String Theory or String Formalism?

[utesfan100]

I have a few question on the nature of the body of knowledge referred to as string theory.

Is this an actual new physical theory of reality, or a new mathematical framework for expressing possible physical theories?

If it is the former, what new behaviors of the universe, beyond those of QM and GR, are anticipated? Does string theory require QM and GR, or merely allow them?

If it is the latter, what processes can be explained more concisely using string theory rather than tensor arithmetic? What level of explanatory power would a rival split-octonion representation need to achieve to rival string theory?

[Reality Check]

String theory is an existing framework trying to reconcile quantum mechanics and general relativity. It has plenty of predictions but none that are testable so far.

[utesfan100]

String theory is an existing framework trying to reconcile quantum mechanics and general relativity. It has plenty of predictions but none that are testable so far.

That looks like a vote for a new physical theory. The leading mainstream speculation.

String theory claims to aim to unify GR and QM. The linked article states that ST conforms to QM and GR (in the low energy limit, I presume to the PPN limit). It also states that ST does not provide any experimentally verifiable predictions using modern technology. Does ST make any calculations easier than using QM and GR?

[Reality Check]

That looks like a vote for a new physical theory.

It is a vote for a "new mathematical framework for expressing possible physical theories" (note the lack of testable predictions).
ST does not make make any calculations easier than using QM or GR.

[Cougar]

Is this an actual new physical theory of reality, or a new mathematical framework for expressing possible physical theories?

I am not qualified to speak authoritatively about string theory. That said, I'll tell you what I think I know.

I would lean toward the latter, since the theory must reside in a 10-dimensional setting, and it can describe 10⁵⁰⁰ different universes. Still, it seeks to explain the workings of the universe we inhabit.

If it is the former, what new behaviors of the universe, beyond those of QM and GR, are anticipated? Does string theory require QM and GR, or merely allow them?

Actually, one of the most interesting results from string theory is Maldecena's anti-deSitter/conformal field theory correspondence. As wiki notes:

An example is the duality between Type IIB string theory on AdS₅ × S⁵ space (a product of five dimensional AdS space with a five dimensional sphere) and a supersymmetric N = 4 Yang–Mills gauge theory (which is a conformal field theory) on the 4-dimensional boundary of AdS₅

[utesfan100]

So far consensus appears to lean towards:

If it is the latter, what processes can be explained more concisely using string theory rather than tensor arithmetic? [None, yet] What level of explanatory power would a rival split-octonion representation need to achieve to rival string theory?

Clearly to be consistent with observation one must agree with GR to the PPN formalism. What are the requirements for a theory to be called a quantum theory?

Is the Dirac equation enough? How about a natural closed algebra over a lattice with integer and half integer points?

[amensae]

It has plenty of predictions but none that are testable so far.

Do you mean that none of the predictions made so far are testable, or that the predictions that have been made are not yet testable?
(In message # 5 you appear to be implying the former.)

[Reality Check]

The majority of predictions that have been made are not yet testable, e.g. predict particles at > 1 TeV.
The models that have made predictions that are testable at the LHC have failed (so far).
See Testability and experimental predictions

[Selfsim]

Some tests and BAUT commentary on String Theory are here. (I attempted to create the thread to keep track of known ST tests as they develop).

Most here see String Theory more as either a very self-consistent hypothesis or as pure mathematics. We've hammered it out several times since I've been here .. here and here ..

Most of the tests I've seen so far are primarily theoretical tests.

String Theory appears to have the 'knack' of being able to produce results which align very nicely with already known observations or measurements, to certain levels of qualitative descriptiveness. Its ability to do this is probably its key feature, and it draws upon extra dimensions, AdS/CFT correspondence and Supersymmetry, to make such achievements.

Regards

[Andrew D]

Disclaimer: jargon heavy post.

String theory is the former. The mathematical framework is called "Algebraic Topology." It is similar to differential geometry, where tensors live, but the main tools are much more abstract; it describes the similarities between topological spaces which are a generalization of the metric spaces we find in differential geometry.

String theories describe universes in which natural laws are emergent from the "underlying structure" of the space. You can put a topological space into a "homology", a generalization of a "functor", which is a type of mapping between two "chain complexes" which are "chains" of "homomorphic groups" that satisfy certain axioms. The groups you get out of the homology describe the properties of the space, ie. how rotations, reflections, transformations, etc conserve or change properties of the space or of subspaces. This way you can establish relationships between different topological spaces (eg, cougar's example above) by examining relationships between the groups.

