The varieties of material existence

digitado ⋅ 19 de September de 2018

Status: Rough and speculative working notes, very quickly written
– basically, a little raw thinking and
exploration. Knowledgeable corrections welcome!

William James wrote a book with the marvellous title “The
Varieties of Religious Experience”. I like the title because it
emphasizes just how many and varied are the ways in which a human
being can experience religion. And it invites followup questions, like
how aliens would experience religion, whether other animals could have
religious experiences, or what types of religious experience are
possible in principle.

As striking as are the varieties of religious experience, they pale
beside the variety of material things that can possibly exist in the
universe.

Using electrons, protons, and neutrons, it is possible to build: a
waterfall; a superconductor; a living cell; a Bose-Einstein
condensate; a conscious mind; a black hole; a tree; an iPhone; a
Jupiter Brain; a working economy; a von Neumann replicator; an
artificial general intellignece; a Drexlerian universal constructor
(maybe); and much, much else.

Each of these is astounding. And they’re all built from arrangements
of electrons, protons, and neutrons. As many people have observed,
with good enough tweezers and a lot of patience you could reassemble
me (or any other human) into a Bose-Einsten condensate, an iPhone, or
a black hole.

We usually think of all these things as separate phenomena, and we
have separate bodies of knowledge for reasoning about each. Yet all
are answers to the question “What can you build with electrons,
protons, and neutrons?”

For the past decade or so, when friends ask me what is the most
exciting thing happening in science, one of the subjects I often
burble about excitedly is quantum matter – very roughly, the
emerging field in which we’re engineering entirely new states of
matter, with intrinsically quantum mechanical properties. It turns out
there’s far more types of matter, with far weirder properties, than
people ever dreamed of.

I’m not an expert on quantum matter, I only follow it from afar. Yet
what I see makes me suspect something really profound and exciting is
going on, something that may, in the decades and centuries to come,
change our conception of what matter is.

Furthermore, it seems to me that many other very interesting nascent
ideas have a similar flavour: things like programmable matter, smart
dust, utility fog, synthetic biology, and so on. In a detailed
technical sense these are very different from the work on quantum
matter (though there are likely overlaps). But in some broader sense
all smell like things that might change our conception of what matter
is.

Because of this, I decided to write some quick notes about how we
think about matter, and what it might be possible to build. It’s a
brain dump of questions for myself, ideas, and pointers, basically
just me thinking out loud, trying to reduce some of my confusion, and
increase my understanding.

On the phrase “state (or phase) of matter”: This phrase
has a technical meaning in physics, coming from the theory of
statistical mechanics. In that technical sense, solids, liquids, and
gases are all states of matter (as are superconductors, superfluids,
and numerous other more exotic phases), while things like life or
consciousness or universal computers are not.

Of course, there’s an everyday sense in which something like life
(etc) is a state of matter. To resolve the ambiguity, I’ll use the
phrase “phase of matter” for the physicist’s specific
meaning. And I’ll use the phrase “state of matter” for the
broader sense. I’m interested in both in these notes – I’m not
just interested in new phases of matter, I’m interested in what new
states of matter are possible, broadly speaking.

The flux in “phases of matter”: Actually, there’s a
further issue: the meaning of “phase of matter” is in flux
amongst physicists themselves. In the 20th century a pretty good
theory of phases of matter was developed, by Landau, Wilson, Fisher,
Kadanoff, and others. Circa 1980 physicists “knew” what a
phase of matter was. And then things became very exciting, with the
discovery of the Haldane model, the AKLT model, and, especially,
fractional quantum Hall systems. These all showed new phases of
matter, but didn’t fit within the Landau-Wilson et al
understanding. Instead, in the decades since we’ve been trying to
figure out the right way of understanding these new ideas. It turns
out that there are many new “topological” phases of
matter, and we’re just at the beginning of understanding them. We
don’t yet have a good understanding. Even the basic theory and
questions are unclear at this point.

What are the most interesting states of matter which have not yet
been imagined? It’s remarkable that human consciousness, universal
computing, superconductors, fractional quantum Hall systems (etc) are
all pretty recent arrivals on planet Earth. Each is an amazing step, a
qualitative change in what is possible with matter. What other states
of matter are possible? What qualitatively new types of phenomena are
possible, going beyond what we’ve yet conceived? Can we invent new
states of matter as different from what came before as something like
consciousness is from other states of matter? What states of matter
are possible, in principle? In a sense, this is really a question
about whether we can develop an overall theory of design?

