Are The Fundamental Constants Delicately Tuned? | The Naturalness Problem

Thank you to Anydesk for supporting PBS. Did God have any choice in creating the world? So asked Albert Einstein. He was being poetic. What he really meant was whether the universe could have been any other way. It have different laws of physics driven by different fundamental constants. Or is this one vast and complex universe the inevitable result of an inevitable and unique underlying principle, perhaps expressible as a supremely elegant theory of everything?

It certainly seems that Einstein thought that this should be the case, that God had no choice in whether or how to create the world. It seems like a pretty armchair philosophical and perhaps unanswerable question, but the modern problem of naturalness may lead to an answer. Hey everyone, a couple of quick announcements before we get started. Our second Patreon interview with Dr. Midhana Yoganathan is available.

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Or fine-tuning problems in general are those in which some property of the universe seems oddly specific, as though whatever process decided on the parameters of the natural laws cared that this particular property has the does. We've been talking about this stuff a bit, including in two recent episodes where we discussed why many physicists

that the small value of the mass of the Higgs boson seems unnatural. This is the hierarchy problem. The idea, if you recall, is that there should be some processes influencing the Higgs mass that operate at very high energies. Which should in turn lead to a very high Higgs mass unless there are precision suppressions of those influences. Those influences are interactions with quantum fields, and the suppression is supposed to be that those interactions cancel each other out.

No natural mechanism has yet been discovered to achieve such high precision and coordinated cancelling. But the alternative to coordinated cancelling is fortuitous cancelling If the latter is true, then it looks like the various cancellations were finely tuned to achieve the small Higgs mass, which feels unnatural. Another supposed fine-tuning problem is the apparent very small value of the cosmodule constant.

So we observe that the expansion of the universe is accelerating, and a possible culprit is vacuum energy. The faint energy density. Quantum fields that fill all of space. We call this influence dark energy and describe it with the cos module constant in the Einstein equation. And for basically the same reason that physicists are confused by the low Higgs mass, many are also confused that dark energy isn't extremely strong due to the contribution of high energy component to those fields.

And again, quantum cancellations could reduce this energy. It's not such a stretch to imagine a perfect cancellation if there's a high level of symmetry in those contributions, but to cancel almost but not quite perfectly seems an oddly specific result. Finely tuned, in fact. So far we've been talking about these issues in Mechanistic terms, that's a potential source of confusion. Because, in a sense, the mechanisms don't matter.

There's a much more general way to express the problem that gets to the heart of the question we started with. in our very particular universe inevitable. I'm gonna get to that after a few more words to put this mechanistic picture to bear. Quantum field theory describes essentially everything in terms of myriad interactions between quantum fields, expressed in the theory in terms of virtual particle interaction.

Many, and perhaps most physicists, understand this virtual stuff to be just a mathematical tool representing the messy interactions of quantum fields. But even if the Feynman sums in QFT are mathematical fictions, We can still consider the complex field interactions that they represent as being real in some sense.

The astonishing success of the standard model of particle physics, itself a quantum-field theory, means that we kind of have to take quantum-field interaction seriously. That includes ideas like Field interactions contributing to particle mass, and even the idea of field interactions cancelling each other's influence. There's also independent evidence that this virtual activity is in a sense real, for example, in the Casimir effect.

In which a measurable force is induced between supposed virtual field modes from between two conducting plates. The clockwork behind the standard model, the mechanism of quantum field interactions and cancellations, make very sensible predictions in and nonsensical ones in other cases. In particular, prior to being fixed, the QFT behind the standard model energy should be enormous. So can we just ignore those predictions?

In the case of the standard model, the answer is yes, at least if all we want to do is to use the theory within its domain of applicability. The supposed exploding masses of the particles can be dealt with if we just input by hand their true masses, as measured in the lab. The process is called renormalization and it involves adding some made up cancelling terms to get the

exploding masses back down to where we know they should be. With this change, those particle masses are no longer predicted by the theory, but rather become free parameters of the theory. In this way, the standard model becomes internally self-consistent. It doesn't predict very large masses, but that's by construction.