Now, as far as the question "is string theory math or physics?" Math is physics is math. The properties of mathematics are emergent from nature; with string theory we can translate physics problems into number problems or problems in a number of other fields and vice versa. You might say this is a "new behavior" of the universe.

"Easier calculations" are not the end goal. The calculations are ridiculous. A more complete picture of nature is the goal, and string theory is incredibly successful in this endeavor.

[utesfan100]

Sorry for the delay in response.

Disclaimer: jargon heavy post.

String theory is the former. The mathematical framework is called "Algebraic Topology." It is similar to differential geometry, where tensors live, but the main tools are much more abstract; it describes the similarities between topological spaces which are a generalization of the metric spaces we find in differential geometry.

String theories describe universes in which natural laws are emergent from the "underlying structure" of the space. You can put a topological space into a "homology", a generalization of a "functor", which is a type of mapping between two "chain complexes" which are "chains" of "homomorphic groups" that satisfy certain axioms. The groups you get out of the homology describe the properties of the space, ie. how rotations, reflections, transformations, etc conserve or change properties of the space or of subspaces. This way you can establish relationships between different topological spaces (eg, cougar's example above) by examining relationships between the groups.

You appear to be saying that string theory is completely defined by the fundamental units and their neighborhood. All properties of space, including dimension, are then built up from these smaller definitions.

This idea appears to be more explicitly made in holographic universe theories, where higher dimensions are viewed as forming when stresses push the universe into new dimensions. Why should a holographic universe stop at 3 physical dimensions, rather than continue to the dimension where the change in density with radius is maximized?

If we insist on integer dimensions this occurs at D=5, 5.24 if we allow Hausdorff dimensions. If we maximize the density of the surface, rather than the volume, we get D=7, or 7.24.

If physics is derived from only local effects of infinitesimal strings, why is the global structure of the universe flat
and three dimensional?

Now, as far as the question "is string theory math or physics?" Math is physics is math. The properties of mathematics are emergent from nature; with string theory we can translate physics problems into number problems or problems in a number of other fields and vice versa. You might say this is a "new behavior" of the universe.

Can you prove that "the properties of mathematics are emergent from nature?" This appears to be a philosophical paradigm of string theory, not a proven fact of nature.

Are you saying that all of set theory exists in string theory? How does one express Rustle's paradox in string theory?

"Easier calculations" are not the end goal. The calculations are ridiculous. A more complete picture of nature is the goal, and string theory is incredibly successful in this endeavor.

Name one empirical success string theory has provided, showing it has improved our picture of nature in any way.

[Andrew D]

Sorry for the delay in response.

You appear to be saying that string theory is completely defined by the fundamental units and their neighborhood. All properties of space, including dimension, are then built up from these smaller definitions.

That's quite an inference.

This idea appears to be more explicitly made in holographic universe theories, where higher dimensions are viewed as forming when stresses push the universe into new dimensions. Why should a holographic universe stop at 3 physical dimensions, rather than continue to the dimension where the change in density with radius is maximized?

What do you mean by " stresses push the universe into new dimensions"? You can't reason your way to understanding the universe with natural language; this just sounds like silliness, because it is.

If we insist on integer dimensions this occurs at D=5, 5.24 if we allow Hausdorff dimensions. If we maximize the density of the surface, rather than the volume, we get D=7, or 7.24.

How are you making these calculations? What surfaces are you describing?

If physics is derived from only local effects of infinitesimal strings, why is the global structure of the universe flat
and three dimensional?

Is it, even? I don't remember mentioning infinitesimal strings.

Can you prove that "the properties of mathematics are emergent from nature?" This appears to be a philosophical paradigm of string theory, not a proven fact of nature.

How trite. Your objection would be just as philosophical as my supposition, were it so, and unfounded. See http://en.wikipedia.org/wiki/Langlands_program. There exist mappings from structures describing numbers to structures describing nature.

Are you saying that all of set theory exists in string theory? How does one express Rustle's paradox in string theory?

No. I'm saying that the phenomena of nature are just the phenomena of numbers, and vice versa. I think you mean Russell's paradox. If a noun verbs all the nouns that don't verb themselves, then does the noun verb itself? (feel free to choose a noun and verb as you would.)

Name one empirical success string theory has provided, showing it has improved our picture of nature in any way.