How were the most interesting states of matter created or first
conceived? There are a few common mechanisms: extremizing physical
quantities (black holes, Bose-Einstein condensates, superconductors);
evolution (cells, higher forms of life, consciousness, many forms of
technology, including the iPhone); asking fundamental questions
(universal computers, Drexlerian universal constructors, the Utility
Fog). Design and engineering sometimes play a role, although often as
part of a larger evolutionary process (e.g., you can view the iPhone
as the outcome of a 30+ year-long combination of imaginative design
and memetic, market-driven evolution). More recently, some of the most
interesting work on quantum matter has this flavour – people
like Kitaev, Haldane et al.

(I wish I could be more precise about: “asking fundamental
questions”. There’s lots of fundamental questions which don’t give
rise to ideas like this. But I can’t immediately think of a better
characterization.)

What phase of matter is life? It bugs me that I don’t have a really
good answer to this question. Informally, we often think of human
bodies as solids. Certainly, in many everyday respects they behave
much more like solids than they do like liquids or gases, although
they tend to be rather squishy, and there are important exceptions
(like blood, tears, etc). Of course, we’re filled up with liquid
water! But those liquids are hidden away behind membranes, like the
cytosol inside the cell wall. Even human bone contains quite a lot of
water.

Much of my confusion is because the standard classification of matter
into phases relies on that matter being at (or near) thermodynamic
equilibrium. Parts of the human body are near thermodynamic
equilibrium. But much is not. The thing that makes it all go, that
makes life life – our metabolism – is all about energy
flows that keep things away from equilibrium.

Unfortunately, I also don’t understand very well when a physical
system should be at thermodynamic equilibrium. The standard story we
teach undergraduates is that if you put a macroscopic system in
contact with a large heat bath, then over time it will gradually
equilibriate.

That’s not a very good story.

Human beings are in contact with a large heat bath – our
external environment is a pretty good approximation to one.
Certainly, swimming in the ocean this is true! And yet large parts of
us remain stubbornly away from equilibrium. (Though swim in too cold
waters for too long, and you will eventually equilibriate in a most
unpleasant fashion).

Put another way, life seems to be a system designed to resist
equilibrium. And yet at the same time it’s also a system designed to
be (surprisingly) stable in important ways.

Except: that also is only partially true! In fact, much of our body
structure is at (or near) equilibrium – much of the fluid,
much of our bone structure, and so on. My guess is that many of the
essentially fixed, static structures in our body are near enough to
equilibrium.

So my very rough picture is that a (living) human body is a system
with the following properties:

Many static components which are near thermodynamic
equilibrium. These are important structural components in the whole.
Many energy flows and dynamic components which are far away from
thermodynamic equilibrium (and sometimes driving movement of static
components, too).
Despite not being at equilibrium, the system is surprisingly
stable. Scratch your knee or injure a muscle and the injury will
(largely) heal itself. The immune system can fight off many
invaders. Many of the systems in our body are surprisingly
resilient and stable over time. In particular, we have systems which
keep us away from equilibrium in very specific ways.

A big part of the reason this question bothers me is because I have
two broad (and very different) frameworks for thinking about matter.

One of those frameworks is equilibrium statistical mechanics. This is
the framework used by physicists to think about the different phases
of matter, and (often) by chemists and materials scientists to think
about what new materials are possible. It’s a powerful framework, and
most stable matter in the world is of this type.

However, many of the most interesting systems – including
universal computers, conscious minds, cells, economies, and others
– don’t fit well into this framework. Rather, they have the
three properties described above: many static components near
thermodynamic equilibirum; many energy flows and dynamic components
far from equilibrium; and surprising stability and resilience, often
with built in self-healing or error-correction mechanisms.

What, if anything, is the takeaway from all this? Here’s a few
tentative points and questions:

It may be useful to think of “resilient matter” as the
overall class here – types of matter which can be stable
enough that it makes sense to think of objects at all. And that
class can be divided into two types: the stable classes which arise
out of statistical mechanics (equilibrium physics + renormalization
group => appropriate phase of matter); and the stable classes which
arise in some other way (e.g., an immune system, or other types of
built in error-correction and self-healing).
Is there a good unified way of thinking about these two approaches
to building resilient classes of matter?
Interesting things often happen when you try to move from one domain
into the other. For instance, Kitaev’s ideas about naturally
fault-tolerant quantum computation involved replacing complex
designed forms of error-correction with error-correction that occurs
naturally as a consequence of certain thermal processes. Ideas like
designing a system whose ground state is a quantum error-correcting
code are steps in merging the two domains.
Put another way, a good generative question given a designed system
or process may well be: can we find a system in which this same
process occurs intrinsically as a consequence of thermal relaxation?

