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Big things are made of smaller things, and those smaller things are made of
smaller things still. That’s reductionism in a nutshell, and digging our way to the smallest
layer has been one of the primary goals of physics for ever. But what if,
just before we reach the bottom, we find out that reductionism fails?
Just use the code: blackhole at checkout. Links in the descrption. On to the episode
You are made of cells, and your behavior can be thought of as the collective behavior of those
cells—whether it’s the collective throbbing of cardiac cells behind your heartbeat or the
coordinated firing of neurons behind your subjective experience. We don’t need cell
biology to describe your pulse rate—we just need a number of beats per minute,
and we don’t need the neurophysiology of ion channels and action potentials to understand your
fear of clowns—psychology and maybe psychiatry are more useful there. If we go deeper, those heart
and brain cells are made of molecules and then atoms, whose interactions can be understood by
chemistry without much attention paid to the quantum mechanics at work even deeper down.
The universe has layers, roughly sorted according to size, and each layer can be described by its
own set of rules or “dynamics” that we can use without having to know the rules of the layer
below. It’s pretty convenient that we don’t have to do quantum mechanics to understand how people
work. And we take this peculiar feature of our universe for granted, but perhaps we shouldn’t.
It’s also convenient that to understand nature, we only need to look to smaller and smaller scales.
Understand the smallest, then in principle we’ve understood the largest. This notion,
broadly described as reductionism, has been the cornerstone of much of science and certainly
physics since the ancient Greeks. But this too may be an assumption that needs to be questioned.
In a recent episode, we talked about the hierarchy problem—the fact that the Higgs
particle’s small mass doesn’t feel natural in the context of this reductionist worldview.
Some physicists suggest that this is a strike against reductionism. Others,
like Sabine Hossenfelder who responded to our video with one of her own, contends that it’s
this notion of “naturalness” that is misused. But reductionism has been a foundational tenet
of physics for ever, and naturalness has long been considered an important tool.
This video is going to lay down some groundwork to give you a solid sense
of how these concepts are fundamental to much of physics, which will help us
understand why we should be surprised that these approaches seems to fall apart at the bottom.
Let’s start by defining some concepts. The idea that big things can be understood in
terms of small things is called methodological reductionism.
We also have the related concept of theory reductionism that I’ll come back to.
A few other terms: a level of new dynamics arising from a deeper, smaller layer emerges from or is
emergent from that deeper layer. The dynamics—the rules describing the layer—arise from the
potentially very different dynamics of its many parts. And those parts don’t have the emergent
dynamics specifically coded in them. If the emergent dynamics can be described without
any reference to the underlying dynamics, we say the emergent system has dynamical independence.
Perhaps the simplest example is in thermodynamics, where the positions,
momenta of countless particles—literally 10^27 independent-ish numerical properties
or degrees of freedom in the air in a typical room—reduced to a few tightly related variables:
temperature, pressure, density and volume for an ideal gas in equilibrium.
Or take fluid flow. The Navier-Stokes equations predict the time-dependent behavior of fluids
with incredible accuracy, relating the density, momentum, various stresses, etc. of the fluid
with no reference to the nature of the individual particles making up the flow. Their properties
are subsumed in the global parameters of the fluid. For example, the maddeningly complex
attractive interactions between fluid particles just becomes a single number: the viscosity.
There are plenty of other examples where constituent particles of a system have no
knowledge of the emergent dynamics that come from them, from the patterns within a susurration of
starlings to quasi-particles formed by electron holes in superconductors or by skyrmion knots
in magnetic dipole arrays.
In physics, a theory that works in a particular narrow range of some parameter space is called
an effective theory. Newtonian gravity is an effective theory of the more general general
relativity, with Newton only working in cases of relatively weak gravity.
The most prominent type of effective theory in physics is the effective field theory,
which is what it sounds like—an effective theory that’s also a field theory,
meaning it describes properties that extend through space,
like in fluid dynamics or general relativity or quantum field theories.
In an effective field theory, the restriction on the validity of the theory is size scale.
The component parts of an EFT—be they particles of air or quantum elements of
the fabric of space—are small compared to the emergent field. Zoom in close enough and our
EFT fails—things like temperature and viscosity become poorly defined and then meaningless as
we enter the realm of individual elements. But zoomed out far enough, the underlying elements
are so numerous and so small compared to the EFT scale that this behavior can be averaged over;
their statistics are highly predictive, even if the individual elements are not.
