We don't have a theory of quantum gravity, but we have a number of research programs on the case. Steve Carlip has a paper (The Small Scale Structure of Spacetime) which discusses an intriguing fact: many of these otherwise disparate programs display or imply the idea that our familiar four dimensional (3 spacelike + 1 timelike) spacetime may be two dimensional (1+1) at high energies/short distances.
If 4 dimensional spacetime is an emergent phase, and the more fundamental physics is comprised of elementary, causally linked, quantum bits of some sort, you might expect this kind of dimensionality.
Here is the physics arxiv blog article on the paper.
Showing posts with label Quantum Gravity. Show all posts
Showing posts with label Quantum Gravity. Show all posts
Monday, September 13, 2010
Monday, June 14, 2010
Order Underpins Everything
I discovered the work of Kevin H. Knuth, and took a dive into his papers and this recent talk given at the Perimeter Institute. The theme of his research is that a simple ordering relation among elements is more fundamental than, and can be used to derive, more familiar theories. The talk is entitled “The Role of Order in Natural Law”, and was part of a workshop on the topic of laws of nature.
Thursday, January 14, 2010
Another Argument for Emergent Gravity
I have followed with interest a growing body of opinion among physicists that gravity (and space itself) is best thought of as an emergent phenomenon (most recently here). Erik Verlinde has a paper, called On the Origin of Gravity and the Laws of Newton, which presents a heuristic case for gravity as emergent.
Unlike most of the other research papers I've blogged about, this is not a quantum gravity theory, but rather uses a number of concepts in mainstream physics (thermodynamics, the holographic principle) to derive emergent gravity. He says that if one coarse grains a microscopic theory (whose precise dynamics need not be known), and applies the holographic principle to measure information on partition screens between particles, the information on the screens will give rise to an entropic force - this is gravity.
The paper has engendered discussion (I first saw it mentioned by Peter Woit here; there is some appreciation here, and criticism here -- Verlinde responds here). The main criticisms are that Verlinde's points are either not new, or that they embody circular reasoning (since concepts from Newtonian and post-Newtonian physics are used to derive Newtonian gravity). Verlinde responds that he is bringing out a new insight which should help convince people that gravity is not a fundamental force, but is emergent.
I can't adjudicate the disagreements, but I think it's very suggestive that the argument for emergence continues to gain adherents.
I also think it is interesting to note that in Verlinde's model the microscopic theory, while not defined in any detail, must have a well-defined asymmeterical time dimension, as in the emergent quantum gravity theories I've reviewed. "Time is fundamental, while space is not".
[UPDATE 22 Jan.2010: A couple of more related links (HT). A New Scientist article, and an illuminating preprint from Lee Smolin, who works through a Verlinde-type derivation in a different way, utilizing ideas from Loop Quantum Gravity research (altho note the specifics of LQG are actually not very important to the analysis). He does a very good job placing the Verlinde work in context of other research and shows where it seems to add new value.]
Unlike most of the other research papers I've blogged about, this is not a quantum gravity theory, but rather uses a number of concepts in mainstream physics (thermodynamics, the holographic principle) to derive emergent gravity. He says that if one coarse grains a microscopic theory (whose precise dynamics need not be known), and applies the holographic principle to measure information on partition screens between particles, the information on the screens will give rise to an entropic force - this is gravity.
The paper has engendered discussion (I first saw it mentioned by Peter Woit here; there is some appreciation here, and criticism here -- Verlinde responds here). The main criticisms are that Verlinde's points are either not new, or that they embody circular reasoning (since concepts from Newtonian and post-Newtonian physics are used to derive Newtonian gravity). Verlinde responds that he is bringing out a new insight which should help convince people that gravity is not a fundamental force, but is emergent.
I can't adjudicate the disagreements, but I think it's very suggestive that the argument for emergence continues to gain adherents.
I also think it is interesting to note that in Verlinde's model the microscopic theory, while not defined in any detail, must have a well-defined asymmeterical time dimension, as in the emergent quantum gravity theories I've reviewed. "Time is fundamental, while space is not".
[UPDATE 22 Jan.2010: A couple of more related links (HT). A New Scientist article, and an illuminating preprint from Lee Smolin, who works through a Verlinde-type derivation in a different way, utilizing ideas from Loop Quantum Gravity research (altho note the specifics of LQG are actually not very important to the analysis). He does a very good job placing the Verlinde work in context of other research and shows where it seems to add new value.]
Wednesday, December 23, 2009
Why Hard Questions are Hard: The Cosmos as a Phase of Being
Why is reality mysterious? Why should difficult questions persist for so long despite the successes of physical science?
An answer to these meta-questions may lie in the concept of a phase transition. As discussed in prior posts (like this recent one), a school of quantum gravity research has arisen which explores the idea that the visible cosmos (of matter bound in space-time geometry) arises at lower energies from a more fundamental quantum world. This more fundamental level is usually characterized by a network of quantum systems, subject to a directional causal arrow, but otherwise connected in a highly non-local fashion (little or no recognizable spatial geometry).
This model is inspired by the myriad examples of phase transitions observed in nature, and particularly those in the field of condensed matter physics (which utilizes the toolkit of quantum field theory to describe the phenomena). Superconductors, superfluids, etc. display remarkable emergent features which arise under certain pressure/temperature conditions.
Picture our familiar physical cosmos as a portion of reality which condensed into a “classical” phase, but retained subtleties in its nature which reflected its pre-transition roots. If this analogy works, then it would explain our situation: while classical explanations usually work well, some phenomena defy such analysis because their foundations go deeper. This could be the case, for instance, for the arrow of time and for conscious experience itself.
An answer to these meta-questions may lie in the concept of a phase transition. As discussed in prior posts (like this recent one), a school of quantum gravity research has arisen which explores the idea that the visible cosmos (of matter bound in space-time geometry) arises at lower energies from a more fundamental quantum world. This more fundamental level is usually characterized by a network of quantum systems, subject to a directional causal arrow, but otherwise connected in a highly non-local fashion (little or no recognizable spatial geometry).
This model is inspired by the myriad examples of phase transitions observed in nature, and particularly those in the field of condensed matter physics (which utilizes the toolkit of quantum field theory to describe the phenomena). Superconductors, superfluids, etc. display remarkable emergent features which arise under certain pressure/temperature conditions.
Picture our familiar physical cosmos as a portion of reality which condensed into a “classical” phase, but retained subtleties in its nature which reflected its pre-transition roots. If this analogy works, then it would explain our situation: while classical explanations usually work well, some phenomena defy such analysis because their foundations go deeper. This could be the case, for instance, for the arrow of time and for conscious experience itself.
Monday, November 30, 2009
String Theorist Turns to Emergent Gravity Approach
Inspired by phase transitions displayed in condensed matter physics, Petr Hořava has constructed a model where the time dimension is decoupled from space at high energy/short distance while the space-time characteristic of relativity (and Lorentz invariance) emerges at low energy/long distances. The model, which is a quantum field theory, is able to be renormalized in a way GR itself cannot be. The paper, “Quantum Gravity at a Lifshitz Point,” sets out the theory.
Monday, October 12, 2009
3 Links: Math and Physics
[UPDATE 13 October 2009: Edited for typos and clarity]
First, since I’m on the record as a skeptic regarding the existence of actual or concrete infinities, I’m on the lookout for discussion of this topic. Here’s a talk given by mathematician Edward Nelson (hat tip: Not Even Wrong). In it, he expresses deep skepticism not only (in passing) regarding the idea of an actual physical infinity, but also (very controversially) on the concept as used in mathematics itself. I wouldn’t think skepticism about the former need have anything to do with the latter (and I’m certainly no mathematician), but I thought this was interesting reading.
