True Background-Independent Particle Physics

[rogerl]

True Background-Independent String Theory/Particle Physics

Lee Smolin mentions in Trouble with Physics:

"... it is not enough to have a theory with gravitons made from strings wiggling in space. We need a theory about what makes up space, a background-independent theory. As described earlier, the success of general relativity demonstrates that the geometry of space is not fixed. It is dynamical and it evolves in time. This is a basic discovery that cannot be reversed, so any further theory must incorporate it. String theory does not, so if string theory is valid, there must lie behind it a more fundamental theory - one that is background independent. In other words, whether string theory is valid or not, we still have to discover a background-independent theory of quantum gravity"

Questions:

1. Is it really a requirement that any quantum gravity must be background independent (context of this meaning space and time must arise from it, and not serve as a backdrop for the actions of strings)? Or is it only Smolin bias that it has to be so?

2. If string theory really needs to be background independent, how come string theorists don't work toward that end? Maybe because it is not necessarily a requirement?

3. If it is really required for string theory to be background independent, what groups and how many percentage of string theorists are working on it?

4. Is Background Independence not only important in Quantum Gravity but in any particle interaction as well even if strings are not involved? Meaning the particles in QFT like the electrons and quark being thousand of times larger than the Planck scale needs also to be background independent? I think String theory treat electron as strings in Planck scale.. but what if they are not strings.. then electrons are much bigger in size than the Planck.. in this case... do we need them to be background independent too?

5. What would happen if our QFT were adjusted to become background independent. How current experimental results be affected or what new results can the theory predicts?

 

[Fra]

I'm not sure what type of answer you seek but I'll add my point of view.

Questions:
1. Is it really a requirement that any quantum gravity must be background independent (context of this meaning space and time must arise from it, and not serve as a backdrop for the actions of strings)? Or is it only Smolin bias that it has to be so?

The complete solution is not easy, but the conceptual understanding of the problem is not difficult IMHO:

I tried to explain in the other thread.

There are GOOD argument advocating Background INdependence, and there are GOOD arguments advocating Background dependence. One one reviews both of these, the PROBLEM is how to resolve the conflict. This question is open.

Simple versions of arguments...

Argument for BI: The backgrounds corresponds to observer frames and constitutes a gauge choice, and the laws of physics must not depend on this choice. Thus a consistency requirement is that the statements of the theory, are invariant with respect to this choice. Implemented either by covariant formulations or more purely in terms of invariants only. Ie. if two observers make different predictions then that's an inconsistency.

In SR the set of all possible observers are those in different inertial fraames. In GR this symmetry is extended to arbitrary frames.

As long as we deal with classical physics, this argument is almost undeniable.

Argument for BD in measurement theory: Meaurement theory makes statements about outcomes fo specific experiments. Experiments need preparation or context. With this follows a background. Spacetime is of course only a PART of this background. Thus the predictive statements of a measurement theory seems to be bound to be BD by construction.

Very roughly, there are two main routes of of this.

- Formulate a BI theory, where somehow the BD measurement theory perspectice emerges or slices out of this. How to do this? (I think of this as loosely Rovelli style logic)

- Formulate a BD measurement theory, and somehow show that the BI master theory emerges out of the set of all possible BD theories. How do to this? (I think of this loosely as String logic)

/Fredrik

 

[rogerl]

I'm not sure what type of answer you seek but I'll add my point of view.



The complete solution is not easy, but the conceptual understanding of the problem is not difficult IMHO:

I tried to explain in the other thread.

There are GOOD argument advocating Background INdependence, and there are GOOD arguments advocating Background dependence. One one reviews both of these, the PROBLEM is how to resolve the conflict. This question is open.

Simple versions of arguments...

Argument for BI: The backgrounds corresponds to observer frames and constitutes a gauge choice, and the laws of physics must not depend on this choice. Thus a consistency requirement is that the statements of the theory, are invariant with respect to this choice. Implemented either by covariant formulations or more purely in terms of invariants only. Ie. if two observers make different predictions then that's an inconsistency.

In SR the set of all possible observers are those in different inertial fraames. In GR this symmetry is extended to arbitrary frames.

As long as we deal with classical physics, this argument is almost undeniable.

Argument for BD in measurement theory: Meaurement theory makes statements about outcomes fo specific experiments. Experiments need preparation or context. With this follows a background. Spacetime is of course only a PART of this background. Thus the predictive statements of a measurement theory seems to be bound to be BD by construction.

Very roughly, there are two main routes of of this.

- Formulate a BI theory, where somehow the BD measurement theory perspectice emerges or slices out of this. How to do this? (I think of this as loosely Rovelli style logic)

- Formulate a BD measurement theory, and somehow show that the BI master theory emerges out of the set of all possible BD theories. How do to this? (I think of this loosely as String logic)

/Fredrik

Hmm.. about string theory.. so you think string theorists are forcing the model to be background-dependent so they can still make measurements? Or don't they make it because it is just difficult and only an unknown M-Theory needs it??

