Oli todella mielenkiintoisella tavalla haastava kokemus yrittää selittää ymmärrettävästi joitain nykyfysiikan suurimmista mysteereistä perusopiskelijatason kuulijoille. Saamani palautteen perusteella onnistuin jopa kohtuullisen hyvin, vaikka ainakin omasta mielestäni parannettavaakin riittää rutkasti seuraavaan kertaan, jos sellainen on tullakseen.
maanantai 13. huhtikuuta 2015
A Pedestrian Introduction to Quantum Gravity
Pari viikkoa sitten pidin johdantoluennon kvanttigravitaatiosta otsikolla "A Pedestrian Introduction to Quantum Gravity" Tampereen teknillisen yliopiston fysiikan laitoksen opiskelijaseminaarissa. Kuvasin videon tilaisuudesta ja laitoin YouTubeen jakoon:
Oli todella mielenkiintoisella tavalla haastava kokemus yrittää selittää ymmärrettävästi joitain nykyfysiikan suurimmista mysteereistä perusopiskelijatason kuulijoille. Saamani palautteen perusteella onnistuin jopa kohtuullisen hyvin, vaikka ainakin omasta mielestäni parannettavaakin riittää rutkasti seuraavaan kertaan, jos sellainen on tullakseen.
Oli todella mielenkiintoisella tavalla haastava kokemus yrittää selittää ymmärrettävästi joitain nykyfysiikan suurimmista mysteereistä perusopiskelijatason kuulijoille. Saamani palautteen perusteella onnistuin jopa kohtuullisen hyvin, vaikka ainakin omasta mielestäni parannettavaakin riittää rutkasti seuraavaan kertaan, jos sellainen on tullakseen.
maanantai 2. helmikuuta 2015
Quantum gravity and some of my favorite approaches to it (englanniksi)
Enpä ole taas onnistunut postaamaan mitään tänne pitkään aikaan --- suppeaa suhteellisuusteoriaa käsittelevä raapustukseni on edelleen puristuksissa työn alla. Korvatakseni tämän hiipivän hiljaisuuden ajattelin kopioida tänne kotisivuani varten kirjoittamani lyhyehkön englanninkielisen johdannon kvanttigravitaatioon. Nauttikaa, jos voitte.
The pair of words "quantum gravity" has several possible meanings with different degrees of specificity, but the most practical and general definition is probably also the one that most people can agree on: Quantum gravity is the field of theoretical high energy physics that tries to understand the microscopic structure and behavior of spacetime (although not necessarily exclusively). According to this definition, "quantum gravity" is not any particular theory of physics, but a particular field of physics determined by the questions that it poses. This is also my favorite definition (as well as the one used by Wikipedia), since we simply don't know at this stage what is the correct approach to develop a theory that describes space and time at very short distances or, equivalently, very high energies. In my experience, anyone who claims otherwise is either seriously misinformed or writing a research proposal.
The problem of quantum gravity is extremely fascinating, because it is one of the last frontiers of fundamental physics, if not the last. While its solution will not rid the world of starvation or disease in the foreseeable future, I believe it does present to us an opportunity to revolutionize our conception of physical reality --- as did the discoveries of its predecessors quantum mechanics and general relativity. The importance of such revolutions has never stemmed from their immediate practical implications (which may be plenty, as in the case of quantum mechanics), but rather from their profound effect on our conception of the universe we inhabit, and ultimately our self-image as momentary patterns in that universe. However, in my mind, above all such noble philosophical motivations arises the fact that, due to our complex evolutionary history as a species of primates, we humans are exteremely curious creatures by nature. We just simply love to learn new things and find out more about pretty much everything --- no matter how esoteric or impractical! Indeed, this innate instinct of ours is certainly one of the key factors in our success as a species.
(Too often it appears to me, however, that our societies and educational systems have been built around the goal of stifling this instinctive curiosity within people by promoting obedience and passive consumerism instead of active creative participation.)