Second, I enjoyed reading this (lengthy) overview of quantum gravity research by R.P.Woodard. The main focus of the paper is a “pedagogical explanation” of just why the techniques used in creating quantum versions of classical theories didn’t work when it came to general relativity (I thought this was helpful even if one can't follow all the formalisms). There is also a short section on the state of current research. Woodard makes this comment in the section discussing Causal Dynamical Triangulations (p.67): “…exact calculations are unlikely to be unattainable for quantum gravity, so the most fruitful way of questioning perturbation theory [i.e. the QFT method which is also the basis of original string theory – Steve] is to develop better approximation techniques.” The idea of finding a theory of everything (TOE) which consists of a set of equations with exact solutions looks like it is not going to happen. Finding a well-motivated approximate description of the ultra-high energy regime from which GR and QFT matter fields co-emerge at lower energies is probably the way things will go (I fearlessly predict).
Lastly, here’s a link which is just plain cool. Experimental physicists have been trying to place larger and larger molecules in quantum superposition: here’s a proposal for designing an experiment which could achieve this for a virus. Hat tip goes to the Physics and Cake blog.
First, since I’m on the record as a skeptic regarding the existence of actual or concrete infinities, I’m on the lookout for discussion of this topic. Here’s a talk given by mathematician Edward Nelson (hat tip: Not Even Wrong). In it, he expresses deep skepticism not only (in passing) regarding the idea of an actual physical infinity, but also (very controversially) on the concept as used in mathematics itself. I wouldn’t think skepticism about the former need have anything to do with the latter (and I’m certainly no mathematician), but I thought this was interesting reading.
Second, I enjoyed reading this (lengthy) overview of quantum gravity research by R.P.Woodard. The main focus of the paper is a “pedagogical explanation” of just why the techniques used in creating quantum versions of classical theories didn’t work when it came to general relativity (I thought this was helpful even if one can't follow all the formalisms). There is also a short section on the state of current research. Woodard makes this comment in the section discussing Causal Dynamical Triangulations (p.67): “…exact calculations are unlikely to be unattainable for quantum gravity, so the most fruitful way of questioning perturbation theory [i.e. the QFT method which is also the basis of original string theory – Steve] is to develop better approximation techniques.” The idea of finding a theory of everything (TOE) which consists of a set of equations with exact solutions looks like it is not going to happen. Finding a well-motivated approximate description of the ultra-high energy regime from which GR and QFT matter fields co-emerge at lower energies is probably the way things will go (I fearlessly predict).
Lastly, here’s a link which is just plain cool. Experimental physicists have been trying to place larger and larger molecules in quantum superposition: here’s a proposal for designing an experiment which could achieve this for a virus. Hat tip goes to the Physics and Cake blog.
Tuesday, June 09, 2009
Physics Links and Notes
Here are three interesting things I read recently.
1. Lee Smolin has an article titled “The unique universe” in physicsworld (hat tip: Not Even Wrong). It covers some of the same ground as the video I had earlier posted here. In it he argues against some ideas which have been recently popular among physicists when considering the shape of the next fundamental theory of cosmology. First, many now argue that our universe is just one of a vast or infinite number of others: the multiverse. Also, it is argued that the fundamental theory will be timeless, since they see our experience of the flow of time as an emergent local phenomenon. This leaves us with a vision of a timeless and static multiverse.
Smolin says advocates of this vision are led by mistaken reasoning. One problem arises when physicists take the essentially Newtonian schema we use to evaluate systems within the universe (deterministic laws + initial conditions) and try to apply it to the entire cosmos. This leads them to try to describe a process for selecting our universe from a landscape of many universes (anthropically or otherwise). Smolin argues that we would do better to explore theories which take time to be fundamental, and where laws can vary in a process of cosmic evolution.
2. Many people are optimistic that an information-theoretic perspective will lead to new insights in exploring the foundations of quantum mechanics, and this multi-authored paper, called “A new physical principle: Information Causality”, is an interesting effort in this regard. Information causality is, according to the authors, a principle which helps pick out QM from a space of possible theories which, like QM, feature entangled correlations but allow no faster than light signaling. While the principle seems simple when stated (“communication of m classical bits causes information gain of at most m bits”), the fact that other (hypothetical) theories which feature strong correlations don’t meet it is notable. Hat tip goes to this post by the Quantum Pontiff which has some helpful discussion.
3. I had come across the essay “Free will, undecidability, and the problem of time in quantum gravity” by Rodolfo Gambini, which was submitted to the FQXi contest (see here), but I didn’t immediately catch on to his arguments. But now having reviewed two papers on Arxiv by Gambini and colleagues (here and here) I have a better idea what his program is. The key starting point is this: the mathematics of quantum mechanics treat time as an external infinitely divisible classical variable; Gambini et.al. think that fundamental limitations on the practical measurement of time within the physical world have implications for how we should interpret the problem of quantum measurement. For instance, if we look at decoherence theory, we see that a quantum superposition involving a system, a measuring device and the environment can evolve such that the degrees of freedom responsible for interference are dispersed. But decoherence itself says nothing about a measurement taking place -- the system is still evolving unitarily. Gambini et.al. argue that a point comes where no possible mechanism is available to tell whether or not a measurement outcome (or event) has or has not taken place. They think this undecidability threshold can be seen as the marker for when an event has occurred. (Then, in the essay, Gambini waxes philosophical and speculates that this undecidability between evolution and collapse might create space for free will.) A thread about this in physicsforums is here.
I liked reading Gambini’s papers, but I think the calculations regarding the undecidability point are controversial, given that a full explanation would require a theory of quantum gravity. And if my preferred approach to QG is right -- where time is a fundamental aspect of a pre-gravity microscopic quantum theory, and the particles and space-time geometry of current theories are emergent regularities -- then I suspect that the constraints on describing a physical clock would not arise in the same way as it does here.
1. Lee Smolin has an article titled “The unique universe” in physicsworld (hat tip: Not Even Wrong). It covers some of the same ground as the video I had earlier posted here. In it he argues against some ideas which have been recently popular among physicists when considering the shape of the next fundamental theory of cosmology. First, many now argue that our universe is just one of a vast or infinite number of others: the multiverse. Also, it is argued that the fundamental theory will be timeless, since they see our experience of the flow of time as an emergent local phenomenon. This leaves us with a vision of a timeless and static multiverse.
Smolin says advocates of this vision are led by mistaken reasoning. One problem arises when physicists take the essentially Newtonian schema we use to evaluate systems within the universe (deterministic laws + initial conditions) and try to apply it to the entire cosmos. This leads them to try to describe a process for selecting our universe from a landscape of many universes (anthropically or otherwise). Smolin argues that we would do better to explore theories which take time to be fundamental, and where laws can vary in a process of cosmic evolution.
2. Many people are optimistic that an information-theoretic perspective will lead to new insights in exploring the foundations of quantum mechanics, and this multi-authored paper, called “A new physical principle: Information Causality”, is an interesting effort in this regard. Information causality is, according to the authors, a principle which helps pick out QM from a space of possible theories which, like QM, feature entangled correlations but allow no faster than light signaling. While the principle seems simple when stated (“communication of m classical bits causes information gain of at most m bits”), the fact that other (hypothetical) theories which feature strong correlations don’t meet it is notable. Hat tip goes to this post by the Quantum Pontiff which has some helpful discussion.
3. I had come across the essay “Free will, undecidability, and the problem of time in quantum gravity” by Rodolfo Gambini, which was submitted to the FQXi contest (see here), but I didn’t immediately catch on to his arguments. But now having reviewed two papers on Arxiv by Gambini and colleagues (here and here) I have a better idea what his program is. The key starting point is this: the mathematics of quantum mechanics treat time as an external infinitely divisible classical variable; Gambini et.al. think that fundamental limitations on the practical measurement of time within the physical world have implications for how we should interpret the problem of quantum measurement. For instance, if we look at decoherence theory, we see that a quantum superposition involving a system, a measuring device and the environment can evolve such that the degrees of freedom responsible for interference are dispersed. But decoherence itself says nothing about a measurement taking place -- the system is still evolving unitarily. Gambini et.al. argue that a point comes where no possible mechanism is available to tell whether or not a measurement outcome (or event) has or has not taken place. They think this undecidability threshold can be seen as the marker for when an event has occurred. (Then, in the essay, Gambini waxes philosophical and speculates that this undecidability between evolution and collapse might create space for free will.) A thread about this in physicsforums is here.