Btw... you said the particles of QFT and atomic physics doesn't influence the geometry, even outside Planckscale. Hmm.. you sure of it ? Maybe our theory just ignored it. There maybe be an influence. This is because if the strings being smaller can influence it, more so the bigger electron in stringless theories. No? Why?

 

[Fra]

Btw... you said the particles of QFT and atomic physics doesn't influence the geometry, even outside Planckscale.

What I meant is that the geometry of the context; the asymptotic laboratory frame isn't affected.

The inside geometry might change at short range, but this is almost inseparable from exactly how interactions are renormalized. And thus at extremely short ranges, it becomes hard to distinguisha the interactions as seen from the asymptotic perspective. So we stumble also upon the problems of unifications.

/Fredrik

 

[Fra]

Hmm.. about string theory.. so you think string theorists are forcing the model to be background-dependent so they can still make measurements? Or don't they make it because it is just difficult and only an unknown M-Theory needs it??

I don't speak for ST, but there is a logic to the idea that one you specify an observer; with it comes a background.

The problem in ST, is that the master theory that connects all the BD theories aren't known and that we can't attached our reality to a unique choice of background.

Ie. string theory has generated a hypotetical landscape of possible "theories" and we can't identify what corresponds to our world.

One rational idea is that if you take into account that two observers, are interacting, there will take place en evolution and selection of backgrounds. so that ultimately "BI master theory emerges out of the set of all possible BD theories". But this isn't yet realized. Until it is, it's as incomplete as the other route.

I don't use the same reasoning as the string program, but IMHO a landscape of theories is not in conflict with a master theory. On the other hand, in the route of " "BI master theory emerges out of the set of all possible BD theories" the landscape is the arena where they BI is negotiated. I don't see them as conflicting.

/Fredrik

 

[Fra]

4. Is Background Independence not only important in Quantum Gravity but in any particle interaction as well even if strings are not involved?

Yes.

The GENERAL problem and debated of B/I has nothing at all to do with string theory, or any other program for that matter.

In it's most general form, it's a conflict between the requirements of the conflicting observer invariance of the laws of nature, and observer dependent inferences and expectations of the nature in the context of a measurement theory.

This problems "looks different" depending on the research program you look at. String theory has their set of problems. Other programs has theirs.

/Fredrik

 

[rogerl]

Yes.

The GENERAL problem and debated of B/I has nothing at all to do with string theory, or any other program for that matter.

In it's most general form, it's a conflict between the requirements of the conflicting observer invariance of the laws of nature, and observer dependent inferences and expectations of the nature in the context of a measurement theory.

This problems "looks different" depending on the research program you look at. String theory has their set of problems. Other programs has theirs.

/Fredrik

I wonder if observer invariance of the laws of nature is really true. I mean. All this Background Independent stuff only work if General Relativity is 100% true. But Quantum Mechanics and GR can't be united. If string theory and Loop quantum gravity is wrong. Then either GR or QM has to be wrong. Maybe GR is wrong and can be replaced by another spacetime model wherein background independence with particles is NOT necessary? Have you heard of any programme along this line??

 

[Fra]

I wonder if observer invariance of the laws of nature is really true.

Then either GR or QM has to be wrong.

The way I think of it is that both GR and QM are limiting cases or special cases of something we don't yet know.

Given that GR and QM are both sort of special cases, but different special cases, no wonder that the exact special cases combine without deformation.

I personally think neither QM nor GR as it stands will survive revision.

The problem with GR is that it's not a measurement theory at all. It's a realist theory. (the deprivation of physical reality of spacetime Einstein talked about was of course still a revolution, but in a different sense).

The problem with QM as it stands is that it is an EXTRINSIC mesaurement theory.

I think what we need is a reformulation of QM as an INTRINSIC measurement theory. The observer invariant CONSTRAINT of GR, might be replaced by something softer, such as democracy between observers.

Unfortunately I'm not aware of any even partially mature research program that implements this in the way I personally think is the right way.

Until then, all we have to play with is the current research programs. Although there are interesting things in them, I've overall rejected when some seemingly undeniable needed traits are missing.

So our choice is to keep tweaking any of the current researchprograms, or try to define a new program.

But any such radical program, would certainly have to explain why and when QM ang GR emerge as some correspondence principle that always guided new theories. Because there is no denial that both QM ang GR are very successful in the domains where they are currently tested.

/Fredrik

 

[Fra]

I wonder if observer invariance of the laws of nature is really true. I mean. All this Background Independent stuff only work if General Relativity is 100% true.

It should be noted that not everyone shares the most genreal meaning of B/I I refer to here.

Some people just constrain themsevles with it meaning the background spacetime. This is of course the original meaning of GR. But once you look how it's motivated, you see that it's due to the fact that otherwise two observers would make inconsistent predictions.

