I Theories without Fundamental Space and Time

[kiki_danc]

Can string theory be made without time equations?

According to Carlo Rovelli in his latest book "The Order of Time"
https://www.amazon.com/dp/073521610X/?tag=pfamazon01-20

:

"The equations of loop quantum gravity on which I work are a modern version of the theory of Wheeler and DeWitt. There is no time variable in these equations."

then later...

"For this intermediate phase, where time is wholly indeterminate, we still have equations that tell us what happens. Equations without time.

This is the world described by loop theory.

Am I certain that this is the correct description of the world? I am not, but it is today the only coherent and complete way that I know of to think about the structure of spacetime without neglecting its quantum properties.

Loop quantum gravity shows that it is possible to write a coherent theory without fundamental space and time—and that it can be used to make qualitative predictions.

In a theory of this kind, time and space are no longer containers or general forms of the world. They are approximations of a quantum dynamic that in itself knows neither space nor time. There are only events and relations. It is the world without time of elementary physics."A theory that knows neither space nor time appears to be more elegant.. too bad LQG folks still haven't approximated General Relativity in the classical limit. Can string theory be made to work without fundamental space and time too? How?

 

[AgentSmith]

A theory that knows neither space nor time appears to be more elegant.. too bad LQG folks still haven't approximated General Relativity in the classical limit. Can string theory be made to work without fundamental space and time too? How?

What is the difference between spacetime and fundamental space and time?

 

[kiki_danc]

What is the difference between spacetime and fundamental space and time?

Im not sure but I got the word from the passage "Loop quantum gravity shows that it is possible to write a coherent theory without fundamental space and time—and that it can be used to make qualitative predictions."

There are many "fundamental" words in the book.. for example.. a part reads:

"At first no one could understand the significance of an equation without a time variable, perhaps not even Wheeler and DeWitt themselves. (Wheeler: “Explain time? Not without explaining existence! Explain existence? Not without explaining time! To uncover the deep and hidden connection between time and existence . . . is a task for the future.”) The issue was discussed at great length; there were conferences, debates; rivers of ink flowed. I think that the dust has now settled and things have become much clearer. There is nothing mysterious about the absence of time in the fundamental equation of quantum gravity. It is only the consequence of the fact that, at the fundamental level, no special variable exists."

It's a great book.. who has read it too? I got the book about reading Sabine Hossenfelder article about the interview with Rovelli at: http://backreaction.blogspot.com/2018/08/guest-post-tam-hunt-roasts-carlo.html

 

[kiki_danc]

To make the question more tractable.

The movement of strings causes spacetime and spacetime curvature to emerge and in many cases, even some of the initially fixed spacetime can be seen as emerging from the movement of strings. Are the strings only belonging to the graviton particle? Or does other strings like electron string also causes spacetime or spacetime curvature to emerge or causes initially fixed spacetime emerging from the movement of the electron string?

 

[atyy]

Can string theory be made to work without fundamental space and time too?

The AdS/CFT or gauge-gravity correspondence of string theory is a conjecture in which one dimension of space is not fundamental, but emergent: https://www.scientificamerican.com/article/the-illusion-of-gravity-2007-04/.

 

[Fra]

Some years ago i got and started to read up on Rovellis ideas, and in particular to analyse his line of reasoning. At first it seems excellent, brilliant etc, but very soon, early in his logic he imo looses clarify and enters a haze he never seem to escapes from.
https://www.physicsforums.com/threa...n-classical-and-quantum-gravity.220841/page-2

How one thinks about this is related to a more general topic the nature of symmetry, or rather than nature of observer equivalence. If you have thought about this one will see its a chicken and egg situation. Rovelli seems to want to describe the equivalence class itself, without the set that defines it to get rid on the redundancies and get the observer invariance manifest. But this is what i think is wrong, he is throwing the baby out with the bathwater.

A good constrast to Rovellis view is Smolins reality of time. If you check both let me know which you think is the most sound of them both.
https://en.wikipedia.org/wiki/Time_Reborn
and the as far as i know most recent and most promising way out the metalaw dilemma
https://arxiv.org/abs/1205.3707

/Fredrik

 

[kiki_danc]

Some years ago i got and started to read up on Rovellis ideas, and in particular to analyse his line of reasoning. At first it seems excellent, brilliant etc, but very soon, early in his logic he imo looses clarify and enters a haze he never seem to escapes from.
https://www.physicsforums.com/threa...n-classical-and-quantum-gravity.220841/page-2

How one thinks about this is related to a more general topic the nature of symmetry, or rather than nature of observer equivalence. If you have thought about this one will see its a chicken and egg situation. Rovelli seems to want to describe the equivalence class itself, without the set that defines it to get rid on the redundancies and get the observer invariance manifest. But this is what i think is wrong, he is throwing the baby out with the bathwater.

