The Emergence of Space-time in String Theory

A few yesrs ago now I read a First Course in String Theory.

In that book strings were part of normal space-time plus for consitency some extra dimensions. Spin 2 partices natually emerged and so did GR.

I didnt think anything of it at the time (pun intended), but I recently saw a discussion about what time is with Michio Kaku on the pannel. He claimed that the concept of time emerged from String Theory. Others poo-pooed it saying how can you have vibrating strings without time. Michio kept silent, but I thought there must be something to it for him to say it.

So I did a bit of research, including skimming over the A First Course text. The text didnt really illuminate anything but I did discover he following lecture:



As well as the following book that I splurged on and actually purchased (evidently it arrives next Friday):

https://www.amazon.com.au/Emergence-Spacetime-String-Theory/dp/1032177926?tag=pfamazon01-20

Should be interesting. I am about to watch the video.

Thanks
Bill

bhobba said:

He claimed that the concept of time emerged from String Theory.

I would wonder what his basis is for that statement, since as I understand it string theory models still have one timelike dimension; timelike curves/vectors/etc. don't somehow emerge from an underlying model without them. For example, in the 11-dimensional model that seems to be the basis for M-theory, there are 10 spacelike dimensions and one timelike dimension.

PeterDonis said:

in the 11-dimensional model that seems to be the basis for M-theory, there are 10 spacelike dimensions and one timelike dimension.

Yes.

I have watched the video, and it is not entirely clear what is happening.

The video explained that space-time in string theory is much more complicated than in classical physics. But GR still emerges.

That is not the same as the claim that string theory explains time (or space-time).

I think I will need to wait for the book to arrive.

I have found the following that may help clarify the situation before the book arrives:

https://beyondspacetime.net/publica...-of-spacetime-in-quantum-theories-of-gravity/

Off to a delayed lunch - still a fascinating video.

Thanks
Bill

It (emerging time) certainly isn't part of the standard formulation of string theory. But ST is a bit weird in that you start from a string on a flat spacetime, in which then gravitons are part of the spectrum. A coherent state of these gravitons can be constructed which describes a string in a curved background. In that sense it resembled Fierz Pauli theory in which a background dependent formulation can lead (up to some technicalities) to a background independent theory. To me this always indicated that ST wants to tell us about the nature of space(time), which now in the "spacetime from entanglement" program seems to be the case (as Horowitz also treats in the lecture).

Just a quick reflection:

Emergence is one of those buzzwords, and in string theory I think one can maybe say that 4D spacetime emerges FROM a 11D spacetime, but means of the compactifications, but which involves a finetuning problem; so for me at least, it's explanatory value is questionable.

The 11D themselves, are not emergent as far as I know how ST usually puts it, it's put in there to make it consistent.

(The "hope" I have seen in string theory is some interesting turns in string theory is various dualities however, that can can imagine iterating. Where changes dimensonality can be traded in for different dynamics. This is potentially interesting.

This comes to my mind
https://math.ucr.edu/home/baez/nth_quantization.html

The conceptual association I always made of those ideas is that "dimensions" seen just as a continuous "index", can be created by indexing "states of fields". So by starting with a 0-brane in say a 1D spacetime, you can increase the dimensionality by applying quantization. This way previously indistinguishable uncertainy, becomes distinghuishable and "creates" new dimensions. (how this is possible is up to any approcha to explain though) This conceptially is how i envision dimensional emergence in general. But to make this satisfactory, I think one should not explain it by thinking of it as exciting already existing higher dimensions, because leds you to the finetuning trap. Am I not sure if there is any actual work in this direction in string community. The main problem I see for string theory to do this, is that they start out in the continuum, this is whay everything is uncountable from start, wether you have one or 11 dimensions, and then I always wondered - uncountable from which observer.. there my interest in string teory fades)

/Fredrik

Kaku could be talking about the IKKT matrix model, see slide 16 here for something about how the model seems Euclidean but there's a way to define time; I haven't studied it yet,

IKKT is a Japanese model, and Japanese work in string theory sometimes gets neglected in the west.

bhobba said:

I didnt think anything of it at the time (pun intended), but I recently saw a discussion about what time is with Michio Kaku on the pannel. He claimed that the concept of time emerged from String Theory.

Is this discussion available online?

Kontilera said:

Is this discussion available online?

Yes, at the Institute of Arts and Ideas.

That said as a mentor I now feel Michio Kaku certainly meets our standards, some others in that discussion about time do not. Because of that I do not feel comfotable promoting it.

Thanks
Bill

bhobba said:

Michio Kaku certainly meets our standards

His published peer-reviewed papers are not the issue. The issue, if there is one, is with claims he makes in informal contexts, which are often way beyond what can be justified by the peer-reviewed literature. That's why I said I would want to know what his basis is for that statement. Is it something actually demonstrated, or at least argued for, in a peer-reviewed paper? Or is it just his own personal opinion? My money would be on the latter, but the only way to know for sure is to look at the source.