To accept some backgrounds but not others, also becomes very ambigous and incoherent from the point of view of general inference and measurement theory. Then one needs to explain how this symmetry is inferred from experiemtn, but an inside observer. Ie. no use of asymptotic or global observables. I honestly don't see how that can make sense except as an expected equilibrium scenario. But then this should be acknowledged as a conjecture.

/Fredrik

 

[Physics Monkey]

I would argue that string theory is already background independent. Of course, this is not to say that we don't still have a lot to learn about strings and emergent geometry. I'll give several examples I like, although one could say much much more.

1. Perturbative strings in flat space. String theory can describe graviton-graviton scattering using so-called vertex operators [tex] V[/tex] associated with scattering states. Although it looks like you're just simply assuming flat space, a more careful analysis actually shows that flat space is a solution of the theory i.e. the background can't be just anything if certain nice features are to exist. Describing strings moving in a more general background looks like a coherent state of stringy gravitons, something like [tex] e^V [/tex] in the path integral. So it really looks like the strings are becoming semiclassical and creating a new geometry which they in turn propagate in self consistently.

2. Topology change. Strings can describe effective changes in the topology of spacetime. For example, strings can turn a doughnut into a sphere. Strings can also smooth out spacetime singularities like those at the fixed points of orbifolds. This illustrates the point that strings shape their own destiny no matter what background you think you're putting them on. What strings actually see and what you think they see can be very different.

3. Holographic duality. Here there is literally no bulk geometry, it is totally emergent from the dynamics of the gauge theory or field theory. All one specifies is the boundary values of fields at infinity, something one is always supposed to do even in background independent theories like GR, etc.

4. Non-geometric backgrounds. Here classical smooth geometries are glued together using stringy dualities to produce bizarre structures that nevertheless allow strings to smoothly propagate. For example, we can take a small circle and turn it into a large one via T duality. There is no geometrical meaning at all now, but the strings don't care.

Just because string theory in some situations is formulated in terms of a particular background doesn't make the theory background dependent. What matters are the predictions of the theory and whether those are independent of what background you choose. In other words, in string theory I can start with a "background" of flat space, but I can nevertheless correctly described experiments done in curved space. Never mentioning a background at all or mentioning a background but dressing it up until it's unrecognizable can both accomplish the same task of background independence. String theory can do both.

The main objections I see being raised are philosophical or aesthetic. Certain thinkers agitate against the current formulation of string theory because it sometimes refers to particular backgrounds at intermediate stages of calculation. That's my experience anyways.

 

[rogerl]

I would argue that string theory is already background independent. Of course, this is not to say that we don't still have a lot to learn about strings and emergent geometry. I'll give several examples I like, although one could say much much more.

1. Perturbative strings in flat space. String theory can describe graviton-graviton scattering using so-called vertex operators [tex] V[/tex] associated with scattering states. Although it looks like you're just simply assuming flat space, a more careful analysis actually shows that flat space is a solution of the theory i.e. the background can't be just anything if certain nice features are to exist. Describing strings moving in a more general background looks like a coherent state of stringy gravitons, something like [tex] e^V [/tex] in the path integral. So it really looks like the strings are becoming semiclassical and creating a new geometry which they in turn propagate in self consistently.

2. Topology change. Strings can describe effective changes in the topology of spacetime. For example, strings can turn a doughnut into a sphere. Strings can also smooth out spacetime singularities like those at the fixed points of orbifolds. This illustrates the point that strings shape their own destiny no matter what background you think you're putting them on. What strings actually see and what you think they see can be very different.

3. Holographic duality. Here there is literally no bulk geometry, it is totally emergent from the dynamics of the gauge theory or field theory. All one specifies is the boundary values of fields at infinity, something one is always supposed to do even in background independent theories like GR, etc.

4. Non-geometric backgrounds. Here classical smooth geometries are glued together using stringy dualities to produce bizarre structures that nevertheless allow strings to smoothly propagate. For example, we can take a small circle and turn it into a large one via T duality. There is no geometrical meaning at all now, but the strings don't care.

Just because string theory in some situations is formulated in terms of a particular background doesn't make the theory background dependent. What matters are the predictions of the theory and whether those are independent of what background you choose. In other words, in string theory I can start with a "background" of flat space, but I can nevertheless correctly described experiments done in curved space. Never mentioning a background at all or mentioning a background but dressing it up until it's unrecognizable can both accomplish the same task of background independence. String theory can do both.

The main objections I see being raised are philosophical or aesthetic. Certain thinkers agitate against the current formulation of string theory because it sometimes refers to particular backgrounds at intermediate stages of calculation. That's my experience anyways.

