Something is bothering me at the boundary of physics and metaphysics. It seems very likely that a successful theory of quantum gravity will entail that our actual universe is finite. This follows from two considerations. First, in the new theory, the singularities of general relativity will be banished, and the universe will be seen to be grained at the Planck scale. Second, it seems to me that the observable universe can be identified with the actual universe: in what sense should we consider a putative region of the universe beyond the reach of any possible causal contact to be actual? So, it follows that the actual universe is finite.
Now in reading metaphysical papers recently by Ross Cameron and Jonathan Schaffer, (see posts here and here), I was introduced to the argument for the conceivability of “gunk”. Gunk is stuff every part of which has proper parts -- that is, it is infinitely divisible. Now is a world made of gunk conceivable? It seems so. Now, since I have embraced the general stance that conceivability implies possibility, I would have to concede that if the actual world is finite, this is a contingent rather than necessary fact about the world.
For some reason, this just rubs me the wrong way. I don’t like thinking that something as fundamental as the conclusion that our world is finite in extent is just a contingent fact. But given that we are (famously) adept at conceiving infinities, and the strength of my opinion regarding the modal rationalist link between conceivability and possibility, I’m stuck.
The only strategy which I think might work is as follows. I could assert that the conceivability of infinity is grounded by the whole space of possible worlds, and its application to a single possible world is a mistake. The gunky world would itself have to comprise all possible worlds by virtue of its infinite extent. It would itself necessarily constitute the entire modal space, so it couldn’t also be one of the constituents of modal space. Individual possible worlds themselves would be necessarily finite in this scheme.
Friday, May 18, 2007
Tuesday, May 15, 2007
In the Beginning was the Qubit
So, how did this party get started? In Programming the Universe (see also prior posts on this topic), Seth Lloyd would like to retell the cosmological story with qubits instead of elementary particles. However, the section of the book (chapter 3) where he does this doesn’t really add much to the standard account. He interprets fluctuations in quantum fields as superpositions of bits whose possible outcomes "0" and "1" represent low and high energy density. The collapse (or decoherence, following Lloyd’s preferred interpretation) of these superpositions creates pockets of high density which can then be the target of gravitational attraction. If you take out the references to bits, his story seems to be the standard cosmological model. If the universe is really a quantum computer, then matter-energy fields (and space-time) would be derived from qubits.
In other words, the real innovation would come if the computational model helps point us toward a theory of quantum gravity. And here, Lloyd does have some ideas. The book has just a few pages on this, but more detail is found in his paper, “A theory of quantum gravity based on quantum computation”. Some impressions from this paper are below (with the caveat that as usual I can’t understand large portions of it).
The idea is that the metric structure of space-time and the behavior of quantum matter fields “are derived from and arise out of an underlying quantum computer. (p.2)”. One starts with the fact a quantum computer can be thought of as a universal theory for discrete quantum mechanics. Quantum computers represent a causal network (=computational history) of interactions – actually superpositions of such networks. These can be represented as a graph, similar to those in causal set theory. Now, for the matter side of things, note that at each vertex of the graph (=logic gate), qubits can be transformed or not. When they are transformed, this is a scattering event. Each computation is a superposition of different computational histories, one for each pattern of scattering events. The events are the matter.
On the gravity side of things, the superpositions of these computational histories will be seen to correspond to a fluctuation of space-time geometry. Lloyd’s strategy is to “embed the computational graph in a space-time manifold by mapping [the computational graph] C into R4 via an embedding mapping E. (pp.6-7)”. He says that if you do this, then general covariance will follow from the fact that the informational flow through the network is independent of the way the computation is embedded in space-time. The next step (which seems to be the key part of the paper) makes some additional assumptions so that the geometries derived from the computation explicitly obey the Einstein equations (in their discrete Regge calculus form).