I take a pessimistic view on anything a string theorist says about GR. That being said, their concept of emergence I found best to be explained in section 4 here: https://arxiv.org/pdf/1904.03234.pdf (although this isn't about the emergence of 'time' so to speak, but just the overall vibe about emergence)

If Michio Kaku told me my mother loves me, I would check it out. He says...um...lots of things.

Vanadium 50 said:

If Michio Kaku told me my mother loves me, I would check it out. He says...um...lots of things.

Thanks for the heads up. I thought he was in the reliable camp but it looks like I need to think again. You live and learn.

Thanks
Bill

romsofia said:

I take a pessimistic view on anything a string theorist says about GR. That being said, their concept of emergence I found best to be explained in section 4 here: https://arxiv.org/pdf/1904.03234.pdf (although this isn't about the emergence of 'time' so to speak, but just the overall vibe about emergence)

Just gave it a read. You are correct.

Nice paper, though.

My head is groaning from all this string theory stuff I did years ago in A First Course. I still recommend it as a book.

Thanks
Bill

romsofia said:

I take a pessimistic view on anything a string theorist says about GR. That being said, their concept of emergence I found best to be explained in section 4 here: https://arxiv.org/pdf/1904.03234.pdf (although this isn't about the emergence of 'time' so to speak, but just the overall vibe about emergence)

On page 14 (The concepttion of emergence) they write..

" In the philosophical literature, there is a widespread view of emergence as a `delicate balance' between dependence, or rootedness, and independence, or autonomy. Roughly speaking, dependence means that there is a linkage between two levels or theories: usually, a macroscopic and a microscopic theory. Independence can be taken to mean novelty in the macroscopic theory with respect to the microscopic theory
...
For the purposes of this paper, we will take the condition that determines the linkage between the microscopic and the macroscopic theory to be the limit of a large number of degrees of freedom of the system, while keeping appropriate quantities xed. Thus, it is indeed highly reminiscent of a thermodynamic limit.
...
String theory authors have sometimes used the term `emergence' rather liberally, and its occurrence in the technical literature on duality can be confusing.
...
The black holes can be viewed as `built up' of branes, anti-branes and strings" - the latter were "fundamental". Still, it is not clear if one must imagine the black hole description to `emerge' from the quantum microscopics.
...
In the Strominger-Vafa analysis, we are dealing with the comparison of a microphysical state-counting with a thermodynamic entropy. So, can one indeed identify the semiclassical black hole as emergent?"

I would like to see ideas where the continuum object (the strings/branes) as emergent as well in order to have novelty emerge as complexity increase in a deeper way than just in the static thermodynamics sense. The place I would like start is with discrete string models, in a way if you starte from a 0-brane, it's just an index, basically a true/false. And you get rid of the uncountable starting point. This could perhaps better even motivate "strings" from start. After all, a "string" can be seen as a "smeared" point, which was the trick to avoid infiniteis in the first place. But what is the conceptual meaning of this "smearing". A point in turns can be thought of just as a bit (true or false), so about as much as we can reduce anything? I think the quantization induction is an interesting idea. Can we think of the "smearing" on the observers side of the cut (ie ignorance). So we have already there a seed for a duality, between the observer cut screen. Thus a string, or a uncertaint point is in the eye of the beholder. And if the beholder is part fo the interactions, it becomes very interesting and complicated.

/Fredrik

bhobba said:

A few yesrs ago now I read a First Course in String Theory.

In that book strings were part of normal space-time plus for consitency some extra dimensions. Spin 2 partices natually emerged and so did GR.

I didnt think anything of it at the time (pun intended), but I recently saw a discussion about what time is with Michio Kaku on the pannel. He claimed that the concept of time emerged from String Theory. Others poo-pooed it saying how can you have vibrating strings without time. Michio kept silent, but I thought there must be something to it for him to say it.

So I did a bit of research, including skimming over the A First Course text. The text didnt really illuminate anything but I did discover he following lecture:



As well as the following book that I splurged on and actually purchased (evidently it arrives next Friday):

https://www.amazon.com.au/Emergence-Spacetime-String-Theory/dp/1032177926?tag=pfamazon01-20

Should be interesting. I am about to watch the video.

Thanks
Bill

Here is a lecture by the author of the book you linked.

She argues that relativistic spacetime is a mechanical byproduct of string dynamics.

