Are There Viable Alternatives to Quantum Field Theory and Second Quantization?

[waterfall]

It's amazing how one can mess up every little detail. Sorry, don't be surprised about not gettting answers, it's just too far off.

What? It's not my idea but Smolin's. Anyway. I converted all texts of Lee Smolin "Trouble With Physics" to speech and I'll listen to it all day and night in my ipod. Here's Smolin main theme or punchline:

"This is the story of a quest to understand nature at its deepest level. Its protagonists are the scientists who are laboring to extend our knowledge of the basic laws of physics. The period of time I will address - roughly since 1975 - is the span of my own professional career as a theoretical physicist. It may also be the strangest and most frustrating period in the history of physics since Kepler and Galileo began the practice of our craft four hundred years ago. The story I will tell could be read by some as a tragedy. To put it bluntly - and to give away the punch line - we have failed. We inherited a science, physics, that had been progressing so fast for so long that it was often taken as the model for how other kinds of science should be done. For more than two centuries, until the present period, our understanding of the laws of nature expanded rapidly. But today, despite our best efforts, what we know for certain about these laws is no more than what we knew back in the 1970s. How unusual is it for three decades to pass without major progress in fundamental physics? Even if we look back more than two
hundred years, to a time when science was the concern mostly of wealthy amateurs, it is unprecedented. Since at least the late eighteenth century, significant progress has been made on crucial questions every quarter century"

 

[Physics Monkey]

What I find amazing is the unbelievable hubris required to equate a few esoteric questions in high energy physics with the progress of all physics.

 

[friend]

Btw.. why hasn't anyone told me the answer to the "Alternative to QFT " in my thread question is nothing but Loop Quantum Gravity as Smolin mentioned?

Does your concern about the right math in physics come from a perception that present math may not be able to give us a complete theory of everything? Or does it seem that the mathematical origins of QFT seem arbitrary? What would prove that we are using the correct math? We would have to be able to derive QFT from deductive logic in order to show that there is even any chance of proving the completeness of physics. Otherwise, our theories will always be contingent on the next experiment confirming their predictions. We can never measure everything, so their always remains the possibility that our theory can be proven wrong by some experiment.

 

[tom.stoer]

LQG is certainly not the alternative
- it's not a complete theory but work in progress (neither mathematically nor physically)
- it's a theory about gravity only; full inclusion of matter is still missing
- it's by no means a theory aiming for unification
- the definition of obervables is not fully understood
- nobody knows how to do simple low-energy scattering calculations
-...

 

[waterfall]

Does your concern about the right math in physics come from a perception that present math may not be able to give us a complete theory of everything? Or does it seem that the mathematical origins of QFT seem arbitrary? What would prove that we are using the correct math? We would have to be able to derive QFT from deductive logic in order to show that there is even any chance of proving the completeness of physics. Otherwise, our theories will always be contingent on the next experiment confirming their predictions. We can never measure everything, so their always remains the possibility that our theory can be proven wrong by some experiment.

I have to study deeper the math of QFT to be able to answer that. But I heard from Fredrik that even those with Ph.D. in Physics doesn't mean they are already expert in QFT. So it's kinda heartbreaking. From graduate in college of BS in Physics to Ph.D. I think takes 4 to 5 years more for total of 8 years. And yet they are not yet master in it. Are you a physicist? I'm thinking whether to go back to school and become one. Because there is a possibility our physicists may just miss it all and won't see the light even after 20 years or year 2032. This is because they are doing it blind. They don't have any guiding principle much like when Einstein got the insight about the Equivalence Principle and spent 10 years to perfect it to produce GR. I think I have a guiding principle insight too and just need to find the right math. Actually some have the same guiding principle insight but they are just not trained to math to develope it fully. And physics is just so important to leave it to physicists. Important choices to make maybe not just me.. but also you. So is your course related to physics? What do you make of Smolin and Woit book. Woit book is more mathematical and I think I'll try to understand it deeper after learning here that QFT is good for only free fields and Fock space is none-interacting proving Smolin and Woit is not smoking pots but are partly if not more right in their critique of modern physics.

 

[ofirg]

Why is QFT treated here as its definition only makes sense with perturbation theory?
I understood that the path integral definition ( and the canonical formalism also, at least of you can find an appropriate fock space) doesn't rely on perturbation theory, and we use it simply because we aren't able solve the full theory.

 

[marcus]

Hi Waterfall, your thread about a possible wrong turn reminds me of a different discussion we had here a few years back. A mentor named "SelfAdjoint" took part in the discussion.

https://www.physicsforums.com/showthread.php?t=124999

It began with a poll asking when people thought a wrong turn was made.

 

[juanrga]

Why is QFT treated here as its definition only makes sense with perturbation theory?
I understood that the path integral definition ( and the canonical formalism also, at least of you can find an appropriate fock space) doesn't rely on perturbation theory, and we use it simply because we aren't able solve the full theory.

The «full theory» does not exist as QFT... because only free fields are well-defined.

 

[atyy]

after learning here that QFT is good for only free fields and Fock space is none-interacting

First, the renormalization group shows that theories do not have to be defined at all energies to yield great predictions at low energies. QED is such a theory.

Second, it is not true that only free fields are rigourously defined at all energies. Some nonlinear self-interacting quantum fields have been rigourously constructed in 2 and 3 dimensional spacetimes. The rigourous construction of Yang-Mills theory in 4 dimensional spacetime is thought possible because of asymptotic freedom, but it is still being researched. In fact, the Clay Institute is offering a prize of $1 million for a rigourous construction of Yang Mills theory and a demonstration that it has a mass gap.

http://www.claymath.org/millennium/Yang-Mills_Theory/
http://www.claymath.org/millennium/Yang-Mills_Theory/yangmills.pdf

 

[marcus]

LQG is certainly not the alternative
- it's not a complete theory but work in progress (neither mathematically nor physically)
- it's a theory about gravity only; full inclusion of matter is still missing
- it's by no means a theory aiming for unification
- the definition of obervables is not fully understood
- nobody knows how to do simple low-energy scattering calculations
-...

I have no reason to object to any of these 5 points and don't want to argue about any of this.

But I want to mention what my perspective is on your "certainly not the alternative" phrase.

LQG could well be on the correct path to the alternative even though it is itself not the last step nor does try to be.

The LQG program may be *on the path to unification" because it strives for a new (no-prior-geometry) representation of spacetime. One which takes into account how geometry responds to measurement and interacts with matter.

On the path, because it may happen to be necessary to settle on a quantum theory of geometry (interacting with matter) before one can build a new representation of the whole.

And in particular it may be necessary to arrive first at a testable QG model of early universe cosmology, like that of LQC--something which explains how the big bang occurred, resolves some problems with dark matter and inflation, and predicts various features to observe in the background of ancient light.

 

[friend]

Hi Waterfall, your thread about a possible wrong turn reminds me of a different discussion we had here a few years back. A mentor named "SelfAdjoint" took part in the discussion.

https://www.physicsforums.com/showthread.php?t=124999

It began with a poll asking when people thought a wrong turn was made.

That thread ended with

riginally Posted by Mike2
"We don't really know WHY the math is the way it is. "

To which the reply was,
"We never knew that, and we will never know that."

My opinion is that we will never really be satisfied until we can derive physics from the first principles of logic. For that's really the only means of really "knowing' what is true beyond any argument. Otherwise, theories developed by just guessing the math can be falsified by some observation in the future, and we can never be totally sure about them because we can not measure everything to actually prove that the theory predicts all measurements.

So, my efforts have been towards a derivation of physics from logic for the past 5-10 years. I seem to have made progress (at least no one is showing me any blatant errors), and I think I am getting very close. However, my efforts are not on the arXiv yet. So it might still be considered speculative here. But if you really want to examine my work in progress, give me a Private Message.

 

[ohwilleke]

"- it's a theory about gravity only; full inclusion of matter is still missing
- it's by no means a theory aiming for unification
. . .

But I want to mention what my perspective is on your "certainly not the alternative" phrase.

LQG could well be on the correct path to the alternative even though it is itself not the last step nor does try to be.

The LQG program may be *on the path to unification" because it strives for a new (no-prior-geometry) representation of spacetime. One which takes into account how geometry responds to measurement and interacts with matter."

To restate the point Marcus is making in a slightly different way, there is active research underway regarding how existing Standard Model interactions can be formulated in the context of a LQG space-time that seem to be making more progress than efforts express Standard Model interactions in a manner consistent with General Relativity rather than just Special Relativity. LQG efforts are proving more fruitful because one of the main the difficulties in integrating Standard Model interaction with General Relativity flow directly from the simultaneous assumptions that space-time is continuous (from GR) and that fundamental fermions and bosons are point-like (from the Standard Model) which naturally implies that every single particle is a singularity and isn't easily fixed. Point-like Standard Model fundamental fermions and bosons cause far less mischief in LQG because the discreteness of space-time discourages singularities from arising.