Now I can’t follow all the steps here, but what I think he is doing amounts to a demonstration of how a quantum computation could be consistent with the emergence of general relativistic space-time, rather than showing that it would actually do so as a matter of course. He ends up being at least partially circular in invoking our knowledge of the Einstein equations to achieve his explicit results (if someone would like to correct me on this, please do). In contrast, Fotini Markopoulou’s desired ambition (see here and here) is to show that the emergence of space-time is a general consequence of an underlying quantum micro-theory (likewise Olaf Dreyer).
The paper finishes with some ideas on how such a theory would impact a variety of topics in cosmology. For instance, singularities correspond to bits entering or leaving the universe, and black holes do lose information; the model can handle different stages of cosmological evolution, etc. This is interesting stuff, and I’ll be interested in seeing if these ideas are developed further.
Something which intrigues me is how one is supposed to think about this new proposed atom of the universe, the qubit. A practical quantum computer uses properties of familiar particles (spin of an electron or polarization of a photon) as qubits. But if these particles (as well as space-time itself) are derived from these postulated elementary qubits, what are they? Is the superposed atomic qubit just a pure possibility of existence?
[UPDATE: 25 May, 2007. My comments in first paragraph of this post are a bit unfair since later in the book (Ch.8 p.196) Lloyd revisits the story of the history of the universe incorporating some of the ideas from his sections on quantum gravity and complexity. In this discussion, here the computation does indeed have priority status over matter and gravity.]
In other words, the real innovation would come if the computational model helps point us toward a theory of quantum gravity. And here, Lloyd does have some ideas. The book has just a few pages on this, but more detail is found in his paper, “A theory of quantum gravity based on quantum computation”. Some impressions from this paper are below (with the caveat that as usual I can’t understand large portions of it).
The idea is that the metric structure of space-time and the behavior of quantum matter fields “are derived from and arise out of an underlying quantum computer. (p.2)”. One starts with the fact a quantum computer can be thought of as a universal theory for discrete quantum mechanics. Quantum computers represent a causal network (=computational history) of interactions – actually superpositions of such networks. These can be represented as a graph, similar to those in causal set theory. Now, for the matter side of things, note that at each vertex of the graph (=logic gate), qubits can be transformed or not. When they are transformed, this is a scattering event. Each computation is a superposition of different computational histories, one for each pattern of scattering events. The events are the matter.
On the gravity side of things, the superpositions of these computational histories will be seen to correspond to a fluctuation of space-time geometry. Lloyd’s strategy is to “embed the computational graph in a space-time manifold by mapping [the computational graph] C into R4 via an embedding mapping E. (pp.6-7)”. He says that if you do this, then general covariance will follow from the fact that the informational flow through the network is independent of the way the computation is embedded in space-time. The next step (which seems to be the key part of the paper) makes some additional assumptions so that the geometries derived from the computation explicitly obey the Einstein equations (in their discrete Regge calculus form).
Now I can’t follow all the steps here, but what I think he is doing amounts to a demonstration of how a quantum computation could be consistent with the emergence of general relativistic space-time, rather than showing that it would actually do so as a matter of course. He ends up being at least partially circular in invoking our knowledge of the Einstein equations to achieve his explicit results (if someone would like to correct me on this, please do). In contrast, Fotini Markopoulou’s desired ambition (see here and here) is to show that the emergence of space-time is a general consequence of an underlying quantum micro-theory (likewise Olaf Dreyer).
The paper finishes with some ideas on how such a theory would impact a variety of topics in cosmology. For instance, singularities correspond to bits entering or leaving the universe, and black holes do lose information; the model can handle different stages of cosmological evolution, etc. This is interesting stuff, and I’ll be interested in seeing if these ideas are developed further.
Something which intrigues me is how one is supposed to think about this new proposed atom of the universe, the qubit. A practical quantum computer uses properties of familiar particles (spin of an electron or polarization of a photon) as qubits. But if these particles (as well as space-time itself) are derived from these postulated elementary qubits, what are they? Is the superposed atomic qubit just a pure possibility of existence?