These seem to be her main points re/ emergence of spacetime:

i) Instead of interpreting string worldsheets as embedded in some spacetime, interpret them as non-embedded manifolds. Worldsheet spacetime coordinates are reinterpreted as values of fields on these manifolds.

ii) The spacetime metric that appears in string action, that was previously interpreted as the metric of the spacetime the worldsheet was embedded in, is a free parameter, and not a statement about any actual spacetime.

iii) Spacetime emerges in this sense: Gravitons are byproducts of string dynamics, and a their collective behaviour obeying Einstein's field equations is reproduced by string theory

But still: how can one speak of emergence if the +- signature or any information about the worldsheet has to be put in by hand?

haushofer said:

But still: how can one speak of emergence if the +- signature or any information about the worldsheet has to be put in by hand?

The idea as far as I can tell is a choice of metric for the target spacetime is really a choice of a conformal field theory over the worldsheets themselves. So even though a metric with a relevant signature is used, it does not signify any spacetime in which the worldsheets are embedded. See e.g. equation 6 and discussion about it in witten. How satisfactory this is, I can't say. And even if the worldsheets are not embedded in some spacetime put in by hand, they would have their own "auxiliary" metric that could count as an initial spacetime.

[edit] - Actually might have misinterpreted your question. When you said "+-" signature, you were asking about the metric of the worldsheet, as opposed to the metric of the target spacetime?

Morbert said:

The idea as far as I can tell is a choice of metric for the target spacetime is really a choice of a conformal field theory over the worldsheets themselves. So even though a metric with a relevant signature is used, it does not signify any spacetime in which the worldsheets are embedded. See e.g. equation 6 and discussion about it in witten. How satisfactory this is, I can't say. And even if the worldsheets are not embedded in some spacetime put in by hand, they would have their own "auxiliary" metric that could count as an initial spacetime.

[edit] - Actually might have misinterpreted your question. When you said "+-" signature, you were asking about the metric of the worldsheet, as opposed to the metric of the target spacetime?

Yes. One leaves off from a 1+1 dim. superconformal field theory which contains a time-like direction. Then it's no surprise that the target space also contains a time-like direction.

haushofer said:

Yes. One leaves off from a 1+1 dim. superconformal field theory which contains a time-like direction. Then it's no surprise that the target space also contains a time-like direction.

This paper might be relevant
https://arxiv.org/pdf/1207.1635.pdf

We saw before that the action looks like that for a d + 1-dimensional field theory on a 2-dimensional surface, the string. Witten’s proposal is to take that appearance at face value as the ontology of the theory, instead of an ontology of a string in an external spacetime.
[...]
The relative motions of string vibrations (including the graviton modes) are presumably part of the story, but so is the internal spatiotemporal structure of the string, represented by the internal spatial and temporal coordinates. Is time (and space) fundamental after all, but in the guise of string time, τ ?
[...]
Such a conservative view would still leave us with interesting questions about how phenomenal time, as it appears in classical spacetime theories, emerges from stringy time. Here, however, we want to emphasize that string ‘space’ and ‘time’ cannot be simply thought of as like ordinary space and time, just in two dimensions.
[...]
And so τ on the string—the fundamental ‘time’ in Witten’s interpretation—is quite unlike familiar time. In relativity, the time between two events depends on the frame of reference, but it is still the case that a timelike curve has a determinate duration, known as its ‘proper time’—not so in a theory with Weyl symmetry

Vistarini maintains that the string time is distinct from our "emergent" time, because Weyl invariance means lengths assigned by the metric have no physical significance, and proper time is lost.

@bhobba is this the video?

Greg Bernhardt said:

@bhobba is this the video?

I know that video - but I was referring to another one.

I will review it, but if my memory is correct, it just shows the problems philosophers have with physics.

Further discussion likely needs to wait until I get the book.

Thanks
Bill

Book arrived.

I will give it a skim and see if I can get the general idea.

Thanks
Bill

So far, it seems to be the holographic idea:

https://www.quantamagazine.org/one-labs-quest-to-build-space-time-out-of-quantum-particles-20210907/

Thanks
Bill

What I recall in the 80's the hope was 7+4=11, from supergravity and the point that 11D formulations of gravity had a lot of mechanics of tensor decomposition and dualities, favouring objects with a foot in the 7 and other in the 4.

Time itself is a different thing. The best lore is to guess that it emerges from noncommutativity of some algebra.