A good constrast to Rovellis view is Smolins reality of time. If you check both let me know which you think is the most sound of them both.
https://en.wikipedia.org/wiki/Time_Reborn
and the as far as i know most recent and most promising way out the metalaw dilemma
https://arxiv.org/abs/1205.3707

/Fredrik

I'm rereading Time Reborn. I still can't decide whether it's Smolin or Rovelli's..

The main two points of Smolin book that I'm questioning now are the ideas.. firstly:

"THE MAIN MESSAGE OF Part II so far has been that for cosmology to progress, physics must
abandon the idea that laws are timeless and eternal and embrace instead the idea that they
evolve in a real time. This transition is necessary so that we can arrive at a cosmological theory—
one that explains the choices of laws and initial conditions—that is testable and even
vulnerable to falsification by doable experiments."

But is there no way to evolve laws without any real time? Can't the originator of the evolving laws transcend time?

The second point.

"In a word, in general relativity size is universal and time is relative, whereas in shape
dynamics time is universal and size is relative. Remarkably, though, these two theories are
equivalent to each other, because you can—by a clever mathematical trick that isn’t necessary
to go into here—trade the relativity of time for the relativity of size. So you can
describe the history of the universe in two ways, in the language of general relativity or the
language of shape dynamics. The physical content of the two descriptions will be the same,
and any question about an observable quantity will have the same answer."

Let's say Bob is 30 years old. Alice is 10 years old. If Bob is near a black hole. He ages less so when he and Alice met.. Alice is more than 100 years old while Bob is just 31 years old or less (remember the scene in Interstellar). How do you apply Shape Dynamics here where time is universal and yet Alice is 3 times the age of Bob. If they would take Shape Dynamics into perspective. Can or how do they retain their ages?

 

[Urs Schreiber]

According to Carlo Rovelli in his latest book "The Order of Time"
https://www.amazon.com/dp/073521610X/?tag=pfamazon01-20:
"The equations of loop quantum gravity on which I work are a modern version of the theory of Wheeler and DeWitt. There is no time variable in these equations."

As the reference to Wheeler and DeWitt indicates, the general idea of the Hamiltonian constraints in relativistic field theory replacing the Hamiltonian time evolution in non-relativistic field theory is old and, in fact, standard. For instance, quantizing the Hamiltonian constraint for the relativistic Klein-Gordon particle is well-known to yield the Klein-Gordon equation. (See the references at relativistic particle.)

This makes it seem a good idea to quantize gravity, non-perturbatively, by "simply" quantizing the Hamiltonian constraint of general relativity. If it were known how to do this, there would be little to no debate that this is successful non-perturbative quantum gravity.

Unfortunately, what sounds easy turns out to be intractable.

The reason that "LQG" apparently solves this problem is only because it doesn't solve the problem, but changes the problem to something else before solving it (by passage from real connections to "generalized connections"). I have explained this here.

 

[Fra]

But is there no way to evolve laws without any real time? Can't the originator of the evolving laws transcend time?

Time will not be "real" as in a global time. As I see it, reality of time just refers to the reality of a succession of states. Where the generalized sense of state is used where you unify state and law. In Newtonian paradigm we separate things into initial conditions, law and states. In the evolving view, all these things should be treated more unified.

If you take an inference perspective to measurement/observation, and consider an observer to infer/interact with its environment, then ALL the qualifiers must go through the inferential pipeline. This in itself puts interesting "constraints" on what is allowed and what's not. One implication is for example that timeless symmetries has not place. All symmetries must be a result of an inference. And the confidence of the inference is influence by the inference structure and the amount of data.

In this view ther is no fundamental notion of space or time, the fundamental notions are what is somewhat certain and what is uncertai about distinguishable states. Typically the past is certain, the future is uncertain. But the past typically has an arrow of time, based on what is uncertain. Space are them emergent embedding dimensions only in the large complexity limit. And that large scales are 4D is something that should be predicted from this. The spacetime CONTINUUM has no fundamental place in my thinking. The reason is that computationally infinite and in particular uncountable sets are really troublesome. I rather seem the continuum models as a large complexity "approximation" of the real thing, rather than the otherw way around.