[UPDATE: 25 May, 2007. My comments in first paragraph of this post are a bit unfair since later in the book (Ch.8 p.196) Lloyd revisits the story of the history of the universe incorporating some of the ideas from his sections on quantum gravity and complexity. In this discussion, here the computation does indeed have priority status over matter and gravity.]
Friday, May 04, 2007
Notre Dame Phil. Review of Strawson
For those interested, Leopold Stubenberg has a well-written summary of the recent special edition of the Journal of Consciousness Studies featuring Galen Strawson's panpsychism papers and 17 commentaries. (Hat tip - A brood comb's "power-blogroll"). My posts on this topic are here.
Monday, April 30, 2007
Physical Systems Process Information: So What?
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.
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.
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.
Wednesday, March 21, 2007
Merriam's Quantum Relativity
Paul Merriam posted a paper called Quantum Relativity: Physical Laws Must be Invariant Over Quantum Systems in which he puts forth a conceptual strategy for understanding how a relational interpretation addresses the foundational issues of quantum mechanics. Please see this prior post for more background. What follows is a summary and attempted interpretation of what I found to be key aspects of the paper. The usual caveats are in place: my summaries may be not only incomplete (including omission of formalisms) but also misleading due to errors in interpretation. Please read the paper to judge.
The paper starts with a section which discusses why decoherence does not solve the foundational issues of QM. Since I believe this is generally acknowledged (see this recent blog post from Matt Leifer; an old blog post of mine is here), I’ll just focus on the most important part of this discussion. Recall that one of the perceived shortcomings of the relational interpretation of QM revolves around the question of how two or more interacting systems come to “choose” the same basis. Merriam says that decoherence has a “change of basis” problem of its own.
To see this, Merriam returns to the “Wigner’s friend” framework and replaces "Wigner" with the "environment" to create a decoherence version of the scenario. Relative to the environment E, the experimenter (called A) and the system he or she is measuring (S) are in superposition and evolve according the Schrödinger picture. Decoherence would lead to the selection of relatively stable “classical” appearances of the observable which is the basis of the measurement. But suppose A decides to measure a different observable of S (change of basis). Decoherence takes place over a period of time (decoherence time); this time depends on many factors, but the “change of basis” is a problem for the time between zero and the decoherence time. (Decoherence is not measurement).
Next Merriam discusses (repeating the arguments of his older paper) the issues highlighted by the Wigner’s friend setup, arguing again that the quantum state describes a system relative to another system. Quantum mechanics is an intransitive theory.
The next section is titled “Quantum Relativity”. So having acknowledged the perspectivist nature of QM, what’s the next step? When considering two quantum systems: “The essential point of this paper is that since both systems physically exist they are both valid coordinate frames from which the laws of physics must hold. Quantum mechanics is as valid in S as it is in A.” If A describes S in terms of a superposition across some measurement basis, then S will describe A as starting out in a corresponding superposition. When A observes (measures) S to be in some eigenstate, “S must also observe A to be in some corresponding eigenstate…”
The key point is brought out by the word “must” here and in the title of the paper. The conceptual hurdle we are jumping here is as follows: if QM is valid from the point of view of all “quantum systems” (including everything from electrons to physicists), then when they interact they necessarily select the consistent basis for interaction. The basis problem is solved by asserting that basis choices must match if QM is to be valid from all points of view.
Merriam believes this conceptual leap has consequences analogous to special relativity. The next passage (see p. 6) looks at the formalism of the Schrödinger equation from A’s and S’s perspective and wonders how they can be consistent if the mass is so different in the two cases. But he notes the values for length or distance between the two quantum observations do not have to have the same numeral values in both systems. If distance is scaled to the relationship of the masses, then it is possible to create a transformation from the superposition of S as described by A to that of A described by S. There can be a group of such transformations for any number of systems. Merriam derives a transformation constant in analogy to the role the speed of light c plays in relativistic transformation.