I liked reading Gambini’s papers, but I think the calculations regarding the undecidability point are controversial, given that a full explanation would require a theory of quantum gravity. And if my preferred approach to QG is right -- where time is a fundamental aspect of a pre-gravity microscopic quantum theory, and the particles and space-time geometry of current theories are emergent regularities -- then I suspect that the constraints on describing a physical clock would not arise in the same way as it does here.
Thursday, January 22, 2009
More on the Fundamental Status of Time
Here are two more links to arguments for why time is fundamental:
A very good talk by Lee Smolin at a Perimeter Institute conference last fall. I thought he did a very good job in explaining how physics got into the practice of viewing time in a geometric fashion (with no important role for the present moment) and why this will not work when formulating a theory of the universe as a whole.
Here's George Ellis in another entry from the FQXi essay contest explaining why it is a mistake to try to describe the universe without time asymmetry.
A very good talk by Lee Smolin at a Perimeter Institute conference last fall. I thought he did a very good job in explaining how physics got into the practice of viewing time in a geometric fashion (with no important role for the present moment) and why this will not work when formulating a theory of the universe as a whole.
Here's George Ellis in another entry from the FQXi essay contest explaining why it is a mistake to try to describe the universe without time asymmetry.
Friday, December 05, 2008
Markopoulou: Time is Fundamental, Space is Not
The Foundational Questions Institute has run an essay contest on "The Nature of Time" and received a wide variety of responses. These come from well known physicists, other academics, and amateurs alike. Because of time contraints I've only read a few, beginning with authors I recognized (there are likely some "diamonds in the rough" if one plows through all the contributions).
Fotini Markopoulou of the Perimeter Institute, whose work I mentioned in the last post (and several older ones), wrote: "Space does not exist, so time can." She has a talent for writing clearly about these deep concepts, and I find her arguments persuasive (even if her work toward a full theory of quantum gravity still has a long road ahead). So I highly recommend the essay.
Kudos also to cosmologist and blogger Sean Carroll for his nice essay: "What if Time Really Exists" (here is the Cosmic Variance post introducing it). While I don't like some of his specific suggestions (associating time's arrow with macroscopic entropy considerations), I liked the stance he takes in the essay.
For countervailing views you can read the contributions of Carlo Rovelli and Julian Barbour.
UPDATE (7 January 2009): I just found this interesting post by Scott Aaronson - "Time: Different from space" which includes his computer science-derived insight on why time (causal structure)is fundamental.
Fotini Markopoulou of the Perimeter Institute, whose work I mentioned in the last post (and several older ones), wrote: "Space does not exist, so time can." She has a talent for writing clearly about these deep concepts, and I find her arguments persuasive (even if her work toward a full theory of quantum gravity still has a long road ahead). So I highly recommend the essay.
Kudos also to cosmologist and blogger Sean Carroll for his nice essay: "What if Time Really Exists" (here is the Cosmic Variance post introducing it). While I don't like some of his specific suggestions (associating time's arrow with macroscopic entropy considerations), I liked the stance he takes in the essay.
For countervailing views you can read the contributions of Carlo Rovelli and Julian Barbour.
UPDATE (7 January 2009): I just found this interesting post by Scott Aaronson - "Time: Different from space" which includes his computer science-derived insight on why time (causal structure)is fundamental.
Tuesday, November 18, 2008
Aether Makes a Comeback
The nineteenth century version of the ancient concept of the aether (or ether) was killed by the Michelson-Morley experiment and the success of Einstein’s theory of special relativity. Electro-magnetic radiation needed no substance to support wave propagation. Of course we did not revert to a view of space as an void sprinkled with a few solid objects. In modern particle theory, space-time is pictured as filled with matter fields. And in general relativity, space-time is revealed as a dynamic actor, not just a backdrop. Still, space-time remains distinct from matter/energy, and is geometric, rather than substantive. It thus retains a bit of the conceptual flavor of an empty container (a related discussion on the blog is here).
I was surprised to see the number of physics papers on arxiv which invoke the concept of aether (or ether) in the context of theoretical proposals to solving outstanding problems (e.g. dark energy). For me, aether was brought to mind by certain quantum gravity research programs.These propose that the space-time of general relativity is not fundamental: it emerges (along with the matter fields of the standard model) from something more basic – an underlying network of elementary quantum systems. This underlying network is not itself defined against a spatial backdrop and lacks the usual notions of distance or locality. Both space-time geometry and matter as we know them are constituted by the quantum systems: they arise from the aether.
For an example of this kind of work, here’s the second “quantum graphity” paper from Fotini Markopoulou and colleagues (the authors do not invoke the term aether, so don’t blame them!*). The introduction does a good job of discussing the stance they are taking toward the space-time of general relativity, and places this in the context of how other quantum gravity research programs approach the issue.
* Although they do link their work to the model described in this paper: “Quantum ether: photons and electrons from a rotor model” by Levin and Wen.
{UPDATED 19 November, 2008: Minor edits; 8 December 2008: Sean Carroll at Cosmic Variance just posted about his collaboration on aether field models.}
I was surprised to see the number of physics papers on arxiv which invoke the concept of aether (or ether) in the context of theoretical proposals to solving outstanding problems (e.g. dark energy). For me, aether was brought to mind by certain quantum gravity research programs.These propose that the space-time of general relativity is not fundamental: it emerges (along with the matter fields of the standard model) from something more basic – an underlying network of elementary quantum systems. This underlying network is not itself defined against a spatial backdrop and lacks the usual notions of distance or locality. Both space-time geometry and matter as we know them are constituted by the quantum systems: they arise from the aether.
For an example of this kind of work, here’s the second “quantum graphity” paper from Fotini Markopoulou and colleagues (the authors do not invoke the term aether, so don’t blame them!*). The introduction does a good job of discussing the stance they are taking toward the space-time of general relativity, and places this in the context of how other quantum gravity research programs approach the issue.
* Although they do link their work to the model described in this paper: “Quantum ether: photons and electrons from a rotor model” by Levin and Wen.
{UPDATED 19 November, 2008: Minor edits; 8 December 2008: Sean Carroll at Cosmic Variance just posted about his collaboration on aether field models.}
Wednesday, October 22, 2008
What Lies Beyond the Big Bounce
We don’t have a fully developed theory of quantum gravity yet, but there is one consequence of the theory we already know: it will banish general relativity’s space-time singularities from our conception of the universe. In particular, the idea of the big bang needs to be retired after decades of dominating professional and popular views of cosmology: the observed universe did not begin as a singularity but rather grew out of a pre-existing reality – a “big bounce”.
Martin Bojowald had a nice article in SciAm recently ("Follow the Bouncing Universe" in the print edition). Bojowald is a loop quantum gravity theorist: while loop theory has not produced an adequate theory for quantum gravity (and I think it probably won’t), it has produced formalisms that may be useful for constructing models which offer insight into the question of what will replace singularities in QG. This work goes under the rubric “loop quantum cosmology (LQC)”. I also noticed that Bojowald’s senior colleague Abhay Ashtekar has a paper out summarizing the results of work in LQC.
What intrigues me is their exploration of what the region on the other side of the big bounce might be like.
In his article, Bojowald first outlines the idea that space-time in QG is not a continuum, but rather has a fine-scale fundamental structure. These space-time “atoms” follow the rules of quantum mechanics and therefore the physics that prevails at high energies/short distances will differ from general relativity (GR). Specifically, in the loop model, a repulsive force comes into play at high energy densities, preventing singularities. In the case of the big bang, one scenario is that the initial high density state arose when a pre-existing universe collapsed (hence – a “bounce”). Bojowald describes an early, simplified, model which seemed to imply that the pre-existing universe was similar to our own. However, Bojowald says his own subsequent work found that quantum effects would have dominated the immediately pre-existing world:
Bojowald finishes by discussing how we might learn more about the pre-existing universe from astronomical clues.