But wait... Hold your horses. Why is this new "revolution" in physics needed in the first place? Why aren't our current theories sufficient to describe the physical world? After all, (as far as I know) there is currently not a single observation contradicting our two best theories, the Standard Model of elementary particle physics and Einstein's general theory of relativity describing gravity. However, the fact of the matter is that despite the magnificient success of these two most fundamental of theories, they are in an inherent conceptual contradiction with each other. It is only because gravitational forces on elementary particles are so ridiculously weak that they have no practical relevance what-so-ever within the limits of the current observational accuracy, and for the most part we may just neglect them altogether. Most researchers, myself included, blaim the contradiction on the classical deterministic character of the general theory of relativity. We have learned since the conception of quantum mechanics in the beginning of the 20th century that the fundamental description of nature appears not to be deterministic but probabilistic. The probabilities of measurement outcomes are described in the case of simple microscopic systems by quantum mechanics, while the Standard Model describes with an utmost accuracy the probabilities for the highly energetic interaction processes of elementary particles that take place, for example, inside the Large Hadron Collider (LHC) at CERN. One of the main reasons for believing that quantum theories are more fundamental than classical deterministic theories, such as general relativity, is that in several instances a quantum model --- built from a classical model via a set of techniques called quantization --- has turned out to describe nature more faithfully than its original classical counterpart. The quintessential example of this is the development of quantum electrodynamics in the 1940's and 50's that was succesfully obtained from Maxwell's electromagnetic field theory more or less by a direct quantization.
Since Einstein's general theory of relativity, just like Maxwell's electromagnetic theory, has the form of a classical field theory, it is tempting to postulate that by directly quantizing it we should be able to obtain a corresponding quantum theory, thus bringing our descriptions of elementary particles and gravity under the same roof, and removing the fundamental contradiction in modern physics. Indeed, attempts by extremely smart people to do exactly this span now at least 50 years, which already conveys some feeling of the immense difficulty of the task. It turns out that the dynamics of Einstein's theory, as such, has properties that make it extremely adverse to a direct quantization. As a result, many researchers have moved forward to consider other alternative approaches to the problem, some of which are quite faithful to the original vision, and some others that are not so in the least. Anyone interested in fundamental physics these days has probably heard of String Theory and Loop Quantum Gravity, perhaps even about the disputes between the supporters of the two approaches, but these are really only the tip of the iceberg. Hidden behind the most popular directions of research, there is a wild undergrowth of ideas and points-of-view, and I have no intention or pretension to make justice to all or, indeed, any of them here. Instead, I will just very briefly and even more subjectively review two of my own favorites.
1) Quantum gravity as quantum statistics of geometry. The revolutionary idea behind Einstein's general relativity is that gravitational interactions are caused by the curvature of spacetime geometry itself. In the original formulation, the "field" that is the dynamical variable of the theory is the metric of spacetime that describes the geometry of spacetime by determining the lengths and durations of spatial and temporal intervals. Whenever a region of space contains energy (or, equivalently, mass), the dynamics of general relativity dictate that the geometry around the region must be curved. Such curvature causes the trajectories of freely moving objects to deviate from straight lines, thus causing the illusion of a force acting on the objects.
Accordingly, the fundamental insight of general relativity can be expressed as "gravity = spacetime geometry". To cash in on this insight, we may further postulate "quantum gravity = quantum spacetime geometry". It is a natural idea therefore to try to construct quantum theories of geometry, even if they are not obtained via a direct quantization of general relativity. One may still be able to construct models that predict quantum probabilities for spacetime geometric processes that agree with general relativity in the large distance/low energy limit. This is exactly the goal of several approaches to quantum gravity and, in particular, group field theories and tensor models. The "elementary particles" of these quantum models are in fact simple tetrahedra, whose interaction processes correspond to discrete 4-dimensional geometries, which then are hoped to approximate the smooth spacetime structure of general relativity in the classical/low energy/thermodynamical regime.
In a sense, since these models are quantum field theories, they are not fundamentally models of tetrahedra --- just like quantum electrodynamics is not really a theory of just photons and electrons --- even though their construction is based on such discrete geometric considerations. In a quantum field theoretical model, particles are only representations of certain quantities that appear in the perturbative approximation to the theory, and not elements of the full non-perturbative theory as such. (In quantum field theory, one may also consider particles to be clicks of a particle detector, but that's another thing.) Therefore, studying the properties of the full theory, and not just its perturbative expansion, is of crucial importance in trying to understand whether these models can really describe the physical spacetime that we know and love. At the same time, understanding the full theory is also very very challenging, and not much progress has been made so far in the case of realistic 4-dimensional models.
It is also far from clear, for example, what is the correct choice of dynamics for such a model that would reproduce general relativity in the appropriate limit. Some researchers hope that, due to a hypothetical universality of the approximate large-scale behavior --- not unlike in some statistical physics models ---, the details of the microscopic model might not matter that much in the end. I'm not so sure that this would be a good thing though, since it would prevent us from choosing a unique model, and therefore compromise predictivity. (So much for teasing the string theorists about their landscape!)
