Seth Lloyd’s book (see prior post) has a nice passage in a chapter subsection entitled “So What?” (p. 168). If the universe can indeed be viewed as a quantum computer, why should we care? He poses this further question: “Do we really need a whole new paradigm for thinking about how the universe operates?” Lloyd says (and it would seem difficult to disagree) that the dominant paradigm of the age of science has been that of universe as mechanism. He proposes a new paradigm: “I suggest thinking about the world not simply as a machine, but as a machine that processes information (p.169 – emphasis original).” In my opinion, however, Lloyd’s discussion, while often suggestive, doesn't really answer the "so what" question. Actually, he underplays how radical and interesting a notion this new paradigm really could be.
Unfortunately, in the section quoted from above, Lloyd doesn’t follow through in offering a philosophically compelling interpretation of this new paradigm. He goes on to discuss how the view might better (technically) account for complexity and how it could help on the quest for a theory of quantum gravity – both topics of subsequent sections. Other statements of this sort sprinkled throughout the book are neutral in tone and vague in terms of what they really mean. Here’s the typical quote: “All physical systems register information, and when they evolve dynamically in time, they transform and process that information. (Prologue, p. xi.)”.
I became frustrated at this: What does it really mean to say physical systems process information? In my own (perhaps uninformed) view of classical computing, the only true information processors are the human beings who provide input, program, and interpret the output. The semantics of information processing are provided by humans exclusively, the rest is syntax. This issue is discussed in one subsection of Lloyds’ book, entitled “Meaning” (p.24), where Lloyd relates being asked by a student: “’But doesn’t information have to mean something?’” The response: “’You’re right that when we think of information we normally associate it with meaning,’ I answered. ‘But the meaning of ‘meaning’ is not clear.’” In the rest of the section (written presumably after some reflection on this), he fails to improve on this answer. He discusses how bits can represent information, and then says “the interpreter must provide the meaning.” Note there is nothing innovative or even quantum mechanical about this discussion.
Here’s the unstated radical interpretation of Lloyd’s theory: If physical interactions ubiquitously can be described in terms of information processing, this implies that something we think belongs uniquely to human (and some animal) agents is also a feature of more elementary physical systems: that is, possession of semantic properties, or intentionality. If one is unwilling to take this step, that’s fine, but then there is no important difference between the new and the old paradigm when it comes to interpreting how human life and mind can fit into the picture of an otherwise lifeless mechanistic universe.
Postscript:
It’s not a coincidence that Lloyd’s approach to the measurement problem of QM is conservative. He believes the decoherent-histories approach is practical and useful enough to de-emphasize worries about foundational interpretation.
Monday, April 30, 2007
Tuesday, April 24, 2007
Living and Computing in Lloyd's Universe
I recently read Seth Lloyd’s Programming the Universe. This is a thought-provoking (if a bit meandering) book which explains why we should envision the universe as a quantum computer and how doing so may illuminate our understanding of some difficult questions (it is out in paperback – page references below are to this edition). In addition it offers a useful summary of quantum computing for the general reader, along with discussions of cosmology, thermodynamics and introductory quantum mechanics (all with a computing “gloss”). In this post and one or two to follow, I’ll discuss a couple of Lloyds’ ideas. (For a general review, the NYT’s is here).
As a layperson who had read explanatory books and articles about quantum physics for many years before I ever heard about quantum computers, the first theme the book hammered home for me was that quantum computing in an important sense just is quantum physics. A classical computer can be instantiated in a variety of physical set-ups; a quantum computer is itself a quantum system. While you can try to model a quantum system on a classical computer, you will quickly overwhelm its computational resources. So, quantum computing, in addition to its potential for practical acceleration of computing power generally, gives us a useful and appropriate logical framework to analyze the physics of our world.
The next step is to explore the implications of the ability to perform this kind of “quantum simulation”. Here’s a thumbnail sketch of how the simulation is done (p.149): “Every part of the quantum system to be simulated is mapped onto a collection of qubits in the quantum computer, and interactions between these parts become a sequence of quantum logic operations.” In fact: “…quantum computers could function as universal quantum simulators, whose dynamics could be the analog of any desired physical dynamics. (p.151)” At this point, Lloyd makes the conceptual case that, logically, there is no reason to distinguish between what’s happening in the simulation and the original system.