It's the unconstrained, unrenormalized quantum field theory beneath the standard model that predicts large masses. During the development of the standard model, some physicists had hoped. that the quantum field theory on which the model is built would be able to fully explain the masses of the particles. They were not pleased that this feature didn't make it into the release version of the theory.

Richard Feynman, who led the development of quantum electrodynamics, the electromagnetic part of the standard model, called renormalization a shell game and a dippy process. He said, Such hocus pocus has prevented us from proving that the theory of quantum electrodynamics is mathematically self consistent. Paul Durac said he was 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. There are two takeaways here. One is that the underlying mechanics of the Stanton model does lead to stuff about the particle masses if you remove the hocus pocus over renormalization. Some would argue that sans, hocus pocus, if you take this mechanism seriously, there appear to be finely tuned cancellations.

The other takeaway is that the standard model fails to realise the dream of Einstein and of Feynman and Durat. They and perhaps we want a singular ultimate theory, one from which Every property of the world should be derivable in a non-dippy, non-arbitrary, and mathematically self-consistent way. The standard model isn't that.

And so we can imagine a more true general theory, perhaps a theory of quantum gravity, of which the standard model, general relativity, and everything else are slightly crappy approximations, each one with only a limited range of validity. We talked about this stuff last time, how we have these layers of theory with three. Describing larger scales and lower scales. Being coarse graining.

Of deeper theories. But all of those so-called effective theories are entirely defined by the theory at the bottom. At least that's how the world works in the reductionist paradigm. We like to call the more coarse grained, the more zoomed out, more emergent theory the infrared or the IR theory, while the deeper, more fundamental theory is the ultraviolet or the The reason is by analysis.

With the ultraviolet catastrophe which was in the last episode. So let's say we have an IR theory that's a coarse graining of a UV theory. Both are defined by their own set of parameters. For example, there are 19 free parameters in the Model that seem arbitrary in the context of that theory alone. The free parameters of the IR theory, however, are not free in the context of the UV theory from which it comes. Instead, they are calculable in principle from the previous.

of that UV theory. So what are the parameters of the deepest UV theory? We don't know. Knowing that fully means knowing the theory of everything, but we can at least imagine The theory of our universe lives in some sort of platonic space of all imaginable such theories. The UV theory that generates our universe has a specific location in that

space defined by its specific parameters. If we locate that specific UV theory, we should be able to calculate the precise parameters of the IR theory that inevitably emerges from it. At least if Einstein has his way. Einstein would also like the UV theory itself to be inevitable, but we really have no idea how those.

Chosen. Okay, so how does naturalness play into this picture? Imagine making a new universe both Choosing a random spot in this theory space. The resulting UV theory defines the IR parameters like the Higgs mass, etc. You haven't chosen your UV theory with any intention to get specific IR parameters, so you probably wouldn't expect them to be unusual or interesting in any way.

are, it would seem unnatural, not as random as you imagine. Let's actually try an analogy. You shoot an arrow into a barn wall, blindfolded. You look to see where you hit, just some random patch of wood, it turns out. Do you act surprised like what are the chances that I hit this square inch in particular? How lucky? No, you had to hit somewhere, and that's just where you hit. It's perfectly natural.

On the other hand, imagine if there was a target painted on the wall with a very tiny bullseye. You hit the bullseye by chance without even knowing that the target was there. You'd be justified in thinking it was a crazy fluke and not just some spot on the wall. In case you missed it, in this analogy, the barn wall is the space of all possible UV theories.

Each point on the wall is a different set of parameters for that theory, each a different underlying master theory leading to a different universe with different IR parameters. The bullseye is a very particular UV theory and it's special because it happens to lead to a very special IR theory, in our case a small Higgs mass and small cosmological constant. And the blind archer. God perhaps?