Thus, LQG is a promising possible way to formulate the Standard Model and GR in ways that are at least theoretically capable of being consistent with each other at the scale of individual particles.

Moreover, if you can formulate Standard Model interactions in an LQG space-time, then a "Theory of Everything" in which all four fundamental forces are different manifestations of a single deeper form of boson mediated particle interaction becomes a category error. If space-time has the character that LQG tries to model it as then gravity since it flows from the nature of space-time itself, is fundamentally different in kind than the other three fundamental forces. Hence, if you can formulate a mere GUT within an LQG space-time, you have taken the reductionist agenda for fundamental physics as far as it can go.

The genius of this research program is that string theory needs more than four dimensions of space-time almost entirely to accommodate the need to make gravity weak relative to the other three fundamental forces which by themselves can be formulated quite workably in a four dimensional space time. Indeed, the whole braneworld concept, in which string theorists conceive of a world where everything but gravity is confined to a four dimensional brane which is embedded in a larger dimensional space, illustrates how unnatural it is to try to treat gravity and the other three fundamental forces of the Standard Model as different versions of the same thing. In contrast, in LQG, an emergently four dimensional space-time arises naturally, and since you should need extra dimensions to formulate Standard Model equations designed for four dimensional Minkowski space into emergently four dimensional LQG space, you have eliminated the need to deal with unnatural extra dimensions from the get go.

A deep hate for point-like particles is deeply embedded in the very DNA of GR equations formulated in continous, perfectly local, space-time, and the Standard Model is equations are very deeply wedded to having point-like particles, which is what has made the marriage of the two so difficult to navigate. But, neither GR nor the Standard Model are all that deeply wedded to a continuous space-time. Continuity is an assumption thrown into the mix mostly for mathematical convenience and the heuristic that drives calculus itself is the notion that it is possible to exquisitely accurately (and indeed beyond accuracy to the point of a Platonic ideal) model sums of infinitessimal quantities as continuous quantities. LQG simply steps back off this assumption used for mathematical convenience to go to the source of the heuristic and computes quantities the hard way rather than analytically. Indeed, we routinely use discrete numerical methods to approximate Standard Model interactions by themselves, and to approximate GR by itself.

Yes, LQG is a work in progress. The task of formulating the Standard Model interactions in an LQG geometry is not ready for prime time yet. And, even if your ultimate goal is to formulate a GUT within an LQG geometry, there is not point in even trying until you accomplish this prerequisite task. You have to hope that the progress you make in formulating Standard Model interactions in an LQG geometry will point you in the right direction regarding what to do next.

But, once you can accomplish the more doable seeming task of formulating Standard Model interations in an LQG geometry, even the goal of then integrating those interactions into a GUT is less pressing. One of the reasons a Theory of Everything is such an alluring Holy Grail is that this would solve the current mess in which are two most perfect and wonderful theories of fundamental physics (the Standard Model and GR) are theoretically inconsistent with each other in obvious ways, despite the fact that both in their own domains repeatedly manage to describe experimental data with exquisite precision. But, if you formulate Standard Model interactions in an LQG geometry, that isn't a problem that needs to be solved by devising a Theory of Everything any more.

With that problem already solved, the only real problem left to tackle by taking the reformulated Standard Model interactions and integrating them into a GUT is to develop better insight about the physics of extremely high energy systems approaching Big Bang conditions. And, even those problems may not be as acute for the Standard Model interactions embedded in LQG, because the LQG geometry is already going to give rise by its very nature to some subtle high energy system modifications to Standard Model predictions because it integrates GR effects that have only been considered in an ad hoc non-rigorous way to date, for example, in asymptotic gravity driven predictions about Higgs mass and clever suppositions formulated just so necessary to predict Hawking radiation. For example, Standard model interactions embedded in LQG are very likely to have a lower unification energy scale than SUSY or SUSY inspired theories, and the natural UV bounds in LQG also tame a lot of the rigor concerns associated with commonly used renormalization methods.

You probably would still need to make a few leaps of insight to get a GUT embedded within an LQG geometry rather than merely the Standard Model embedded within an LQG geometry, but there is very good reason to think that those leaps of insight would have to be more modest in the LQG context than in the continuous space context, because there are fewer problems less to resolve. Once you've got the Standard Model embedded within LQG, pretty much all you need to do is to come up with a way to describe each of the twelve fundamental fermions (three generations each of two kinds of quarks, one kind of charged lepton and one kind of neutrino; if one does not count variations in the color charge/matter-antimatter/parity directions as different fermions), and each of the twelve Standard Model bosons (photon, 2 Ws and a Z, and eight gluons, ignoring any other possible variations on these bosons) as manifestations of one more fundamental thing. Turning one thing into twenty-four things with variations that have the right properties is tough, but not nearly as Herculean as the task currently facing people trying to devise a TOE via string theory.

I wouldn't be at all surprised to see insight developed in one or another prior GUT (perhaps even the original SU(5) GUTs) that failed and developed pathologies when formulated in Minkowski space, apply quite directly to a Standard Model embedded in LQG geometry that would somehow miraculously resolve the pathologies that arose in previous attempts to apply those insights.

 

[waterfall]

First, the renormalization group shows that theories do not have to be defined at all energies to yield great predictions at low energies. QED is such a theory.

Second, it is not true that only free fields are rigourously defined at all energies. Some nonlinear self-interacting quantum fields have been rigourously constructed in 2 and 3 dimensional spacetimes. The rigourous construction of Yang-Mills theory in 4 dimensional spacetime is thought possible because of asymptotic freedom, but it is still being researched. In fact, the Clay Institute is offering a prize of $1 million for a rigourous construction of Yang Mills theory and a demonstration that it has a mass gap.

http://www.claymath.org/millennium/Yang-Mills_Theory/
http://www.claymath.org/millennium/Yang-Mills_Theory/yangmills.pdf

Fock space is derived from Hilbert space which is derived from the Schrodeinger Equations. We know there are other candidate equations or formulations like Matrix Mechanics and Path Integral Approach for example (although I know they are identical in essence). If we were to return to the early 1900s. What kind of math must happen or approach for the quantum fields to be completely interacting? Or is there none at all? Why? Or maybe Fock Space/Hilbert space is just too coarse for it. Also I wonder if this has to do with quantum interpretations. If we can somehow distinguish the right interpretation, would it make the fields become naturally interacting?

 

[friend]

Yes, LQG is a work in progress. The task of formulating the Standard Model interactions in an LQG geometry is not ready for prime time yet. And, even if your ultimate goal is to formulate a GUT within an LQG geometry, there is not point in even trying until you accomplish this prerequisite task. You have to hope that the progress you make in formulating Standard Model interactions in an LQG geometry will point you in the right direction regarding what to do next.

I have to wonder how the symmetries of the standard model would fit into the LQG scheme of things. How does the U(1)XSU(2)XSU(3) symmetry fit into the descrete spacetime of LQG? I thought these symmetries were continuous. Would discrete spacetime destroy them?

 

[waterfall]

"- it's a theory about gravity only; full inclusion of matter is still missing
- it's by no means a theory aiming for unification
. . .

But I want to mention what my perspective is on your "certainly not the alternative" phrase.

LQG could well be on the correct path to the alternative even though it is itself not the last step nor does try to be.

The LQG program may be *on the path to unification" because it strives for a new (no-prior-geometry) representation of spacetime. One which takes into account how geometry responds to measurement and interacts with matter."

To restate the point Marcus is making in a slightly different way, there is active research underway regarding how existing Standard Model interactions can be formulated in the context of a LQG space-time that seem to be making more progress than efforts express Standard Model interactions in a manner consistent with General Relativity rather than just Special Relativity. LQG efforts are proving more fruitful because one of the main the difficulties in integrating Standard Model interaction with General Relativity flow directly from the simultaneous assumptions that space-time is continuous (from GR) and that fundamental fermions and bosons are point-like (from the Standard Model) which naturally implies that every single particle is a singularity and isn't easily fixed. Point-like Standard Model fundamental fermions and bosons cause far less mischief in LQG because the discreteness of space-time discourages singularities from arising.

Thus, LQG is a promising possible way to formulate the Standard Model and GR in ways that are at least theoretically capable of being consistent with each other at the scale of individual particles.

Moreover, if you can formulate Standard Model interactions in an LQG space-time, then a "Theory of Everything" in which all four fundamental forces are different manifestations of a single deeper form of boson mediated particle interaction becomes a category error. If space-time has the character that LQG tries to model it as then gravity since it flows from the nature of space-time itself, is fundamentally different in kind than the other three fundamental forces. Hence, if you can formulate a mere GUT within an LQG space-time, you have taken the reductionist agenda for fundamental physics as far as it can go.