Stumbled upon an interesting book (Quantum Structure Of Space And Time, The - Proceedings Of The 23Rd Solvay Conference On Physics), and there is a whole section dedicated to the emergence of space-time, and while I'm still reading it, the main speaker has posted their paper on arxiv and there is a section on the emergence of time specifically, but it is somewhat short (starts on page 18): https://arxiv.org/pdf/hep-th/0601234.pdf

And some post comments (that I'll upload as a picture since it isn't included in the arxiv):

As luck would have it, recently at the World Science Festival, Brian Greene led a very distinguished panel that, towards the last 1/3 or so, discusses the emergence:



Thanks
Bill

bhobba said:

So far, it seems to be the holographic idea:

bhobba said:

As luck would have it, recently at the World Science Festival, Brian Greene led a very distinguished panel that, towards the last 1/3 or so, discusses the emergence:

When pondering about the meaning and the still lacking "generalization" of these dualities... I think the reaction of both Witten and Strominger on Greenes analogy of duality of the decimal vs roman numbers is good. They pointed out that the point of the duality is not that one theory is objectively superior, but that each dual version usually has different advantages in different situations.

I associate this to the generalization of the relativity of observers, where in a sense their views of the world are all dual, each generlized observer can easily claim that their inferred theory is by construction the optimal one for them (ie. given their given perspective, and resources). But the duality likes in that another observer coming from a different perspective my rightfully find that a different "dual theory" is optimal.

In this sense, the "space of all possible dual theories" might will be conceptually isomorphic to the "space of all possible observers", and in a way all different strange background geometries in string theory IS a different observer in a sense.

But these spaces as we know seem to get very big, the question is how we can treat this in a fruitful way?

As I see it there are two options, either the space is seem to be just extremely big, possibly even infinite, and we are faced with an unreasonable fine tuning problem (landscape problem). Or we try to solve that as seeing the space of theories itself as emergent from something simpler, but this option would be more of the type Lee Smolin seeks how "laws evolve". But Smolin then takes time to be real, and not emergent.

This "world of dualities" can IMO be thought of as a generalization of "observer equivalence" that is behind SR and GR, but which we apparently has a hard time to grasp, both technically and conceptually. But if it's something that I think is worth taking from string theory regardless of what you think about it all, it's the dualities as it conceptually goes beyond the notion of "strings".

/Fredrik

bhobba said:

A few yesrs ago now I read a First Course in String Theory.

In that book strings were part of normal space-time plus for consitency some extra dimensions. Spin 2 partices natually emerged and so did GR.

I didnt think anything of it at the time (pun intended), but I recently saw a discussion about what time is with Michio Kaku on the pannel. He claimed that the concept of time emerged from String Theory. Others poo-pooed it saying how can you have vibrating strings without time. Michio kept silent, but I thought there must be something to it for him to say it.

So I did a bit of research, including skimming over the A First Course text. The text didnt really illuminate anything but I did discover he following lecture:



As well as the following book that I splurged on and actually purchased (evidently it arrives next Friday):

https://www.amazon.com.au/Emergence-Spacetime-String-Theory/dp/1032177926?tag=pfamazon01-20

Should be interesting. I am about to watch the video.

Thanks
Bill

Thank you for sharing.
This video is now few years old. Today the prevailing opinion seems to be that string theory is ruled out. I do not agree that string theory is dead and useless. It is an important pillar supporting the next stage in building a unified theory of forces and particles, including gravity. I also think that loop quantum gravity will find it place in it.

There is a significant challenge in higher-dimensional theories, including string theory, regarding how to render the extra dimensions unobservable. A commonly employed approach involves assuming that the extra dimensions are compact and small. However, we can sidestep the necessity for compactification by postulating that spacetime is a subspace of a multidimensional configuration space—specifically, the space of possible matter configurations in 4D spacetime. Instead of formulating physics in spacetime, we can formulate physics in configuration space.

A potential avenue in this direction was explored in my talk titled "Extending Physics to Clifford Space: Towards the Unification of Particles and Forces, Including Gravity." I delivered this talk as part of the lecture series "Octonions, Standard Model, and Unification," held from February 24 to December 15, 2023.

The video recordings of these lectures can be accessed at https:. Specifically, the video recording of my lecture is available at .

In the talk there is a section on how string theory can be consistently formulated in a target space with neutral signature (p,q) with p=q. In that setup, the higher dimensional target space is the 16D space, with signature (8,8), of the oriented areas/volumes associated with fundamental objects.

pavsic said:

Thank you for sharing.
This video is now few years old. Today the prevailing opinion seems to be that string theory is ruled out.

I'd rather say it has never been ruled in :P

Yes, it has never been ruled in, if by this you mean a generally accepted theory. Indeed, string theory has never reached the status of a universally accepted theory of quantum gravity and the unification of fundamental forces and particles. Initially hailed as a highly promising avenue of research, its prospects have significantly dimmed. Current scientific discourse suggests a pivot away from string theory, viewing it less as a frontier of exploration and more as a theoretical cul-de-sac. This shift in perspective is regrettable for the reasons as outlined in my post.

pavsic said:

The video recordings of these lectures can be accessed at

Thank you so much for posting these links.

My research into the area is progressing slowly.

But they will undoubtedly be a great help as I gain more knowledge.

Thanks
Bill