Lee Smolin mentioned flat out in the entire book Trouble With Physics that string theory was NOT background independent because string theorists ignored it from the beginning. Are you saying Lee Smolin is incorrect? Hope other string theorists can confirm if this is so or admit that string theory is not really background independent. Implication if the theory is made BI is some forces predicted but not detected can cancel out. Problem with string theory is it predicts so many forces not detected.

 

[Haelfix]

Rogerl. The problem is the word 'background independance' does not have a sharp universal or strict mathematical meaning in physics... Its an example of a loaded phrase. Ditto for the much more innocent looking word 'background'. There are different usages floating around the literature (even for the exact same theory, much less different ones) and they are not necessarily equivalent (though sometimes in some contexts they are).

Typically several a priori different concepts are sometimes taken to be the definition and their physical meanings can be significantly different.

Eg the existence or not of a fully "dynamical tensor field (the metric tensor). The requirement for no prior geometry during the formulation of the theory. The lack of any absolute structures. The existence of a canonical 2 form that further possesses general covariance. Further perturbative formalisms vs nonperturbative formalisms sometimes get intertwined. All of this is further murkied by intermediate calculational steps, whether certain properties are manifest in the formalism or not, etc etc

One of the problems is that only the very weakest sense of the definition is actually a physical requirement of a theory. That is, physics absolutely must be independant of the specifics of the metric tensor. If your theory dynamics take a different form in schwarschild coordinates vs minkowski coordinates, it is ruled out (this is essentially synonymous with general covariance or coordinate invariance). The stronger definitions by contrast are simply more aesthetic and may or may not be truly fundamental.. No one knows!

One of the issues is that pretty much every theory on the board satisfies the weak sense, and a few physicists managed to get into PR wars over which of their competing theories were more or less BI. Further different formalisms of the same exact theory can (again depending on exact definitions) be background independant vs background dependant.

As an example, if you take the 'no prior geometry' requirement as your definition, than General relativity is BI. However the initial value formulation of the theory is manifestly BD!

 

[marcus]

Roger,
when I started watching, back in 2003, "background independence" meant that you could formulate a theory (write it out in a few equations) without specifying any prior spacetime geometry. No prior metric on the manifold, or equivalent prior setup like that.

I don't recall any fuss or defensiveness about this. Nobody quarreled about what the term meant. It was really just a shorthand term that a few LQG researchers used to describe a feature of GR they were trying to imitate in their new approach. (They called it an "approach" because it wasn't a theory yet---didn't have a clear testable formulation.)

GR was recognized as a BI theory because it has a clear standard formulation involving no prior "metric" on the manifold---no prior distance-function that specifies some prior shape or geometry to the spacetime.

BI was just a shorthand phrase for one of the goals of the LQG program. Rovelli used it in his book "Quantum Gravity" that came out in 2004. The goal was to be able to formulate a background independent quantum field theory, or a "general relativistic quantum field theory". A draft of the book is online---the goal statement is in Intro or Chapter 1...

John Wheeler in his classic book "Gravitation", with Misner and Thorne, used the phrase "no prior geometry" which is actually clearer. It is less abstract than "background independence" and less subject to confusion. It is a key phrase that the authors ("MTW") use repeatedly all over the place. Relativity experts like Wheeler was tend to think of it as a really important feature of GR---that helps to characterize the new worldview that theory brought with it. The idea that geometry itself is dynamical and free to evolve.

Sometime after 2005 or 2006, as I recall, the term became contentious. People started bending it, having tug-of-war about it, seeing who could talk the loudest. On the one hand that is GOOD because the vitality of science depends on people having these arguments, and the arguments are often battles over a few words like this But on the other hand there is a downside to this contentiousness because it muddies the meaning of words. The term "background independence" has become almost useless by now, or anyway much less useful.

There is a lot of defensiveness and frantic obfuscation because some folks worry that their pet idea will not seem a "background independent" and some other folks' idea. Or they want to make sure everybody knows their idea is more BI than other folks'.

What I do, for my own private bookkeeping, is return to John Archibald Wheeler's classic phrase "no prior geometry". Also I don't think of any theoretical approach as an actual theory unless it has a definite concise formulation in terms of a few principles/equations. And I look at those equations----do they require postulating a space or spacetime manifold? And if there is a manifold representing the continuum, do the equations make sense only if you specify a prior metric geometry?

So that way I can keep the issue straight in my own mind and let other people argue about what "background independence" means and who got more of it etc.

 

[Haelfix]

Actually Marcus, the quarrel starts in 1920 with Kretschman, becomes embarrasing when Cartan formulated his version of GR several years later and has raged throughout the 60s and 70s when De Witt formulated what a theory of quantum gravity ought to look like, and to this day it confuses philosophers of science and in particular it seems, people on this forum!

For instance MTW and Anderson both have classic texts on GR from the 60s that have different definitions of what BI means. Arguably Anderson's is more useful b/c it explains at length what a fixed vs dynamic structure ought to look like mathematically.

