of string theory, was conceived to solve a problem that we now know that it doesn't solve in the way that it was intended to, called the "hierarchy problem" because even if supersymmetric particles and extra Higgs bosons exist, the Large Hadron Collider has established that they are too heavy to solve the "problem" that they were devised to solve.

There may be glimmers of useful mathematical or physical insight that one can gain from studying it, but it is along the lines of the insights into English grammar and vocabulary that you get from studying French for a year or two, that has no meaningful connection to the real world and doesn't allow you to do anything worthwhile.

But in the end analysis, there is a substantial and growing faction of the fundamental physics community, including both professional physicists and educated laypeople like myself, who have concluded that String Theory and Supersymmetry are both dead ends that have wasted immense amounts of time and resources of a lot of very smart people.


neo said...

So what do you propose instead as the way forward to QG and TOE...LQG?

neo said...

btw my intuition is that QM is not fundamental, and that it leads to incorrect predictions inside a black hole, in that time and space are the same thing, and QM splitting time from space only works in weak gravity.

so in effect there is no QG, because QM is not fundamental. QM is an approximation in weak gravity like newtonian physics

andrew said...

I'm not convinced that there is a GUT or a TOE out there. SM + QG seems realistic. In general, I think that ideas of unification have to hew closer to the SM. I don't, e.g., think that there are right handed neutrinos out there (a very common SM extension), nor do I think that there is more than one Higgs boson (another very common SM extension), nor do I think that there is a fourth generation of SM fermions or supersymmetric partners.

If there is anything BSM, I think that the most plausible would be a boson associated with neutrino oscillation, and while I think supersymmetric partners are unlikely, I think that the most likely of them would be a spin-3/2 gravitino singlet as a DM candidate.

Thomas Andersen said...

Thanks. Great read as usual.

neo said...

what about QG?

andrew said...

There are several ways to approach quantum gravity:

* Loop quantum gravity (quantize space).
* Graviton based gravity (with or without conformal symmetry).
* QCD squared.
* Asymptotic gravity.
* Maybe there is some way to reconcile GR (with some possible minor modifications to it such as f(R) gravity) and/or the SM classically.
* Scalar-tensor, or scalar-vector-tensor, or scalar gravity.
* Emergent gravity (arising out of entanglement on the QM/SM side).

Not all are necessarily mutually exclusive.

I don't think it it actually necessary to have all of string theory, or a TOE to incorporate the QG features of the graviton in String Theory.

neo said...

There are several ways to approach quantum gravity:

ur favorite approach quantum gravity?

seems string and Loop quantum gravity are wrong with no New progress

Mitchell said...

A detail: "swampland" does not refer to possible worlds that are incompatible with observed reality. The swampland refers to field theories that cannot arise from string theory. It's the opposite of the "landscape" of field theories that *can* arise from string theory. (In both cases one is referring to field theories with all couplings specified. So e.g. standard model with certain coupling values should be in the landscape, the empirical question is whether standard model with the *observed* couplings is in the landscape.)

"If there is anything BSM, I think that the most plausible would be a boson associated with neutrino oscillation"

Can you say more about this?

andrew said...

@neo I wouldn't say that LQG is disproven, and no approach is all that far along. Ultimately, I think that Deur's approach, discussed at length in a dedicated page on the sidebar for background, is the correct approach. I give it maybe a 40%-75% chance of being the ultimate solutions to quantum gravity, dark matter and dark energy.

@Mitchell I stand corrected re the "swampland". Nonetheless, the "swampland" literature in recent years has been a blow to String Theory.

""If there is anything BSM, I think that the most plausible would be a boson associated with neutrino oscillation"

Can you say more about this?"

The PMNS matrix and neutrino oscillation are understood in basically a black box sense, while the parallel CKM matrix for quarks has a well understood mechanism involving mediation through a W boson process. The CKM matrix is basically a description of the properties and couplings of the W boson.

It seems plausible to me that there could be an analog to the W boson that mediates neutrino oscillation, even though that is not the conventional wisdom (which talks about misalignments between weak force states and mass eigenstates).

I don't strongly believe that it is there, but I also don't think that it is excluded experimentally, and not much effort has been expended looking for a mechanism while one is looking to just work out the oscillation parameters.

Neutrino oscillation pretty much can't be due to virtual W boson interactions, because neutrino oscillations aren't charged, because the mass disparity is too great, and because it is problematic to get the byproducts of a virtual W boson interaction to cancel out neatly as a result of neutrinos and anti-neutrinos not annihilating at tree level into photons (which also aren't emitted in neutrino oscillation).

Such a neutrino oscillation carrier boson would have to be massive, because neutrino oscillation exhibits CP violation (which massless carrier bosons like photons and gluons can't because massless bosons don't experience the passage of time in their own reference frame where they are always moving at the speed of light), but I would expect it to be much less massive than a W boson (otherwise the virtual interactions would be too challenging to manage). One would expect that it would lack EM charge and strong force charge, interacting only via its own force that couples only to neutrinos or couples also to other things but so faintly that it is lost in the noise of other stronger interactions of EM, weak and color in other particles, and probably not even the weak force because otherwise it would screw up the proportions seen in W and Z boson decays. It might also be the source of the neutrino masses in lieu of the Higgs mechanism which is not an ideal fit to SM neutrinos, possibly in combination with weak force interactions of neutrinos.

I think that there are lots of good reasons to think that neutrinos have Dirac rather than Majorana mass, and are not Majorana particles. But a new neutrino oscillation boson would provide a way to have Dirac mass without resorting to the Higgs mechanism.

Mitchell said...

I am confused by these comments.

"the conventional wisdom (which talks about misalignments between weak force states and mass eigenstates)"

Are you suggesting that these eigenstates *are* aligned? (as they are for the charged leptons) Or that the misalignment doesn't intrinsically lead to oscillation?

andrew said...

The latter.

andrew said...

Also, just mentioning here that the fact that neutrino oscillation happens is probably proof not just that muon neutrinos and tau neutrinos have mass, but also that electron neutrinos have a non-zero mass. Were this not the case, electrons would be massless and would always move at exactly the speed of light and would not experience time in their own reference frame. Therefore, they couldn't change through oscillation and also could not have CP violation in their oscillations.