Merriam also speculates about that one could extend the idea to include gravity by taking the equivalence of gravitational force and acceleration to be relative to the local quantum reference system. He suggests the shape a quantum version of Einstein’s equation would take. I will skip for now further discussion of this idea and a section on how gauge invariance might be impacted, since I think the key concept is in place with the analogue to special relativity.
Key to special relativity is the postulate that physical laws valid from one reference frame should be form-invariant when translated to another frame. To review, we assume that QM gives a valid physical description from the point of view of a system, and each quantum system forms a physically valid coordinate frame. Note that systems only share a reference frame when they interact. We should be able to translate the state of a system S which is in superposition relative to system A to the state of A relative to S. Again, this only works if we stipulate that if an interaction takes place, the “basis choice” is necessarily consistent from both perspectives.
The paper starts with a section which discusses why decoherence does not solve the foundational issues of QM. Since I believe this is generally acknowledged (see this recent blog post from Matt Leifer; an old blog post of mine is here), I’ll just focus on the most important part of this discussion. Recall that one of the perceived shortcomings of the relational interpretation of QM revolves around the question of how two or more interacting systems come to “choose” the same basis. Merriam says that decoherence has a “change of basis” problem of its own.
To see this, Merriam returns to the “Wigner’s friend” framework and replaces "Wigner" with the "environment" to create a decoherence version of the scenario. Relative to the environment E, the experimenter (called A) and the system he or she is measuring (S) are in superposition and evolve according the Schrödinger picture. Decoherence would lead to the selection of relatively stable “classical” appearances of the observable which is the basis of the measurement. But suppose A decides to measure a different observable of S (change of basis). Decoherence takes place over a period of time (decoherence time); this time depends on many factors, but the “change of basis” is a problem for the time between zero and the decoherence time. (Decoherence is not measurement).
Next Merriam discusses (repeating the arguments of his older paper) the issues highlighted by the Wigner’s friend setup, arguing again that the quantum state describes a system relative to another system. Quantum mechanics is an intransitive theory.
The next section is titled “Quantum Relativity”. So having acknowledged the perspectivist nature of QM, what’s the next step? When considering two quantum systems: “The essential point of this paper is that since both systems physically exist they are both valid coordinate frames from which the laws of physics must hold. Quantum mechanics is as valid in S as it is in A.” If A describes S in terms of a superposition across some measurement basis, then S will describe A as starting out in a corresponding superposition. When A observes (measures) S to be in some eigenstate, “S must also observe A to be in some corresponding eigenstate…”
The key point is brought out by the word “must” here and in the title of the paper. The conceptual hurdle we are jumping here is as follows: if QM is valid from the point of view of all “quantum systems” (including everything from electrons to physicists), then when they interact they necessarily select the consistent basis for interaction. The basis problem is solved by asserting that basis choices must match if QM is to be valid from all points of view.
Merriam believes this conceptual leap has consequences analogous to special relativity. The next passage (see p. 6) looks at the formalism of the Schrödinger equation from A’s and S’s perspective and wonders how they can be consistent if the mass is so different in the two cases. But he notes the values for length or distance between the two quantum observations do not have to have the same numeral values in both systems. If distance is scaled to the relationship of the masses, then it is possible to create a transformation from the superposition of S as described by A to that of A described by S. There can be a group of such transformations for any number of systems. Merriam derives a transformation constant in analogy to the role the speed of light c plays in relativistic transformation.
Merriam also speculates about that one could extend the idea to include gravity by taking the equivalence of gravitational force and acceleration to be relative to the local quantum reference system. He suggests the shape a quantum version of Einstein’s equation would take. I will skip for now further discussion of this idea and a section on how gauge invariance might be impacted, since I think the key concept is in place with the analogue to special relativity.
Key to special relativity is the postulate that physical laws valid from one reference frame should be form-invariant when translated to another frame. To review, we assume that QM gives a valid physical description from the point of view of a system, and each quantum system forms a physically valid coordinate frame. Note that systems only share a reference frame when they interact. We should be able to translate the state of a system S which is in superposition relative to system A to the state of A relative to S. Again, this only works if we stipulate that if an interaction takes place, the “basis choice” is necessarily consistent from both perspectives.