The genius of this research program is that string theory needs more than four dimensions of space-time almost entirely to accommodate the need to make gravity weak relative to the other three fundamental forces which by themselves can be formulated quite workably in a four dimensional space time. Indeed, the whole braneworld concept, in which string theorists conceive of a world where everything but gravity is confined to a four dimensional brane which is embedded in a larger dimensional space, illustrates how unnatural it is to try to treat gravity and the other three fundamental forces of the Standard Model as different versions of the same thing. In contrast, in LQG, an emergently four dimensional space-time arises naturally, and since you should need extra dimensions to formulate Standard Model equations designed for four dimensional Minkowski space into emergently four dimensional LQG space, you have eliminated the need to deal with unnatural extra dimensions from the get go.

A deep hate for point-like particles is deeply embedded in the very DNA of GR equations formulated in continous, perfectly local, space-time, and the Standard Model is equations are very deeply wedded to having point-like particles, which is what has made the marriage of the two so difficult to navigate. But, neither GR nor the Standard Model are all that deeply wedded to a continuous space-time. Continuity is an assumption thrown into the mix mostly for mathematical convenience and the heuristic that drives calculus itself is the notion that it is possible to exquisitely accurately (and indeed beyond accuracy to the point of a Platonic ideal) model sums of infinitessimal quantities as continuous quantities. LQG simply steps back off this assumption used for mathematical convenience to go to the source of the heuristic and computes quantities the hard way rather than analytically. Indeed, we routinely use discrete numerical methods to approximate Standard Model interactions by themselves, and to approximate GR by itself.

Yes, LQG is a work in progress. The task of formulating the Standard Model interactions in an LQG geometry is not ready for prime time yet. And, even if your ultimate goal is to formulate a GUT within an LQG geometry, there is not point in even trying until you accomplish this prerequisite task. You have to hope that the progress you make in formulating Standard Model interactions in an LQG geometry will point you in the right direction regarding what to do next.

But, once you can accomplish the more doable seeming task of formulating Standard Model interations in an LQG geometry, even the goal of then integrating those interactions into a GUT is less pressing. One of the reasons a Theory of Everything is such an alluring Holy Grail is that this would solve the current mess in which are two most perfect and wonderful theories of fundamental physics (the Standard Model and GR) are theoretically inconsistent with each other in obvious ways, despite the fact that both in their own domains repeatedly manage to describe experimental data with exquisite precision. But, if you formulate Standard Model interactions in an LQG geometry, that isn't a problem that needs to be solved by devising a Theory of Everything any more.

With that problem already solved, the only real problem left to tackle by taking the reformulated Standard Model interactions and integrating them into a GUT is to develop better insight about the physics of extremely high energy systems approaching Big Bang conditions. And, even those problems may not be as acute for the Standard Model interactions embedded in LQG, because the LQG geometry is already going to give rise by its very nature to some subtle high energy system modifications to Standard Model predictions because it integrates GR effects that have only been considered in an ad hoc non-rigorous way to date, for example, in asymptotic gravity driven predictions about Higgs mass and clever suppositions formulated just so necessary to predict Hawking radiation. For example, Standard model interactions embedded in LQG are very likely to have a lower unification energy scale than SUSY or SUSY inspired theories, and the natural UV bounds in LQG also tame a lot of the rigor concerns associated with commonly used renormalization methods.

You probably would still need to make a few leaps of insight to get a GUT embedded within an LQG geometry rather than merely the Standard Model embedded within an LQG geometry, but there is very good reason to think that those leaps of insight would have to be more modest in the LQG context than in the continuous space context, because there are fewer problems less to resolve. Once you've got the Standard Model embedded within LQG, pretty much all you need to do is to come up with a way to describe each of the twelve fundamental fermions (three generations each of two kinds of quarks, one kind of charged lepton and one kind of neutrino; if one does not count variations in the color charge/matter-antimatter/parity directions as different fermions), and each of the twelve Standard Model bosons (photon, 2 Ws and a Z, and eight gluons, ignoring any other possible variations on these bosons) as manifestations of one more fundamental thing. Turning one thing into twenty-four things with variations that have the right properties is tough, but not nearly as Herculean as the task currently facing people trying to devise a TOE via string theory.

I wouldn't be at all surprised to see insight developed in one or another prior GUT (perhaps even the original SU(5) GUTs) that failed and developed pathologies when formulated in Minkowski space, apply quite directly to a Standard Model embedded in LQG geometry that would somehow miraculously resolve the pathologies that arose in previous attempts to apply those insights.

I didn't focus on LQG years ago because the spin networks couldn't even approximate General Relativity in the classical limit. I wonder if it is more optimistic now or still the same problem. If anyone has references concerning updates of how to make LQG approximate the manifold of GR. Let me know.

 

[atyy]

Fock space is derived from Hilbert space which is derived from the Schrodeinger Equations. We know there are other candidate equations or formulations like Matrix Mechanics and Path Integral Approach for example (although I know they are identical in essence). If we were to return to the early 1900s. What kind of math must happen or approach for the quantum fields to be completely interacting? Or is there none at all? Why? Or maybe Fock Space/Hilbert space is just too coarse for it. Also I wonder if this has to do with quantum interpretations. If we can somehow distinguish the right interpretation, would it make the fields become naturally interacting?

I don't know.

Maybe you could take a look at the known successful constructions of interacting quantum fields referenced in Jaffe and Witten's http://www.claymath.org/millennium/Yang-Mills_Theory/yangmills.pdf.

The rigourous construction of quantum Yang-Mills theory remains http://www.claymath.org/millennium/Yang-Mills_Theory/. Douglas describes the http://www.claymath.org/millennium/Yang-Mills_Theory/ym2.pdf.

Gupta's Introduction to Lattice QCD could also be helpful. Gupta references a proof of Osterwalder-Schrader reflection positivity which is a condition for the rigourous construction of quantum fields, including an appropriate Hilbert space. A description of all the Osterwalder-Schrader conditions, and why they lead to a rigourous construction of quantum field theory, is found in Glimm and Jaffe's book.

 

[waterfall]

I don't know.

Maybe you could take a look at the known successful constructions of interacting quantum fields referenced in Jaffe and Witten's http://www.claymath.org/millennium/Yang-Mills_Theory/yangmills.pdf.

The rigourous construction of quantum Yang-Mills theory remains http://www.claymath.org/millennium/Yang-Mills_Theory/. Douglas describes the http://www.claymath.org/millennium/Yang-Mills_Theory/ym2.pdf.

Gupta's Introduction to Lattice QCD could also be helpful. Gupta references a proof of Osterwalder-Schrader reflection positivity which is a condition for the rigourous construction of quantum fields, including an appropriate Hilbert space. A description of all the Osterwalder-Schrader conditions, and why they lead to a rigourous construction of quantum field theory, is found in Glimm and Jaffe's book.

Ok. I'll take a look at them. For an hour now. I kept looking for Peter Woit "Not Even Wrong" in my attic and I can't seem to find it. The book is deeply mathematical and when I read it years ago. It was hard to follow, but now I'll try it again.. it mentioned about S-matrix and other mathematical techniques that I'm sure others who haven't read with more mathematical background can appreciate it more.

Anyway. I think there are two ways of looking at it. If space is discrete, etc. then it is the physical description that is not complete, this means the math ultraviolet divergence for example is due to the physical problem and not the math. But if space is continuous, then it is the math limitation. I think people will agree to this catogorizing...

 

[marcus]

I didn't focus on LQG years ago because the spin networks couldn't even approximate General Relativity in the classical limit. I wonder if it is more optimistic now or still the same problem. If anyone has references concerning updates of how to make LQG approximate the manifold of GR. Let me know.

A recent paper:
http://arxiv.org/abs/1201.2187
A spin-foam vertex amplitude with the correct semiclassical limit
Jonathan Engle
(Submitted on 10 Jan 2012)
Spin-foam models are hoped to provide a dynamics for loop quantum gravity. All 4-d spin-foam models of gravity start from the Plebanski formulation, in which gravity is recovered from a topological field theory, BF theory, by the imposition of constraints, which, however, select not only the gravitational sector, but also unphysical sectors. We show that this is the root cause for terms beyond the required Feynman-prescribed exponential of i times the action in the semiclassical limit of the EPRL spin-foam vertex. By quantizing a condition isolating the gravitational sector, we modify the EPRL vertex, yielding what we call the proper EPRL vertex amplitude. This provides at last a vertex amplitude for loop quantum gravity with the correct semiclassical limit.
Comments: 4 pages

Some other recent papers:
https://www.physicsforums.com/showthread.php?p=3755045#post3755045

 

[atyy]

Ok. I'll take a look at them. For an hour now. I kept looking for Peter Woit "Not Even Wrong" in my attic and I can't seem to find it. The book is deeply mathematical and when I read it years ago. It was hard to follow, but now I'll try it again.. it mentioned about S-matrix and other mathematical techniques that I'm sure others who haven't read with more mathematical background can appreciate it more.