Anyway, here's the obvious problem when dealing with for instance String theory if we utilize your definition. In the other thread it was pointed out there exist nongeometric vacua where there is no obvious notion of dimensionality or indeed even classical spacetime. In other words they have no "backgrounds" (your definition) at all.

Thus a transition between two of these states would be maximally background independant (hell you could call it background free) under your definition. However what are we to make of this, when you realize that these same exact vacua are dual to geometric vacua, and worse they are only superselection sectors of a much larger entity. Still under this definition it is appropriate to call S.T maximally BI b/c of this. Alternatively, you must enlarge the definition to encompass these subleties.

Really the problem is that the definition is woefully incomplete b/c a string background really has a lot more structure (both geometric and other) than merely a metric tensor. Instead it is more appropriate to say it is just one object amongst many other 'stringy states' (like the dilaton, axion etc ) that's required to specify the configuration of the system at any unit of time. Therefore people usually say that string perturbation theory is BD b/c we fix the full classical saddle point solution a priori (metric tensor + all other objects), before expanding around it. But it is not clear how perturbation series could be any other way, in the same way that you require a point to taylor expand around.

Further we now know a lot about nonperturbative physics in S.T. Is that background dependant or independant?

Consider another example.. Newtons theory. BI or BD under your definition? Well at first glance BD b/c it fixes Guv to be an eternal static 4 dimensional space with all diagonal 1 values. But wait, Cartan formulated Newton's laws as a geometric theory (called appropriately, Newton-Cartan theory) where Guv is not fixed at all, and entirely dynamical. The theory is completely isomorphic to the original formulation, but now, under your definition it is BI. The price to pay is that you have a certain preferred direction in the theory (a fixed structure, but not the metric tensor). MTW deals with this too.

So, can you *still* not see just how loaded and ambigous what's going on is?

 

[Fra]

I fully agree that the concept is ambigous.

Why not go back to the origin of these principles. I can't speak for the dead masters, but to speak for my own understanding, there is, and was, only rational justification for this as far as I ever understood it:

In CLASSICAL physics: The laws of physics must look the same to all observers, or we have a contradiction.

This is IMHO the root of the B/I argument.

Diff invariance follows merely from considering that the set of observers are related by diffeomorphisms, or poincare transformastions in SR. The logic is the same. The PARTICULAR symmetry class is of not relevance to the core argument. It's "observer invariance" that is the most general statement, is it not?

Would anyone disagree?

Edit: This view, is also what in the cleanest possible ways leads to the clash between observer invarant fixed laws and measurement theory. If we hide from the core problem how are we ever going to solve them?

/Fredrik

 

[martinbn]

Haelfix, I don't understand your example about Newton-Cartan. It seems to me like an example of _two_ theories, that describe the same phenomena, one of which is BD the other BI. Newton's theory is BD and Newton-Cartan's is BI. No?

The ambiguity whether string theory is BD or BI seems to be not because the concept of background independence is ambiguous but because string theory is. If (when) people can give an unambiguous formulation of string theory then it will be easy to say if it is BI.

 

[rogerl]

I think there is an easy distinction of what the term "Background Independent" means. For purposes of this thread. Background Independence means there is no spacetime in the background at all. It is when there are particles that spacetime somehow is created. We treat spacetime as like an entity. But spacetime is just a model. So in Background Independence model, the particles created the spacetime! I think Lee Smolin wants to use reserve the term BI for Loop Quantum Gravity. Isn't it that in LQG, spacetime arises from the particle itself. Some said the AdS/CFT conjecture in string theory also has this feature where the strings produce spacetime itself, right?

Hmm... in Quantum Field Theory, particles and field are united as one entitiy with particles being just momentum of the field. Maybe it is the right thing to do to unite mass-stress-energy with spacetime itself such that matter itself give rise to spacetime. This is more elegant and profound, isn't it?

Can someone refute this model where matter give rise to spacetime itself (true meaning of BI)? Any fatal flaw in this conjecture?

 

[atyy]

This is not usually called "background independence". For example, in GR, which is usually given as the example of background independence, spacetime does not emerge from the motions of particles. In GR, particles cause spacetime curvature - that is the idea of background independence in GR.

The idea you have of spacetime not existing until particles move in a certain way is called "emergent spacetime". In perturbative string theory, there is some fixed spacetime, so the theory is not fully background independent (although this can be debated), but certainly parts of spacetime, including parts of its curvature, emerge from strings. This is true of all of string theory, not just AdS/CFT. AdS/CFT is only one sector of string theory. In AdS/CFT, the emergence is even more dramatic, since only the boundary is fixed, while the entire bulk emerges, ie. not even a part of the bulk is fixed, unlike in perturbative string theory.

 

[rogerl]

This is not usually called "background independence". For example, in GR, which is usually given as the example of background independence, spacetime does not emerge from the motions of particles. In GR, particles cause spacetime curvature - that is the idea of background independence in GR.

