What is the underlying connection between geometry and matter in string theory?

[SW VandeCarr]

Would it be sufficient for the validation of a string theory if it could make the same predictions as those already validated under QM and GR? Would it be necessary for such a theory to make additional predictions that could be tested at available energies?

 

[mgb_phys]

It would be nice if it could come up with existing effects from self consistent internal theories, rather than using the existing measurements to fix parameters in the theory.

 

[DecayProduct]

Would it be sufficient for the validation of a string theory if it could make the same predictions as those already validated under QM and GR? Would it be necessary for such a theory to make additional predictions that could be tested at available energies?

The way I understand it, no string theory has yet tested valid across all the known quantities and constants. So, while a string model may make a valid prediction about some known GR behavior, that same theory gets the mass of the proton wildly wrong, etc. If a theory makes all the right predictions of other tested theories, and makes new predictions that are testable, then I would think that that theory is correct. No string theory has done it, and some physicists are beginning to suspect that none ever will. That is, some are starting to get the idea that string theory and its cousins, while certainly interesting mathematically, is the wrong path entirely.

 

[Adrian59]

Would it be sufficient for the validation of a string theory if it could make the same predictions as those already validated under QM and GR? Would it be necessary for such a theory to make additional predictions that could be tested at available energies?

The gold standard for any new theory is to make new predictions that are experimentally verified. I would favour any new theory that confirmed existing experimental data providing it was derived from fewer starting premises and required less fine tuning cf the standard model's need for its constants. However, string theory has potentially a greater challenge since it postulates extra dimensions and particles so that just equalling the experimental predictions of the standard model without experimental conformation of these extra phenomena would be untenable.

 

[tom.stoer]

I would agree that in general a new theory should add additional predictions to existing theories - or should cure its physical weaknesses. For string theory the sitiuation is tricky because in the regimes that are accessable by experiment its new predictions are not testable - or let's turn it the other way round: no experiment requires a new theory beyond the standard model.

I would accept string theory if it came up with exactly the same predictions as the standard model - but with a much simpler explanation! This would be a very good starting point, even if additional dimensions are not testable directly (you always have physical or mathematical principles that are not testable directly, e.g. gauge invariance).

Unfortunately string theory neither predicts new (falsifiable) effects nor are its explanations simpler (of course one could start arguing what "simpler" means :-)

 

[marcus]

Van, you might want to read what David Gross had to say recently. He is the one who always seems to be chosen to sum things up at the big Strings conferences. Gave the closing summary talk at the 2007 and 2008, and this time the opening lecture at Strings 2009.
I'll give some sample excerpts and a link to the whole PDF slide set.

==sample excerpts from David Gross Strings 2009 slides==

"4. What is the nature of string perturbation theory?

Our present understanding of string theory has
been restricted to perturbative treatments. Does
this perturbation theory converge? Most likely it
does not. In that case when does it give a reliable
asympototic expansion of physical quantities? How
can one go beyond perturbation theory and what is
the nature of nonperturbative string dynamics?
This question is particularly difficult since we
currently lack a useful nonperturbative formulation
of the theory. "

"5. String Phenomenology?

Here there are many questions that can all be
summarized by asking whether one can construct a
totally realistic four-dimensional model which is
consistent with string theory and agrees with
observation?
Great progress, but still not constructed."

"8. Is There a Measurable, Qualitatively Distinctive
Prediction of String Theory?

... It would be nice to predict
a phenomenon, which would be accessible at
observable energies and is uniquely
characteristic of string theory."

"How many more string revolutions
are required?

What is the fundamental
formulation of string theory?

Quantum Space of all 2-d field theories
Second Quantized Functionals of loops (SFT)
M-theory . . .​

Is string theory a framework, not a theory?
What is missing?"
===end of sample excerpts===
http://strings2009.roma2.infn.it/talks/Gross_Strings09.pdf

 

[tom.stoer]

1. WHAT IS THE NATURE OF STRING PERTURBATION THEORY?

2. CAN ONE CONSTRUCT A TOTALLY REALISTIC FOUR-DIMENSIONAL MODEL WHICH IS CONSISTENT WITH STRING THEORY AND AGREES WITH OBSERVATION?