So the abstractions i look at are mathematical models for inference, whose "execution" corresponds to time evolution. They can grow or release "control" of complexions in their environment to gain or loose mass. And when a collection of such things interact, where will be an evolution of the population of "preferred" mathematical structures. Thats briefly my version of what's along the lines of smolins suggested direction. But this is really abstract and even more "from scratch" than string theory.

So i think evolution without time as we know it is possible. But the evolution itself is a progress indicator that is at least partially objective, at least in certain approximations. But its certainly not the kind of time that can be lined out as complete histories because tracing the history is not a reversible process informationwise.

/Fredrik

 

[Urs Schreiber]

It's hard for me to see what you guys are really trying to understand here. Let's take a step back:

Are you all familiar with what is called generally covariant differential equations of motion? Such as Maxwell's equations or, notably, Einstein's equations? Do these fit your bill of "laws not evolving with time"? I suppose the latter is meant to refer to Hamiltonian formulations of field theory?

 

[Fra]

Do these fit your bill of "laws not evolving with time"?

Yes

A system of differential equations constitute "fixed laws" and the only evolution is that of the state in time, within a given state space. Ie. But the solution is the entire system. This kind of "time" is not real. Its just an independent parameter.

My perspective is really that of inference, and the "fixed laws" corresponds to "100% confident deductive rules", so what is important to me is if we think there are elements that are not subject to evolution/change/revision. The "time" itself is not the big thing for me. Time just happens to be what we call the "parameters" we use to describe a history of states.

/Fredrik

 

[Urs Schreiber]

Yes

Okay, in that case one can say something concrete as to the relation of such general covariant laws to Hamiltonian laws depending on time, and on the quantization in the two perspectives. Namely, this is the perspective of the "covariant phase space" in contrast to the phase space associated with any given Cauchy surface. This is the topic of Chapter 8: Phase space of the PhysicsForums QFT lecture notes.

 

[Fra]

Okay, in that case one can say something concrete as to the relation of such general covariant laws to Hamiltonian laws depending on time, and on the quantization in the two perspectives. Namely, this is the perspective of the "covariant phase space" in contrast to the phase space associated with any given Cauchy surface. This is the topic of Chapter 8: Phase space of the PhysicsForums QFT lecture notes.

I don't think we are talking about the same things after all. It seems you refer how to change from the observer invariant (diff invariant in this case) view to inside view (where an observer is chosen). I understand this, but in my view the observer invariant perspective per see is not observable in the physical sense. Note that i don't have any problem with the mathematical relation here between gauge symmetries and gauge choices, the problem is to me where to attach reality/physics in these abstractions. To talk about quantizing an observer invariant object needs to be phased in form of a real inference, and my conclusion is that no observer CAN infer a perfect invariant (not observable).

With laws evolving in time, i don't mean laws explicity evolving in time as per a deterministic rule. That is indeed equivalent to a fixed law as long as the dependence on time is given. This would then correspond to a "meta law". The core problem of smolins view is to understand what evolution of law means, without adding from behind a "meta law", which in fact is just another law again.

The key is rater to find an intrinsic evolutionary model where only the evolutionary steps are given, and where the future possible states can not be predicted without the actual backreaction from the environment. And for reasons of computability and information limits, this can not be capture in a confident certain rule.

Have you read anything about Smolins views of evoling law? I really enjoy your insights, and mathematical perspective, and I agree more stringency is needed. But there are also the part where one need to somehow attach the abstractios to physics and conceptal understanding. I might guess you find smolins talk fuzzy, but would really like to hear your sincere opinon if you really read any of it. The reason is that it puts the finger on the observer problem, and that laws need to be, not "observer", but in the generalization "inferred/abduced" from interactions, and that therefore all laws must be the result of evolution (or i would say inference). I think smoling could be clearer.

And how do you interpret all this in terms of categories of observers? Where you need another category to even define the category of categories?

/Fredrik

 

[Urs Schreiber]

Have you read anything about Smolins views of evoling law?

No. But, to be frank, if you are trying to advertise any insights that might be found there, you are not doing them a favor here, because they come across as really confused.