Or perhaps we should think of it as representing the mechanism by which the parameters of the UV theory are set. This could be random meaning the whole barn wall is fair game, Or those parameters could be set by some mechanism that's intrinsic to the UV theory itself, a mechanism that only permits a single outcome. Only one spot on the barn wall was ever possible in the first place.

And once you know the UV theory, you see that no other set of UV parameters are possible. That seems to be what Einstein preferred, God has no choice. But whether the UV parameters are set randomly or are unique and inevitable, the archer is still blind and we still do have the problem of fine-tuning. How so? The blindness of the archer doesn't really represent the freedom of the UV theory to have different parameters. What it really represents is a combination of two things.

1. Our own lack of knowledge of those parameters. We know nothing about them, so they could be anything. The whole barn wall is open as far as our prior knowledge is concerned. And two, the fact that the UV theory is blind to the IR theory. So even if the mechanisms that set the parameters of the UV theory have no choice in where they land. They aren't doing that with the emergent IR theory in mind. At least that's the default assumption of reductionism.

So that's the situation we're in. We find an arrow in the bullseye, and it seems that the arrow was put in place by a process that had no idea that the bullseye existed. We can talk about all of this in terms of Bayesian reasoning by assessing likelihoods relative to our prior knowledge. When physicists talk about a prior distribution for a parameter space for the UV theory, they typically aren't talking about some real process that sets the parameters of that theory.

Instead, they usually mean a probability distribution that quantifies our degree of knowledge and ignorance. about some aspect of the world. It's the possible range for the parameters given what little we know, what we call abayan prior. In reality, the true parameters of the UV theory just are what they are, presumably a set of well defined values. But with little prior knowledge, their possible distribution with respect to that knowledge is vast.

In our Bayesian reasoning, we'd use a wide Bayesian prior because Its job is exclusively to represent our knowledge. Now, let's say we know that this wide open UV theory space maps to some as yet unmeasured infrared parameter. We go to measure the parameter and ask how much of the theory space in our Bayesian prior could produce an IR parameter like the one we just measured? If the answer is vanishingly small, then we might be suspicious.

That's the case with the Higgs mass and the cos module constant. it's the arrow being suspiciously in the bull's eye. We would be justified in assuming that the archer actually peaked, or that there's some powerful collusion in the UV theory that propagates down to the IR theory. In this case,

working to make the IR theory the low-energy theory that it is. And it doesn't even matter if the mechanism for setting the IR parameters, such as the suppression of the Higgs mass, is quantum cancellations or anything else. As long as our UV theory natively lives at much higher energy than the IR theory, Either collusion between the high energy mechanics or extreme chance is needed to yield that stable low energy theory.

So that's why it's reasonable to wonder at things like the smallness of the Higgs mass and the cosmological constant. Not because they're actually unnatural, but because they seem unnatural given the mechanisms that we think are at work behind them. Nature is obviously being perfectly natural, and so it means we're missing something. Either the archer peak That's the UV theory being influenced by the IR theory, it sees the target.

The archer shot many, many arrows, and the whole barn wall is a pincushion of alternate universes, and of course we're in one of the extremely rare bullseye universes with survivable Higgs masses and so on. I keep saying that we'll come back to these ideas, the idea of UV IR mixing and anthropic reasoning. And we still will. But for today, let me just say that the choice between these two options may be our answer to Einstein's question. Did God have a choice in creating the world?

If no, then there was only one arrow, and that seems to demand a connection between the fundamental and the emergent that we don't fully understand. If yes, then the arrow could have landed anywhere on the barn wall, and perhaps it did, solving naturalness but generating a multiverse.

Of course, in that case, we can just redefine the multiverse as the world and say that it is singular and inevitable and Einstein gets to be right again. Just like he was with all that stuff about curbed space-time.

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