3. WHAT PICKS THE CORRECT VACUUM?
- WHY DON’T WE LIVE IN TEN DIMENSIONS?
- DOES THE THEORY POSSESS A UNIQUE VACUUM OR IS THE VACUUM TRULY DEGENERATE?
- DOES THE VANISHING OF THE COSMOLOGICAL CONSTANT SURVIVE THE MECHANISM THAT LIFTS THE VACUUM DEGENERACY?

4. IS THERE A MEASURABLE, QUALITATIVE, DISTINCTIVE PREDICTION OF STRING THEORY?

5. WHAT IS STRING THEORY? WHAT IS IT’S FUNDAMENTAL FORMULATION?

Is this something like Hilbert's program for the 21st century string theory research?

 

[marcus]

Is this something like Hilbert's program for the 21st century string theory research?

 

[flatmaster]

String theory is held together by it's namesake. -Matthew Lee Obley

I've been practicing making witty quotes.

 

[Fra]

Personal opinon

I don't mean to nitpick, but we know the drill that no theory is validated as in "verified true" no more than organisms in nature are validated. The closest thing to validation is the corroboration, which means that some get to live on (but usually not forever), some die off - there is variaton and selection.

So the question isn't which theory is right and which is wrong, the question is which theories are WORTH keep testing (ie who gets to live another day). We should keepin mind that testing a hypothesis, means competing with resources from other hypothesis, and our resources are limited.

So I think this leads to the question of what is the origin of the confidence in string theory as a scientific framework, ie a framework constraining the set of possible theories? If string theory WAS this, it would be quite ambitous.

But it's exactly when you see it as a candidate of such, that you lead to ponder not just what is STRING theory, but rather what is a scientific theory in general, and what is physical law which is usually the form our theories are coded? Ie. what physical law "gets to live"? And by consistency of reasoning this must apply to the process description as well, so the framework and theory is inseparable, both must evolve.

But it's exactly in this setting that string theory makes even less sense, since it isn't constructed in this spirit. It is more of a mathematical fantasy. I think this is also what has lead to the landscape problem. The framework provides a set of possibilities, but no selection principle.

I see two problems, the first is the lack of selection principle. BUT, maybe equally bad, is that due to the way the "landscape" is defined, there is not guarantee that even if there was a selection, that the theory will stay withing the landscape. Then the question becomes wether the darwinian selection is faster than the expansion of the landscape. It doesn't appear very promising at all.

This is what I find amusing. Some grand visions and defence of string theory, is to see it as a framework, and that idea per see is I think good. But it's exactly when you look at it as such, that the weakness in design seems even more clear.

To me the lack of conceptual depth and insight and physical basis makes me look at string theory as a mathematically inspired crapshot. It's worth as much chance as any other crapshot but at some point the motivation must fade unless it's confidence is supported by new events.

/Fredrik

 

[tom.stoer]

@Marcus: why the smiley? That was a grave question.

 

[marcus]

Oh, I really thought you were joking, Tom. It struck me as very funny.
For me, both Hilbert and his list of problems have a proven greatness.
Maybe it is just a difference of perspective.

Like for example, in 2006 Witten was out at UC Berkeley to give a series of 3 lectures on what he was working on. I attended all three 90 minute lectures and he didn't mention string. Finally someone asked him about string at the very end and he gave a bland one-sentence answer.
The Strings 2007 conference was in Madrid. Witten was there but his talk was about a non-string topic (3D gravity as I recall). Someone asked him about string at the end and he put the question off. He did not participate in Strings 2008. He was invited to give a public lecture at Strings 2009 and did so but the lecture was not anything about string.

What I've been seeing is beginning to look like a mass exodus, by the top people. Disinterest. For instance Steve Giddings used to do string. Now when he gives a conference talk it is about something else. If it were just an isolated case of one or two individuals it would mean nothing. But it's not just one or two individuals.

Three or four years ago, the whole feel was different. Did you ever watch the video of the Panel Discussion from Strings 2005 (Toronto)?

My guess is that the talks at Strings 2009 (Rome) that got the most attention were by Nima Arkani-Hamed (not about string) and by Petr Horava (not about string).

This is just a vague impression, of course. You may have an entirely different view. But when I saw your list of questions they struck me as little questions, not ones of lasting consequence. Not the kind of questions a David Hilbert would ask, or a Carl Gauss either.)

That's why I laughed. (Out of politeness I would be inclined not to discuss this, but you asked why: I really thought you were joking.)