The idea you have of spacetime not existing until particles move in a certain way is called "emergent spacetime". In perturbative string theory, there is some fixed spacetime, so the theory is not fully background independent (although this can be debated), but certainly parts of spacetime, including parts of its curvature, emerge from strings. This is true of all of string theory, not just AdS/CFT. AdS/CFT is only one sector of string theory. In AdS/CFT, the emergence is even more dramatic, since only the boundary is fixed, while the entire bulk emerges, ie. not even a part of the bulk is fixed, unlike in perturbative string theory.

Hmm... Is Lee Smolin using the word "background independent" for "emergent spacetime"? Isn't it that in Loop Quantum Gravity, it is related to emergent spacetime?

You said that in perturbative string theory, there is some fixed spacetime. What if the spacetime is curved, does it become background independent? or is there such thing as a fixed curved spacetime (which is emphasized by Marcus.. I hope he can elaborate too).

 

[atyy]

Hmm... Is Lee Smolin using the word "background independent" for "emergent spacetime"? Isn't it that in Loop Quantum Gravity, it is related to emergent spacetime?).

I haven't read that book, so I can't say what he means.

You said that in perturbative string theory, there is some fixed spacetime. What if the spacetime is curved, does it become background independent? or is there such thing as a fixed curved spacetime (which is emphasized by Marcus.. I hope he can elaborate too).

Curved spacetime alone does not mean background independence. The crucial idea of background independence is that if particles move in a different way, then spacetime curvature is different, ie. each pattern of spacetime curvature corresponds to one pattern of particle motion. In a curved fixed spacetime (ie. no background independence), each pattern of spacetime curvature can correspond to more than one pattern of particle motion.

 

[rogerl]

I haven't read that book, so I can't say what he means.



Curved spacetime alone does not mean background independence. The crucial idea of background independence is that if particles move in a different way, then spacetime curvature is different, ie. each pattern of spacetime curvature corresponds to one pattern of particle motion. In a curved fixed spacetime (ie. no background independence), each pattern of spacetime curvature can correspond to more than one pattern of particle motion.

Interesting distinctions. How do the Einstein Field Equation and mass-stress-energy coupling differ in each of the 2 cases you mentioned?

 

[atyy]

Interesting distinctions. How do the Einstein Field Equation and mass-stress-energy coupling differ in each of the 2 cases you mentioned?

In curved fixed spacetime, there is no coupling between the energy of the particles that move and the curvature of spacetime.

In contrast, Einstein's equation says that the energy of all particles couples to spacetime curvature.

The reason we often use approximations in which some particles don't cause spacetime curvature is that the system may contain some very large masses and some very small masses. Then the spacetime curvature is due mainly to the large masses, and we can ignore the curvature produced by the small masses. In this approximation, spacetime will "appear" curved and fixed from the "point of view" of the small masses, since their movements change spacetime curvature negligibly.

 

[rogerl]

In curved fixed spacetime, there is no coupling between the energy of the particles that move and the curvature of spacetime.

But if there is no coupling, how can there be space curvature in the first place? Isn't it the EFE is about mass-stress-energy causing spacetime curvature because it is coupled to it. What exactly do you mean by "coupling"?

In contrast, Einstein's equation says that the energy of all particles couples to spacetime curvature.

The reason we often use approximations in which some particles don't cause spacetime curvature is that the system may contain some very large masses and some very small masses. Then the spacetime curvature is due mainly to the large masses, and we can ignore the curvature produced by the small masses. In this approximation, spacetime will "appear" curved and fixed from the "point of view" of the small masses, since their movements change spacetime curvature negligibly.

 

[atyy]

But if there is no coupling, how can there be space curvature in the first place? Isn't it the EFE is about mass-stress-energy causing spacetime curvature because it is coupled to it. What exactly do you mean by "coupling"?

By "coupling", I just meant that mass-energy produces spacetime curvature.

Although spacetime curvature is caused by all masses, if there are large and small masses, we will be pretty accurate even if we pretend that the small masses don't cause spacetime curvature (ie. even if we pretend that the small masses don't couple to spacetime curvature). Spacetime is still curved because of the large masses. (Actually, there are solutions of Einstein's equations with curvature without matter, but that's a technical detail.)

 

[rogerl]

By "coupling", I just meant that mass-energy produces spacetime curvature.

Although spacetime curvature is caused by all masses, if there are large and small masses, we will be pretty accurate even if we pretend that the small masses don't cause spacetime curvature (ie. even if we pretend that the small masses don't couple to spacetime curvature). Spacetime is still curved because of the large masses. (Actually, there are solutions of Einstein's equations with curvature without matter, but that's a technical detail.)

