Something I don't understand about String Theory

[Liger20]

Hello, I have read a few books on the subject of String theory, including The Elegant Universe and Fabric of the Cosmos by Brian Greene (that guy is AWESOME!). Anyway, Mr. Greene may have answered my questions somewhere in his books, but the other day, I heard someone say that strings are tiny vibrating strands of energy. Correct me if I'm wrong, but isn't everything in the universe, including energy supposed to be made up of strings, according to this theory? So, if I'm right in saying that, there seems to be a paradox here. How can strings be pure energy if they make up energy?

 

[BenTheMan]

I think that the statement is ``Everything is made of energy, including strings.'' Or, perhaps, ``Strings are made of energy, electrons are made of strings. Therefore electrons are made of energy.'' A==B, B==C, therefore A==C.

Sorry if this wasn't the profound answer you were looking for :)

 

[Liger20]

Hmmm...that makes sense. Although if it's true, doesn't it mean that our whole definition of energy is rendered obsolete since a string is composed of energy and nobody knows what makes up strings since they're fundamental?

 

[BenTheMan]

I don't think so. Before you read ``Elegant Universe'' and knew anything about string theory, were you ok with the notion of electrons being made out of energy? If so, then nothing has changed :)

 

[Liger20]

Hmmmmm...yes that is a good point. But still, I always thought that strings made up fermions (matter particles) and bosons (force particles) and bosons were considered energy and a string was simply a fundamental particle that made up both of them depending on their vibration configurations. What is really going on here?

 

[BenTheMan]

Well the different ``configurations'' of strings can make up bosons or fermions.

And if bosons are energy, what about heat? Or sound. You can have heat energy or sound energy right?

 

[Demystifier]

According to string theory, strings are fundamental entities. By being fundamental, they are not made of something else (such as energy). Instead, they possesses energy as one of its properties. More precisely, energy of a string is determined by its shape and velocity, which, of course, are easily conceivable properties of a string.

In more conventional theories which assume that particles or fields (rather than strings) are fundamental entities, the same can be said for particles or fields. (Of course, particles do not have a shape.)

 

[arivero]

It'ld be interesting to track how the concept of "made of energy" appears. Probably it comes from some interpretation of Einstein work. Before E=mc2, the concept of Energy was still a secondary object, near of its original definition as "ability to produce Work".

In a comment to my post at Dorigo's blog, Kea has recalled some old say of Heisenberg (It should be nice to have the exact reference), about the concept of fundamental being meaningless in quantum field theory, as particles can disintegrate into others. On the other hand, a string can not disintegrate except into another modes of the same string.

 

[Demystifier]

It'ld be interesting to track how the concept of "made of energy" appears. Probably it comes from some interpretation of Einstein work. Before E=mc2, the concept of Energy was still a secondary object, near of its original definition as "ability to produce Work".

I would say that the Einstein work has not changed the concept of energy, but of mass. Now mass is also a kind of "ability to produce work".

 

[Demystifier]

On the other hand, a string can not disintegrate except into another modes of the same string.

That is not strictly true. Namely, a string can split into two or more strings. Even a classical string can do that:
http://xxx.lanl.gov/abs/hep-th/9502049
But, if you define a single string as ANY function of the form
[tex]X^{\mu}(\sigma,\tau)[/tex]
including discontinuous functions as well, then a splitted string can also be thought of as a single string.

 

[Fra]

Like Demystifier also wrote: If you consider the general question of any distinguishable "structure" or "object", wether we call it string, point or anything else, energy is best throught of as a property of the object, and since usually any object is described in terms of it's properties, the object and it's properties are inseparable. To give a description of what an object is, independent of it's properties really makes no sense. The set of distinguishable properties IS the best description of the object we have.

I personally think of energy as a measure of an objects relative significance or potential influence in a particular sense. An object with zero energy is insignificant, while a high energy object has the potential to have a much higher impact on your state of information.

I think it may be possible to give a information theoretic meaning of energy as a measure of relational capacity that therefore bounds entropies. I have been fascinated by the speculative entropy bounds and it's relations to mass and area, and I think there is some deeper stuff in there yet to be uncovered.

Any observer in my thinking must have en information equivalent of "energy" or storage capacity, which limits it's impact on the environment, and also provides intertia to resist impacts.

