Understanding String Tension in String Theory: Explained and Debunked

[oldman]

I'm not clear why the "string tension" of string theory is so called. Perhaps folk here can help with this elementary point.

It is not really the same as the "string tension" of a musical instrument, say a guitar or a piano, although such a musical-instrument analogy is often used.

In stringed instruments tension is but one kind of internal stress in a composite object made of strings and a body. The internal stress in the string part of the instrument is tensile and is compensated for by compressive stresses in its body part (exactly if the instrument is free-standing). These internal stresses arise from distortions of the stuff of which the instrument is made, and are electromagnetic in nature. But the strings of string theory are not made of stuff that is distorted, nor are they parts of some composite object. So in its details the musical-instrument analogy breaks down.

Neither is "string tension" quite the same as a one-dimensional version of the "tension" in a liquid surface, even though surface tension has the same units as surface energy, just as "string tension" has the same units as energy per unit length. But surface tension arises because surface atoms are less strongly bound than those inside the liquid, whereas strings are thought to be one-dimensional and such distinctions don't arise. Nor are strings known to be made of smaller entities, as liquids are. So this isn't a close analogy, either, and "tension" is perhaps an inappropriate word to use.

"String tension" seems to me to be just the energy (or mass) per unit length of a one-dimensional entity; an energy which is both sufficiently large to account for quantum gravity and to make the entity shrink to Planck-scale dimensions. Is this all "string tension" is?

Finally, I don't understand why strings eventually stop shrinking. What's to stop them making like http://en.wikipedia.org/wiki/Oozlum_bird"

 

[shalayka]

The denser a violin (or supersymmetric) string, the more tension it has under unit displacement (ex: from being plucked). More density implies more mass per unit length. So, I do believe that your assumption regarding tension is correct. I wish I could be of more help at this point, sorry. I have Zwiebach's book, but I am making a slow go of it.

 

[arivero]

You guys are thinking about stress and strain tensors, are you?

 

[shalayka]

Considering that I'm obsessed with General Relativity, that's kind of a rhetorical question. I think about this in my sleep. :)

If you would like to expand on using tensors to describe the mechanics of a violin string, please be our guest. I am hesitant to do so myself, lest I lead someone astray.

 

[oldman]

The denser a violin (or supersymmetric) string, the more tension it has under unit displacement (ex: from being plucked). More density implies more mass per unit length...

I don't believe that a violin string analogy for the tension of the strings of string theory is a "sound" (ha ha) one, because a violin string is deliberately fixed in a stretched state, whereas strings can change energy/mass by expanding or contracting; they're free souls, as it were --- I was just making use of the equivalence of mass and energy here --- I still don't understand how strings stabilise at around the Planck length. I'm sorry if I was being obscure about all this. But thanks for your kind reply, shalayka. I wish you luck with the book.

You guys are thinking about stress and strain tensors, are you?

I hadn't got down to this nitty-gritty level, arivero -- I don't think anyone would invoke them in the case of strings --- they would only be relevant if strings were shown to be made out of something elastic, which doesn't seem to be a string theory proposal.