Now, the step which motivates the book title: while we can’t do it yet, in principle the universe (the accessible part, anyway) is finite in extent, and hypothetically could be simulated in a quantum computer. But, following the point above, since the computer has the same number of qubits as the universe, and since the operations on the qubits simulate the universe’s dynamics, we can say: “Such a quantum computation would constitute a complete description of nature, and so would be indistinguishable from nature. Thus, at bottom, the universe can be thought of as performing a quantum computation. (p.154, emphasis original).”
So what does it mean? What can this view do for us? I think there are two possible answers, one concrete and one more intangible. First, ideas from quantum computing may help in the quest for a theory of quantum gravity. Second, it may offer an improved paradigm for interpreting and understanding the physical world. I’ll follow up on these in future posts.
As a layperson who had read explanatory books and articles about quantum physics for many years before I ever heard about quantum computers, the first theme the book hammered home for me was that quantum computing in an important sense just is quantum physics. A classical computer can be instantiated in a variety of physical set-ups; a quantum computer is itself a quantum system. While you can try to model a quantum system on a classical computer, you will quickly overwhelm its computational resources. So, quantum computing, in addition to its potential for practical acceleration of computing power generally, gives us a useful and appropriate logical framework to analyze the physics of our world.
The next step is to explore the implications of the ability to perform this kind of “quantum simulation”. Here’s a thumbnail sketch of how the simulation is done (p.149): “Every part of the quantum system to be simulated is mapped onto a collection of qubits in the quantum computer, and interactions between these parts become a sequence of quantum logic operations.” In fact: “…quantum computers could function as universal quantum simulators, whose dynamics could be the analog of any desired physical dynamics. (p.151)” At this point, Lloyd makes the conceptual case that, logically, there is no reason to distinguish between what’s happening in the simulation and the original system.
Now, the step which motivates the book title: while we can’t do it yet, in principle the universe (the accessible part, anyway) is finite in extent, and hypothetically could be simulated in a quantum computer. But, following the point above, since the computer has the same number of qubits as the universe, and since the operations on the qubits simulate the universe’s dynamics, we can say: “Such a quantum computation would constitute a complete description of nature, and so would be indistinguishable from nature. Thus, at bottom, the universe can be thought of as performing a quantum computation. (p.154, emphasis original).”
So what does it mean? What can this view do for us? I think there are two possible answers, one concrete and one more intangible. First, ideas from quantum computing may help in the quest for a theory of quantum gravity. Second, it may offer an improved paradigm for interpreting and understanding the physical world. I’ll follow up on these in future posts.
Monday, April 16, 2007
Geometrogenesis
This is a very cool new word. The context of its coining is the exploration of a new genre of background independent quantum gravity theories. The term appears in 3 recent papers posted on arxiv. Geometrogenesis refers to the emergence of space-time geometry (and matter simultaneously) from a pre-geometric micro-theory of interacting quantum systems.
It looks like the term first appeared in “Quantum Graphity”, a paper by Tomasz Konopka, Fotini Markopoulou, and Lee Smolin. Here, the authors created a model intended as a demonstration of how such a theory could proceed. In the model, degrees of freedom lie on a graph which in a disordered high temperature state can only be described in quantum mechanical terms. The system transitions to an orderly lattice structure at low temperatures.
Markopoulou then added two more (mostly overlapping) papers which step back and survey how theories featuring geometrogenesis fit into the taxonomy of quantum gravity theories and how they differ from other so-called background independent theories like loop quantum gravity.
In the paper “New Directions in Background Independent Quantum Gravity,” Markopoulou describes the “traditional” path to background independent quantum theories of gravity (e.g. LQG) as ones which create microscopic geometric degrees of freedom and then consider quantum superposition or path integrals of these geometries. One challenge for such an approach is that the quest for finding classical dynamical space-time in the low energy limit is made difficult by the fact that the starting point is a timeless, not a dynamical theory. (Note though that Causal Dynamical Triangulations is an approach, discussed in this prior post, which has had some success in getting at least the right large scale dimensionality to emerge from a micro-geometric starting point).
Here is what Markopoulou says in section 1.6.1 of the paper (p.18) about the geometrogenesis picture:
She goes on to credit Olaf Dreyer (see this paper, for instance) and quantum computational theorist Seth Lloyd (see here) for advocating this concept of emergence with regard to dynamical space-time.