We say that an EFT integrates over the many degrees of freedom of its underlying elements.
We also call this process coarse-graining, in that our pixel scale is coarse enough that we
can’t resolve the underlying elements. At this point, we see ensemble parameters,
and find relationships between those parameters. Sometimes those coarse-grained relationships are
exquisitely reliable and robust, and the erratic behavior of the underlying parts are no longer
needed to predict the system’s behavior. This is the dynamical independence I mentioned.
But an effective theory breaks when we move beyond its range of validity. An effective field
theory breaks down below a certain size, when the graining is too coarse to capture the increasingly
important behavior of the constituent elements of the emergent field. A key requirement for an
effective field theory to work is a separation of scales—it has to be big enough compared to
its parts that it’s not overly sensitive to the random messiness of those parts Here’s an example
of pushing an effective theory too far: at the end of the 19th century, physicists were trying to
calculate the spectrum produced by hot objects—the blackbody spectrum—the light radiated by particles
colliding or vibrating with thermal energy. Based on the assumptions of classical physics,
physicists were able to correctly calculate the spectrum produced by hot objects,
but only for the low energy, long wavelength end of that spectrum—the infrared or IR in the case of
the Sun’s spectrum. When they tried to calculate the short wavelength ultraviolet, UV side,
they found that high energy particles contributed far too much intensity, causing the spectrum to
brighten indefinitely in that direction. The calculations didn’t match reality. This was
the so-called ultraviolet catastrophe. It was solved when Max Planck realised that classical
physics didn’t give a good description of how particles vibrate, and that description got
worse the higher the energy. His solution was the birth of quantum mechanics. We’ve talked about it.
The ultraviolet catastrophe resulted from pushing classical mechanics beyond its
limit of applicability. By analogy, we often call the limit of an effective theory the “UV
cutoff”--that’s the energy where it stops working and we need to transition to the more general,
more true description. In this case, it was quantum mechanics. By the way,
once we’re in the quantum realm, the UV cutoff corresponds both to a maximum
energy of validity and to a minimum size, for reasons we’ve discussed.
Let’s step back a second. We can describe the world in terms of effective theories that are
emergent from deeper theories. Those deeper theories are, in principle, more fundamental,
but in general are, themselves, also effective theories with their own UV cutoffs. They are
course-grainings of something even deeper. This process of zooming in to smaller and more and more
fundamental layers of reality has led us through classical physics to quantum mechanics with an
ultimate eye to a single, most fundamental theory. Via this methodological reductionism
we hope to also achieve the other type of reductionism: theory reductionism,
which proposes that all effective theories are just different manifestations,
or special cases of a single, underlying mastering theory—a theory of everything.
At least that was the hope. But we saw hints that this program might
be in trouble when we looked at the hierarchy problem recently. Let me refresh your memory.
Let’s go all the way down to the smallest scale at which we have a well-tested field theory.
That’s the Standard Model of particle physics, which describes the elementary particles like
electrons and quarks in terms of oscillations in quantum fields. If we accept the premise of
theory reductionism then all of nature should be explainable in the context of a single,
master theory. The Standard Model is not that theory because it doesn’t include gravity.
That makes it an effective field theory—a coarse-graining of some deeper theory.
But where is the UV cutoff of the Standard Model? We could argue that the deepest
layer of all could be at the size-scale of the Planck length, at 10^-32m. That’s around 17
orders of magnitude smaller than the scale of the heavier of the Standard Model particles. This is
where we know that general relativity and quantum mechanics come into hopeless conflict and so both
of them fail as effective field theories and we need a theory of quantum gravity.
So the quantum gravity scale could be our UV cutoff. But many physicists argue that the
cutoff is much closer in energy to the Standard Model. That makes sense if we take our lead from
the ultraviolet catastrophe. Max Planck solved it when he showed that contributions to the blackbody
spectrum by high energy particle oscillations are suppressed in the more “true” quantum theory. This
suppression kicks in at the same energy that the classical theory stopped making good predictions.
So where does the Standard Model stop becoming predictive? Some would argue that
it’s when we try to predict particle masses. Particle masses are a free parameter of the
Standard Model—something measured in labs rather than predicted by the theory. But,
as good reductionists, we expect that the mechanism explaining these masses is hidden
in the deeper layer, beneath the Standard Model’s UV cutoff. It’s a bit confusing,
because the mechanics of the Standard Model—quantum field theory—does actually
explain mass—at least in principle. Mass arises from a type of interaction with quantum fields.