Anyway. I think there are two ways of looking at it. If space is discrete, etc. then it is the physical description that is not complete, this means the math ultraviolet divergence for example is due to the physical problem and not the math. But if space is continuous, then it is the math limitation. I think people will agree to this catogorizing...

The big problem is gravity which is perturbatively not UV renormalizable. The Wilson-Kadanoff picture of renormalization as a way of seeing how a theory looks like at low energies points to two different approaches. The first is that the theory is incomplete, and new degrees of freedom enter - this is the approach of string theory. The second is that the theory could be UV complete if the renormalization flow is non-perturbatively reversed to high energies - this approach is called Asymptotic Safety.

 

[marcus]

...- this approach is called Asymptotic Safety.

If the FGZ program is successful then LQG could turn out to be in effect a background-independent form of Asymptotic Safety.

The FGZ idea is to reformulate classical GR using graphs to truncate GR to finitely many degrees of freedom. So "loop classical gravity" LCG would simply be an alternative formulation of GR. This seems to capture the kinetics of GR. What remains to examine is dynamics.

For sure you know the paper Atyy, anyone not familiar with it can google "freidel geiller ziprick" and get http://adsabs.harvard.edu/abs/2011arXiv1110.4833F

 

[atyy]

If the FGZ program is successful then LQG could turn out to be in effect a background-independent form of Asymptotic Safety.

The FGZ idea is to reformulate classical GR using graphs to truncate GR to finitely many degrees of freedom. So "loop classical gravity" LCG would simply be an alternative formulation of GR. This seems to capture the kinetics of GR. What remains to examine is dynamics.

For sure you know the paper Atyy, anyone not familiar with it can google "freidel geiller ziprick" and get http://adsabs.harvard.edu/abs/2011arXiv1110.4833F

After this, I know I'm not the only one who finds a Freidel paper cryptic. When you watch this it's essential to watch the discussion too. At first Smolin finds the whole thing trivial, saying that the answer to the question they are posing was known in the late 1980s! Then after clarification, he realizes that they are proposing a new way of figuring out if LQG makes sense.

 

[waterfall]

If the FGZ program is successful then LQG could turn out to be in effect a background-independent form of Asymptotic Safety.

The FGZ idea is to reformulate classical GR using graphs to truncate GR to finitely many degrees of freedom. So "loop classical gravity" LCG would simply be an alternative formulation of GR. This seems to capture the kinetics of GR. What remains to examine is dynamics.

For sure you know the paper Atyy, anyone not familiar with it can google "freidel geiller ziprick" and get http://adsabs.harvard.edu/abs/2011arXiv1110.4833F

Hi Marcus (and other quantum gravity experts),

I read up on the paper about Asymptotic Safety linked by Atty, and found the following passage:

http://arxiv.org/pdf/0709.3851v2.pdf

"Even more radically, it is possible that gravity is just the “low energy” manifestation of some
Asymptotic Safety completely different physics, as suggested in the article by Dreyer. This
would probably imply a failure of the asymptotic safety programme, for example a failure to find a fixed point when certain couplings are considered."

Looking up the article/paper of Dreyer referenced above:

http://arxiv.org/pdf/hep-th/0409048v2.pdf

"Background Independent Quantum Field Theory and the Cosmological Constant Problem"

"We will see that the cosmological constant problem arises only when one regards the quantum fields as living on the background. This is where this problem connects with the conceptual problem of background dependence. If, instead, it is the quantum fields that make the spacetime appear in the first place, and they are not treated as living on the background, then the cosmological constant problem disappears."

Now what I'd like to know is this. If say the above were true and it was "quantum fields that make the spacetime appear in the first place" meaning spacetime is emergent. Would this dissolve or falsify Loop Quantum Gravity or would it make it compatible with it such that the spin networks in LQG that make up spacetime is some sort of quanta of the quantum fields?

(For experts in Superstrings (I think Marcus is expert only on LQG), would this dissolve Superstring theory or would it make it compatible with Superstrings theory too?)

 

[martinbn]

I kept looking for Peter Woit "Not Even Wrong" in my attic and I can't seem to find it. The book is deeply mathematical and when I read it years ago. It was hard to follow, but now I'll try it again.. it mentioned about S-matrix and other mathematical techniques that I'm sure others who haven't read with more mathematical background can appreciate it more.

The book is popular and not mathematical.

 

[waterfall]

The book is popular and not mathematical.

I mean the concepts are abstractly mathematical and not exactly for normal laymen. For example. I randomly picked a page and saw the following paragraph.

"The Chern-Simons theory could be defined for any three-dimensional space, so it gave not only the Jones polynomials for knots in standard three-dimensional space, but analogues for any other space with three dimensions. The most surprising part of the theory was its Hilbert space. The Hilbert space was finite dimensional with a dimension given by the Verlinde formula first discovered in conformal field theory. Packed into Witten's new quantum field theory defined by its single Chern-Simons term were amazing and unexpected relations between the topology of knots and three-dimensional spaces, the theory of Kac-Moody groups and their representations, conformal field theoriees, index theory and much else besides". (from page 137 of Peter Woit "Not Even Wrong")

That is what I mean it is very mathematical book (in words) but may not be for all laymen.

 

[marcus]

...
Now what I'd like to know is this. If ... it was "quantum fields that make the spacetime appear in the first place" meaning spacetime is emergent. Would this dissolve or falsify Loop Quantum Gravity or would it make it compatible with it such that the spin networks in LQG that make up spacetime is some sort of quanta of the quantum fields?
...

It's basic to the current formulation of LQG that geometry is a quantum field. The spin networks are quantum states of this field. So LQG is accord with the actual quote itself. But one can find that same message in many other places both antedating Dreyer and also more recent. I would separate that important idea from the 2004 article by Olaf Dreyer, and focus on the idea expressed in the quote, that the basic thing is the field.

Spacetime as such (e.g. some mathematical continuum, or differential manifold, some x,y,z,t space construction) does not appear in the current LQG theory. There is no mathematical object in the theory which you can point to and say that is space, or that is spacetime. It is not needed.

The fundamental object is the field---the quantum states of that field---namely geometry.
The basic philosophy is that a quantum theory is not about what nature IS but more accurately how nature responds to measurement.

In the case of geometry this means the network of geometrical measurements, including ones about which one may have only an expectation or a a probability amplitude. There may be indefiniteness.

In that sense in LQG (see http://arxiv.org/abs/1102.3660) "spacetime" is purely emergent. The focus is on the web of interrelated geometrical measurements (distances, angles, areas, volumes, durations) that specify quantum states of geometry.

Mind you I'm not talking about the various miscellaneous earlier LQG formulations or what somebody said in 2004 or 2006. There is too much variation to keep track of or generalize about including a kind of revolution that started around 2008. I'm just talking about the current formulation (in the Zakopane Lectures I linked to) which many people seem to think encompasses the Loop mainstream of the past 3 or 4 years.

Thanks for attributing expertise, waterfall I watch the current QG research scene with active interest, but am not an authority. I also follow cosmology and AsymSafe QG research, not only Loop, but can't claim to be an expert!

 

[waterfall]

It's basic to the current formulation of LQG that geometry is a quantum field. The spin networks are quantum states of this field.
Spacetime as such (e.g. some mathematical continuum, or differential manifold, some x,y,z,t space construction) does not appear in the theory. There is no mathematical object in the theory which you can point to and say that is space, or that is spacetime.

The fundamental object is the field---the quantum states of that field---namely geometry.
The basic philosophy is that a quantum theory is not about what nature IS but more accurately how nature responds to measurement.

In the case of geometry this means the network of geometrical measurements.

In that sense in LQG (see http://arxiv.org/abs/1102.3660) spacetime is purely emergent. The focus is on the web of interrelated geometrical measurements (distances, angles, areas, volumes, durations) that specify quantum states of geometry.

So the Cosmological Constant Problem disappears too in LQG? If not, how does LQG differs to the mentioned idea of emergent spacetime referenced in the Asymptotic Safety paper in the following??

http://arxiv.org/pdf/hep-th/0409048v2.pdf

"Background Independent Quantum Field Theory and the Cosmological Constant Problem"

"We will see that the cosmological constant problem arises only when one regards the quantum fields as living on the background. This is where this problem connects with the conceptual problem of background dependence. If, instead, it is the quantum fields that make the spacetime appear in the first place, and they are not treated as living on the background, then the cosmological constant problem disappears."

