Did God have any choice in creating the聽 world?

So asked Albert Einstein.

He was being poetic.

What he really meant, was whether聽 the universe could have been any other way.

Could it have had different laws of physics, driven by聽 different fundamental constants.

Or is this one vast and complex universe the inevitable result聽 of an inevitable and unique underlying principle, perhaps expressible as a supremely elegant Theory聽 of Everything.

It certainly seems that Einstein thought this should be the case … that God had  no choice in whether or how to create the world.

It seems like a pretty arm-chair聽 philosophical and perhaps unanswerable question, but the modern “problem”  of naturalness may lead to an answer.

Naturalness or fine-tuning problems in general are聽 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 value it does.聽 We’ve been talking about this a bit, including in two recent episodes where we discussed why many聽 physicists think that the small value of the mass of the Higgs boson seems unnatural—this is called  the hierarchy problem.

The idea, if you recall, is that there should be processes influencing the聽 Higgs mass that operate at very high energies, which should in turn lead to a very high Higgs聽 mass unless there’s some precision suppression of those influences.

Those influences聽 are interactions with quantum fields, and the suppression is supposed to be that they聽 cancel each other out.

No “natural” mechanism has yet been discovered to achieve such high precision聽 and coordinated cancelling, but the alternative to coordinated canceling is fortuitous cancelling.

If聽 the latter is true then it looks like the various cancellations were “finely tuned” to achieve  that small Higgs mass, which feels unnatural.

Another supposed fine-tuning problem is聽 the apparently very small value of the cosmological constant.

So we observe that the聽 expansion of the universe is accelerating, and a possible culprit is vacuum energy—a faint  energy density in the quantum fields that fill all of space.

We call this influence dark energy聽 and describe it with the cosmological constant in the Einstein equations.

And for basically the聽 same reason that physicists are confused by the low Higgs mass, many are also confused聽 that dark energy isn’t extremely strong due to the contributions of high-energy聽 components of those fields.

And again, quantum cancellations could reduce this energy.聽 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聽 oddly specific result.

Finely tuned, in fact.

So far we’ve been talking about these  issues in very 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 questions we started with: Is聽 our very particular universe inevitable?

I’m going to get to that after a few more  words to put the mechanistic picture to bed.

Quantum field theory describes essentially聽 everything in terms of myriad interactions between quantum fields, expressed in this theory聽 in terms of virtual particle interactions.

Many, perhaps most physicists understand this virtual聽 stuff to be just a mathematical tool representing the messy interactions of quantum fields.

But聽 even if the Feynman sums in QFT are mathematical fictions, we can still consider the complex聽 field interactions they represent as being “real” in some sense, whatever real really means.

The astonishing success of the standard model of particle physics, itself a QFT, means we kind of have to聽 take quantum field interactions seriously.

That includes ideas like field interactions聽 contributing to particle mass and even the idea of field interactions canceling each others’  influence.

There’s also independent evidence that this “virtual” activity is in a sense real—for  example the Casimir effect, in which a measurable force is induced by excluding supposed virtual聽 field modes from between two conducting plates.

So, the clockwork behind the Standard Model—the  mechanism of quantum field interactions and cancelations—make very sensible predictions  in some cases, and nonsensical ones in other cases.

In particular, prior to being fixed, the聽 QFT behind the standard model predicted the Higgs mass and dark energy should be enormous.聽 Can we just ignore those predictions?

In the case of the standard model, the answer was yes.

At least,聽 if all we want to do is to use the theory in its domain of applicability.

The supposed exploding聽 masses of the particles can be dealt with if we just input by hand their true masses as measured聽 in the lab.

The process is called renormalization, and it involves adding some made-up canceling聽 terms to get the exploding masses back down to where we know they should be.

With this change,聽 those particles' masses are no longer predicted by the theory, but rather become free parameters.聽 In this way the Standard Model became internally self-consistent.

It doesn’t predict very large  masses, but that’s by construction.

It’s the unconstrained, un-renormalized quantum field theory underneath the standard model that predicts large masses.

During the development of the Standard Model,聽 some physicists had hoped that the quantum field theory on which the model is built would be able聽 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聽 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聽 self-consistent”.

Paul Dirac said he was, “very dissatisfied with the situation because  this so-called 'good theory' does involve neglecting infinities which appear in its聽 equations, ignoring them in an arbitrary way.” There are two takeaways here.

One is that the聽 underlying mechanics of the Standard Model does lead to confusing stuff about the particles masses聽 if you remove the hocus-pocus of renormalization.

And some would argue that sans-hocus-pocus,聽 if you take this mechanism seriously, there appear to be finely tuned cancellations聽 in order to get the masses reasonable.

The other takeaway is that the Standard Model聽 fails to realize the dream of Einstein, Feynman and Dirac.

They, and perhaps we, want a singular聽 ultimate theory, one from which every property of the world should be derivable in a non-dippy,聽 non-arbitrary, and mathematically self-consistent way.

The Standard Model isn’t that, and so we can  imagine a more true, more general theory—perhaps a theory of quantum gravity—of which the Standard  Model, general relativity, and everything else are slightly crappy approximations, each聽 with only a limited range of validity.

We talked about this stuff last time—how we  have these layers of theory, with theories describing larger scales and lower energies聽 being “course-grainings” of deeper theories.

But all of those so-called effective theories聽 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 course-grained, more zoomed-out, more聽 emergent theory the infrared or IR theory, while the deeper, more fundamental聽 theory is the ultraviolet or UV theory.

The reason is by analogy with the ultraviolet聽 catastrophe, which was in the last episode.