It keeps laymen with no knowledge or respect for mathematical abstraction from having any clue what they are saying in a discussion of "how things really are", which is certainly entertaining, though perhaps not an "empirical success." Its success is that it allows us to discuss things we couldn't discuss otherwise, which may or may not be true, regardless of what names we give them. It allows us to address particle and gravitational phenomena in the same theory.

[utesfan100]

Thank you, everyone, for the many nuanced views expressed here. I am enjoying the diversity of opinions.

I do want to address a few points, where I was questioned directly.

What do you mean by " stresses push the universe into new dimensions"? You can't reason your way to understanding the universe with natural language; this just sounds like silliness, because it is.

This is my understanding of what the Holographic principle is stating. Our third dimension is a projection from a two-dimensional surface. Why not project to higher dimensions?

How are you making these calculations? What surfaces are you describing?

This is the ratio of a hyper-sphere to a hyper-cube in the given dimension, or the surface of a hyper-sphere to a hyper-cube of one less dimension.
http://en.wikipedia.org/wiki/N-sphere

Is it, even? I don't remember mentioning infinitesimal strings.

My understanding of string theory is that physics, including space-time, is derived from the local interactions of strings small enough to be treated as infinitesimal in our every day existence. Is this in error?

How trite. Your objection would be just as philosophical as my supposition, were it so, and unfounded. See http://en.wikipedia.org/wiki/Langlands_program. There exist mappings from structures describing numbers to structures describing nature.

The difference is that I raised my objection as a possibility that should be excluded, where your point was stated as fact.

Mathematics is far richer than the Peano axioms describing numbers.

No. I'm saying that the phenomena of nature are just the phenomena of numbers, and vice versa. I think you mean Russell's paradox. If a noun verbs all the nouns that don't verb themselves, then does the noun verb itself? (feel free to choose a noun and verb as you would.)

Express "There is no set of all sets that do not contain themselves" in physics. This is a mathematical fact. If physics embodies all math, this should be expressible as a physical law.

It keeps laymen with no knowledge or respect for mathematical abstraction from having any clue what they are saying in a discussion of "how things really are", which is certainly entertaining, though perhaps not an "empirical success." Its success is that it allows us to discuss things we couldn't discuss otherwise, which may or may not be true, regardless of what names we give them. It allows us to address particle and gravitational phenomena in the same theory.

String theory certainly obfuscates our understanding to a point that alienates the uninitiated, giving its practitioners the illusion of a superior understanding that may turn out to be an overly complex fools errand.

Other than the hypothetical strings of the theory, I don't see anything in string theory that can't be discussed without it. We regularly address particles and gravitational phenomena using perturbation methods in the weak field limit sufficiently for all empirical results obtainable by state of the art equipment.

[swampyankee]

Currently, I would say that string theory does not qualify as a theory, but only as a hypothesis: it's not been subject to repeated, rigorous experimental verification. In other words, calling it "string theory" is the sort of abuse of the scientific term theory that results in creationists saying "...it's only a theory."

No experimental verification => not a theory.

[Andrew D]

It's semantic. String theory is a "a self-contained formal mathematical system" and thus a "theory," like "Ring theory" is a theory.

[noncryptic]

a "a self-contained formal mathematical system" and thus a "theory,"

Yet it is at least a distinctly different sort of theory than quantum theory and GR, in that it is purely mathematical and perhaps more importantly, none of the predictions that it makes has been verified by observation. It seems to me it does not conform to the definition of scientific theory.

[Andrew D]

Yet it is at least a distinctly different sort of theory than quantum theory and GR, in that it is purely mathematical and perhaps more importantly, none of the predictions that it makes has been verified by observation. It seems to me it does not conform to the definition of scientific theory.

Of course.

[swampyankee]

It's semantic. String theory is a "a self-contained formal mathematical system" and thus a "theory," like "Ring theory" is a theory.

Exactly; it's a question of semantics: "self-contained formal mathematical system" is not sufficient for something to be a scientific theory. In addition to being internally consistent, it has to demonstrate, empirically, that it's consistent with reality. Without that step, it's just mathematical games.

[Andrew D]

Exactly; it's a question of semantics: "self-contained formal mathematical system" is not sufficient for something to be a scientific theory. In addition to being internally consistent, it has to demonstrate, empirically, that it's consistent with reality. Without that step, it's just mathematical games.