And how do you interpret all this in terms of categories of observers? Where you need another category to even define the category of categories?

I wish I knew what you are asking here, because then I would really try to help. But I fail to make sense of what you are saying or asking or trying to understand. What is "all this"? Which "categories of observers"? And how on Earth should something purely formal like the (large) category of all (small) categories suddenly make any appearance here?

To be frank, it does sound quite crackpottish! Maybe it's not, sometimes people sound this way when they are beginning to acquaint themselves with scientific thinking.

Could you try to boil down your question to something more or less well defined? Maybe stick to something concrete, like Maxwell's equations. What is it you would like to know or say about them?

 

[ohwilleke]

Im not sure but I got the word from the passage "Loop quantum gravity shows that it is possible to write a coherent theory without fundamental space and time—and that it can be used to make qualitative predictions."

There are many "fundamental" words in the book.. for example.. a part reads:

"At first no one could understand the significance of an equation without a time variable, perhaps not even Wheeler and DeWitt themselves. (Wheeler: “Explain time? Not without explaining existence! Explain existence? Not without explaining time! To uncover the deep and hidden connection between time and existence . . . is a task for the future.”) The issue was discussed at great length; there were conferences, debates; rivers of ink flowed. I think that the dust has now settled and things have become much clearer. There is nothing mysterious about the absence of time in the fundamental equation of quantum gravity. It is only the consequence of the fact that, at the fundamental level, no special variable exists."

It's a great book.. who has read it too? I got the book about reading Sabine Hossenfelder article about the interview with Rovelli at: http://backreaction.blogspot.com/2018/08/guest-post-tam-hunt-roasts-carlo.html

The issue which I think is confusing you is that in loop quantum gravity, dimensions of space-time are emergent rather than fundamental properties of the theory.

Thus, rather than simply saying that "space-time has three space dimensions and one time dimension" as we do in general relativity, or "space-time has 11 dimensions" as we do in M-theory (which is the master theory of all string theories), loop quantum gravity says "points can be connected to other points according to these rules". From that source principle emerges an approximately four dimensional space-time in the world we see in every day life, and an approximate but not absolute ordering of points in the emergent space-time that creates the illusion of locality and smoothness of what is fundamentally a non-local, discrete theory. In loop quantum gravity, dimensions are approximate descriptions of a space-time in which any two points can, in theory, be connected to each other.

(Incidentally, not all theories of the loop quantum gravity type that try to quantize space-time rather than particles in space-time lack causality. Many kindred theories, e.g. causal dynamic triangles, instead assume a flow of time as an organizing principle that makes time an inherently different kind of dimension than space.)

It is also important that you be clear that string theory (which quantizes a carrier boson of gravity rather than space-time itself) and loop quantum gravity, are competing theories that differ greatly in their fundamental assumptions. You can't carry over something said in one of these theories to the other.

 

[ohwilleke]

To make the question more tractable.

The movement of strings causes spacetime and spacetime curvature to emerge and in many cases, even some of the initially fixed spacetime can be seen as emerging from the movement of strings. Are the strings only belonging to the graviton particle? Or does other strings like electron string also causes spacetime or spacetime curvature to emerge or causes initially fixed spacetime emerging from the movement of the electron string?

This sounds like a confounding of two different theories. In string theory, the movement of strings causes spacetime curvature to emerge, but does not cause spacetime to emerge. In string theory, the dimensionality of spacetime is set, a priori, as an assumed fundamental part of the theory. Sometimes string theory articulates spacetime itself as a "brane" which is not a string.

String theory is based on the assumption that all of the Standard Model particles, the graviton, and probably additional fundamental particles that have not been discovered yet, all arise from vibrations of a single kind of more fundamental particle called a string. Heuristically, the fact that, in string theory, all particles are basically the same thing deep down, and that all mass and all forces are associated with particles, makes the universal application of gravity to everything that has mass or energy make more sense.

 

[kiki_danc]

This sounds like a confounding of two different theories. In string theory, the movement of strings causes spacetime curvature to emerge, but does not cause spacetime to emerge. In string theory, the dimensionality of spacetime is set, a priori, as an assumed fundamental part of the theory. Sometimes string theory articulates spacetime itself as a "brane" which is not a string.

But according to Science Advisor atyy.. the movement of strings causes spacetime to emerge. This is his exact words:

"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."