So let’s say we have an IR theory  that’s a course-graining of a UV theory.

Both are defined by their聽 own set of parameters.

For example, there are 19 free parameters in the Standard Model聽 that seem arbitrary in the context of that theory alone.

The free parameters of the IR theory聽 are not free in the context of the UV theory from which it comes.

Instead they are “calculable” in principle  from the parameters of the UV theory.

What are the parameters of the deepest UV theory?聽 We don’t know.

Knowing that fully means knowing the Theory of Everything.

But we can at least聽 imagine that the UV theory of our universe lives in some sort of platonic space of all imaginable聽 such theories.

The UV theory that generates our universe has a specific location in that space聽 defined by its specific parameters.

If we locate that specific UV theory and you should be able to聽 calculate the precise parameters of the IR theory that inevitably emerges from it.

At least if聽 Einstein has his way.

Einstein would also like the UV theory itself to be inevitable, but really we聽 have no idea how those parameters were “chosen”.

OK, how does naturalness play into this picture?聽 Imagine making a new universe by choosing a random spot in theory-space.

The resulting UV theory聽 defines the IR parameters like the Higgs mass etc.

You haven’t chosen your IR theory with  any intention to get specific IR parameters, so you probably wouldn’t expect them to  be unusual or interesting in any way.

If they are, it would seem unnatural聽 … not as random as you imagined.

Let’s 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.

Do you  act all surprised, like, “What are the chances that I hit this square inch in particular?聽 How lucky!” No, you had to hit somewhere, and that’s where you hit.

Perfectly natural.

On  the other hand, imagine if there was a target painted on the wall with a very tiny bullseye.

You聽 hit the bullseye by chance without even knowing it was there.

You’d be justified in thinking it a  crazy fluke, and not “just some spot on the wall”.

In case you missed it, in this analogy the聽 barn wall is the space of possible UV theories.

Each spot on the wall is a different set of聽 parameters for that theory—each a different underlying master theory leading to a聽 different universe with different IR parameters.

The bullseye is a very particular聽 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聽 perhaps we could think of it as representing the mechanism by which the parameters of the聽 UV theory are set.

This could be random, meaning the whole barn wall is fair game.

Or those聽 parameters could be set by some mechanism that’s intrinsic to the UV theory—a mechanism that only  permits a single outcome—only one spot on the barn wall was ever possible in the first place.

And聽 once you know the UV theory, you see that no other set of UV parameters are possible.

That seems to聽 be what Einstein preferred.

God has no choice.

But whether the UV parameters are set randomly聽 or are unique and inevitable, the archer is still blind and we do still have the problem of fine聽 tuning.

How so?

Well, 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:聽 1) Our own lack of knowledge of those parameters.

We know nothing about them, and so they could be聽 anything—the whole barn wall is open as far as our prior knowledge is concerned.

And 2) the fact聽 that the UV theory is blind to the IR theory.

So even if the mechanisms that set the parameters of聽 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聽 that had no idea that the bullseye existed.

We can talk about all of this in terms of Bayesian聽 reasoning—by assessing likelihoods relative to our prior knowledge.

When physicists talk about a聽 “prior distribution” for the parameter space of the UV theory, they typically aren’t talking  about some real process that sets the parameters of that theory.

Instead, they usually mean聽 a probability distribution that quantifies our degree of knowledge and ignorance about聽 some aspect of the world.

It’s the possible range for the parameters given what little聽 we know what we call a Bayesian prior.

In reality the true parameters of聽 the UV theory are what they are, presumably a set of well defined values.

But聽 with little prior knowledge, their possible distribution with respect to that knowledge聽 is vast.

In our Bayesian reasoning we’d use a wide Bayesian prior because its job is聽 exclusively to represent our knowledge.

Now let's say we know that this wide-open UV聽 theory-space maps to some as-yet unmeasured infrared parameter.

We go to measure the parameter and聽 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 a vanishingly small fraction, then we might be suspicious.

That’s the case with  the Higgs mass and cosmological constant.

It’s the arrow being suspiciously in the bullseye.聽 We would be justified in assuming that the archer actually peeked, or that there’s some powerful  collusion in the UV theory that propagates down to the IR theory, in this case working to make聽 the IR theory the low-energy theory that it is.

And it doesn’t really matter if the mechanism  for suppressing IR parameters such as the Higgs mass is quantum cancellations or聽anything else.

As long as our UV theory natively lives at much higher energy than聽 the IR theory, either collusion between the high-energy mechanics or extreme chance is聽 needed to yield that stable low energy theory.

So that’s why it is reasonable to wonder  at things like the smallness of the Higgs mass and cosmological constant.

Not because聽 they’re actually unnatural, but because they seem unnatural given the mechanisms we think are聽 at work behind them.

Nature is obviously being perfectly natural, and so it means we’re missing  something.

Either the archer peeked—that’s the UV theory being influenced by the IR theory—it  sees the target.

Or the archer shot many, many arrows and the whole barn wall is聽 a pin-cushion of alternate universes and of course we’re in one of the extremely rare  bullseye universes with Survivable higgs mass and so on.

I keep saying we’ll come back to these  ideas of UV-IR mixing and anthropic reasoning, and we still will.

But the choice between聽 these two may be our answer to Einstein’s question.

Did God have a choice in creating the聽 world?

If no then there was only one arrow and that seems to demand a connection between聽 the fundamental and the emergent that we don’t fully understand.

If yes then the arrow  could have landed anywhere on that wall and perhaps did, solving naturalness but generating a multiverse.聽 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聽 all that stuff about curved spacetime.