If you happen to be interested in this kind of an approach in more detail, I can recommend the following two reviews to begin with:
2) Spacetime as a structure of quantum dynamics. Despite the apparent immediateness of the above "gravity = spacetime geometry" reasoning, there are in fact strong indications that this is perhaps too naive an approach. In a world described by classical physics, including general relativity, one is able to measure space and time with an arbitrarily good precision. However, we don't live in that world! Instead, when one takes into account the quantum behavior of matter, this asymptotically perfect accuracy turns out not to hold any longer, but there appear inherent limitations to measurements of spacetime geometry. For example, one can never resolve spacetime points by real physical measurements that always exhibit quantum uncertainties. Therefore, already the starting point to the previous approach of spacetime as a geometric manifold --- a set of points (with some additional structure) --- seems to be seriously undermined by such considerations. (I should emphasize, however, that in group field theory, for example, the geometries that the models describe are not really classical, but quantized à la Loop Quantum Gravity.) Accordingly, quantum gravity as quantization of (classical) geometry seems also to lose its meaningfulness. In the face of such a deep conceptual contradiction, one feels tempted to throw one's hands in the air and exclaim: "No wonder then that the last 50 years have not led to any progress!"
But if spacetime loses its geometric nature in the ultra-high energies, what kind of a structure could take over? There are many different suggestions available in the research literature --- the problem with a complete departure from the classical physics' notion of spacetime being that it is extremely hard to find another well-justified basis, on which to build the hypothetical replacement. However, there is at least one successful example of exactly such a development in the history of quantum physics: The discovery of matrix mechanics by Werner Heisenberg in 1925. Of course, Heisenberg had the great advantage (in addition to staying alone on an isolated island in the middle of nowhere due to a particularly severe case of an allergic reaction) of having a wealth of unexplained experimental data at hand to almost immediately verify his theoretical ideas, whereas we have no experimental data on possible quantum gravitational effects. Nevertheless, his approach to focus on the observable quantities may offer some valuable guidance.
So, let's then consider what exactly is the immediate physical meaning of spacetime geometry, that is, how do we observe and measure it. We cannot directly smell or taste spacetime. In fact, to measure the geometry of spacetime we must always employ material objects that evolve according to some dynamics. Usually the construction of dynamics for a quantum system is based (at least in part) on the geometry of spacetime, on which the system lives, so that the dynamics is local with respect to the geometry. However, since we must necessarily use the dynamics of matter to determine the spacetime geometry, it may as well be that the geometry is in fact "only" a property of the matter dynamics --- an organization of the system's degrees of freedom such that the dynamics becomes local, at least in some appropriate limit. There are then at least two immediate problems to solve: 1) How to construct and represent the dynamics of a quantum system in the total absence of a background spacetime geometry? 2) How to reconstruct the (possibly approximate) spacetime geometry from the dynamics?
We are currently trying to develop an approach to quantum gravity that could provide answers to these fascinating theoretical questions. The algebraic formulation of quantum physics seems --- in addition to being the most general and rigorous one --- to be the most appropriate framework for the construction of quantum systems in the absence of background geometry. However, many important aspects for taking this approach seriously are still covered in a thick mist of confusion and ignorance.
Here you can find one of my past (rejected) research proposals, which contains some more ideas and technical details on the topic. If any questions/comments/suggestions/criticisms come to your mind, don't hesitate to contact me! In the mean while, the work goes on...
The pair of words "quantum gravity" has several possible meanings with different degrees of specificity, but the most practical and general definition is probably also the one that most people can agree on: Quantum gravity is the field of theoretical high energy physics that tries to understand the microscopic structure and behavior of spacetime (although not necessarily exclusively). According to this definition, "quantum gravity" is not any particular theory of physics, but a particular field of physics determined by the questions that it poses. This is also my favorite definition (as well as the one used by Wikipedia), since we simply don't know at this stage what is the correct approach to develop a theory that describes space and time at very short distances or, equivalently, very high energies. In my experience, anyone who claims otherwise is either seriously misinformed or writing a research proposal.
The problem of quantum gravity is extremely fascinating, because it is one of the last frontiers of fundamental physics, if not the last. While its solution will not rid the world of starvation or disease in the foreseeable future, I believe it does present to us an opportunity to revolutionize our conception of physical reality --- as did the discoveries of its predecessors quantum mechanics and general relativity. The importance of such revolutions has never stemmed from their immediate practical implications (which may be plenty, as in the case of quantum mechanics), but rather from their profound effect on our conception of the universe we inhabit, and ultimately our self-image as momentary patterns in that universe. However, in my mind, above all such noble philosophical motivations arises the fact that, due to our complex evolutionary history as a species of primates, we humans are exteremely curious creatures by nature. We just simply love to learn new things and find out more about pretty much everything --- no matter how esoteric or impractical! Indeed, this innate instinct of ours is certainly one of the key factors in our success as a species.