Friday, March 16, 2007
Exploring the Borderlands
Recent books on atheism and religion have been the focus of much debate recently, which I think is a good thing. It’s no surprise that the debate is dominated by traditional religious believers on the one hand, and those who hold to a traditional materialist strain of atheism on the other. Of course, there is a wide, if seemingly less populated, territory between these views. I think the truth lies in the border regions.
If one is a realist, as I am, about first-person experience and the existence of some degree of freedom, then materialism is inadequate. On the other hand, one’s worldview must be shaped by valid inferences from the success of science. Because of this, I find traditional supernatural entities and interventions highly implausible, and have in the past characterized my own worldview has an enriched or expanded version of naturalism.
My more recent ruminations on modal realism and abstract entities have led me to consider that my realist commitments may actually require a necessary ground of possibilities underlying and penetrating our contingent concrete world. While at the end of the day labels aren't important, it seems as if a commitment to the idea that reality extends beyond our world in this way may get me expelled from the naturalist club.
I’m very reluctant to name this necessary existent “God”, since that unavoidably summons up a cluster of attributes and associations which go far beyond my commitments. But there is no getting around the fact that I may be moving into the vicinity of theism.
If one is a realist, as I am, about first-person experience and the existence of some degree of freedom, then materialism is inadequate. On the other hand, one’s worldview must be shaped by valid inferences from the success of science. Because of this, I find traditional supernatural entities and interventions highly implausible, and have in the past characterized my own worldview has an enriched or expanded version of naturalism.
My more recent ruminations on modal realism and abstract entities have led me to consider that my realist commitments may actually require a necessary ground of possibilities underlying and penetrating our contingent concrete world. While at the end of the day labels aren't important, it seems as if a commitment to the idea that reality extends beyond our world in this way may get me expelled from the naturalist club.
I’m very reluctant to name this necessary existent “God”, since that unavoidably summons up a cluster of attributes and associations which go far beyond my commitments. But there is no getting around the fact that I may be moving into the vicinity of theism.
Monday, March 12, 2007
Priority Monism
[UPDATE: 25 Sept.2009: Links fixed, but note the post refers to an earlier draft of the paper]
As a follow-up to the last post, I want to very briefly take note of Jonathan Schaffer’s noble attempt to argue that the fundamental (ontologically prior) level is the whole rather than the parts – “priority monism”.
The draft paper “Monism: the Priority of the Whole” includes a fairly lengthy discussion of a historical context in which the case for monism has mostly gone unappreciated (it is often caricatured and dismissed as the position that there exists exactly one thing). He takes some time explicating the idea that both the whole and the parts exist, one of these must be prior, and the choice of either the whole or the parts is an exclusive and exhaustive list of options. Then it is “game on” to see which prevails.
There are four sections to the argument over priority. Two of these I consider a tie: the argument over which comports best with common sense, and which option better explains the apparent heterogeneity of the world (he’s right to say that saying pluralism explains heterogeneity begs the question).
The next section asks what fits best with science. Here, I think Schaffer makes a mistake. He invokes the idea of entanglement from quantum mechanics and infers that the whole world is entangled, making reference to a wave function for the entire universe. In my opinion, this is wrong. The entire world would be entangled only from a perspective standing outside the universe. There is no wave function for the entire universe. The interactions (measurements) between the many quantum systems in the world constitute concrete reality, and the whole of the concrete world is the relational network of these many interactions.
The last section asks which view on priority best deals with the possibility of the world being made of “gunk”, which is stuff with no proper parts (or to put it another way, stuff which is infinitely divisible). Schaffer references a couple of scientific theories and speculations that physical entities might be infinitely divisible. Here I think the existence of the Planck scale is actually good evidence of a limit to divisibility, so again his attempt to invoke science doesn't succeed.
