By Michael Nielsen

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