# Size of strings in string theory

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In summary, In 10 dimensional space time, the states of M theory should have width. However, it is not clear if fermionic states of the superstring of the same size have the same width as the bosonic states.

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Quite a long time ago, I read about length of strings in string theory. And, if I remember correctly, expected length was in light years. I looked at Wikipedia today, and I see currently expected length of string is very small, around Plank size.
Is it changed over time, or the expected length was from start of the theory and I simply read something wrong?

Ans said:

Sounds like it.

ohwilleke and arivero
Thanks!
And what about width of strings? Are they one dimensional or they expected to have non zero width?

Ans said:
Quite a long time ago, I read about length of strings in string theory. And, if I remember correctly, expected length was in light years.
Maybe you were reading about "cosmic strings". A web search will give you lots of hits. Here's a randomly found article from 10 years ago. The introduction gives an overview. Read past the introduction at your own risk.

ohwilleke
Ans said:
And what about width of strings? Are they one dimensional or they expected to have non zero width?
For some reason, no one answered you. I'm not an expert on strings, but as the name suggests, a string is a one-dimensional object that has no width. However, most likely, it is meant that it has no width in the Minkowski space, and in extra dimensions, variants with the dimension of the string itself are possible. Let the experts answer.

And I have an additional question. If the strings were one-dimensional in the augmented Minkowski space, how fair would it be to interpret the string as a one-dimensional topological singularity of a vector field given in this space? By the topological feature of a vector field I mean the closure of the streamline of a vector field.

bayakiv said:
By the topological feature of a vector field I mean the closure of the streamline of a vector field.
A simple example. Suppose we have a vector field on an infinite cylinder, whose streamlines are helical lines of the cylinder. Then it will be a vector field without topological singularities. But if we deform the vector field (and with it its streamlines) so that in some areas of the cylinder the helical streamlines are transformed into circles homeomorphic to the defining circle of the cylinder, then we will have a vector field with topological singularities. In this regard, the question arises as to how justified the expectation of the identity of the topological features of the vector field and strings. And in general, is not string theory a disguised theory of aether?

Ans said:
Thanks!
And what about width of strings? Are they one dimensional or they expected to have non zero width?
hmm The states of M theory should have width when seen in 10 dimensional space time, shouldn't them

And while we are in the topic... are fermionic states of the superstring of the same size that the bosonic states?

arivero said:
And while we are in the topic... are fermionic states of the superstring of the same size that the bosonic states?
If the augmented Minkowski space is endowed with a pseudo-Euclidean metric, then the analogy of bosonic states with zero mass and strings with zero length, respectively, fermionic states and strings with nonzero length suggests itself. For example, if it is a torus endowed with a pseudo-Euclidean metric, then the defining circle will have zero length, and the torus (2,3) -node (trefoil) will have nonzero length.

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bayakiv said:
bosonic states with zero mass and strings with zero length, respectively, fermionic states and strings with nonzero length suggests itself
well, perhaps it is better to compare same mass, ie, susy partners. Curiously, I had thought differently: bosons can make classical fields so long-range forces, fermions can not. So a bosonic state could be non zero length while a fermionic should be zero.

arivero said:
Curiously, I had thought differently: bosons can make classical fields so long-range forces, fermions can not. So a bosonic state could be non zero length while a fermionic should be zero.
On the contrary, fermions create long-range classical fields, and bosons are quantum fields obtained as a result of compactification of the classical field. If we turn to my example with the vector field of a torus (or cylinder), then the classical field there is a twist of helical streamlines without violating their topology, and a boson is a single twist (local full revolution) of a helical streamline.

Not obvious that the width of a string is well defined and the open string v. closed string cases would influence what definition might make sense to describe the width of a string. A closed string theory probably would have a meaningful way to define a string width, an open string case might not.

@ ohwilleke,
From your explanation, I realized that string theory does not have a clear and precise definition of the width of a string, but in principle, string theory does not exclude the two-dimensionality of a string. In that case, let me note that the topological feature of a vector field can also be multidimensional. For illustration, one can imagine a pair of vortex vector fields (given in different planes of the Cartesian product) at a point in 4-dimensional space, a singularity of which can have a 2-torus topology.

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