 

[waterfall]

So the Cosmological Constant Problem disappears too in LQG? If not, how does LQG differs to the mentioned idea of emergent spacetime referenced in the Asymptotic Safety paper in the following??

http://arxiv.org/pdf/hep-th/0409048v2.pdf

"Background Independent Quantum Field Theory and the Cosmological Constant Problem"

"We will see that the cosmological constant problem arises only when one regards the quantum fields as living on the background. This is where this problem connects with the conceptual problem of background dependence. If, instead, it is the quantum fields that make the spacetime appear in the first place, and they are not treated as living on the background, then the cosmological constant problem disappears."

Since you mentioned there was a difference and (I think) the Cosmological Constant problem remains in LQG. How do you adjust LQG such that the Cosmological Constant problem would disappear too? And how come Dreyer idea of emergent spacetime can make it disappear in comparison to LQG where it doesn't disappears?

 

[marcus]

So the Cosmological Constant Problem disappears too in LQG? If not, how does LQG differs to the mentioned idea of emergent spacetime referenced in the Asymptotic Safety paper in the following??

http://arxiv.org/pdf/hep-th/0409048v2.pdf

"Background Independent Quantum Field Theory and the Cosmological Constant Problem"

This is a fast evolving field and it's not advisable to get wrapped up in outdated sources.
Whatever Dreyer thought was "the cosmological constant problem" back in 2004 is not likely to mean very much to us today.

I'd say focus on more recent sources. Two people who really are QG experts have written a recent (2010) article disposing of "the cosmological constant problem". They basically make fun of all the HYPE about it. They say "what's the problem?" The cosmological constant is a constant that appears naturally in Gen Rel just like the constant G does.

My advice would be to flush Dreyer 2004 and read this more recent discussion.
http://arxiv.org/abs/1002.3966 or google "bianchi prejudices against constant"
To directly answer your question as best I can: LQG does not have a "cosmological constant problem". So I guess you could say it "disappears", or that it appeared in the first place.

The Bianchi Rovelli article "Why All These Prejudices Against a Constant?" has been known to distress some who view the matter from a background-dependent quantum field theory perspective.

Maybe an additional note for clarification: a field can be defined mathematically without being defined ON anything. One does not need an underlying set (like a manifold). Or if one is used as a temporary technical convenience one can get rid of it later by showing that it is "gauge"--not physically significant.

The aim with QG is to define the gravitational field in this (background independent) way so that other fields (matter) can be defined with the geometry as a basis: located in terms of the gravitational field, that being just another name for geometry.

 

[waterfall]

This is a fast evolving field and it's not advisable to get wrapped up in outdated sources.
Whatever Dreyer thought was "the cosmological constant problem" back in 2004 is not likely to mean very much to us today.

I'd say focus on more recent sources. Two people who really are QG experts have written a recent (2010) article disposing of "the cosmological constant problem". They basically make fun of all the HYPE about it. They say "what's the problem?" The cosmological constant is a constant that appears naturally in Gen Rel just like the constant G does.

My advice would be to flush Dreyer 2004 and read this more recent discussion.
http://arxiv.org/abs/1002.3966 or google "bianchi prejudices against constant"
To directly answer your question as best I can: LQG does not have a "cosmological constant problem". So I guess you could say it "disappears", or that it appeared in the first place.

The Bianchi Rovelli article "Why All These Prejudices Against a Constant?" has been known to distress some who view the matter from a background-dependent quantum field theory perspective.

Maybe an additional note for clarification: a field can be defined mathematically without being defined ON anything. One does not need an underlying set (like a manifold). Or if one is used as a temporary technical convenience one can get rid of it later by showing that it is "gauge"--not physically significant.

The aim with QG is to define the gravitational field in this (background independent) way so that other fields (matter) can be defined with the geometry as a basis: located in terms of the gravitational field, that being just another name for geometry.

Back in 2004. LQG researchers stated how the Glast satellite can detect signs of it.

http://www.skyandtelescope.com/news/39867717.html

|Gamma-Ray Burst Hints of Space-Time Foam|

In 2008. There seemed to be positive results as detailed above. I have been searching for archives here and can't find any discussions about it. Isn't the result significant enough? So far. Do you think it's the only way to test for proof of LQG?

But then, if Glast results were proven that high energy gamma ray were more delayed. Aren't there other theories that is not LQG that also predicts it? What's the lastest about this?

 

[negru]

The latest was that Fermi ruled out to very high confidence the LQG prediction, and that LQG people were trying to say it was not in fact a prediction.

see eg http://news.stanford.edu/news/2009/october26/fermi-telescope-discovery-102809.html

 

[waterfall]

This is a fast evolving field and it's not advisable to get wrapped up in outdated sources.
Whatever Dreyer thought was "the cosmological constant problem" back in 2004 is not likely to mean very much to us today.

I'd say focus on more recent sources. Two people who really are QG experts have written a recent (2010) article disposing of "the cosmological constant problem". They basically make fun of all the HYPE about it. They say "what's the problem?" The cosmological constant is a constant that appears naturally in Gen Rel just like the constant G does.

My advice would be to flush Dreyer 2004 and read this more recent discussion.
http://arxiv.org/abs/1002.3966 or google "bianchi prejudices against constant"
To directly answer your question as best I can: LQG does not have a "cosmological constant problem". So I guess you could say it "disappears", or that it appeared in the first place.

The Bianchi Rovelli article "Why All These Prejudices Against a Constant?" has been known to distress some who view the matter from a background-dependent quantum field theory perspective.

Maybe an additional note for clarification: a field can be defined mathematically without being defined ON anything. One does not need an underlying set (like a manifold). Or if one is used as a temporary technical convenience one can get rid of it later by showing that it is "gauge"--not physically significant.

The aim with QG is to define the gravitational field in this (background independent) way so that other fields (matter) can be defined with the geometry as a basis: located in terms of the gravitational field, that being just another name for geometry.

I'm interested in Dreyer not because of his cosmological constant thing but because he is related to Fotini of the Perimeter Institute along with Lee Smolin. Fotini wrote this paper with many illustrations of Emergent Spacetime via Geometrogenesis:

http://www.matmor.unam.mx/eventos/loops07/talks/PL5/Markopoulou.pdf

What do you think of the concept there? How it differs to LQG is in this paper:

http://arxiv.org/pdf/gr-qc/0703097v1.pdf

"New directions in Background Independent Quantum Gravity"

"The different approaches to quantum gravity can be classified according to the role that spacetime plays in them. In particular, we can ask two questions of each approach: 1) Is spacetime geometry and general relativity fundamental or emergent? 2) Is spacetime geometry, if present, dynamical or fixed?
Reviewing the different approaches we find that they split into four categories. First, there are the quantum field theory-like approaches, such as string theory and its relatives. Here general relativity is to be an emergent description, however, the spacetime that appears in the initial formulation of the theory is fixed and not dynamical. Next are the so-called background independent approaches to quantum gravity, such as loop quantum gravity, spin foams, causal sets and causal dynamical triangulations. Geometry and gravity here is fundamental, except
quantum instead of classical. These approaches implement background independence by some form of superposition of spacetimes, hence the geometry is not fixed. Third, there are condensed matter approaches (see Volovik, 2006). While it is clear that relativity is to be emergent, there
is confusion on question 2 above. These are condensed matter systems, so it seems clear that there is a fixed spacetime in which the lattice lives, however, it can be argued that it is an auxilliary construction, an issue we shall not resolve here.
Our main focus in this chapter is a new, fourth, category that is currently under development and constitutes a promising and previously unexplored direction in background independent quantum gravity. This is pre-geometric background independent approaches to quantum gravity.
These start with an underlying microscopic theory of quantum systems in which no reference to a spatiotemporal geometry is to be found. Both geometry and hence gravity are emergent. The geometry is defined intrinsically using subsystems and their interactions. The geometry
is subject to the dynamics and hence itself dynamical."

What do you make of it? Note that GLAST produced null-results that almost falsify LQG just like MMX experiment falsified the Aether a century ago. And with Superstring theory not likely. We need other plausible alternatives. Is Fotini's plausible?

 

[atyy]

If you are interested in Fotini Markopoulou's condensed matter inspired approach, I suggest you look at the gauge/gravity or AdS/CFT duality. The gauge theory is like a condensed matter theory, which when interpreted holographically gives rise to a theory of quantum gravity. This sort of quantum gravity probably does not model our universe, but it should give hints as to what other theories of quantum gravity may look like. The gauge/gravity duality comes form string theory, but it has inspired string theorists to work on condensed matter;)

McGreevy, Holographic duality with a view toward many-body physics
Hartnoll, Lectures on holographic methods for condensed matter physics
Herzog, Lectures on Holographic Superfluidity and Superconductivity

 

[marcus]

...

What do you make of it? Note that GLAST produced null-results that almost falsify LQG just like MMX experiment falsified the Aether a century ago. And with Superstring theory not likely. We need other plausible alternatives. Is Fotini's plausible?