Reference https://www.physicsforums.com/threads/true-background-independent-particle-physics.484720/page-2

Here, atyy stated that the movement of strings causes spacetime to emerge. You don't agree.

So does the movement of strings causes spacetime to emerge or not? Maybe it's the context.. so I hope atyy and ohwilleke can resolve this.​

String theory is based on the assumption that all of the Standard Model particles, the graviton, and probably additional fundamental particles that have not been discovered yet, all arise from vibrations of a single kind of more fundamental particle called a string. Heuristically, the fact that, in string theory, all particles are basically the same thing deep down, and that all mass and all forces are associated with particles, makes the universal application of gravity to everything that has mass or energy make more sense.

 

[kiki_danc]

The issue which I think is confusing you is that in loop quantum gravity, dimensions of space-time are emergent rather than fundamental properties of the theory.

But again, according to Science Advisor atyy in the thread referenced above: "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."

You and atyy are two of a kind. Non-physicists but well versed in physics technicalities so I hope you can settle on the context and perhaps let a full time physicist declares what is the correct concepts and terms to use.

Thus, rather than simply saying that "space-time has three space dimensions and one time dimension" as we do in general relativity, or "space-time has 11 dimensions" as we do in M-theory (which is the master theory of all string theories), loop quantum gravity says "points can be connected to other points according to these rules". From that source principle emerges an approximately four dimensional space-time in the world we see in every day life, and an approximate but not absolute ordering of points in the emergent space-time that creates the illusion of locality and smoothness of what is fundamentally a non-local, discrete theory. In loop quantum gravity, dimensions are approximate descriptions of a space-time in which any two points can, in theory, be connected to each other.

(Incidentally, not all theories of the loop quantum gravity type that try to quantize space-time rather than particles in space-time lack causality. Many kindred theories, e.g. causal dynamic triangles, instead assume a flow of time as an organizing principle that makes time an inherently different kind of dimension than space.)

It is also important that you be clear that string theory (which quantizes a carrier boson of gravity rather than space-time itself) and loop quantum gravity, are competing theories that differ greatly in their fundamental assumptions. You can't carry over something said in one of these theories to the other.

 

[Urs Schreiber]

in loop quantum gravity, dimensions of space-time are emergent rather than fundamental properties of the theory.

This is not really correct, at least not in the original "canonical" LQG (maybe in some variant of CDT). The definition of LQG is to start from a Hamiltonian formulation of 3+1 dimensional gravity, then encode the field variables as SU(2)-connections, then encode these as parallel transport, then pass to "generalized connections" (which is where they go astray) and then quantize.

The reason that Ashtekar variables involve SU(2) (whence the whole business of "spin" networks) is directly related to 3+1 dimensions.

 

[Urs Schreiber]

This sounds like a confounding of two different theories. In string theory, the movement of strings causes spacetime curvature to emerge, but does not cause spacetime to emerge.

That's about right. In a sigma-model ("geometric") string background, a target spacetime is fixed, and the string perturbation series provides an S-matrix for perturbative quantum gravity on this background spacetime, encoding, if you wish, perturbative quantum fluctuations of the metric tensor, hence of the curvature of spacetime. As you said.

One subtlety here is that a string background need not be defined by a geometric sigma-model. A priori it is defined simply by specifying a suitable 2d conformal field theory on the worldsheet. In this perspective, no target spacetime geometry is manifest. But then one may still compute the string perturbation series, and then ask which QFT on which actual spacetime has the same scattering amplitudes (S-matrix) like that, at low energy. If one finds such a QFT, one may regard the spacetime that it is defined on as having "effectively emerged" from the excitation spectrum of the worldsheet theory.

This is just as in Connes-style NCG, just with worldlines promoted to worldsheets. There is a PF-Insights article with more on this kind of "emergence" at Spectral Standard Model and String Compactifications

 

[Fra]

To be frank, it does sound quite crackpottish! Maybe it's not, sometimes people sound this way when they are beginning to acquaint themselves with scientific thinking.

I don't blame you for this impression! I supposed i thought you would connect without having to write more, but i was clearly wrong.

I have a physics education and would say i have been thinking about the logic of science more than many working physicists. However I made the decision to leave the academic route, because i have too strong ideas on my own that i need to work on, and i could not bring myself to align with mainstream.

So my main "problem" is I have far too little time to wokr on this, so progress is slow.