Ashtekar’s paper discusses the same research more formally; in addition he also deals with LGC models for black holes, where again singularities are replaced by quantum regions (somewhat surprisingly to me, black holes are somewhat more difficult to model than the big bang itself). He concludes his discussion of the big bang/bounce this way: “Big bang is not the Beginning nor the big crunch the End. Quantum space-time appears to be vastly larger than what general relativity had us believe!”
My takeaway is that a realm of quantum possibilia extends beyond and surrounds us our island of observable cosmos. The old idea of the universe as a relatively straightforward, neatly bounded space-time container must be discarded.
Martin Bojowald had a nice article in SciAm recently ("Follow the Bouncing Universe" in the print edition). Bojowald is a loop quantum gravity theorist: while loop theory has not produced an adequate theory for quantum gravity (and I think it probably won’t), it has produced formalisms that may be useful for constructing models which offer insight into the question of what will replace singularities in QG. This work goes under the rubric “loop quantum cosmology (LQC)”. I also noticed that Bojowald’s senior colleague Abhay Ashtekar has a paper out summarizing the results of work in LQC.
What intrigues me is their exploration of what the region on the other side of the big bounce might be like.
In his article, Bojowald first outlines the idea that space-time in QG is not a continuum, but rather has a fine-scale fundamental structure. These space-time “atoms” follow the rules of quantum mechanics and therefore the physics that prevails at high energies/short distances will differ from general relativity (GR). Specifically, in the loop model, a repulsive force comes into play at high energy densities, preventing singularities. In the case of the big bang, one scenario is that the initial high density state arose when a pre-existing universe collapsed (hence – a “bounce”). Bojowald describes an early, simplified, model which seemed to imply that the pre-existing universe was similar to our own. However, Bojowald says his own subsequent work found that quantum effects would have dominated the immediately pre-existing world:
“So the bounce was not a brief push by a repulsive force, like the collision of billiard balls. Instead, it may have represented the emergence of our universe from an almost unfathomable quantum state – a world in highly fluctuating turmoil.”
Bojowald finishes by discussing how we might learn more about the pre-existing universe from astronomical clues.
Ashtekar’s paper discusses the same research more formally; in addition he also deals with LGC models for black holes, where again singularities are replaced by quantum regions (somewhat surprisingly to me, black holes are somewhat more difficult to model than the big bang itself). He concludes his discussion of the big bang/bounce this way: “Big bang is not the Beginning nor the big crunch the End. Quantum space-time appears to be vastly larger than what general relativity had us believe!”
My takeaway is that a realm of quantum possibilia extends beyond and surrounds us our island of observable cosmos. The old idea of the universe as a relatively straightforward, neatly bounded space-time container must be discarded.
Friday, June 27, 2008
Reduce Everything to Space-time?
[UPDATED 25 Sept.2009: Fixed Links]
I want to quickly comment on an interesting post by Justin at Panexperientialism. In it he reviews a book by Freya Mathews (called The Ecological Self) and also discusses a draft paper by Jonathan Schaffer (Spacetime the One Substance). Please check out his post, which discusses many aspects of Mathews’ ideas in particular beyond what I’m picking up on here (I have not read the book).
Both Mathews and Schaffer advocate a monistic metaphysical view where matter is effectively reduced to space-time.
I agree with these authors that the dual scheme of {space-time container plus material objects} must be rejected, but think they are slightly off-track in wanting to reduce the properties of matter fields to space-time (at least space-time anything like we currently think of it).
These brief comments focus on the relationship of this idea to the work of theoretical physicists. Mathews acknowledges that an early attempt to derive this reduction from general relativity failed (Wheeler’s Geometrodynamics), but still likes the metaphysical vision for philosophical reasons. In his paper Schaffer argues toward a similar goal, but along the way I think he overstates the degree to which GR and (especially) quantum field theory as we know them are congenial to this vision. QFT has matter fields housed in a separate space-time container. In GR the matter and space-time are dynamically intertwined, but the fact that you can model the geometry while leaving out matter shows that they remain distinct.
In some ways the quest for a theory of quantum gravity can (should?) be viewed as a quest for a monistic theory which is rid of the dual scheme. I continue to try to follow the different theories as a layperson to see how they come down on this issue.
String theory: originally an extension of QFT which retained the feature of having fields on a background space-time. Has evolved in many ways over the years and maybe can overcome this starting point (?).
Loop Quantum Gravity and Causal Dynamical Triangulations: these seek to formulate a quantum version of space-time with the promise of integrating matter into the picture later. I’m not sure if this promised integration would be more monistic than GR.
Causal Sets; Quantum Causal Histories/Geometrogenesis; Internal Relativity; Quantum Computing and Condensed Matter-based approaches: these programs seem best on this question as they try to specify a monistic underlying micro-theory from which space-time and matter fields as we know them may simultaneously emerge.
I would note that if the latter sort of approach works, it doesn’t support Schaffer’s advocacy of priority monism (see my previous post on this topic). The underlying network would not be a very coherent whole, but a fairly ill-behaved evolving pluralism of micro-events. Even though Schaffer wants to overcome the container/object scheme, his view of space-time as the holistic fundamental object still has a bit of a hangover from the container idea in my opinion.
I want to quickly comment on an interesting post by Justin at Panexperientialism. In it he reviews a book by Freya Mathews (called The Ecological Self) and also discusses a draft paper by Jonathan Schaffer (Spacetime the One Substance). Please check out his post, which discusses many aspects of Mathews’ ideas in particular beyond what I’m picking up on here (I have not read the book).
Both Mathews and Schaffer advocate a monistic metaphysical view where matter is effectively reduced to space-time.
I agree with these authors that the dual scheme of {space-time container plus material objects} must be rejected, but think they are slightly off-track in wanting to reduce the properties of matter fields to space-time (at least space-time anything like we currently think of it).
These brief comments focus on the relationship of this idea to the work of theoretical physicists. Mathews acknowledges that an early attempt to derive this reduction from general relativity failed (Wheeler’s Geometrodynamics), but still likes the metaphysical vision for philosophical reasons. In his paper Schaffer argues toward a similar goal, but along the way I think he overstates the degree to which GR and (especially) quantum field theory as we know them are congenial to this vision. QFT has matter fields housed in a separate space-time container. In GR the matter and space-time are dynamically intertwined, but the fact that you can model the geometry while leaving out matter shows that they remain distinct.
In some ways the quest for a theory of quantum gravity can (should?) be viewed as a quest for a monistic theory which is rid of the dual scheme. I continue to try to follow the different theories as a layperson to see how they come down on this issue.
String theory: originally an extension of QFT which retained the feature of having fields on a background space-time. Has evolved in many ways over the years and maybe can overcome this starting point (?).
Loop Quantum Gravity and Causal Dynamical Triangulations: these seek to formulate a quantum version of space-time with the promise of integrating matter into the picture later. I’m not sure if this promised integration would be more monistic than GR.
Causal Sets; Quantum Causal Histories/Geometrogenesis; Internal Relativity; Quantum Computing and Condensed Matter-based approaches: these programs seem best on this question as they try to specify a monistic underlying micro-theory from which space-time and matter fields as we know them may simultaneously emerge.
I would note that if the latter sort of approach works, it doesn’t support Schaffer’s advocacy of priority monism (see my previous post on this topic). The underlying network would not be a very coherent whole, but a fairly ill-behaved evolving pluralism of micro-events. Even though Schaffer wants to overcome the container/object scheme, his view of space-time as the holistic fundamental object still has a bit of a hangover from the container idea in my opinion.