If this is the case and it is that simple. Meaning the effect is negligible that is why we don't need the coupling to occur in a particle that is located in a tiny region of spacetime that we can for all practical purposes described as flat. Then why does some folk insist we need a background independent formulation when the effect is negligible?

Maybe Smolin keeps emphasizing about BI because in Loop Quantum Gravity, it is automatically BI because it has emergent spacetime. And the reason Smolin emphasizes the BI portion of LQG is simply to promote and advertise LQG?

 

[fzero]

If this is the case and it is that simple. Meaning the effect is negligible that is why we don't need the coupling to occur in a particle that is located in a tiny region of spacetime that we can for all practical purposes described as flat. Then why does some folk insist we need a background independent formulation when the effect is negligible?

The effects of QG are negligible in everyday physics, or even at particle accelerators like the LHC, but they do become important in the situations that were explained to you in https://www.physicsforums.com/showthread.php?t=483811 So it is very important to understand QG, even if we can still understand quite a lot of physics without understanding QG.

 

[atyy]

If this is the case and it is that simple. Meaning the effect is negligible that is why we don't need the coupling to occur in a particle that is located in a tiny region of spacetime that we can for all practical purposes described as flat. Then why does some folk insist we need a background independent formulation when the effect is negligible?

Maybe Smolin keeps emphasizing about BI because in Loop Quantum Gravity, it is automatically BI because it has emergent spacetime. And the reason Smolin emphasizes the BI portion of LQG is simply to promote and advertise LQG?

Well, the formalism of particles on a fixed curved background is only an approximation. We do expect the motion of all particles to modify the 4D spacetime. So Smolin is right to emphasize background independence.

However, I don't think background independence is what really distinguishes string theory and loop quantum gravity. I think the question the distinction is between emergent and non-emergent spacetime.

In string theory, spacetime is emergent ie. the fundamental dynamical entities are not related to spacetime in any simple way. In loop quantum gravity, the fundamental entities are essentially pieces of spacetime, so spacetime is not as drastically emergent.

The main problem in strings at the moment is that there isn't a non-perturbative formulation of the theory, ie. we don't know the full structure of the theory. There are non-perturbative formulations of some sectors due to AdS/CFT in which the boundary is fixed, but the bulk is fully emergent and dynamical.

The main problem in loop quantum gravity is that it hasn't been shown that all the little pieces of spacetime join up to make a classical spacetime that obeys Einstein's equations.

 

[rogerl]

Well, the formalism of particles on a fixed curved background is only an approximation. We do expect the motion of all particles to modify the 4D spacetime. So Smolin is right to emphasize background independence.

However, I don't think background independence is what really distinguishes string theory and loop quantum gravity. I think the question the distinction is between emergent and non-emergent spacetime.

In string theory, spacetime is emergent ie. the fundamental dynamical entities are not related to spacetime in any simple way. In loop quantum gravity, the fundamental entities are essentially pieces of spacetime, so spacetime is not as drastically emergent.

I think you err at this point. In string theory, spacetime is not emergent.. maybe only in the AdS/CFT conjecture. Smolin said many times in the book Trouble with Physics such as "Since string theory is limited to the description of strings and branes moving in fixed-background spacetime gemoeties, it offers nothing for someone who wants to break new ground..."

 

[atyy]

I think you err at this point. In string theory, spacetime is not emergent.. maybe only in the AdS/CFT conjecture. Smolin said many times in the book Trouble with Physics such as "Since string theory is limited to the description of strings and branes moving in fixed-background spacetime gemoeties, it offers nothing for someone who wants to break new ground..."

It is true that spacetime isn't fully emergent in perturbative string theory (or at least not obviously so). However, it is true that the movement of strings causes spacetime (and spacetime curvature) to emerge. Furthermore, in many cases, even some of the initially fixed spacetime can be seen as emerging from the movement of strings.

 

[rogerl]

It is true that spacetime isn't fully emergent in perturbative string theory (or at least not obviously so). However, it is true that the movement of strings causes spacetime (and spacetime curvature) to emerge. Furthermore, in many cases, even some of the initially fixed spacetime can be seen as emerging from the movement of strings.

You keep saying this that the movement of strings causes spacetime to emerge. This may only be true in the AdS/CFT conjecture but all the 5 superstring theories don't have background independence. Smolin said that "As described earlier, the success of general relativity demonstrates that the geometry of space is not fixed. It is dynamical and it evolves in time. This is a basic discovery that cannot be reversed, so any further theory must incorporate it. String theory does not, so if string theory is valid, there must lie behind it a more fundamental theory - one that is background independent."

Are you saying that Smolin is misrepresenting string theory or literally lying to get his idea of Loop Quantum Gravity across to the public? You keep saying strings causes spacetime to emerge. Smolin, on the other hand, keep denying it. If mainstream string theory is not BI but only the small minority AdS/CFG conjecture is. Then mainstream string theory is not BI. Hope someone else can confirm what is really the case. This is making my head spin already.