 

[Fra]

So the question isn't which theory is right and which is wrong, the question is which theories are WORTH keep testing (ie who gets to live another day). We should keepin mind that testing a hypothesis, means competing with resources from other hypothesis, and our resources are limited.

Here is a paper that was discussed before, perhaps also relating a little bit to Toms question.
The author Moataz H. Emam is apparently a professional string theorist.

So what will you do if string theory is wrong?
"I briefly discuss the accomplishments of string theory that would survive a complete falsification of the theory as a model of nature and argue the possibility that such a survival may necessarily mean that string theory would become its own discipline, independently of both physics and mathematics."
-- Moataz H. Emam, http://arxiv.org/abs/0805.0543

Snipped quotes from the paper

"In fact, string theory has so far failed to conform to the definition of a scientific theory
...
The failure to satisfy Popper’s definition is however a serious drawback that string theory critics will, justly, continue to point out
...
So why do people continue to work on string theory?
"

Then he replies to his own quesion:

"There are several reasons.

We often hear that the theory is aesthetically attractive and that it would be a shame if nature had not picked such an elegant structure to use as the basis of the universe. Furthermore, it is the only model that aspires to not just be a theory of quantum gravity, but also a theory of everything; unifying, in principle, all of known physics. The hope is that eventually we will have a complete nonperturbative quantum theory which leads to the standard model plus general relativity in the low energy, dimensionally reduced limit. Not only that, we would like this reduction to happen in a unique way. However, the possible ways we can dimensionally reduce the ten-dimensional string theory to four spacetime dimensions allows for many possible outcomes, so large that they are collectively known as the “string theory landscape” [10, 11]. The often quoted estimate of the number of these product theories is 10500! If the physics we observe is just one of 10500 possibilities, what of the remaining 10500 − 1 wrong ones? Why are they there? To date this is an open question. An added complication is that the well-studied portions of the landscape are far from being perfectly connected to each other."

I think these are no serious arguments at all.

The he says

"So even if someone shows that the universe cannot be based on string theory, I suspect that people will continue to work on it. It might no longer be considered physics, nor will mathematicians consider it to be pure mathematics. I can imagine that string theory in that case may become its own new discipline; that is, a mathematical science that is devoted to the study of the structure of physical theory and the development of computational tools to be used in the real world."

The latter statement here sound very ambitious, and if it really was this, I for one would embrace it. But IMHO string theory is not even near a plausible candidate from such a great ambition; I don't see a single plausability argument for this conjecture, maybe it could evolve into one (just like anthing can evolve into anything given time), and end up nothing like the original ideas of string theory, but then it's not string theory and is not argument for the current endavour as a physical science, I suspect all other programs will also converge to something else given enough time. So this is still no argument for the specifics of string theory as a physical theory, or even framework for physical theory as it is today.

Edit: I confess I thought Tom was joking too :)

/Fredrik

 

[tom.stoer]

@Marcus: thanks for the explanation!

Explanation from my side: it is not that I am claiming it could be something like Hilbert's program. It is simply that Gross is opening the string conference with this list of questions - questions that may not be as deep as Hilbert's but perhaps more difficult to answer. So in order to answer we should ask Gross :-)

Look at Hilbert's questions: deeper questions, less people to work on, but nevertheless most of theme have been answered quite soon. So perhaps Hilbert's genius was to ask the right questions about the right subject.

 

[tom.stoer]

@Marcus again: what would Marcus' program for 21st century physics be?

 

[marcus]

off the top of my head, without taking time to consider
(and speaking not as an expert/researcher but merely as interested observer)

1. to understand the origin of geometry

2. to understand how the combined geometry-and-matter entity arises
(why geometry responds to matter and why matter follows geometry, they must be fundamentally the same underlying thing because of this close interaction, what is this thing?)

3. what causes Newton laws and Einstein law? what are straight lines and why do light and other things go in straight lines? what is inertia?

4. to construct quantum field theory without a geometric background (because the geometry is also one of the fields---one on which the others are defined). We will understand matter fields better when the QFT of matter is backgroundless, and joined to the QFT of geometry.

5. any successful geometry-and-matter theory will explain dark matter and dark energy effects, and will explain inflation if that did in fact occur, and will describe events around the start of expansion in such a way that it makes testable predictions regarding details of the microwave sky and other observable early universe relics.

It is ridiculous of me to be numbering these as separate problems. I admit that they are all one problem. I am not very imaginative this morning, a bit like a broken vinyl record that plays the same musical phrase over and over. I'll think about this and perhaps say something else about it later.