Tuesday, June 24, 2008
CDT in Scientific American
Surprising and promising results have not come too frequently in quantum gravity research, but the Causal Dynamical Triangulations program led by Renate Loll, Jan Ambørn and Jerzy Jurkiewicz had an exciting moment in 2004. A computer simulation showed that a space-time model with the right dimensionality arose from a path integral superposition of fairly generic microscopic geometric building blocks. The team has kept up a steady stream of research investigating and seeking to extend this result, and now they have published a popular article in the latest Scientific American.
I recommend the article, if one has access to it. I also discussed (as best I could) the basics of the CDT approach in this earlier post, so I won’t repeat all that here. Also, I coincidentally had just read a recent paper by the team which showed how they have generated not just the right dimensionality, but also specifically find a de Sitter universe in a simulation.
The thing I find most interesting about CDT is that it may give some evidence that selecting asymmetric time and causality as fundamental features is important in quantum gravity (a caveat is that their simulation uses globally synchronized time, and I wonder if they can relax this assumption).
One reason to be cautious is that CDT at this point only deals with space-time, not matter. Like in Loop Quantum Gravity, there is an expectation that matter fields can be coupled to the theory later on. This is in contrast to research by Fotini Markopoulou and Olaf Dreyer (see posts here and here), who think that it is the matter fields which are to emerge from a micro-quantum substrate, and that space-time geometry is to be inferred from the matter. If this works, it seems conceptually more appealing, since you’ve dealt with both space-time and matter at once. (See also this recent FQXi article on Markopoulou and Dreyer).
One last interesting aspect which I hadn’t thought much about before was discussed in the recent paper. This is the fact that CDT (and I assume other “emergence-style” programs) need to be investigated by computer simulation, rather than by deriving a specific analytical result through mathematical formalism. This essentially means giving up on the traditional idea of a “theory of everything” which can be written down in a set of equations. The CDT team doesn’t see this as a weakness, and cites condensed matter theory (see also this post) for example as a field where emergent behaviors are profitably studied without the possibility of precise description at the micro-level. They also invoke the idea of “self-organizing” complex systems. Here’s a quote:
“Think of quantum gravity as a strongly coupled system of a very large number of microscopic constituents, which by its nature is largely inaccessible to analytic pen-and-paper methods. This is no reason for despair, but a common situation in many complex systems of theoretical interest in physics, biology and elsewhere, and merely calls for a dedicated set of technical tools and conceptual notions.”
I recommend the article, if one has access to it. I also discussed (as best I could) the basics of the CDT approach in this earlier post, so I won’t repeat all that here. Also, I coincidentally had just read a recent paper by the team which showed how they have generated not just the right dimensionality, but also specifically find a de Sitter universe in a simulation.
The thing I find most interesting about CDT is that it may give some evidence that selecting asymmetric time and causality as fundamental features is important in quantum gravity (a caveat is that their simulation uses globally synchronized time, and I wonder if they can relax this assumption).
One reason to be cautious is that CDT at this point only deals with space-time, not matter. Like in Loop Quantum Gravity, there is an expectation that matter fields can be coupled to the theory later on. This is in contrast to research by Fotini Markopoulou and Olaf Dreyer (see posts here and here), who think that it is the matter fields which are to emerge from a micro-quantum substrate, and that space-time geometry is to be inferred from the matter. If this works, it seems conceptually more appealing, since you’ve dealt with both space-time and matter at once. (See also this recent FQXi article on Markopoulou and Dreyer).
One last interesting aspect which I hadn’t thought much about before was discussed in the recent paper. This is the fact that CDT (and I assume other “emergence-style” programs) need to be investigated by computer simulation, rather than by deriving a specific analytical result through mathematical formalism. This essentially means giving up on the traditional idea of a “theory of everything” which can be written down in a set of equations. The CDT team doesn’t see this as a weakness, and cites condensed matter theory (see also this post) for example as a field where emergent behaviors are profitably studied without the possibility of precise description at the micro-level. They also invoke the idea of “self-organizing” complex systems. Here’s a quote:
“Think of quantum gravity as a strongly coupled system of a very large number of microscopic constituents, which by its nature is largely inaccessible to analytic pen-and-paper methods. This is no reason for despair, but a common situation in many complex systems of theoretical interest in physics, biology and elsewhere, and merely calls for a dedicated set of technical tools and conceptual notions.”
Monday, April 07, 2008
Group Field Theory and Emergent Space-Time
This paper by Daniele Oriti includes some ambitious ideas toward a theory of quantum gravity. In its first sections, he introduces his preferred formalism, called Group Field Theory (GFT). He shows how this formalism offers a framework general enough to incorporate aspects of other quantum gravity approaches. He then draws some lessons from these other approaches to suggest a path toward a successful theory by which space-time may be seen to emerge from a discrete quantum micro-structure using a GFT. Interestingly, in light of my last QG post, he takes inspiration from condensed matter theory in advocating his ideas. (My thanks to the anonymous commenter who suggested I look at this paper).
I had come across Oriti’s work before, and my first casual impression was that if GFT was a generalization of quantum field theory which hoped to incorporate gravity, then it might not be too interesting. I had taken to heart the criticisms that approaches which start by extending QFT (like the original string theory) were flawed by not being “background-independent”. Field theory is formulated against a flat space-time background, so how can you get space-time back out of it? As Oriti describes the formalism, while it is a true species of QFT, the way he uses it can be interpreted as modeling pre-geometric discrete quantum gravity elements. If so, then the QFT origin of the mathematical structure may not be an issue. In any case, I’m in no position to make judgments about the merits of the formalism, so I’ll just try to summarize here some the interesting ideas which arise as Oriti explores this framework.
He says the GFT can describe a quantum field in terms of fundamental variables which can be represented either as spin network vertices or elementary (d-1) simplices. Therefore he can draw connections to both the loop quantum gravity/spin foam and dynamical triangulations research programs. He says while there are open issues here, it appears that the GFT formalism can be seen to incorporate enough of these theories (and quantum Regge calculus as well) that he can draw some new lessons from examining certain features of these models from within the GFT framework.
Let me try to see if I can relate what he says the main lesson is (section 3.4 of the paper). These theories have tried to get dynamics from path integrals of the discrete structures they start with. Oriti says what results are the physics of (only) “few-particles”; these approaches lack a way to get interesting large –scale “many-particle” physics which would offer a chance to reveal an emergent space-time “continuum”. GFT offers a way to do a second quantization and field-theoretic analysis of the same starting structures in order to study the complex features which come in the many-particle regime. It is in this regime where we would hope to find an approximation of the continuum space-time described by General Relativity.
One exception to these perceived limitations of the other theories is the Causal version of Dynamical Triangulations (my post on this is here). In this approach, the micro-variables are stripped down to include only causally ordered ones, and the resulting path integral analysis has given interesting results in terms of an emergent four dimensional structure. Oriti suspects, though, that the strict limitations put imposed in CDT may lead one to again prefer analyzing the more general results which can come from using the GFT approach.
Oriti says that condensed matter physics shows the usefulness of field-theoretic and 2nd quantization approaches to studying the collective behavior and statistical properties of many-particle physics. He thinks we should consider quantum space-time as a condensed matter system, with the discrete structures of the GFT formalism as the atoms of space-time, and the continuum space-time as an emergent collective regime. General Relativity would be a hydrodynamic effective description of a quantum space-time fluid. Condensed matter techniques, themselves based on QFT, can point the way for how to research this possibility within GFT. Toward the end of the paper, Oriti offers a speculation that the Bose-Einstein condensate may be the specific analogue to look at (section 7 of the paper). His outline for how this would work is hard for me to follow. Some of the choices one makes in setting the terms in the GFT model seem important, but I can’t offer any opinions on this.