(Too often it appears to me, however, that our societies and educational systems have been built around the goal of stifling this instinctive curiosity within people by promoting obedience and passive consumerism instead of active creative participation.)
But wait... Hold your horses. Why is this new "revolution" in physics needed in the first place? Why aren't our current theories sufficient to describe the physical world? After all, (as far as I know) there is currently not a single observation contradicting our two best theories, the Standard Model of elementary particle physics and Einstein's general theory of relativity describing gravity. However, the fact of the matter is that despite the magnificient success of these two most fundamental of theories, they are in an inherent conceptual contradiction with each other. It is only because gravitational forces on elementary particles are so ridiculously weak that they have no practical relevance what-so-ever within the limits of the current observational accuracy, and for the most part we may just neglect them altogether. Most researchers, myself included, blaim the contradiction on the classical deterministic character of the general theory of relativity. We have learned since the conception of quantum mechanics in the beginning of the 20th century that the fundamental description of nature appears not to be deterministic but probabilistic. The probabilities of measurement outcomes are described in the case of simple microscopic systems by quantum mechanics, while the Standard Model describes with an utmost accuracy the probabilities for the highly energetic interaction processes of elementary particles that take place, for example, inside the Large Hadron Collider (LHC) at CERN. One of the main reasons for believing that quantum theories are more fundamental than classical deterministic theories, such as general relativity, is that in several instances a quantum model --- built from a classical model via a set of techniques called quantization --- has turned out to describe nature more faithfully than its original classical counterpart. The quintessential example of this is the development of quantum electrodynamics in the 1940's and 50's that was succesfully obtained from Maxwell's electromagnetic field theory more or less by a direct quantization.
Since Einstein's general theory of relativity, just like Maxwell's electromagnetic theory, has the form of a classical field theory, it is tempting to postulate that by directly quantizing it we should be able to obtain a corresponding quantum theory, thus bringing our descriptions of elementary particles and gravity under the same roof, and removing the fundamental contradiction in modern physics. Indeed, attempts by extremely smart people to do exactly this span now at least 50 years, which already conveys some feeling of the immense difficulty of the task. It turns out that the dynamics of Einstein's theory, as such, has properties that make it extremely adverse to a direct quantization. As a result, many researchers have moved forward to consider other alternative approaches to the problem, some of which are quite faithful to the original vision, and some others that are not so in the least. Anyone interested in fundamental physics these days has probably heard of String Theory and Loop Quantum Gravity, perhaps even about the disputes between the supporters of the two approaches, but these are really only the tip of the iceberg. Hidden behind the most popular directions of research, there is a wild undergrowth of ideas and points-of-view, and I have no intention or pretension to make justice to all or, indeed, any of them here. Instead, I will just very briefly and even more subjectively review two of my own favorites.
1) Quantum gravity as quantum statistics of geometry. The revolutionary idea behind Einstein's general relativity is that gravitational interactions are caused by the curvature of spacetime geometry itself. In the original formulation, the "field" that is the dynamical variable of the theory is the metric of spacetime that describes the geometry of spacetime by determining the lengths and durations of spatial and temporal intervals. Whenever a region of space contains energy (or, equivalently, mass), the dynamics of general relativity dictate that the geometry around the region must be curved. Such curvature causes the trajectories of freely moving objects to deviate from straight lines, thus causing the illusion of a force acting on the objects.
Accordingly, the fundamental insight of general relativity can be expressed as "gravity = spacetime geometry". To cash in on this insight, we may further postulate "quantum gravity = quantum spacetime geometry". It is a natural idea therefore to try to construct quantum theories of geometry, even if they are not obtained via a direct quantization of general relativity. One may still be able to construct models that predict quantum probabilities for spacetime geometric processes that agree with general relativity in the large distance/low energy limit. This is exactly the goal of several approaches to quantum gravity and, in particular, group field theories and tensor models. The "elementary particles" of these quantum models are in fact simple tetrahedra, whose interaction processes correspond to discrete 4-dimensional geometries, which then are hoped to approximate the smooth spacetime structure of general relativity in the classical/low energy/thermodynamical regime.