There are no distances or metrics in the micro-theory; distance is recovered as emerging from the relations among the quantum sub-systems. She also notes that is a feature of this idea that these emergent excitations of the microscopic degrees of freedom define not only geometry but the structure of matter at the same time. Matter and gravity are unified in the pre-geometric phase. The ambition of this approach is highlighted by Markopoulou’s saying that the approach “provides a path towards explaining gravity rather than just quantizing it (emphasis original).”
She discusses some of the challenges the approach faces. One is that the introduction of dynamics in the micro-theory reintroduces time in a theory that is supposed to be background independent (I personally think if local time and causality exist in the micro-theory, that’s OK). Second and more important, can such a theory show that geometry will emerge, or just that it could emerge. In other words will we need to posit a fine-tuning mechanism to have a geometric phase? She thinks some of the early approaches offer the hope that the geometric phase is a generic consequence of the theory.
In the paper, she then goes on to describe a specific approach she’s been working on, which invokes the quantum computing concept of noiseless sub-systems to drive emergence. I have a prior post about this work, so I’ll leave off discussing it here.
I don’t have any right to have an opinion, but I find a lot of intuitive appeal in this approach to quantum gravity. The ground level of reality consists of elementary quantum systems linked in a causal network; it is a natural consequence of this reality that our world emerges at the large scale.
It looks like the term first appeared in “Quantum Graphity”, a paper by Tomasz Konopka, Fotini Markopoulou, and Lee Smolin. Here, the authors created a model intended as a demonstration of how such a theory could proceed. In the model, degrees of freedom lie on a graph which in a disordered high temperature state can only be described in quantum mechanical terms. The system transitions to an orderly lattice structure at low temperatures.
Markopoulou then added two more (mostly overlapping) papers which step back and survey how theories featuring geometrogenesis fit into the taxonomy of quantum gravity theories and how they differ from other so-called background independent theories like loop quantum gravity.
In the paper “New Directions in Background Independent Quantum Gravity,” Markopoulou describes the “traditional” path to background independent quantum theories of gravity (e.g. LQG) as ones which create microscopic geometric degrees of freedom and then consider quantum superposition or path integrals of these geometries. One challenge for such an approach is that the quest for finding classical dynamical space-time in the low energy limit is made difficult by the fact that the starting point is a timeless, not a dynamical theory. (Note though that Causal Dynamical Triangulations is an approach, discussed in this prior post, which has had some success in getting at least the right large scale dimensionality to emerge from a micro-geometric starting point).
Here is what Markopoulou says in section 1.6.1 of the paper (p.18) about the geometrogenesis picture:
“It is a factor of about twenty orders of magnitude from the physics of the Planck scale described by the microscopic theory to the standard subatomic physics. By analogy with all other physical systems we know, it is reasonable to expect that physics at the two scales decouples to a good approximation. We can expect at least one phase transition interpolating between the microscopic BI phase and the familiar one in which we see dynamical geometry. We shall use the word geometrogenesis for this phase transition.”
She goes on to credit Olaf Dreyer (see this paper, for instance) and quantum computational theorist Seth Lloyd (see here) for advocating this concept of emergence with regard to dynamical space-time.
There are no distances or metrics in the micro-theory; distance is recovered as emerging from the relations among the quantum sub-systems. She also notes that is a feature of this idea that these emergent excitations of the microscopic degrees of freedom define not only geometry but the structure of matter at the same time. Matter and gravity are unified in the pre-geometric phase. The ambition of this approach is highlighted by Markopoulou’s saying that the approach “provides a path towards explaining gravity rather than just quantizing it (emphasis original).”
She discusses some of the challenges the approach faces. One is that the introduction of dynamics in the micro-theory reintroduces time in a theory that is supposed to be background independent (I personally think if local time and causality exist in the micro-theory, that’s OK). Second and more important, can such a theory show that geometry will emerge, or just that it could emerge. In other words will we need to posit a fine-tuning mechanism to have a geometric phase? She thinks some of the early approaches offer the hope that the geometric phase is a generic consequence of the theory.
In the paper, she then goes on to describe a specific approach she’s been working on, which invokes the quantum computing concept of noiseless sub-systems to drive emergence. I have a prior post about this work, so I’ll leave off discussing it here.
I don’t have any right to have an opinion, but I find a lot of intuitive appeal in this approach to quantum gravity. The ground level of reality consists of elementary quantum systems linked in a causal network; it is a natural consequence of this reality that our world emerges at the large scale.
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