Why is this so disreputable? Something interesting about many of the
ideas I’ve described is that they are (or were) a little
disreputable. Universal constructors, artificial general intelligence,
quantum computers, Jupiter Brains, and so on – all have gone
through periods when they were not regarded as serious subjects.

One interesting example is Eric Drexler’s writing on
nanotechnology. He wrote a remarkable book in 1986. This book has
an interesting status among scientists. For many it’s too far-out,
beyond-the-pale speculation, not backed up by any serious chemistry, a
form of science fiction. At the same time it seems pretty clear to me
that Drexler has helped set the agenda for what many of those people
dream about. Basically: ubiquitous, scalable, rapid, programmable,
atomically precise engineering of atomic systems, and a legitimization
of the question: what could we build if this were all possible and
inexpensive?

There’s a funny thing about norms here. I think it’s pretty common
that two communities, A and B, will do a body of work on overlapping
subjects. Community B will borrow a lot of ideas and inspiration from
Community A. Yet it will feel embarassed to be doing so, and will
often deny doing so, since Community A isn’t playing by what Community
B has internalized as the correct rules. But those very same rules
actually prevented Community B from seeing the things that Community A
saw. I think this is what happened with nanotechnology, and it’s a
common dynamic in all of human life.

(Related: the futurist Peter Schwartz’s observation that the great
thing about being a science fiction writer is that you get to
determine what the next generation of scientists and engineers will
dream of making.)

There are exceptions. Prestigious enough individuals get something of
a pass. Richard Feynman wrote pieces about nanotechnology
and quantum computing, and those were taken much more seriously
than they might otherwise have been (and eventually held up as
validating the fields) because it was Feynman. But even in those
essays, Feynman is somewhat apologetic – he knows he’s doing
something not regarded as entirely okay by his community of peers.

Of course, I’m not immune to this feeling. I feel somewhat embarassed
thinking in this speculative mode. And yet the question is an
important one: what fundamentally new modes of matter might it be
possible to create? And it’s worth spending at least a little time
exploring the question, from a variety of speculative points of view.

What could designer matter mean? One natural and pretty common
conception is that it means the ability to reconfigure shape in real
time. This is central to concepts such as the Utility Fog, much
of the work of the Tangible Media Group, DARPA’s program on
progammable matter (e.g., and others. I’m fascinated, though, by
questions which go beyond reconfiguring shape and basic quantities
such as density. Ideally, you’d like to be able to program all
macroscopic quantities, things like thermal and electrical
conductivity, brittleness, elasticity, ductility, and so on. How wide
a range of parameters is in principle possible?

It seems likely that, unlike in computation, it’s not possible to
design a single substrate which can reconfigure itself across the
entire possible range for these macroscopic quantities. But you might
be able to design a substrate factory which could, upon being given
specifications for a desired substrate’s range of possible properties,
say whether or not such a substrate was possible, and if so
manufacture it. In that sense, a universal substrate would not be
possible, but a universal substrate factory might be.

I’ve listed out a set of macroscopic quantities. But I want to return
again to the question: what is missing from that list of macroscopic
properties? In a Bose-Einstein condensate the macrosopic property is
the (non-zero!) fraction of particles all simultaneously occupying the
ground state(!); this type of property could perhaps (just) barely
have been conceived 100 years ago, and it certainly couldn’t even have
been conceived 200 years ago. Presumably there are many, many such
properties still waiting to be discovered. What fundamental new types
of property of matter are possible? Apart from the historical
strategies described above, I have few ideas for how to answer that
question!

To read: on magnetoresistance (and related effects, like giant
magnetoresistance), where an externally applied magnetic field can
be used to change the resistance of a material.

Universality in electrostatics: It’s easy to design a programmable
device which is universal for electrostatics in any given closed
region of space. You need two abilities: (1) the ability to create
arbitrary charge densities within the region; and (2) a set of
electrodes bounding the space, to which can be applied arbitrary
potentials. Standard results about boundary-value problems then imply
that both: (1) the electric field is completely determined within the
region; and (2) any electric field which is possible in electrostatics
may be created in this way. It should, in fact, be relatively easy to
build a crude prototype for such a system, although of course there
will be limits on the achievable charge densities and potentials. (I
wouldn’t be surprised if this was routine, and I simply don’t know the
name of this type of device.)