In a sense, since these models are quantum field theories, they are not fundamentally models of tetrahedra --- just like quantum electrodynamics is not really a theory of just photons and electrons --- even though their construction is based on such discrete geometric considerations. In a quantum field theoretical model, particles are only representations of certain quantities that appear in the perturbative approximation to the theory, and not elements of the full non-perturbative theory as such. (In quantum field theory, one may also consider particles to be clicks of a particle detector, but that's another thing.) Therefore, studying the properties of the full theory, and not just its perturbative expansion, is of crucial importance in trying to understand whether these models can really describe the physical spacetime that we know and love. At the same time, understanding the full theory is also very very challenging, and not much progress has been made so far in the case of realistic 4-dimensional models.
It is also far from clear, for example, what is the correct choice of dynamics for such a model that would reproduce general relativity in the appropriate limit. Some researchers hope that, due to a hypothetical universality of the approximate large-scale behavior --- not unlike in some statistical physics models ---, the details of the microscopic model might not matter that much in the end. I'm not so sure that this would be a good thing though, since it would prevent us from choosing a unique model, and therefore compromise predictivity. (So much for teasing the string theorists about their landscape!)
If you happen to be interested in this kind of an approach in more detail, I can recommend the following two reviews to begin with:
- Daniele Oriti, The Microscopic Dynamics of Quantum Space as a Group Field Theory, arXiv:1110.5606 [hep-th]
- Vincent Rivasseau, The Tensor Track, III, arXiv:1311.1461 [hep-th]
2) Spacetime as a structure of quantum dynamics. Despite the apparent immediateness of the above "gravity = spacetime geometry" reasoning, there are in fact strong indications that this is perhaps too naive an approach. In a world described by classical physics, including general relativity, one is able to measure space and time with an arbitrarily good precision. However, we don't live in that world! Instead, when one takes into account the quantum behavior of matter, this asymptotically perfect accuracy turns out not to hold any longer, but there appear inherent limitations to measurements of spacetime geometry. For example, one can never resolve spacetime points by real physical measurements that always exhibit quantum uncertainties. Therefore, already the starting point to the previous approach of spacetime as a geometric manifold --- a set of points (with some additional structure) --- seems to be seriously undermined by such considerations. (I should emphasize, however, that in group field theory, for example, the geometries that the models describe are not really classical, but quantized à la Loop Quantum Gravity.) Accordingly, quantum gravity as quantization of (classical) geometry seems also to lose its meaningfulness. In the face of such a deep conceptual contradiction, one feels tempted to throw one's hands in the air and exclaim: "No wonder then that the last 50 years have not led to any progress!"
But if spacetime loses its geometric nature in the ultra-high energies, what kind of a structure could take over? There are many different suggestions available in the research literature --- the problem with a complete departure from the classical physics' notion of spacetime being that it is extremely hard to find another well-justified basis, on which to build the hypothetical replacement. However, there is at least one successful example of exactly such a development in the history of quantum physics: The discovery of matrix mechanics by Werner Heisenberg in 1925. Of course, Heisenberg had the great advantage (in addition to staying alone on an isolated island in the middle of nowhere due to a particularly severe case of an allergic reaction) of having a wealth of unexplained experimental data at hand to almost immediately verify his theoretical ideas, whereas we have no experimental data on possible quantum gravitational effects. Nevertheless, his approach to focus on the observable quantities may offer some valuable guidance.
So, let's then consider what exactly is the immediate physical meaning of spacetime geometry, that is, how do we observe and measure it. We cannot directly smell or taste spacetime. In fact, to measure the geometry of spacetime we must always employ material objects that evolve according to some dynamics. Usually the construction of dynamics for a quantum system is based (at least in part) on the geometry of spacetime, on which the system lives, so that the dynamics is local with respect to the geometry. However, since we must necessarily use the dynamics of matter to determine the spacetime geometry, it may as well be that the geometry is in fact "only" a property of the matter dynamics --- an organization of the system's degrees of freedom such that the dynamics becomes local, at least in some appropriate limit. There are then at least two immediate problems to solve: 1) How to construct and represent the dynamics of a quantum system in the total absence of a background spacetime geometry? 2) How to reconstruct the (possibly approximate) spacetime geometry from the dynamics?
We are currently trying to develop an approach to quantum gravity that could provide answers to these fascinating theoretical questions. The algebraic formulation of quantum physics seems --- in addition to being the most general and rigorous one --- to be the most appropriate framework for the construction of quantum systems in the absence of background geometry. However, many important aspects for taking this approach seriously are still covered in a thick mist of confusion and ignorance.
Here you can find one of my past (rejected) research proposals, which contains some more ideas and technical details on the topic. If any questions/comments/suggestions/criticisms come to your mind, don't hesitate to contact me! In the mean while, the work goes on...
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