Could you try to boil down your question to something more or less well defined? Maybe stick to something concrete, like Maxwell's equations. What is it you would like to know or say about them?

Hmm Maxwells equations is not the best starting point. My questions does not concern specifically differential equations per see, its related to the logica systems.

Maybe can rewind to this thread https://www.physicsforums.com/threads/why-higher-category-theory-in-physics-comments.899167/ But let me go back and read up on your (excellet) ncat pages on homotopy type theory and i will try to see if i can rephrase my points in something that is more your technical language. As I am not fluent in that mathematics, it takes some time to read up. Let me get back on this. I see that you may have insights that i have not seen yet - so this interests me, but i am a man that has the ambition to make serious progress having at hand not many hours per week. Otoh, those hours i can focues exactly where i want without compromising and not have to worry about publications or funding, or risk having my own idea beeing biased by those. Its pros and cons.

So sorry for the incoherence, let me get back when i had time to read your ncat pages and phrase it at least a little closer to your terms.

/Fredrik

 

[Fra]

As there is wast body of simply terminology of the field here, that easily obscures the core points, i will start by linking to where i feel we are on the same page.

First very conceptually.

"Hence if we ask “What is an observer?” at a truly fundamental level, in a realm of genuinely fundamental Planck scale physics where everyday intuition will have broken down and the pure mathematics is all that remains, then a promising way to find an answer to this is to make sense of formalizations of physical theory within type theory.

Interestingly enough, type theory, being an incarnation of constructive mathematics, is an intrinsically observational formalization of mathematics in itself. In type theory, the proof of any truth is provided by finding “terms” of a certain “type”, and these terms, once found, are called “witnesses exhibiting (conclusive) evidence” (e.g. section 1.11 of (1)). Hence for a fundamental physical theory formalized in homotopy type theory, every truth about the physics is to be exhibited by a mathematical observation in this sense, as if the logic of the universe were observing its own derivation. In terms of the identification of mathematical proof with experimental observation, at the most fundamental level of reality, in the presence of genuinely mathematical laws of nature, to observe anything in nature is to find mathematical truth in the mathematical system describing it, and vice versa."
-- Froms David Corfield and Urs Schreiber, https://ncatlab.org/schreiber/show/Physics+of+the+Observer

The bold things where are indeed what i refer to. The infereces is talk about, are loosely speaking "constructive proofs". And these "constructive proofs" are the abstractions of observation and interactions. For example, i argue that even physical law, are subject to the constraints of subjective proof, (i use the term looseley here) i call it general inference, and i am not sure if its 100% one-to-one to homotopty theory, but its ceratinly close enough and related.

more later...(jsut to set the perspective here, the above is also fuzzy, but as its from Urs own page i presume it is suffient to get us to the same page)

/Fredrik

 

[kiki_danc]

But according to Science Advisor atyy.. the movement of strings causes spacetime to emerge. This is his exact words:

"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."

Reference https://www.physicsforums.com/threads/true-background-independent-particle-physics.484720/page-2

Here, atyy stated that the movement of strings causes spacetime to emerge. You don't agree.

So does the movement of strings causes spacetime to emerge or not? Maybe it's the context.. so I hope atyy and ohwilleke can resolve this.​

May I know what versions of string theory where the "initially fixed spacetime can be seen as emerging from the movement of strings" and the thing about the movement of strings causes spacetime to emerge. Atyy stated it to be so, then it may be so since he is very well read and familiar with it all.

 

[atyy]

May I know what versions of string theory where the "initially fixed spacetime can be seen as emerging from the movement of strings" and the thing about the movement of strings causes spacetime to emerge. Atyy stated it to be so, then it may be so since he is very well read and familiar with it all.

Perhaps I was too loose with my language there. I was thinking that gravitons are vibrations of strings, and curved spacetime can be thought of as a coherent state of gravitons. This is discussed in https://books.google.com.sg/books?id=jbM3t_usmX0C&source=gbs_navlinks_s, section 3.7.

 

[kiki_danc]

Perhaps I was too loose with my language there. I was thinking that gravitons are vibrations of strings, and curved spacetime can be thought of as a coherent state of gravitons. This is discussed in https://books.google.com.sg/books?id=jbM3t_usmX0C&source=gbs_navlinks_s, section 3.7.