As I’ve said before, I like the idea of having a theory where a discrete quantum micro-physics leads to the space-time of GR in an emergent regime. So Oriti’s work is one I will try to follow as I have the other programs which have this feature. I also like that he wants to incorporate condensed matter physics as a guide to how this works. The parallels between condensed matter physics and fundamental physics are so suggestive that this link should be pursued. I still have a residual worry about the use of a field-theoretic approach which has space and time coordinates in the configuration of the micro-theory. I have this idea that a causal network of elementary quantum systems with absolutely no space-like metric would be a philosophically more appealing starting point. But perhaps this will turn out to be an unfounded worry. I look forward to reading more from Oriti in the future.
Emergent Quantum Gravity Research Series (in chronological order):
What’s New in Quantum Gravity
A section of Lee Smolin’s recent book discusses new approaches.
Causality First
Rafael Sorkin’s Causal Sets and Fotini Markopoulou’s Quantum Causal Histories.
Emerging From the Noise
More on Markopoulou’s approach.
Caution: Universe under Construction
The Causal Dynamical Triangulation program.
Geometrogenesis
More papers from Markopoulou and colleagues.
In the Beginning was the Qubit
Seth Lloyd’s quantum computing-inspired take on quantum gravity.
Dreyer's Internal Relativity
Olaf Dreyer's approach to finding emergent gravity from a quantum mechanical base.
The Superfluid Universe
Grigory Volovik looks for the answers to fundamental physics in the surprising phenomena displayed in condensed matter physics.
I had come across Oriti’s work before, and my first casual impression was that if GFT was a generalization of quantum field theory which hoped to incorporate gravity, then it might not be too interesting. I had taken to heart the criticisms that approaches which start by extending QFT (like the original string theory) were flawed by not being “background-independent”. Field theory is formulated against a flat space-time background, so how can you get space-time back out of it? As Oriti describes the formalism, while it is a true species of QFT, the way he uses it can be interpreted as modeling pre-geometric discrete quantum gravity elements. If so, then the QFT origin of the mathematical structure may not be an issue. In any case, I’m in no position to make judgments about the merits of the formalism, so I’ll just try to summarize here some the interesting ideas which arise as Oriti explores this framework.
He says the GFT can describe a quantum field in terms of fundamental variables which can be represented either as spin network vertices or elementary (d-1) simplices. Therefore he can draw connections to both the loop quantum gravity/spin foam and dynamical triangulations research programs. He says while there are open issues here, it appears that the GFT formalism can be seen to incorporate enough of these theories (and quantum Regge calculus as well) that he can draw some new lessons from examining certain features of these models from within the GFT framework.
Let me try to see if I can relate what he says the main lesson is (section 3.4 of the paper). These theories have tried to get dynamics from path integrals of the discrete structures they start with. Oriti says what results are the physics of (only) “few-particles”; these approaches lack a way to get interesting large –scale “many-particle” physics which would offer a chance to reveal an emergent space-time “continuum”. GFT offers a way to do a second quantization and field-theoretic analysis of the same starting structures in order to study the complex features which come in the many-particle regime. It is in this regime where we would hope to find an approximation of the continuum space-time described by General Relativity.
One exception to these perceived limitations of the other theories is the Causal version of Dynamical Triangulations (my post on this is here). In this approach, the micro-variables are stripped down to include only causally ordered ones, and the resulting path integral analysis has given interesting results in terms of an emergent four dimensional structure. Oriti suspects, though, that the strict limitations put imposed in CDT may lead one to again prefer analyzing the more general results which can come from using the GFT approach.
Oriti says that condensed matter physics shows the usefulness of field-theoretic and 2nd quantization approaches to studying the collective behavior and statistical properties of many-particle physics. He thinks we should consider quantum space-time as a condensed matter system, with the discrete structures of the GFT formalism as the atoms of space-time, and the continuum space-time as an emergent collective regime. General Relativity would be a hydrodynamic effective description of a quantum space-time fluid. Condensed matter techniques, themselves based on QFT, can point the way for how to research this possibility within GFT. Toward the end of the paper, Oriti offers a speculation that the Bose-Einstein condensate may be the specific analogue to look at (section 7 of the paper). His outline for how this would work is hard for me to follow. Some of the choices one makes in setting the terms in the GFT model seem important, but I can’t offer any opinions on this.
As I’ve said before, I like the idea of having a theory where a discrete quantum micro-physics leads to the space-time of GR in an emergent regime. So Oriti’s work is one I will try to follow as I have the other programs which have this feature. I also like that he wants to incorporate condensed matter physics as a guide to how this works. The parallels between condensed matter physics and fundamental physics are so suggestive that this link should be pursued. I still have a residual worry about the use of a field-theoretic approach which has space and time coordinates in the configuration of the micro-theory. I have this idea that a causal network of elementary quantum systems with absolutely no space-like metric would be a philosophically more appealing starting point. But perhaps this will turn out to be an unfounded worry. I look forward to reading more from Oriti in the future.
Emergent Quantum Gravity Research Series (in chronological order):
What’s New in Quantum Gravity
A section of Lee Smolin’s recent book discusses new approaches.
Causality First
Rafael Sorkin’s Causal Sets and Fotini Markopoulou’s Quantum Causal Histories.
Emerging From the Noise
More on Markopoulou’s approach.
Caution: Universe under Construction
The Causal Dynamical Triangulation program.
Geometrogenesis
More papers from Markopoulou and colleagues.
In the Beginning was the Qubit
Seth Lloyd’s quantum computing-inspired take on quantum gravity.
Dreyer's Internal Relativity
Olaf Dreyer's approach to finding emergent gravity from a quantum mechanical base.
The Superfluid Universe
Grigory Volovik looks for the answers to fundamental physics in the surprising phenomena displayed in condensed matter physics.
Friday, February 01, 2008
The Superfluid Universe
Several advocates of an “emergence” approach to fundamental physics come from the world of condensed matter physics (an old blog post which briefly discussed Robert B. Laughlin’s views is here).
Grigory Volovik is a prominent (and award-winning) theorist who has been working on applying the knowledge gained in his research on superfluids to the case of explaining how gravity and the matter fields of current theory may themselves be emergent features of a deeper reality – a sort of “super” quantum vacuum. {UPDATED 2 February 2008 -- minor edits}
Until recently I had only read a little about superfluids or condensed matter physics. Superfluids have surprising collective behaviors (like zero viscosity) which can be topologically stable despite micro-physical imperfections. Although their characteristics are exhibited at a macroscopic scale, the tools of quantum field theory are needed to explain them. As he explains in this older article (from 1999), Volovik thinks one particular variety of superfluid even displays characteristics which make it a good model for the entire universe: this is the one created by supercooling the He-3 helium isotope. In reaching this conclusion, he explains that the condensed matter system used must be fermionic. We need both fermionic and bosonic fields and in the He-3 superfluid the atoms behave as fermions, and quantum bose fields appear as low-energy collective modes. (Interestingly, in He-4 superfluid, the atoms behave as bosons – who knew? – and I guess there is no analogous way to recover fermions as some collective mode). Now, a He-3 superfluid is not the only fermionic system (or Fermi system) known, and Volovik explains how the topologies differ between the alternatives (he looks at systems which feature a “Fermi surface” as opposed to the “Fermi point” of He-3). He concludes the He-3 superfluid’s topology has the symmetries which create analogous features with the quantum fields of particle physics and also of gravity. It is hard for me to follow the details, but it looks like an impressive match, although Volovik concedes in the article that he hasn’t shown that analogies exist for quite the whole particle zoo of the standard model.
Now, in this recent paper, “Emergent Physics: Fermi point scenario”, one can see that Volovik’s confidence that his work shows the right path to fundamental physics has grown. In the paper, he begins by discussing the cosmological constant problem and the particle mass hierarchy problem, as a prelude to explaining why they are more natural expectations of his model.
First he explains that in a Fermi point vacuum all of physical laws (except for quantum mechanics itself) can be seen as effective laws which naturally emerge at low energy. He discusses again how the symmetries of the Fermi point system give one the fields of particle physics and gravity. He then shows how vacuum energies get nullified in a way that leads to consistency with a low cosmological constant. When it comes to the hierarchy problem, the Fermi point system has elements which come from macroscopic (topologically robust) emergent features and ones which come from micro-structure. The observed masses (or zero masses) of various particles are shown to be consistent (in approximate order of magnitude) with the model. (Again, I have trouble following the specific arguments here, so please see the paper.)