Why not say "Without that step, it's just a mathematical theory"? Then your post wouldn't have been offensive at all, but just correct. Don't forget that the name "imaginary number" was introduced pejoratively into language by René Descartes. He was right, no? They are completely useless in real science.

get it? real science?

You're trying to empirically draw ontological conclusions about something which very few people actually understand, maybe none.

[swampyankee]

Why not say "Without that step, it's just a mathematical theory"? Then your post wouldn't have been offensive at all, but just correct. Don't forget that the name "imaginary number" was introduced pejoratively into language by René Descartes. He was right, no? They are completely useless in real science.

get it? real science?

You're trying to empirically draw ontological conclusions about something which very few people actually understand, maybe none.

Descartes is good company to be placed into. If you're saying that string theory is a mathematical tool being used by some theoretical physicists, that's fine, but that's not how it's being portrayed, even by some of the physicists involved. As for imaginary numbers, I use them all the time, as I still solve ODE and, on rare occasion, PDE. They're a nice tool, in the same category as real numbers, wrenches, and Lagrangians; they are one of the useful tools from mathematics. String theory is not, currently, being touted as a mathematical theory, but as a scientific one; as such it has to meet the criteria for a scientific theory. It doesn't.

I'm not arguing about its validity as a scientific hypothesis, as it does seem to successfully eliminate or explain the contradictions between QM and GR that occur at extreme conditions, such as those near a singularity, and it doesn't require the sort of appeal to supernatural authority that ID or creationism are based on.

[mutleyeng]

ive heard Brian Greene say the same thing many times

[noncryptic]

That it is called theory anyway is more out of habit (the term was used early on in the popular press and it stuck) than because it actually is a theory. Indeed it is more a hypothesis than a theory. (which means theory has not gone ahead of observation).

If i recall correctly, in the documentary "The Elegant Universe" Witten and others do acknowledge as much.

[swampyankee]

That it is called theory anyway is more out of habit (the term was used early on in the popular press and it stuck) than because it actually is a theory. Indeed it is more a hypothesis than a theory. (which means theory has not gone ahead of observation).

If i recall correctly, in the documentary "The Elegant Universe" Witten and others do acknowledge as much.

That's all well and good, but the term "string theory" still confuses the non-scientific among us. Since I'm trying to teach high school science, it's especially confusing for the students "well, they call string theory a theory, but the Nobel-prize winning scientists are abusing the definition your high school teacher is giving you."

Please, at least in things written by scientists, science writers, and school teachers, let's eschew the term "string theory."

[noncryptic]

swampyankee,

I'm in complete agreement.
And the term "string theory" is not the only case.

The popular press plays its part in this, but scientists talking to the popular press are also a cause.
In science often every-day words are used in specific meanings, either formally or informally. Scientists who talk amongst themselves know what they mean because they spend all day on it, but many seem to be insufficiently aware that without explanation of the specific meanings, those words/statements might mean something different to laypersons than they do to scientists.

[Andrew D]

Peano: Hey Tortoise, if I had one apple in a bucket, and I'm dropping another one apple in, how many apples will be in the bucket?

Tortoise: Two apples?

Peano: Hmmm. It appears that my mathematical prediction of two apples, which I arrived at using the mathematics of numbers, is consistent with reality. Tortoise, you're on to something.

Tortoise: Can I have those apples now?

[Selfsim]

Well, I find the last few posts preceding this one, most unfortunate.

String Theory reaches deeply into fundamental physics in ways which don't reveal themselves easily to many amateur skillsets. I have been quietly following this thread, as I find the delicately poised status of String Theory in Physical Science, to be a major challenge when it comes to conducting discussions such as this, in public fora.

Personally, I am also of the view that String Theory represents a relatively new type of approach in theoretical science, which I think we're going to see a lot more of, in the immediate future.

The portrayal of String Theory in the public media is usually carefully couched in terms such as: 'if this is right .. then…' or, 'if this is the way the universe works … then ...', etc, etc.

Perhaps we should sensitise our critical thinking perceptions to the more subtle context in such presentations, and mimic a similar communications approach in future discussions about ST (??)

Regards

[Andrew D]

That earns an infraction for rudeness.

...it's just mathematical games.

And that doesn't? I happen to put food in my fridge by teaching abstract "games" to future scientists and engineers. This forum is backwards. Go ahead and just ban me, I have no desire to participate any longer. Have fun trying to see the big picture through your pinhole; I'll come back and let you know when some fool who wastes his time just playing games has news on which direction you should look.