There are two separate statements.. does the above address the first or the second...

the first is: "initially fixed spacetime can be seen as emerging from the movement of strings"
the second is: "the thing about the movement of strings causes spacetime to emerge"

Did you mean your "I was thinking that gravitons are vibrations of strings" being an answer to "initially fixed spacetime can be seen as emerging from the movement of strings"

and your "curved spacetime can be thought of as a coherent state of gravitons" being an answer to "the thing about the movement of strings causes spacetime to emerge"?

Please confirm if the above is correct or your answer is only to either one of them only?

 

[atyy]

There are two separate statements.. does the above address the first or the second...

the first is: "initially fixed spacetime can be seen as emerging from the movement of strings"
the second is: "the thing about the movement of strings causes spacetime to emerge"

Did you mean your "I was thinking that gravitons are vibrations of strings" being an answer to "initially fixed spacetime can be seen as emerging from the movement of strings"

and your "curved spacetime can be thought of as a coherent state of gravitons" being an answer to "the thing about the movement of strings causes spacetime to emerge"?

Please confirm if the above is correct or your answer is only to either one of them only?

You should forget about what I said (since that was in the context of another thread, and I don't want to keep looking that up).

 

[kiki_danc]

This sounds like a confounding of two different theories. In string theory, the movement of strings causes spacetime curvature to emerge, but does not cause spacetime to emerge. In string theory, the dimensionality of spacetime is set, a priori, as an assumed fundamental part of the theory. Sometimes string theory articulates spacetime itself as a "brane" which is not a string.

The context of what it means the movement of strings causes spacetime to emerge is this: "graviton=spacetime emerges from strings, and gravitons contribute to spacetime curvature"... this is the punchline.

String theory is about particles.. so it has graviton which General Relativity doesn't have.. Therefore you can look at it dually.. either as classical spacetime or graviton. Now if strings are gravitons.. perhaps this is what atyy meant strings causes spacetime to emerge.. or strings being graviton being spacetime emerged from strings.

Therefore the statement "the movement of strings causes spacetime to emerge" is only true if you take into account gravitons and not classical spacetime. Because when you use the context of classical spacetime, then the statement is wrong.

My analysis is correct above?

String theory is based on the assumption that all of the Standard Model particles, the graviton, and probably additional fundamental particles that have not been discovered yet, all arise from vibrations of a single kind of more fundamental particle called a string. Heuristically, the fact that, in string theory, all particles are basically the same thing deep down, and that all mass and all forces are associated with particles, makes the universal application of gravity to everything that has mass or energy make more sense.

 

[Fra]

Don´t take this precise as I have not case my work into your language mainly because i am not fluent in it. But here is a quick attempt to put the ideas i talk about, as well as my take on evolving law a little close to your context. Let's see if this makes any sense to you?

The background is that this the abstractions i personally use in my own research; but the point here is not my personal views, but the general abstractions i referred to. I have some conjectures and visions about what an Observer is and how it interacts with its environment, refining this in a way that explains physical law from general rules of inference is my resaarch problem.

For any given observer O, there is a category of all possible set of microstructures as i label it.
Ignore the details, but we should roughly associate this to the quantum state relative to a given observer (but observer in a generalized meaning).

Ob(O) / "objects" ~ All possible ways to ENCODE the observers information about its environent, given
the resources of the observers (here is a builtin, cutoff complexity M that limits the amount of data that
can be coded) meaning this structure contains an "inferred" picture of its own environment. Let's ignore the explicit details of these structurs.

hom(O) / "transformations" ~ All possible ways to transform one state of the information in Ob(O) to another state. This corresponds to internal alternative ways fo datacompression.

Informally the deterministic time evolution of QM, in this abstractions follows from that the category has a natural internal flow. Ie a given class has spontaneous transformations that transformst the objects. This by design is unitary, and can be understood conceptually simply as the momentum of hte "inference" that keeps in motion in between information updates. And i propose that the physical law, is implicitly encoded in this class.

Next, we consider many such classes interacting with each other. Wich can be understood so that different observers has different "views" on physical law; and this in itself is the explanatory power of some interaction. They can be _explained_ but the difference views. This is analogous to conflict psychology, some conflices are fully explained by the two parties having inconsistent views on each other.

The category of all Observers, K
Here we allow the complexity of the observer to change, and change in this picture includs the measurement, so we do NOT have unitary evolution here. Instead its more like a learning model.