In a concluding section, Volovik explains the contrast between his approach, which treats gravity as an effective emergent theory, and other approaches to quantum gravity which treat general relativity as something fundamental and then try (so far unsuccessfully) to unify it with the standard model.
(Note also that Volovik has a full-length book on this topic, which I have not read, called: The Universe in a Helium Droplet)
This is the first time I’ve grappled with Volovik’s approach and any thoughts I have are extremely tentative. I would say at this point that his model adds to a growing argument that emergent approaches to fundamental physics are promising. On the other hand, it still seems to be more of an analogy rather than a candidate for a fundamental theory. The reason I say this is that the toolkit for analyzing the Fermi point system (and other condensed matter systems) is quantum field theory. The approach, then, seems to have a circular aspect to it: one is trying to explain gravity (among other things) using a theory which has a formalism which embeds a background (flat, special relativistic) space-time. If there could be a way to get the same kind of outcome starting only with (a network of?) elementary quantum mechanical systems, that might be a better candidate for a fundamental theory.
Grigory Volovik is a prominent (and award-winning) theorist who has been working on applying the knowledge gained in his research on superfluids to the case of explaining how gravity and the matter fields of current theory may themselves be emergent features of a deeper reality – a sort of “super” quantum vacuum. {UPDATED 2 February 2008 -- minor edits}
Until recently I had only read a little about superfluids or condensed matter physics. Superfluids have surprising collective behaviors (like zero viscosity) which can be topologically stable despite micro-physical imperfections. Although their characteristics are exhibited at a macroscopic scale, the tools of quantum field theory are needed to explain them. As he explains in this older article (from 1999), Volovik thinks one particular variety of superfluid even displays characteristics which make it a good model for the entire universe: this is the one created by supercooling the He-3 helium isotope. In reaching this conclusion, he explains that the condensed matter system used must be fermionic. We need both fermionic and bosonic fields and in the He-3 superfluid the atoms behave as fermions, and quantum bose fields appear as low-energy collective modes. (Interestingly, in He-4 superfluid, the atoms behave as bosons – who knew? – and I guess there is no analogous way to recover fermions as some collective mode). Now, a He-3 superfluid is not the only fermionic system (or Fermi system) known, and Volovik explains how the topologies differ between the alternatives (he looks at systems which feature a “Fermi surface” as opposed to the “Fermi point” of He-3). He concludes the He-3 superfluid’s topology has the symmetries which create analogous features with the quantum fields of particle physics and also of gravity. It is hard for me to follow the details, but it looks like an impressive match, although Volovik concedes in the article that he hasn’t shown that analogies exist for quite the whole particle zoo of the standard model.
Now, in this recent paper, “Emergent Physics: Fermi point scenario”, one can see that Volovik’s confidence that his work shows the right path to fundamental physics has grown. In the paper, he begins by discussing the cosmological constant problem and the particle mass hierarchy problem, as a prelude to explaining why they are more natural expectations of his model.
First he explains that in a Fermi point vacuum all of physical laws (except for quantum mechanics itself) can be seen as effective laws which naturally emerge at low energy. He discusses again how the symmetries of the Fermi point system give one the fields of particle physics and gravity. He then shows how vacuum energies get nullified in a way that leads to consistency with a low cosmological constant. When it comes to the hierarchy problem, the Fermi point system has elements which come from macroscopic (topologically robust) emergent features and ones which come from micro-structure. The observed masses (or zero masses) of various particles are shown to be consistent (in approximate order of magnitude) with the model. (Again, I have trouble following the specific arguments here, so please see the paper.)
In a concluding section, Volovik explains the contrast between his approach, which treats gravity as an effective emergent theory, and other approaches to quantum gravity which treat general relativity as something fundamental and then try (so far unsuccessfully) to unify it with the standard model.
(Note also that Volovik has a full-length book on this topic, which I have not read, called: The Universe in a Helium Droplet)
This is the first time I’ve grappled with Volovik’s approach and any thoughts I have are extremely tentative. I would say at this point that his model adds to a growing argument that emergent approaches to fundamental physics are promising. On the other hand, it still seems to be more of an analogy rather than a candidate for a fundamental theory. The reason I say this is that the toolkit for analyzing the Fermi point system (and other condensed matter systems) is quantum field theory. The approach, then, seems to have a circular aspect to it: one is trying to explain gravity (among other things) using a theory which has a formalism which embeds a background (flat, special relativistic) space-time. If there could be a way to get the same kind of outcome starting only with (a network of?) elementary quantum mechanical systems, that might be a better candidate for a fundamental theory.
Friday, January 04, 2008
Smolin and Rovelli Respond to Edge's Annual Question
The Edge annual question for this year, asked of over 100 scientists, journalists, and assorted intellectual types was “What have you changed your mind about and why?” I checked out the responses of some of the physicists who participated.
Lee Smolin’s entry discusses the impact that his evolving views about time have had on his quantum gravity work. His earlier research was on loop quantum gravity (LQG), which as it seeks to quantize the geometry described by general relativity results in a basically “timeless” theory (unlike quantum mechanics itself, where a background time is part of the picture). Now, however, Smolin has come to believe that time, in the guise of causality, needs to be a fundamental element of a theory. This leads him to be interested in theories where causality is built in at the ground level and where the more familiar “laws of physics” (general relativity and quantum field theory) are emergent features which may themselves evolve in time (for more see my previous post on Smolin).
It was interesting to me to note a contrast with fellow loop quantum gravity pioneer Carlo Rovelli. Rovelli’s entry was about his realization that the standard interpretation of quantum mechanics made sense, but not if you tried to apply it to the whole universe. The insight led to his formulation of relational quantum mechanics a bit over 10 years ago. Now, from my outsider’s perspective, it seems that Rovelli’s relational qm is philosophically in harmony with Smolin’s interest in “emergent” quantum gravity approaches which start with a causal network of quantum systems at the fundamental level. However, while Rovelli says that relational qm has “affected substantially” his quantum gravity work, in his case, it appears this involves inspiring the ongoing extensions to the loop program rather than working on approaches which have a different fundamental starting point.
Finally, relevant to this topic is John Baez on why he decided to stop working on quantum gravity.
Lee Smolin’s entry discusses the impact that his evolving views about time have had on his quantum gravity work. His earlier research was on loop quantum gravity (LQG), which as it seeks to quantize the geometry described by general relativity results in a basically “timeless” theory (unlike quantum mechanics itself, where a background time is part of the picture). Now, however, Smolin has come to believe that time, in the guise of causality, needs to be a fundamental element of a theory. This leads him to be interested in theories where causality is built in at the ground level and where the more familiar “laws of physics” (general relativity and quantum field theory) are emergent features which may themselves evolve in time (for more see my previous post on Smolin).
It was interesting to me to note a contrast with fellow loop quantum gravity pioneer Carlo Rovelli. Rovelli’s entry was about his realization that the standard interpretation of quantum mechanics made sense, but not if you tried to apply it to the whole universe. The insight led to his formulation of relational quantum mechanics a bit over 10 years ago. Now, from my outsider’s perspective, it seems that Rovelli’s relational qm is philosophically in harmony with Smolin’s interest in “emergent” quantum gravity approaches which start with a causal network of quantum systems at the fundamental level. However, while Rovelli says that relational qm has “affected substantially” his quantum gravity work, in his case, it appears this involves inspiring the ongoing extensions to the loop program rather than working on approaches which have a different fundamental starting point.
Finally, relevant to this topic is John Baez on why he decided to stop working on quantum gravity.