Remember you are dealing with a mathematical science. Back in 2002 Rovelli published a paper showing that LQG was compatiible with Lorentz invariance, not with Lor. violation. No rigorous proof or derivation has ever shown that LQG implies Lorentz violation. Various people thought that it MIGHT and tried to prove it, but failed. By now the opposite has been shown, in fact!

Here's a 2010 paper about this:
C. Rovelli and S. Speziale, “Lorentz covariance of loop
quantum gravity,” arXiv:1012.1739.

GLAST or FERMI results in no sense came near falsifying Loop. By now, at this stage, that is just ignorant talk. Or perhaps in some cases malicious.
The main Loop spokesperson, the one they usually invite to write a review articles and give overview talks etc, is Rovelli, and if not him then it's Asktekar. Neither ever suggested that the theory predicted Lor. violation. Or energy-dependent speed of light etc.
So here is what one of them had to say in 2010:
http://arxiv.org/pdf/1012.4707v1.pdf page 18

Recent Planck-scale observations appear to support local Lorentz invariance [144]. This has been er- roneously presented by some authors as evidence against loop gravity. I want to stress the fact that loop gravity does not imply a violation of Lorentz invariance. In particular, the naive argument, often heard, that a minimal length is incompatible with Lorentz invariance is wrong, because it disregards quantum theory. The same argument would imply that a minimum value for a component of the angular momentum would be incompatible with rotation invariance, a conclusion manifestly contradicted by the quantum mechanics of angular momentum. For a complete discussion of this point, see [145]. The Lorentz invariance of the loop and spinfoam formalism can be made manifest: see [18] and references therein. For the moment, existing theoretical evidence is against Lorentz violations [149], and in accord with observations. So, for now we have no useful information from this direction.
The most likely window of opportunity at present seems to come from early cosmology. Quantum effects could be significative shortly before the onset of inflation and could affect, for instance, the CMB at multiple moments somewhat higher than the ones presently measured. The hope that the theory could provide an input to early cosmology sufficient for predicting observable quantum effects, and interesting attempts in this direction exist [150– 155]. But for the moment, I see no definite prediction that could be used to falsify the theory. To make loop (or any other) quantum theory of gravity, physically credible, this must change.​

The reference [18] is to the paper I mentioned: http://arxiv.org/abs/1012.1739 proving covariance.

 

[waterfall]

Remember you are dealing with a mathematical science. Back in 2002 Rovelli published a paper showing that LQG was compatiible with Lorentz invariance, not with Lor. violation. No rigorous proof or derivation has ever shown that LQG implies Lorentz violation. Various people thought that it MIGHT and tried to prove it, but failed. By now the opposite has been shown, in fact!

GLAST or FERMI results in no sense came near falsifying Loop. By now, at this stage, that is just ignorant talk. Or perhaps in some cases malicious.
The main Loop spokesperson, the one they usually invite to write a review articles and give overview talks etc, is Rovelli, and if not him then it's Asktekar. Neither ever suggested that the theory predicted Lor. violation. Or energy-dependent speed of light etc.
So here is what one of them had to say in 2010:
http://arxiv.org/pdf/1012.4707v1.pdf page 18

Recent Planck-scale observations appear to support local Lorentz invariance [144]. This has been er- roneously presented by some authors as evidence against loop gravity. I want to stress the fact that loop gravity does not imply a violation of Lorentz invariance. In particular, the naive argument, often heard, that a minimal length is incompatible with Lorentz invariance is wrong, because it disregards quantum theory. The same argument would imply that a minimum value for a component of the angular momentum would be incompatible with rotation invariance, a conclusion manifestly contradicted by the quantum mechanics of angular momentum. For a complete discussion of this point, see [145]. The Lorentz invariance of the loop and spinfoam formalism can be made manifest19: see [18] and references therein. For the moment, existing theoretical evidence is against Lorentz violations [149], and in accord with observations. So, for now we have no useful information from this direction.
The most likely window of opportunity at present seems to come from early cosmology. Quantum effects could be significative shortly before the onset of inflation and could affect, for instance, the CMB at multiple moments somewhat higher than the ones presently measured. The hope that the theory could provide an input to early cosmology sufficient for predicting observable quantum effects, and interesting attempts in this direction exist [150– 155]. But for the moment, I see no definite prediction that could be used to falsify the theory. To make loop (or any other) quantum theory of gravity, physically credible, this must change.​

This means Loop Quantum Gravity is no longer falsifiable. Gamma burst GLAST seemed to be one way to check it out. But now it is invalid. So there is no longer any way to test LQG and even Superstrings? The latter has 10^300 solutions. The former well.. maybe if it could be worked out to describe how an apple could fall down and the right velocity. Then perhaps this is how we can say LQG is true or not? Hmm...

We ought to entertain other candidates because if these two main alternatives fail. We may not have others.

 

[marcus]

This means Loop Quantum Gravity is no longer falsifiable...

No, there's a growing literature of ways to test using the CMB spectrum. Early universe cosmology (EUC) seems like the most promising arena for testing, and there has been a lot of research activity, publication recently.

Here's a search that digs up some of the papers from 2008 to 2011 that have to do with testable phenomena (so-called phenomenology, research related to testing Lqg). Have a look at some titles, or read the abstracts if you want:
http://inspirehep.net/search?ln=en&...earch=Search&sf=&so=d&rm=citation&rg=100&sc=0

What I quoted was written in 2010. Have to keep abreast.

I keep an eye on half a dozen alternative QG. Been doing so at least as far back as 2005.

If you are urging doing that you are preaching to the converted.

I tend to study and report on what currently has the most activity, is making the most progress in things like modeling EUC, and attracting the most young researchers (PhD students, postdocs) relative to its size. Percentage growth kind of thing.

Right now I see the most progress happening and the most growth in AsymSafe QG and in Loop.

I've noticed an actual LOSS of interest in some of the other QG gambits some of which I used to think were pretty cool. Just how it is. You may operate on entirely different principles

 

[waterfall]

No, there's a growing literature of ways to test using the CMB spectrum. Early universe cosmology (EUC) seems like the most promising arena for testing, and there has been a lot of research activity, publication recently.

What I quoted was written in 2010. Have to keep abreast.

I keep an eye on half a dozen alternative QG. Been doing so at least as far back as 2005.

If you are urging doing that you are preaching to the converted.

I tend to study and report on what currently has the most activity, is making the most progress in things like modeling EUC, and attracting the most young researchers (PhD students, postdocs) relative to its size. Percentage growth kind of thing.

Right now I see the most progress happening and the most growth in AsymSafe QG and in Loop.

I've noticed an actual LOSS of interest in some of the other QG gambits some of which I used to think were pretty cool. Just how it is. You may operate on entirely different principles

I guess you exclude Fotini's Geometrogenesis idea because it's not popular but you have a point. If LQG doesn't have mechanism yet of how apple falls to ground, Fotini's idea doesn't have mechanism of how there is apple in the first place. Such hopelessness.

Hope one of the programme would be right. Or if all attempts including all aspects of Supersting Theory wrong and LQG, etc. wrong then we would be back in the days of Newton. Or worse, we would be back in the dark ages before Newton... where instead of witches casting spells.. we would have math wizards (physicists) brewing and casting math spells (where some may work, some don't.)

 

[waterfall]

Remember you are dealing with a mathematical science. Back in 2002 Rovelli published a paper showing that LQG was compatiible with Lorentz invariance, not with Lor. violation. No rigorous proof or derivation has ever shown that LQG implies Lorentz violation. Various people thought that it MIGHT and tried to prove it, but failed. By now the opposite has been shown, in fact!

Here's a 2010 paper about this:
C. Rovelli and S. Speziale, “Lorentz covariance of loop
quantum gravity,” arXiv:1012.1739.

GLAST or FERMI results in no sense came near falsifying Loop. By now, at this stage, that is just ignorant talk. Or perhaps in some cases malicious.
The main Loop spokesperson, the one they usually invite to write a review articles and give overview talks etc, is Rovelli, and if not him then it's Asktekar. Neither ever suggested that the theory predicted Lor. violation. Or energy-dependent speed of light etc.
So here is what one of them had to say in 2010:
http://arxiv.org/pdf/1012.4707v1.pdf page 18

Recent Planck-scale observations appear to support local Lorentz invariance [144]. This has been er- roneously presented by some authors as evidence against loop gravity. I want to stress the fact that loop gravity does not imply a violation of Lorentz invariance. In particular, the naive argument, often heard, that a minimal length is incompatible with Lorentz invariance is wrong, because it disregards quantum theory. The same argument would imply that a minimum value for a component of the angular momentum would be incompatible with rotation invariance, a conclusion manifestly contradicted by the quantum mechanics of angular momentum. For a complete discussion of this point, see [145]. The Lorentz invariance of the loop and spinfoam formalism can be made manifest: see [18] and references therein. For the moment, existing theoretical evidence is against Lorentz violations [149], and in accord with observations. So, for now we have no useful information from this direction.
The most likely window of opportunity at present seems to come from early cosmology. Quantum effects could be significative shortly before the onset of inflation and could affect, for instance, the CMB at multiple moments somewhat higher than the ones presently measured. The hope that the theory could provide an input to early cosmology sufficient for predicting observable quantum effects, and interesting attempts in this direction exist [150– 155]. But for the moment, I see no definite prediction that could be used to falsify the theory. To make loop (or any other) quantum theory of gravity, physically credible, this must change.​

The reference [18] is to the paper I mentioned: http://arxiv.org/abs/1012.1739 proving covariance.