Ob(K) / "objects" ~ All possible categories O
hom(K) / "transformations" ~ all possible deforming transformation that brings one observer into another one, in a way that is non-unitary, and it also allows for loosing or gaiing complexity.

But the point now, is that the explanatory power is tehre only for the class which has made this inference from observing such fellow classes interact, and abduced this from data. This is then analogous to the gauge symmetry, one needs a class of much higher complexity to make this transformation POSSIBLE. This is possible for HEP when the observer is the lab fram, but breaks down for hyopothetical Planck scale observer.

Is here that the "evolution of law" enters the picture. As per the logic of reality of law as per smoling, the state of final fixed law is never reach for cosmological models. Ignoring this leads to what he calls cosmological fallacy. Ie. applying things we know work from HEP - to cosomology. This is a fallacy.

Anyway, the open problem as it see it, is howto from this picture of evolving categories (which given that one observer, can observer other groups of observers in the environment) leades to evolving categories of categories - make some generic insights that help us get real predictability out of this, rather than just descriptions.

It was in this sense i wonder if you have any insights? For example, this is analogous to a hypothetical landscape of theories, where you may ponder in HOW the different theories evolve into each other, and wether this is to be understood as a physical process or not? My perspective is that is is a physical process, but one that requires new framework for foundational physics, and our understanding of symmetries etc.

But I have a feeling that while one can probably phrase this question in terms of higher categories, the physical problem lies in the relation and evolution of these categories, and i suspect that the key to make progress here might not like in these category theories? Unless you are aware of some extremely clever theorems or something that physicists simply hasnt understood the possible use of?

In view the categories of categories or just a refinement of the microstructure of the Objects, and the set of possible transformation of the morphisms, so instead of an hierarchy, i expet that we have an evolving classes - that interact - and we are looking for some preferred popupation of classes that are "consistent" with each other, and this corresponds to the laws of physics. but paradoxalyl to understand this consistent state i think we need to relax it and see that there is not physical law that we should use as constraints.

That task is then to, out of these pure abstractions (singled out preferred mathematical structures) identify all the "baggage" such as 4D spacetime, mass. and of course all interactions.

This is very abstract, so it is hard to explain shorly, and which is why i have lots fo work todo before i will seriously publish any of this. I usually don't bother, but from reading some of Urs work I think there is a chance that you might understand my main points, even though indeed all i write here is just words. I have not phrased or cleaned this up in a proper formal way. Thats also quite some work as i am not used to this mathematics, nor am i familiary wit all the symbolic notation. I also suspect the quality and denseness of your technica work is hard to digest for many physicists, but you have done a really good job on the ncat pages to start to explain why this is relevant to physics.

Does this many any sense? or still too fuzzy? IF so, rephrasing this deeper will take more time i have at ahdn for the moment. To be hoenst, in the stuff i work on secretly now, i use a basic probabilistic notation, in terms of combinatorics and microstructures. So i do not so far cast anything in any "advanced framework", as i do not yet KNOW which the right framework is, except i know its general inference. And computational theory and the types and terms are indeed related to this. The observers microstructure are then also ~ types. And terms are transformatiosn.

But in the category of categories, we have a type that is evolving also constrained by the original terms. And ther terms i view as spontaneouis processes. So no ad hoc laws are needed as input.

/Fredrik

 

[Fra]

Forgot to mention this:

When thinking about this one should associate the difference in computational complexity of dual theories (generalizations of Ads/CFT) as a clue to the physical selecetion mechanism for WHICH observer classes that are "preferred" and thus populate our universe. In this, the inequivalence lies no in the results, but in the smaller computatioanl resources requires, and that tehy can litterarly be fitted into less complex observers.

/Fredrik

 

[kiki_danc]

I don't know what reference I read it before.. about combining loop quantum gravity with string theory. I can't find it now. Any papers about this?

String theory is about particles.. about gravitons... but what if you want string theory version of something that precedes space-time (where space-time is really emergent... remember loop quantum gravity doesn't really have emergent spacetime as Urs argued earlier that "The definition of LQG is to start from a Hamiltonian formulation of 3+1 dimensional gravity, then encode the field variables as SU(2)-connections, then encode these as parallel transport, then pass to "generalized connections" (which is where they go astray) and then quantize."

I want something where spacetime and the dimensions are truly emergent (something that creates spacetime.. which string theory can't do because once you have strings.. or particles.. you already assume there is spacetime).

We need more complex theories with more degrees of freedom.