I'm going to go hang out with Dr. Rocket.

[syzygy42]

That's all well and good, but the term "string theory" still confuses the non-scientific among us. Since I'm trying to teach high school science, it's especially confusing for the students "well, they call string theory a theory, but the Nobel-prize winning scientists are abusing the definition your high school teacher is giving you."

Please, at least in things written by scientists, science writers, and school teachers, let's eschew the term "string theory."

I can appreciate your confusion. As a basic researcher in molecular biology, perhaps I can provide a behind the scenes perspective. In all my years, I cannot recall one discussion as to whether a conceptual framework represented a theory according to the scientific philosophy of Popper. Over time, names for conceptual frameworks, models, and phenomena were coined and adopted by the community, becoming part of the language members of the scientific community used to communicate with one another. I am not sure how the term "string theory" came into use, but a quick Google ngram search shows that the term came into use around 1980. With 30+ years of use, it's not going to go away any time soon.

Perhaps, you can use it to teach your students the difference between the colloquial use of the word theory, and the strict use of the term in Karl Popper's philosophy. In the latter, it has meaning that is much more than a simple definition can embody. One has to work through Popper's argument to gain a deeper understanding of his philosophy of science. In the long run for your students, it's more important to understand how science functions to deepen our understanding of nature than to merely be able to repeat a recipe.

How does one learn science? Science is an activity that encompasses much more than the physical performance of an experiment. A necessary complement to experiment is the development of a model to test. This is an activity that begins by taking observations and turning them into abstract concepts that can be mentally manipulated. In fact, the only way that one comes to understand a concept is through mental manipulation, specifically, gedanken experiments. You continually test your model for consistency internally and externally with known observations. Bash your model until it breaks. When it does, you have learned something new and can refine your concept. This practice allows you to then look elsewhere to recognize patterns in observations and in other related concepts. Learning science is then a continuous activity of model building. I think it was Feynman who said that science is imagination in a straightjacket. The straitjacket is the scientific method that functions as a check to make sure that you are not fooling yourself. Imagination is the internal creation of a conceptual model, and the various disciplines of science are collections of models that are continuously being tested and extended.

Unfortunately, the science curriculum that most people are exposed to consists of a presentation fully formed, usually simplified, models with only a tenuous connection as to how they were developed. Moreover, exams primarily test "knowledge" in the form of recitation of facts and figures. It's therefore not surprising that students and the public at large perceive science as an activity of accumulating facts. One only needs to see the furor caused by Pluto becoming an ex-planet to see this fact-based understanding at work. Pluto is still Pluto, an interesting object regardless of whatever name is attached to it. The New Horizons probe will tell us a lot about the outer solar system and help to shape our models about how the solar system formed. No doubt, it must be confusing to many when old models are modified and new ones are formed. How can so many of the facts one learns in high school and college turn out to be wrong or incomplete just a few years later?

I return to the discussion of string theory in the context of the above discussion. It is a model system that is under construction. It can be seen as one in a line of models that extend back to the beginnings of quantum mechanics and general relativity. It is incomplete and has its problems. Will it blossom into a fully functional scientific theory in the Popperian sense? Nobody knows. Yet it has provided inspiration and application in pure mathematics and several areas of physics outside of gravity and particle physics. It can also be seen as a theory based upon Hilbert's program of grounding physics on a rigorous axiom-based formalism. As such, it is a theory of both mathematics and physics. Indeed, Ed Witten received a Fields Medal for his work in mathematical physics.

Physics was always a source of stimulus and inspiration for Mathematics so that Mathematical Physics is a legitimate part of Mathematics. -- Ludwig Faddeev (1990) Address describing Witten's work at the award session.

You also said

Originally Posted by swampyankee

Exactly; it's a question of semantics: "self-contained formal mathematical system" is not sufficient for something to be a scientific theory. In addition to being internally consistent, it has to demonstrate, empirically, that it's consistent with reality. Without that step, it's just mathematical games

.

Here, I would disagree with the connotation of "just mathematical games". It is such mathematical or conceptual play that is required to keep science progressing. Play is essential to model building, and models such as string theory will be essential once the Higgs particle is firmly identified (probably). Beyond that, the Standard Model is silent. We shall have to wait and see what emerges from these and other investigations. One thing that I can predict is that we will be surprised.

Cheers