Btw.. I have a question. It is said that "the discrete nature of space causes higher-energy gamma rays to travel slightly faster than lower-energy ones". Why is that? I saw this claimed in 2004. How did Rovelli banish the problem? I read the following in Smolin article in Scientific American in January of 2004 (I know it's old news but I can't understand the above paper):

"RADIATION from distant cosmic explosions called gamma-ray bursts might provide a way to test whether the theory of loop quantum gravity is correct. Gamma-ray bursts occur billions of light-years away and emit a huge amount of gamma rays within a short span. According to loop quantum gravity, each photon occupies a region of lines at each instant as it moves through the spin network that is space (in reality a very large number of lines, not just the five depicted here). The discrete nature of space causes higher-energy gamma rays to travel slightly faster than lower-energy ones. The difference is tiny, but its effect steadily accumulates during the rays’ billion-year voyage. If a burst’s gamma rays arrive at Earth at slightly different times according to their energy, that would be evidence for loop quantum gravity. The GLAST satellite, which is scheduled to be launched in 2006, will have the required sensitivity for this experiment."

Again, what is the reason for the statement "The discrete nature of space causes higher-energy gamma rays to travel slightly faster than lower-energy ones" and how did Rovelli make the problem go away??

 

[marcus]

If LQG doesn't have mechanism yet of how apple falls to ground, ..

who says that?

Back around 2007, work started on graviton propagator, aimed at recovering the inverse square law.
Largely satisfactory, eventually, as far as recovering Newton law at some level of approximation.

There was a paper just last year, I'll see if I can find it. Yeah, here:

http://arxiv.org/abs/1109.6538
Lorentzian spinfoam propagator
Eugenio Bianchi, You Ding
(Submitted on 29 Sep 2011)
The two-point correlation function is calculated in the Lorentzian EPRL spinfoam model, and shown to match with the one in Regge calculus in a proper limit: large boundary spins, and small Barbero-Immirzi parameter, keeping the size of the quantum geometry finite and fixed. Compared to the Euclidean case, the definition of a Lorentzian boundary state involves a new feature: the notion of past- and future-pointing intertwiners. The semiclassical correlation function is obtained for a time-oriented semiclassical boundary state.
13 pages

 

[marcus]

...
Again, what is the reason for the statement "The discrete nature of space causes higher-energy gamma rays to travel slightly faster than lower-energy ones" and how did Rovelli make the problem go away??

There never was a problem. Smolin was never able to prove that starting from actual LQG you could derive that, mathematically/logically.
And around 2005 he got several people interested in trying to prove it, by 2007 the main guy had given up. A talented mathematical physicist named Jerzy Kowalski-Glikman.
Basically Smolin had an intuitive feeling---sometimes he said the higher energy would travel faster. Sometimes other people said they would travel slower. But based on LQG they could never prove that the theory predicted any such thing.

So there was no problem that anyone needed to make go away. Just a logical void, some intuition, and talk. However the research did have a nice spin-off in some other directions (some work by Bee Hossenfelder and some by Laurent Freidel and others.)

There was, and still is, another theory called DSR (doubly special relativity) in some version of which you can get results like that, I believe, but it is not derivable from LQG. Separate theory.

 

[waterfall]

who says that?

Back around 2007, work started on graviton propagator, aimed at recovering the inverse square law.
Largely satisfactory, eventually, as far as recovering Newton law at some level of approximation.

There was a paper just last year, I'll see if I can find it. Yeah, here:

http://arxiv.org/abs/1109.6538
Lorentzian spinfoam propagator
Eugenio Bianchi, You Ding
(Submitted on 29 Sep 2011)
The two-point correlation function is calculated in the Lorentzian EPRL spinfoam model, and shown to match with the one in Regge calculus in a proper limit: large boundary spins, and small Barbero-Immirzi parameter, keeping the size of the quantum geometry finite and fixed. Compared to the Euclidean case, the definition of a Lorentzian boundary state involves a new feature: the notion of past- and future-pointing intertwiners. The semiclassical correlation function is obtained for a time-oriented semiclassical boundary state.
13 pages

When I mentioned apple not falling, I meant general relativity not being recovered but you addressed it already in post # 68. Don't you edit wikipedia pages? In the wiki entry on LQG it is stated:

http://en.wikipedia.org/wiki/Loop_quantum_gravity

"Problem

Presently, no semiclassical limit recovering general relativity has been shown to exist. This means it remains unproven that LQG's description of spacetime at the Planck scale has the right continuum limit (described by general relativity with possible quantum corrections). It is thus unclear if the theory is in agreement with any experiment ever made."

Maybe some LQG enthusiasts can modify the page?

I'm surprised there are so many papers on LQG now and it's getting more popular. Maybe it has to do with Lee Smolin book "Trouble with Physics" criticizing Superstrings and support LQG? Also what's happening to Superstrings community now? I haven't heard of latest from Witten and the crew. Why is no one sharing on Supestrings in this forum?

 

[negru]

Most recently Witten is working on infrared issues of scattering amplitudes in string theory

 

[suprised]

Why is no one sharing on Supestrings in this forum?

There have been threads on this, you may need to invest a few minutes of search. But at any rate, this forum is by no means representative of what is actually happening in science. You should listen to actual scientists. It is the wrong place the get a fair impression of the field, as are those books.

 

[waterfall]

There never was a problem. Smolin was never able to prove that starting from actual LQG you could derive that, mathematically/logically.
And around 2005 he got several people interested in trying to prove it, by 2007 the main guy had given up. A talented mathematical physicist named Jerzy Kowalski-Glikman.
Basically Smolin had an intuitive feeling---sometimes he said the higher energy would travel faster. Sometimes other people said they would travel slower. But based on LQG they could never prove that the theory predicted any such thing.

So there was no problem that anyone needed to make go away. Just a logical void, some intuition, and talk. However the research did have a nice spin-off in some other directions (some work by Bee Hossenfelder and some by Laurent Freidel and others.)

There was, and still is, another theory called DSR (doubly special relativity) in some version of which you can get results like that, I believe, but it is not derivable from LQG. Separate theory.

I found the entire Lee Smolin article "The Atom of Space and Time" here:

http://www.phys.lsu.edu/faculty/pullin/sciam.pdf

Go to page 74. It is mentioned "In the past several years, however, a few imaginative young researchers have thought up new ways to test the predictions of loop quantum gravity that can be done now. These methods depend on the propagation of light across the universe. When light moves through a medium, its wavelength suffers some distortions, leading to effects such as bending in water and the separation of different wavelengths, or colors. These effects also occur for light and particles moving through the discrete space described by a spin network."

It is based on the idea of light traveling in a medium with wavelength distortion. How do you (or Rovelli counter this?)

Continuing: "A gamma-ray burst spews out photons in a range of energies in a very brief
explosion. Calculations in loop quantum gravity, by Rodolfo Gambini of the University of the Republic in Uruguay, Jorge Pullin of Louisiana State University and others, predict that photons of different energies should travel at slightly different speeds and therefore arrive at slightly different times [see illustration above]. We can look for this effect in data from satellite observations of gamma-ray bursts. So far the precision is about a factor of 1,000 below what is needed, but a new satellite observatory called GLAST, planned for 2006, will have the precision required."

 

[marcus]

I found the Gambini and Pullin reference for you, in case you are interested:
http://arxiv.org/abs/gr-qc/9809038
It's impressive how much the theory has evolved since 1998.

 

[marcus]

WF, you seem intelligent and motivated enough so that you could, I think, make a big improvement in quality by quoting only from peer-reviewed sources. And preferably ones that are reasonably current, at least from the past 5 or 6 years.

Personally I have a real high regard for Gambini and Pullin, and I'd guess that other people do as well (but I don't want to speak for others). Their 1998 paper was peer-reviewed and published in Physical Review series D.

They carefully qualified their calculation, making clear what assumptions it was based on. A formulation of LQG which, as it happens, was not covariant and I haven't heard much about for many years. And a proposed Hamiltonian dynamics which was already being criticised by the Loop researchers in 1998. Its author had abandoned it by 2003 or so and gone back to the drawing board. If you are interested in Loop history, as you seem to be, you can follow up some of the references in the Gambini Pullin article.