I think that if we’re speaking of our concrete world, then the parts are prior to the whole. The possibility is open, however, that there is a holistic non-concrete ground of possibilia which supports the parts, but this would be a different discussion.
As a follow-up to the last post, I want to very briefly take note of Jonathan Schaffer’s noble attempt to argue that the fundamental (ontologically prior) level is the whole rather than the parts – “priority monism”.
The draft paper “Monism: the Priority of the Whole” includes a fairly lengthy discussion of a historical context in which the case for monism has mostly gone unappreciated (it is often caricatured and dismissed as the position that there exists exactly one thing). He takes some time explicating the idea that both the whole and the parts exist, one of these must be prior, and the choice of either the whole or the parts is an exclusive and exhaustive list of options. Then it is “game on” to see which prevails.
There are four sections to the argument over priority. Two of these I consider a tie: the argument over which comports best with common sense, and which option better explains the apparent heterogeneity of the world (he’s right to say that saying pluralism explains heterogeneity begs the question).
The next section asks what fits best with science. Here, I think Schaffer makes a mistake. He invokes the idea of entanglement from quantum mechanics and infers that the whole world is entangled, making reference to a wave function for the entire universe. In my opinion, this is wrong. The entire world would be entangled only from a perspective standing outside the universe. There is no wave function for the entire universe. The interactions (measurements) between the many quantum systems in the world constitute concrete reality, and the whole of the concrete world is the relational network of these many interactions.
The last section asks which view on priority best deals with the possibility of the world being made of “gunk”, which is stuff with no proper parts (or to put it another way, stuff which is infinitely divisible). Schaffer references a couple of scientific theories and speculations that physical entities might be infinitely divisible. Here I think the existence of the Planck scale is actually good evidence of a limit to divisibility, so again his attempt to invoke science doesn't succeed.
I think that if we’re speaking of our concrete world, then the parts are prior to the whole. The possibility is open, however, that there is a holistic non-concrete ground of possibilia which supports the parts, but this would be a different discussion.
Monday, March 05, 2007
Must there be a Ground-Floor Turtle?
I have a strong intuition that there is a fundamental level of reality which ultimately grounds the phenomena of the world. This intuition forms a basis for preferring certain philosophical arguments over others. For instance, take the cosmological argument. In one traditional formulation, the argument goes something like this: every effect has a cause, and if you follow the chain backwards in time, there must be a first cause. I’ve never felt this argument was very forceful – what’s wrong with an infinite chain of causes? Now, however, if you recast the argument as saying that the contingent facts of the world ultimately and necessarily depend on a fundamental fact or collection of facts, then suddenly I start nodding my head affirmatively. There can’t be an infinite chain of contingent facts depending on other contingent facts, can there? Ontological priority seems to need a starting point more urgently than temporal priority. In the famous expression invoked by Ross P Cameron in his recent paper on this topic (found via OPP): it can’t be turtles all the way down, right?
Our desire for explanations seems to drive the intuition. If an entity is shown to depend on something else, it is thought to be explained. We want this search for explanation to find an ending point in terms of ultimate constituents. In our world, we seem indisputably to encounter composite things which seem comprised of parts; this drives our search for reductionist explanations. I guess it is possible to think that perhaps the “ceiling” rather than the “floor” is fundamental; perhaps the whole of the universe is the fundamental thing and the parts ontologically depend on the whole. Now, this seems counterintuitive to me: if we start with a whole, why should there be any parts? In any case, the direction of dependence is probably less important for this discussion than the idea that there is some fundamental level.
In his paper, Cameron asks whether there is a good argument for the truth of this intuition that there cannot be an unending chain of ontological dependence. Can we, for instance, argue that if there were no fundamental level grounding other entities, then nothing would be real? Cameron concludes that this would essentially be restating the intuition, rather than providing an argument. He considers a couple of other strategies in the paper and finds no satisfactory argument. On the other hand, he doesn’t see any good arguments against the intuition either. In fact the search for a metaphysical argument for the intuition may be seen to parallel the search for a deeper and deeper ontological level: you have to start somewhere, don’t you? Why not with an intuition? He notes as an example that Leibniz never argues for the Principle of Sufficient Reason, it’s just his starting point. Now, one can’t thereby defeat a skeptic who doesn’t share the intuition, but at the end of the day I don't find that the skeptics and deflationists of the world provide very good metaphysical explanations themselves.