Miscellaneous ideas, questions, and observations

How useful will the immune system be as a source of design or
engineering ideas?
Physics will be gradually reinvented as a design science. It’s
notable that computer science began with its theory of everything
(the Turing machine). And yet it still sees a steady stream of
fundamental advances, new types of abstraction, even entirely new
layers of abstraction, and radical reconceptions of the basics. I
think physics will transition to being a similar kind of design
science over the coming decades and centuries.
To what extent is it possible to make properties of matter
composable? So, e.g., you design foglets that can be composed to
achieve some desnity, and those dense super-foglets can be composed
to achieve some ductility? Etc.
Is it possible to imagine life inside an exotic phase of matter,
e.g., life evolving inside a superconductor? Frankly, I’m not
entirely sure what this question even means – as I said
earlier, life seems to be intrinsically an out-of-equilibrium
phenomenon. But perhaps it’s possible for something like this to
happen to the same kind of extent as we often think of human bodies
as solid+liquid hybrids. (Dandelion Mane tells me of Dragon’s
Egg, a novel set on the surface of a neutron star.)
Observation: a lot of people are working on quantum matter, and a
great deal is known. To do striking work, you’d need to bring in
some very interesting external ideas.
That said, it’s clear there is extraordinary power in the design of
simple, “unrealistic” model systems in quantum
matter. Renormalization and universality means there often are real
systems which exhibit very similar behaviour. So getting a picture
of the zoo of basic model systems may well be extremely
valuable. And developing some skill as a designer of such systems
also seems fun. What design principles are there?
It’s notable that engineering conceptions of programmable matter
tend to emphasize actuators, sensors, communication, and power. A
physics conception tends to focus more on physical properties like
density, elasticity, and so on. I’m not sure what this means –
I just wonder about the different cultures present in thinking about
this kind of problem, and the benefits of pushing those cultures up
against one another.
To what extent does the notion of fundamental particles even make
sense? It’s extremely common for a theory to have two or more
(equivalent) descriptions in terms of different sets of basic
particles or fields. E.g., the use of
the Jordan-Wigner transform shows that there is an equivalence
between certain spin chains and systems of free Fermi particles.
The answer to the question “Is the system really a set of spins or a
set of free fermions?” is ambiguous. It depends not on properties
intrinsic to the system, but rather on other external systems to
which it is coupled (for, e.g., state preparation and
measurement). This is absolutely remarkable! It means the question
“what is this system made of?” in some sense depends on the other
systems which interact with it, that is, is not entirely an
intrinsic property of the system itself. Change those other systems,
and there may be a sense in which you change what the system is
built of.
To drive this point home, suppose you worked very hard to build a
spin chain which had such a “reinterpretation” in terms of free
Fermions. It’s tempting to think of this reinterpretation as merely
a convenience, or fortuitous coincidence. But then someone hands
you a measurement probe which couples to degrees of freedom in the
Fermi gas, and perhaps allows you to control those degrees of
freedom, reset them, etc. The more powerful and flexible the probe,
the more you’d start to think of the system as “really” being made
of fermions.
It’s conventional to write down the action for physics in terms of
the familiar particles and fields – electrons, photons,
quarks, and so on. I wonder, though, what equivalent quasiparticle
descriptions are possible? Maybe this is a silly question, or
obviously not possible, at least for the standard modelq. But that’s
not at all obvious to me. And if some other quasiparticle
description is possible, then I can imagine doing physics in other
phases of matter where it wasn’t “natural” to discover electrons,
photons, etc, but rather we would naturally discover a very
different set of basic particles and fields. (It was this thought
that motivated me to wonder about life native to other phases of
matter.)
Related: the work of Xiao-Gang Wen, e.g. this paper, and many
others.
What’s the analogue of the Church-Turing thesis for programmable
matter? What’s the analogue of the strong Church-Turing thesis?
Presumably there is some universal factory that can reasonably
efficiently produce near-optimal substrates. What is the nature of
that factory?
It’s interesting to think about overarching divisions of matter we
use in the everyday world. Different phases of matter. Living versus
non-living. Conscious versus non-conscious. Systems which process
(or carry) information versus those which do not. When you start to
push hard on the boundaries between these divisions, things get
interesting.
I’ve implicitly often made a distinction here between microscopic
and macroscopic scales. I’m uncomfortable with the
dichotomy. Somehow, you want to understand the transition, and
ideally perhaps even have several different layers of intermediate
abstraction.

A few things to read, or to read more deeply

Some of Kitaev’s early models: 1, 2.
Kitaev and Laumann review on topological phases and quantum computation
Kitaev on the Sachdev-Yu-Kitaev (SYK) model, and connections to
holography: 1, 2, 3.
Kitaev on a periodic table for topological insulators and superconductors.
David Deutsch on constructor theory.

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