 

[atyy]

You keep saying this that the movement of strings causes spacetime to emerge. This may only be true in the AdS/CFT conjecture but all the 5 superstring theories don't have background independence. Smolin said that "As described earlier, the success of general relativity demonstrates that the geometry of space is not fixed. It is dynamical and it evolves in time. This is a basic discovery that cannot be reversed, so any further theory must incorporate it. String theory does not, so if string theory is valid, there must lie behind it a more fundamental theory - one that is background independent."

Are you saying that Smolin is misrepresenting string theory or literally lying to get his idea of Loop Quantum Gravity across to the public? You keep saying strings causes spacetime to emerge. Smolin, on the other hand, keep denying it. If mainstream string theory is not BI but only the small minority AdS/CFG conjecture is. Then mainstream string theory is not BI. Hope someone else can confirm what is really the case. This is making my head spin already.

Smolin is not wrong that most string theory can only be formulated perturbatively on a fixed background, and that the more complete theory is unknown at the moment. However, he probably said that strings contain perturbative quantum gravity or something like that, ie. a particular vibration mode of the string is the graviton - a particle of spacetime. So the graviton=spacetime emerges from strings, and gravitons contribute to spacetime curvature.

I haven't read his book, but he has in the past said "Given that string theory solves this problem and, more generally, that the only known perturbative quantum field theories that describe consistently the coupling of gravitons to themselves and other fields are perturbative string theories[38], it seems that any acceptable quantum theory of gravity, whatever its ultimate formulation, is likely to reduce to a perturbative string theory in the appropriate limit." http://arxiv.org/abs/gr-qc/9508064

 

[Fra]

Are you saying that Smolin is misrepresenting string theory or literally lying to get his idea of Loop Quantum Gravity across to the public? You keep saying strings causes spacetime to emerge. Smolin, on the other hand, keep denying it. If mainstream string theory is not BI but only the small minority AdS/CFG conjecture is. Then mainstream string theory is not BI. Hope someone else can confirm what is really the case. This is making my head spin already.

Smolin isn't lying, but I think there is no replacement for eventually trying to make up your own opinion. There is no such thing as unbiased information.

The single biggest difference is exactly how you define background independence. First of all there is the notion to a background, what do you include in this background? a 4D metric? a 10D metric? even more, topolody dimensionality? hilbert spaces? etc...

Given what you included in the "background", one can talke about manifest or non-manifest BI like string people do. Manifest BI means you write the math without any reference to a background. non-manifest men you mean you do write it with a reference, but you show that the reference is arbitrary or gauge.

To assess a theory, decided for yourself what is important. In fact it does not matter what labels we put on this.

/Fredrik

 

[Haelfix]

Haelfix, I don't understand your example about Newton-Cartan. It seems to me like an example of _two_ theories, that describe the same phenomena, one of which is BD the other BI. Newton's theory is BD and Newton-Cartan's is BI. No?

Yes that's the point. Question: In what way is gr special as a theory of nature as opposed to say Newtons laws? Answer most commonly given: it has a bi formulation under the restricted definition Marcus gave. Counterexample: Newton caftan theory implying that Newtonian physics is no different. Eg they both admit bi formulations and they both admit bd formulations.

Consequently the principle used as a sieve to distinguish between theories seems to fail. Nor is it clear what if anything is physical about wanting to make the theory bi. Again Newton caftan theory is not something you want to use to learn about Newtonian gravity. It makes calculations really difficult. By contrast gr is far more aesthetically beautiful and powerful when written in the fully geometric bi language.

It could be the case that whatever final theory of gq is correct ends up having it's most useful form just like Newton caftan theory. I don't think so, but nothing in the argument implies it one way or the other.

But anyway I digress. The other key point is that a classical background most likely is too restrictive a notion when dealing with a quantum theory. Eg people would call a theory of noncommutative geometry background dependent if there was an existing non commutative manifold in place a priori. Eg it's an obvious generalization of the definition.

 

[martinbn]

Haelfix, I see your point now.

 

[atyy]

1. Perturbative strings in flat space. String theory can describe graviton-graviton scattering using so-called vertex operators [tex] V[/tex] associated with scattering states. Although it looks like you're just simply assuming flat space, a more careful analysis actually shows that flat space is a solution of the theory i.e. the background can't be just anything if certain nice features are to exist. Describing strings moving in a more general background looks like a coherent state of stringy gravitons, something like [tex] e^V [/tex] in the path integral. So it really looks like the strings are becoming semiclassical and creating a new geometry which they in turn propagate in self consistently.

Just trying to see if I understand. Does this correspond to the statement that any consistent background for perturbative string theory must be Ricci flat?

Also, is it true that any Ricci flat background that has the same topology can be obtained from Minkowski spacetime (or in the first place, what are the Ricci flat solutions with the same topology)?