Cameron says we can justify the intuition against infinitely descending chains of dependence by appeal to theoretical utility. We can give better explanations for entities if we identify an ultimate ontological basis in a collection of independent entities. This may be reason enough. He notes that this won’t convince someone who thinks the search for metaphysical explanation is misguided to begin with. On the other hand he says: ”…if you believe in metaphysical explanation you should believe it bottoms out somewhere.” He ends the paper by noting that given the pragmatic way the use of the principle is being justified, we should be modest about holding forth about the necessity of its truth.
Also interesting in this context is David Chalmers' recent paper: Ontological Anti-Realism (see blog post with links). His support for anti-realism in the paper (most of which is devoted to a mapping out of the terrain of meta-ontological stances) holds out the possibility of an exception for realism about the fundamental level. Jonathan Schaffer, in his commentary on the paper argues that Chalmers’ framework actually requires realism about the fundamental level. If Schaffer’s arguments are right, it seems to help to bolster the case that if you want to pursue metaphysical explanations, you need to be a realist about the fundamental level.
Our desire for explanations seems to drive the intuition. If an entity is shown to depend on something else, it is thought to be explained. We want this search for explanation to find an ending point in terms of ultimate constituents. In our world, we seem indisputably to encounter composite things which seem comprised of parts; this drives our search for reductionist explanations. I guess it is possible to think that perhaps the “ceiling” rather than the “floor” is fundamental; perhaps the whole of the universe is the fundamental thing and the parts ontologically depend on the whole. Now, this seems counterintuitive to me: if we start with a whole, why should there be any parts? In any case, the direction of dependence is probably less important for this discussion than the idea that there is some fundamental level.
In his paper, Cameron asks whether there is a good argument for the truth of this intuition that there cannot be an unending chain of ontological dependence. Can we, for instance, argue that if there were no fundamental level grounding other entities, then nothing would be real? Cameron concludes that this would essentially be restating the intuition, rather than providing an argument. He considers a couple of other strategies in the paper and finds no satisfactory argument. On the other hand, he doesn’t see any good arguments against the intuition either. In fact the search for a metaphysical argument for the intuition may be seen to parallel the search for a deeper and deeper ontological level: you have to start somewhere, don’t you? Why not with an intuition? He notes as an example that Leibniz never argues for the Principle of Sufficient Reason, it’s just his starting point. Now, one can’t thereby defeat a skeptic who doesn’t share the intuition, but at the end of the day I don't find that the skeptics and deflationists of the world provide very good metaphysical explanations themselves.
Cameron says we can justify the intuition against infinitely descending chains of dependence by appeal to theoretical utility. We can give better explanations for entities if we identify an ultimate ontological basis in a collection of independent entities. This may be reason enough. He notes that this won’t convince someone who thinks the search for metaphysical explanation is misguided to begin with. On the other hand he says: ”…if you believe in metaphysical explanation you should believe it bottoms out somewhere.” He ends the paper by noting that given the pragmatic way the use of the principle is being justified, we should be modest about holding forth about the necessity of its truth.
Also interesting in this context is David Chalmers' recent paper: Ontological Anti-Realism (see blog post with links). His support for anti-realism in the paper (most of which is devoted to a mapping out of the terrain of meta-ontological stances) holds out the possibility of an exception for realism about the fundamental level. Jonathan Schaffer, in his commentary on the paper argues that Chalmers’ framework actually requires realism about the fundamental level. If Schaffer’s arguments are right, it seems to help to bolster the case that if you want to pursue metaphysical explanations, you need to be a realist about the fundamental level.
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