 

[friend]

4. to construct quantum field theory without a geometric background (because the geometry is also one of the fields---one on which the others are defined). We will understand matter fields better when the QFT of matter is backgroundless, and joined to the QFT of geometry.

I'm not so sure it's possible to define QFT or particles independent of a background. For particles are defined by how they move with respect to a background. And fields are inherently defined at various points of a background. It might be more a question of how do particles properties change as the local background changes. Or how do particles interact with a changing background?

 

[tom.stoer]

1. What is the origin of space-time; what is the reason for four dimensions

2. What is the origin of the fundamental interactions; what is the reason for the standard model symmetries and its particle and field content

3. What is the nature of geometry and quantum (gauge) field theory

4.What is the reason that mathematics is the language of the universe; why are mathematical structures realized in nature

 

[Fra]

I'm not so sure it's possible to define QFT or particles independent of a background. For particles are defined by how they move with respect to a background. And fields are inherently defined at various points of a background. It might be more a question of how do particles properties change as the local background changes. Or how do particles interact with a changing background?

I don't think either we can do away with a background to measurements completely.

I think the natural solution here is to look for the "background" in the observer. And thus to do away with the background completely, is to do away with observers. But then we're also doing away with physical measurement theory. Here I disagree with Rovelli's reasoning.

As I see it, the observers is the only possible container for the background. Informationally, the only background at hand, is the observers prior information, that has resulted from evolution. Informationally, the prior information structure, is the only background we have and need.

It also gives a natural view on a geodesic. It's the path of evolution, that follows from the inside-information at hand. The system deviates from the geodesic only when forced to by new evidence along the way (which acutally causes the spacetime to deform), or because the confidence in the geodesic is so low that some random walk around the probabilistic geodesic occurs.

One specific question I ask in this direction is

How does the spacetime as we know it, emerge from the general conjectured information structure? Clearly here the matter/space issue does not lead to the question of how to unify them, the problem is rather how to separate them from their common origin - properties of a general information structure.

It is a decoding problem where the question is whay a particular decoding is to be preferred and thus considered right? I think to answer that we need to take the life of the decoder into account as well. Maybe it's simply a game where the competition selects for particular coding/decoding systems that are the effective evolving "laws of nature". Those habitants that fail to implement these specific coding simply won't live to tell about it.

Edit: To throw in a bad analogy, consider society. The laws of society, are not about true and false and right and wrong in a universal sense, they are simply a neogtiated system of rules for mutual existence. Those who follow them do well, those who don't are punished by society. Yet, it is still possible to chang the rules, but it's a slow process and it can not be done simply by breaking them. The process involves inducing motivation for change into your environment. Thus, there are then also "effective rules" for how the rules must change.

/Fredrik

 

[marcus]

I'm not so sure it's possible to define QFT or particles independent of a background...

When the QG people talk about "background independent" the technical meaning of "background" is a fixed (pseudo) Riemannian metric on a manifold or any other kind of fixed geometry.

In the sense, 1915 General Relativity is background independent. It does not start with a fixed metric.

Of course if you interpret "background" in a vague general way, then everything has a background. Everything has some kind of context. But that is not what we are talking about---I think you and I would agree on that.

All we want is something that comes up to the standard set in 1915 of being free of any fixed geometric background. So what I am wondering is why you think it might be impossible to define a quantum field theory (without first fixing a metric geometry)?

You may be right, but I don't understand why it would be impossible. GR works and is background independent, so why wouldn't one be able for example to define some fields on top of GR? (Regardless of whether it would be useful or have merit as physics, I'm just illustrating with an example.)

 

[atyy]

Random thought - if time is emergent like Rovelli and Motl hope - then shouldn't we have more background independence than GR by allowing the signature to also be dynamic (since it's the signature that makes the metric pseudo-Riemannian, which means there's spacelike and timelike vectors)?

 

[friend]

So what I am wondering is why you think it might be impossible to define a quantum field theory (without first fixing a metric geometry)?

My hesitation stems from considering that any dynamics of particles and fields usually has derivatives with respect to time and space, thus implying the existence of a background metric. But maybe I'm forgetting some way of formulating dynamics in differential geometric terms.

 

[tom.stoer]

But covariance guarantuees that you do not need a specific background metric. A metric that is itself subject to a field equation and therefore dynamical will do the job.