My feeling is that life is too short to go back and study a 1998 calculation based on now obsolete formulations. But you may be historically inclined and less interested in the situation NOW. It's a matter of taste.

If on the other hand you want to learn about the situation now then I'll suggest a peer-reviewed source that I think is accessible. The two people who come closest to speaking for the field as a whole, these days, are Ashtekar and Rovelli. When a journal wants a review article surveying the status, results, open problems, they get asked. When a conference or school is organized they typically get asked to give the introduction or main lectures.

(A conference will have some brilliant younger people to talk about specific research initiatives and results. It's like any area of physics. Every few years there are comprehensive survey articles written by recognized leaders. Most of the active younger researchers in the field have been PhD students and or postdocs working with a few central figures.)

So if you are interested in knowing something about the actual state of Lqg theory, and want help finding accessible peer-referreed overview stuff, or Loops conference videos that you can understand, just ask.

 

[waterfall]

A recent paper:
http://arxiv.org/abs/1201.2187
A spin-foam vertex amplitude with the correct semiclassical limit
Jonathan Engle
(Submitted on 10 Jan 2012)
Spin-foam models are hoped to provide a dynamics for loop quantum gravity. All 4-d spin-foam models of gravity start from the Plebanski formulation, in which gravity is recovered from a topological field theory, BF theory, by the imposition of constraints, which, however, select not only the gravitational sector, but also unphysical sectors. We show that this is the root cause for terms beyond the required Feynman-prescribed exponential of i times the action in the semiclassical limit of the EPRL spin-foam vertex. By quantizing a condition isolating the gravitational sector, we modify the EPRL vertex, yielding what we call the proper EPRL vertex amplitude. This provides at last a vertex amplitude for loop quantum gravity with the correct semiclassical limit.
Comments: 4 pages

Some other recent papers:
https://www.physicsforums.com/showthread.php?p=3755045#post3755045

Has anyone actually read the above paper entirely? I can't understand the arguments. But based on your reading and by other experts, Is it agreed now by the majority that the semiclassical limit recovering general relativity has been shown to exist categorically in LQG? If so. How come I didn't hear this in the news that "LQG spin foam has recovered general relativity in the classical limit!". This is almost the same as saying LQG is on the right path! Can anyone find any weakness in any arguments in the paper that prevent it from making headlines just like Lisa Randall RS1 and RS2 papers which became talk of the town?

 

[marcus]

Has anyone actually read the above paper entirely? I can't understand the arguments. But based on your reading and by other experts, Is it agreed now by the majority that the semiclassical limit recovering general relativity has been shown to exist categorically in LQG? If so. How come I didn't hear this in the news that "LQG spin foam has recovered general relativity in the classical limit!". This is almost the same as saying LQG is on the right path! Can anyone find any weakness in any arguments in the paper that prevent it from making headlines just like Lisa Randall RS1 and RS2 papers which became talk of the town?

This is an example of why I suggest you read a careful balanced peer-reviewed summary, rather than rely on paraphrase and scuttlebut.
Read this. It will put things into perspective for you.
LQG the first 25 years (December 2010)
Rovelli is good at laying out the gaps and unresolved issues. Avoids hype. describes limitations and unfinished business. But also knows what progress has been made in the past 3 or 4 years.
This is an invited review article by a scholarly journal.

Google "loop first twenty-five years"
or go directly to http://arxiv.org/abs/1012.4707

 

[waterfall]

This is an example of why I suggest you read a careful balanced peer-reviewed summary, rather than rely on paraphrase and scuttlebut.
Read this. It will put things into perspective for you.
LQG the first 25 years (December 2010)
Rovelli is good at laying out the gaps and unresolved issues

Ok Thanks. http://arxiv.org/pdf/1012.4707.pdf (updated Jan. 31, 2012)

"Classical limit. There is substantial circumstantial evidence that the large distance limit of the theory is correctly general relativity, from asymptotic analysis and from large distance calculations of npoint functions and in spinfoam cosmology; and there are open directions of investigations to reinforce this evidence. The degrees of freedom are correct and the theory is generally covariant: the low-energy limit is not likely to be much else than general relativity. But there is no solid proof yet."

So there is no solid proof yet. Let's just wait for the breakthrough paper that will put it in the level of Einstein's "On the Electrodynamics of Moving Bodies."

I wonder if anyone here has read or own this book:

https://www.amazon.com/dp/0199590753/?tag=pfamazon01-20

"A First Course in Loop Quantum Gravity"

Please review it those who have read it esp as it talks about QFT too. Thanks.

 

[waterfall]

It's basic to the current formulation of LQG that geometry is a quantum field. The spin networks are quantum states of this field. So LQG is accord with the actual quote itself. But one can find that same message in many other places both antedating Dreyer and also more recent. I would separate that important idea from the 2004 article by Olaf Dreyer, and focus on the idea expressed in the quote, that the basic thing is the field.

Spacetime as such (e.g. some mathematical continuum, or differential manifold, some x,y,z,t space construction) does not appear in the current LQG theory. There is no mathematical object in the theory which you can point to and say that is space, or that is spacetime. It is not needed.

The fundamental object is the field---the quantum states of that field---namely geometry.
The basic philosophy is that a quantum theory is not about what nature IS but more accurately how nature responds to measurement.

In the case of geometry this means the network of geometrical measurements, including ones about which one may have only an expectation or a a probability amplitude. There may be indefiniteness.

In that sense in LQG (see http://arxiv.org/abs/1102.3660) "spacetime" is purely emergent. The focus is on the web of interrelated geometrical measurements (distances, angles, areas, volumes, durations) that specify quantum states of geometry.

Mind you I'm not talking about the various miscellaneous earlier LQG formulations or what somebody said in 2004 or 2006. There is too much variation to keep track of or generalize about including a kind of revolution that started around 2008. I'm just talking about the current formulation (in the Zakopane Lectures I linked to) which many people seem to think encompasses the Loop mainstream of the past 3 or 4 years.

Thanks for attributing expertise, waterfall I watch the current QG research scene with active interest, but am not an authority. I also follow cosmology and AsymSafe QG research, not only Loop, but can't claim to be an expert!

Marcus, I don't really have a good mathematical background only knowing calculus concepts by words only and don't do any calculations. Therefore I can't understand any of the paper at its core. This is my weakness. Therefore I just want to understand something. Many of us laymen just want a bird eye view without necessary having to take 7 years course or spent that much to master the rigorous math.

What I want to know is this. In Superstrings, the gravitons produce effects similar to the curvature of General Relativity. So the curvature is not really there in 4D spacetime but only effects brought about by gravitons. As way of illustration. For example. If you have 4D vision, you would see the spacetime curvature in General Relativity. But with the same 4D vision aiming at universe with Superstrings, you won't see any curvature of space and time but only see gravitons making it appear like there is curvature. Now aiming the same 4D vision at Loop Quantum Gravity. Is it supposed to recreate the metric of General Relativity as in really there in 4D spacetime, or do the dynamics of the spin foams recreate the effects of gravity just like gravitons without necessarily having to actually create the curvature in 4D spacetime? This is what I'm not sure about.

We just need this concept for now so as to appreciate the difference and the aim of LQG. Again, I and general laymen didn't have the math training to even understand any of Rovelli paper at its core so a bird eye view is enough to introduce us what's the programme all about in the metric level.

 

[marcus]

Marcus, I don't really have a good mathematical background only knowing calculus concepts by words only and don't do any calculations. Therefore I can't understand any of the paper at its core. This is my weakness. Therefore I just want to understand something. Many of us laymen just want a bird eye view without necessary having to take 7 years course or spent that much to master the rigorous math.

What I want to know is this. In Superstrings, the gravitons produce effects similar to the curvature of General Relativity. So the curvature is not really there in 4D spacetime but only effects brought about by gravitons. As way of illustration. For example. If you have 4D vision, you would see the spacetime curvature in General Relativity. But with the same 4D vision aiming at universe with Superstrings, you won't see any curvature of space and time but only see gravitons making it appear like there is curvature. Now aiming the same 4D vision at Loop Quantum Gravity. Is it supposed to recreate the metric of General Relativity as in really there in 4D spacetime, or do the dynamics of the spin foams recreate the effects of gravity just like gravitons without necessarily having to actually create the curvature in 4D spacetime? This is what I'm not sure about.

We just need this concept for now so as to appreciate the difference and the aim of LQG. Again, I and general laymen didn't have the math training to even understand any of Rovelli paper at its core so a bird eye view is enough to introduce us what's the programme all about in the metric level.

Strange idea! Who told you that? Do the gravitons also make it appear that space is expanding? And expanding at different rates at different times and places? Do they make the expansion appear accelerate by various amounts, but it isn't really accelerating?

Sounds like someone sold you a load of bunkum, WF.