An interesting question is the unification of memory capacity of an observer vs maximum information capacity of a physical object. There is seemingly interesting relations between storage capacity, information capacity limits of uncertainty as well as physical mass and energy.

I don't think we understand all this quite yet.

/Fredrik

 

[arivero]

That is not strictly true. Namely, a string can split into two or more strings. Even a classical string can do that:
http://xxx.lanl.gov/abs/hep-th/9502049

Hey, thank very much! I am interested on results on string decay rates... the idea being to investigate if it could be possible to explain the equality of reduced decay widths of composite bosons and elementary ones (ej pion, J/Psi and Z0) by reinterpretation as open and closed versions of the same string.

But, if you define a single string as ANY function of the form
[tex]X^{\mu}(\sigma,\tau)[/tex]
including discontinuous functions as well, then a splitted string can also be thought of as a single string.

Yes, that is a point. But most importantly, it implies that all the sheet pieces of the worldsheet are solution of the same dynamical equations, so also in this sense it can be say that the splitted strings are of the same kind that the original one.

 

[BenTheMan]

According to string theory, strings are fundamental entities. By being fundamental, they are not made of something else (such as energy). Instead, they possesses energy as one of its properties. More precisely, energy of a string is determined by its shape and velocity, which, of course, are easily conceivable properties of a string.

In more conventional theories which assume that particles or fields (rather than strings) are fundamental entities, the same can be said for particles or fields. (Of course, particles do not have a shape.)

I guess the proper statement is that, for example, a photon is an excitation of an electromagnetic field, and that excitation costs some energy to make. Liger is referring to the ``tiny vibrating bands of pure energy'' description that Brian Greene uses, I think.

 

[Demystifier]

I guess the proper statement is that, for example, an electron is an excitation of an electromagnetic field, and that excitation costs some energy to make.

You mean photon (not electron) I guess.

 

[javierR]

That is not strictly true. Namely, a string can split into two or more strings. Even a classical string can do that:
http://xxx.lanl.gov/abs/hep-th/9502049
But, if you define a single string as ANY function of the form
[tex]X^{\mu}(\sigma,\tau)[/tex]
including discontinuous functions as well, then a splitted string can also be thought of as a single string.

Well, string theory (in contrast to string field theory) does not a priori include string splitting or other interactions; just as in relativistic quantum mechanics (sometimes called the "first quantized" framework), you must include the processes of splitting and other interactions with other strings "by hand". The string interaction diagrams are then smooth 2-dimensional surfaces (described by the functions mentioned above), one for each genus ("number of holes" in the surface). You wouldn't say there is one string in a decay just because it's described by a single surface, e.g., just as you wouldn't in a particle decay that is diagrammed as a single connected graph (though, there is only one type of fundamental string). Anyway, as has already been covered here, in string theory the idea is that strings (or the string field) are to be fundamental objects as elementary particles (or quantum fields) were considered.

 

[marcus]

According to string theory, strings are fundamental entities. By being fundamental, they are not made of something else (such as energy). Instead, they possesses energy as one of its properties. More precisely, energy of a string is determined by its shape and velocity, which, of course, are easily conceivable properties of a string.

Demy, thanks for clearing that up. I can't imagine how Brian Greene or anyone else would say strings are "tiny vibrating strands of energy" except drunk at a cocktail party. But that leaves open the question
What is space made of?

Strings are fundamental, not made of anything, but they are in space. They can't vibrate unless space has some metric (geometric) properties. So what is geometry made of? Is space made of strings too?

 

[josh1]

What is mass, and in particular, what do we mean when we talk about the mass and spin of an elementary particle? Well, mass and spin simply label the irreducible representations of the Lorentz group under which the mathematical objects describing the particles transform. What is energy? Well, energy is defined to be the property that is conserved in a system when it is invariant under translations in time. What is momentum? It is the property that is conserved when a system is invariant under translations in space. The point is that on the most fundamental level, we can only think about these properties relative to a specific mathematical description of our universe. This is simply the best we can do. Of course we can talk about such properties in more qualitative or descriptive terms as people are trying to in this thread, but this is just imagery, which of course can be very useful, but it is still just imagery.