 

[Fra]

Of course if you interpret "background" in a vague general way, then everything has a background. Everything has some kind of context. But that is not what we are talking about---I think you and I would agree on that.

All we want is something that comes up to the standard set in 1915 of being free of any fixed geometric background. So what I am wondering is why you think it might be impossible to define a quantum field theory (without first fixing a metric geometry)?

You may be right, but I don't understand why it would be impossible. GR works and is background independent, so why wouldn't one be able for example to define some fields on top of GR? (Regardless of whether it would be useful or have merit as physics, I'm just illustrating with an example.)

I understand what you say about the LQG meaning of background independence, it is indeed more definite than the vauge general independence I associated to.

Here is a brief additional plausability argument for the quest for a general background independence.

But what I think is a good reason to keep looking for a more definite form of this general independence is that I find that it's required by consistency of reasoning if you insist on looking for an intrinsic measurement theory. To me the general background is simply the prior information of an observer. This encodes the measure and the spacetime structure from the reference in question.

The symmetry transformations that makes all observers equivalent (diff symmetry) are often given realist interpretations. I think this has no place in an intrinsic measurement theory. I mean from a scientific standpoint, and physical measurement standpoitn, what is the origin of the powerful information that there are these symmetries? Even symmetries must be inferred from real interactions, and thus the process by which this happens is more fundamental.

In the reasoning of rovelli, I don't see that he is looking for a physical measurement theory. As I see it the information he seems to make use of (say the various symmetries) represent "background information", ie information that is injected into the reasoning, without physical reason. Ie. there is a realist view of these symmetries, they are somehow not subject to questioning. This, does to me, break the intrinsic reasoning. Intrinsic processes can not make use of any external references.

To put this in some kind of current context, Smolins idea of evolving law, is one possible response to this "issue". Dreyers internal relativity is too (judging prematurely from his program description).

So I think the fact that this is currently vague, doesn't necessarily mean it's a useless or flawed idea.

/Fredrik

 

[Thomas Larsson]

My hesitation stems from considering that any dynamics of particles and fields usually has derivatives with respect to time and space, thus implying the existence of a background metric.

Derivatives only imply the existence of a smooth structure. Actually, if we only allow derivatives up to order p we only assume a C^p structure. A background metric is a stronger condition.

 

[friend]

Derivatives only imply the existence of a smooth structure. Actually, if we only allow derivatives up to order p we only assume a C^p structure. A background metric is a stronger condition.

I would think that if the Standard Model could be formulated in a background independent form or in terms of differential forms, it already would have been.

 

[Haelfix]

The entire standard model can be formulated in terms of differential forms!

 

[Adrian59]

The hope is that eventually we will have a complete nonperturbative quantum theory which leads to the standard model plus general relativity in the low energy, dimensionally reduced limit. Not only that, we would like this reduction to happen in a unique way. However, the possible ways we can dimensionally reduce the ten-dimensional string theory to four spacetime dimensions allows for many possible outcomes, so large that they are collectively known as the “string theory landscape” [10, 11]. The often quoted estimate of the number of these product theories is 10500! If the physics we observe is just one of 10500 possibilities, what of the remaining 10500 − 1 wrong ones? Why are they there? To date this is an open question. An added complication is that the well-studied portions of the landscape are far from being perfectly connected to each other."[/I]
/Fredrik

I thought it was worse than this. Hasn't the string landscape 10^500 solutions in some scenarios going up to infinite for others.

 

[Fra]

I thought it was worse than this. Hasn't the string landscape 10^500 solutions in some scenarios going up to infinite for others.

Yes that's just a scrambling during copy&paste. The ^ must have disappeared. It's 10 raised to 500.

/Fredrik

 

[Adrian59]

Thanks Fredrik for your clarification

 

[Adrian59]

2. to understand how the combined geometry-and-matter entity arises
(why geometry responds to matter and why matter follows geometry, they must be fundamentally the same underlying thing because of this close interaction, what is this thing?)

...

You have posed what I would agree is a fundamental question. One could say that Einstein’s great leap of imagination was to recognise because of the equivalence of inertial mass with gravitational mass that mass was warping space. However, to my interpretation the surprise is that this works. Einstein assumed that matter warping space created gravity & derived his general theory of relativity from this assumption so the surprise is that it works so well without a clear understanding why. As you said, Marcus, it’s this relationship between the geometry of space-time & matter that needs an explanation.