Tuesday, December 04, 2007
Markopoulou Article
The Foundational Questions Institute (home page here) has a "community" web-page which features articles and blog posts relating to the work of those who have received grants. They have put up an article (in pdf) on Fotini Markopoulou and her quantum gravity program. (my posts on Markopoulou's work in reverse chronological order are here, here, and here).
Tuesday, November 13, 2007
Dreyer's Internal Relativity
In recent years, a new school of quantum gravity research has come into view. The research programs in this group attempt to demonstrate that neither the matter fields nor the space-time geometry described by our present theories are fundamental, but instead both co-emerge from a pre-geometric quantum mechanical foundation. (Links to my prior posts on this research are at the end of this post). Olaf Dreyer is a theoretician working in this mode. He recently presented this paper, “Why Things Fall”, which nicely summarized his work to-date (hat tip: this thread maintained by marcus at Physics Forums).
What helps make the paper accessible is that Dreyer’s approach has been to work at a very stylized conceptual level. He wants to show how the path to a full theory should go, with the goal of filling in crucial details later. It is clear that this kind of theory has a long way to go, in particular to show that Einstein’s equations will specifically emerge.
In the introduction, Dreyer describes the approach where gravity is not assumed at the outset but is emergent. He breaks this down further by discussing the constraint that there is to be is no clean distinction between the emergent gravity and matter degrees of freedom (as opposed to an approach like early string theory where the graviton emerged as part of the particle family). Rather, it is only through the matter degrees of freedom that we infer the geometry. He says: “…we are taking seriously the fact that we only know geometry through matter…geometry alone is not accessible to us. (p.2)” This description of the emergence of geometry is in contrast to an approach like loop quantum gravity, where the space-time geometry of general relativity is taken as given and then quantized. What makes the theory a quantum theory of gravity is that the matter degrees of freedom and inferred geometry will emerge from a foundation which is quantum mechanical. One consequence of adopting a QM system as fundamental is that background time is assumed at this foundational level, although it will have no relationship to emergent space-time. I have no problem with this: something has to be fundamental and I think time and asymmetric causality are good candidates for this role.
The term “internal relativity” is meant to stress a key point: we ask what geometry obtains from observed degrees of freedom from a point of view within the system. Dreyer believes that if we do this, relativity naturally will emerge.
As a prepatory example, Dreyer shows (in section 3) how something like this happens in a classical theory. Specifically, if we start with an electro-magnetic field (on a Newtonian background of absolute space and time), we can see how special relativity emerges from considering how the dynamics of charged particles gives rise to contraction/dilation effects from a point of view inside the system.
Section 4 presents the main model of the paper. Dreyer begins with a simple quantum mechanical system in a ground state (level 0). Then he allows for excitations (traveling spin waves in the model). This is level 1, and the excitations are meant to be analogues of elementary particles of our world. Level 2 is given by bound states of these excitations. These bound states are meant to be analogues of the solid objects of our world. They do not leave the parameter on ground state of level 0 unchanged. Dreyer analyzes the effect of the objects on the distribution of the level 0 parameter and is able to derive Newton’s law of gravitation between the objects in a low velocity approximation. He then says the presence of Newtonian gravity means that the geometry seen by internal observers will be not flat but curved (a curved Lorentzian manifold). So while Newtonian gravity was derived, the overall framework implies something which goes beyond Newtonian gravity. He notes that the model falls short of showing that the gravitational mass implied for the bound objects is actually the same as the inertial mass.
Section 5 concludes with some discussion. Dreyer reiterates the concepts involved in having matter degrees of freedom and gravitation emerge from a fundamental level that has distinct degrees of freedom. He discusses how certain problems don’t arise in this conceptual framework, such as the “problem of time” which arises when one quantizes space-time, and the problem of incorrect predictions for the value of the cosmological constant. He also discusses some very preliminary ideas for observable consequences which may follow from this kind of theory.
Emergent Quantum Gravity Research Series (in chronological order):
What’s New in Quantum Gravity
A section of Lee Smolin’s recent book discusses new approaches.
Causality First
Rafael Sorkin’s Causal Sets and Fotini Markopoulou’s Quantum Causal Histories.
Emerging From the Noise
More on Markopoulou’s approach.
Caution: Universe under Construction
The Causal Dynamical Triangulation program.
Geometrogenesis
More papers from Markopoulou and colleagues.
In the Beginning was the Qubit
Seth Lloyd’s quantum computing-inspired take on quantum gravity.
What helps make the paper accessible is that Dreyer’s approach has been to work at a very stylized conceptual level. He wants to show how the path to a full theory should go, with the goal of filling in crucial details later. It is clear that this kind of theory has a long way to go, in particular to show that Einstein’s equations will specifically emerge.
In the introduction, Dreyer describes the approach where gravity is not assumed at the outset but is emergent. He breaks this down further by discussing the constraint that there is to be is no clean distinction between the emergent gravity and matter degrees of freedom (as opposed to an approach like early string theory where the graviton emerged as part of the particle family). Rather, it is only through the matter degrees of freedom that we infer the geometry. He says: “…we are taking seriously the fact that we only know geometry through matter…geometry alone is not accessible to us. (p.2)” This description of the emergence of geometry is in contrast to an approach like loop quantum gravity, where the space-time geometry of general relativity is taken as given and then quantized. What makes the theory a quantum theory of gravity is that the matter degrees of freedom and inferred geometry will emerge from a foundation which is quantum mechanical. One consequence of adopting a QM system as fundamental is that background time is assumed at this foundational level, although it will have no relationship to emergent space-time. I have no problem with this: something has to be fundamental and I think time and asymmetric causality are good candidates for this role.
The term “internal relativity” is meant to stress a key point: we ask what geometry obtains from observed degrees of freedom from a point of view within the system. Dreyer believes that if we do this, relativity naturally will emerge.
As a prepatory example, Dreyer shows (in section 3) how something like this happens in a classical theory. Specifically, if we start with an electro-magnetic field (on a Newtonian background of absolute space and time), we can see how special relativity emerges from considering how the dynamics of charged particles gives rise to contraction/dilation effects from a point of view inside the system.
Section 4 presents the main model of the paper. Dreyer begins with a simple quantum mechanical system in a ground state (level 0). Then he allows for excitations (traveling spin waves in the model). This is level 1, and the excitations are meant to be analogues of elementary particles of our world. Level 2 is given by bound states of these excitations. These bound states are meant to be analogues of the solid objects of our world. They do not leave the parameter on ground state of level 0 unchanged. Dreyer analyzes the effect of the objects on the distribution of the level 0 parameter and is able to derive Newton’s law of gravitation between the objects in a low velocity approximation. He then says the presence of Newtonian gravity means that the geometry seen by internal observers will be not flat but curved (a curved Lorentzian manifold). So while Newtonian gravity was derived, the overall framework implies something which goes beyond Newtonian gravity. He notes that the model falls short of showing that the gravitational mass implied for the bound objects is actually the same as the inertial mass.
Section 5 concludes with some discussion. Dreyer reiterates the concepts involved in having matter degrees of freedom and gravitation emerge from a fundamental level that has distinct degrees of freedom. He discusses how certain problems don’t arise in this conceptual framework, such as the “problem of time” which arises when one quantizes space-time, and the problem of incorrect predictions for the value of the cosmological constant. He also discusses some very preliminary ideas for observable consequences which may follow from this kind of theory.
Emergent Quantum Gravity Research Series (in chronological order):
What’s New in Quantum Gravity
A section of Lee Smolin’s recent book discusses new approaches.
Causality First
Rafael Sorkin’s Causal Sets and Fotini Markopoulou’s Quantum Causal Histories.
Emerging From the Noise
More on Markopoulou’s approach.
Caution: Universe under Construction
The Causal Dynamical Triangulation program.
Geometrogenesis
More papers from Markopoulou and colleagues.
In the Beginning was the Qubit
Seth Lloyd’s quantum computing-inspired take on quantum gravity.
Friday, May 18, 2007
Quantum Gravity and Gunk
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.
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.
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.]
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