Strings are fundamental, not made of anything, but they are in space. They can't vibrate unless space has some metric (geometric) properties. So what is geometry made of? Is space made of strings too?

Einstein said that the geometry of spacetime is just the large-structural property of the gravitational field. At very high energies, these structural properties as they’re described by the gravitational field equations of General Relativity break down and we need to understand gravity in a way that goes beyond classical physics. In lqg we have the idea of a spin-network and in string theory the quantum of the gravitational field is a string, as are all the quanta of the four known fundamental interactions according to string theory.

We also need to understand how high energy gravitational fields congeal at lower energies to once again yield solutions of the Einstein equations, i.e., a geometrical description of the gravitational field. String theory is a clear success in this regard, but the situation with lqg etc is not so clear, which is a bit odd since lqg provides a description of the gravitational field which even at high energies has a simple geometrical interpretation. On the other hand, whether or not nature requires a background-independent description of gravity is an open question. It ‘s difficult to see how such a formulation wouldn’t be required, but who knows? I don’t think there are many people who believe such a description will ever prove to be unnecessary.

 

[Demystifier]

Demy, thanks for clearing that up. I can't imagine how Brian Greene or anyone else would say strings are "tiny vibrating strands of energy" except drunk at a cocktail party. But that leaves open the question
What is space made of?

Strings are fundamental, not made of anything, but they are in space. They can't vibrate unless space has some metric (geometric) properties. So what is geometry made of? Is space made of strings too?

In the usual formulation of string theory, space is assumed to exist independently of the existence of strings. Gravity is just like any other force acting in space. The a priori metric is fixed (usually taken to be flat), but at low energies gravity acts as if the effective metric was curved in a dynamic manner. This, of course, makes string theory background dependent, which, indeed, may be thought of as a drawback of the usual formulation of string theory. But no theory is perfect, of course. But I guess that you already knew that.

 

[Fra]

It seems one major difference between opinions here is what significance/relevance is assigned to this "drawback".

Is it insignificant enough to be waved away, or is it significant enough to demand a resolution, that is the question.

I think some common defense of ignoring this, is that it's hard to get around it. How would you actully construct something truly background independent? Is it even possible? That's a fair point, and certainly if we don't see any other way, then, any way is what we've got to try.

And how much effort does one invest is solving this problem, when there might be easier problems to solve, that at least in the short run gives more "results" albeit possibly "skewed"?

/Fredrik

 

[Demystifier]

How would you actully construct something truly background independent? Is it even possible?

Let me note that LQG (as well as classical Einstein gravity) in the usual formulation does not need a background metric, but does need a background topological space (manifold).

By the way, does anybody know the answer to the following question?:
Are there classical solutions of the Einstein equation in which the signature of the metric changes (say from +--- to ----)?

 

[Fra]

Let me note that LQG (as well as classical Einstein gravity) in the usual formulation does not need a background metric, but does need a background topological space (manifold).

Yes, actually my question was more rethorical :) since it seems not everyone thinks background independence makes sense, even though I do. Perhaps someone will want to argue why a background doesn't NOT make sense?

Usually there are also various degrees of background independence, just like you indicate. This is often another argument I've seen. Ie. people argue that a completely background independend method is hard to find.

A straight background metric is quite obvious, but other background "structures" is still annoying IMO.

As for the actual spacetime metric, I personally think of this should be looked for as emergent structure, sort of along the ideas of information geometry, where minimum action principles are associated with minimum uncertainty principles. But I'd expect the topology and dimensionality can also also be emergent. I think these things are probably very fundamental and need to be understood. I make strong associations with the emergence of these structures, to a learning logic. There may be no initial preconception, and when you start interacting, perhaps there is a logic behind how your perception is formed. Some conceptual framworks are simply more likely to survive.

/Fredrik

 

[Fra]

Ultimately I see as one of the the main problem with the reasoning along the lines "some conceptual framworks are more likely", is exactly how to define the implied probability space. It's easy to end up considering imaginary spaces that again introduces background structures. This is why I like to introduce an alternative probability formalism which uses the concept of estimated probability space, which seems to be very natural in learning. The basic quest is to generate stability, when there is not background reference anywhere. so it must somehow be selfsupporting and adapt ot be self-preserving. Just like life itself!

/Fredrik