But, in a manner analogous to the ultraviolet catastrophe, particle mass can become very
large—even infinite—if you naively add the contributions from high energy oscillations
in those quantum fields. The main culprit is the Higgs boson, which in turn grants mass
to other elementary particles. Rewatch the last video for the nitty gritty.
The point here is that the power of the Standard Model to explain nature appears
to fail at around the mass of the Higgs boson. Taking their queue from, among other things,
the ultraviolet catastrophe, many physicists expected to find new physics close to this
mass—physics that would suppress or cancel high energy contributions. They did not find
that physics. At least, the Large Hadron Collider hasn’t yet, and it’s probed
quite a bit deeper than where this physics was supposed to appear in the form of new particles.
So could the mechanics that define the Standard Model’s parameters lie much deeper
than is accessible to the LHC, or perhaps even to any plausible future accelerator?
Could this so-called UV theory only emerge many orders of magnitude larger in energy and smaller
in size than the scale of the Standard Model, perhaps even at the Planck scale?
Many would say that this feels “unnatural”, claiming it requires very precise tuning
of the parameters of that UV theory. In an upcoming episode I’ll properly address the
fine-tuning argument more rigorously, including whether we should expect to
expect the Standard Model parameters and the UV parameters from which they emerge
to be anything other than what they are. Some, like Sabine, think we should not.
For now, I want to end with an illustration of the strangeness of the situation, in terms of size,
not energy. What is the typical separation of scales between familiar dynamically independent
levels? Think starling flocks to individual birds to bird cells to molecular machinery to atoms to
the elementary particles of the Standard Model. We zoom in 2-4 orders of magnitude each time,
and then we have this chasm that could be up to 17 orders of magnitude between these
elementary particles and the deepest layer. There’s as much difference between the Planck
scale to the scale of the Higgs as there is between the atom and the blue whale. Imagine
we tried to find out what blue whales are made of and we found no supporting structure
for 17 orders of magnitude—no organs, no cells, no molecules. Just atoms of
blue whale that somehow managed to get their act together to make a cetacean.
This is a problem because it gives us a sense that the atoms knew what they were trying to build,
which contradicts the whole idea of our methodological reductionism. The parts
should not know about the whole—emergence goes from small to big. This requirement
is a bit more nuanced than that. There IS feedback between the generating and emergent
layers. For example, a cell can’t live without its host organism, molecular machinery requires a
stable environment of the cell, even the lowerly quark can only exist in composite particles.
There’s a feedback between scales—small generates large, large stabilizes small.
But this feedback acts locally typically each scale directly influences a layer above and
stabilizes a layer below—similar to how the dynamics within each
layer is spatially local. Throughout most of nature, this interplay between emergence and
stabilizing feedback works when the separation of scales is not too small but also not too large.
It's hard to imagine a mechanism for that feedback over the 17 orders of magnitude
from the Higgs to the quantum gravity scale. If this is true,
it seems like there are really only two broad possible explanations. Option
1 is that the UV theory that ultimately underlies and defines the Standard Model
just is the way it is. It’s doing its thing, oblivious to the fact that incredible richness
arises many orders of magnitude away in scale. That does seem a bit lucky, or finely tuned.
We could also invoke the anthropic principle here, in that only universes with such a quality end up
getting observed - by blue whales presumably. There’s a solid case to be made for this, but
you do need a ridiculous number of universes to make it work. We’ll come back to that some time.
Or option 2) Perhaps a type of downward causation or large-to-small feedback is stronger than the
standard reductionist paradigm generally permits. Perhaps the Higgs does tell the
lower levels how to get their act together over vast scales to stabilize its mass,
or perhaps the Higgs mass is stabilized not from below but rather from above.
The general term for this kind of anti-reductionist reversal of
influence between the small and large, the ultraviolet and infrared, is UV-IR mixing.
And there’s some strong motivation to think that this might be an answer—we already see
UV-IR mixing in one very familiar case—that of gravity. But that’s also for another time.
In either case, something weird and cool is going on at the bottom of reality,
and the clue is in the separation of reality’s emergent layers,
from blue whales down to the quantum fabric of spacetime.