String Theory Query

Question

I listened to a lecture by Sean Carroll who gave a representation of "Strings" (as in string theory) by comparing them to a violin string.

He said "A violin string can vibrate in lots of different ways (being a string attached at two points) and will have a fundamental and natural overtones."

I appreciate it is an analogy for dummies like me but it leads me to ask a question.

A violin string is attached at two ends but does it really have many modes of vibration?

One could pluck it or bow it in different ways to produce different sounds, affecting the volume (loudness/amplitude) and harshness or richness of tone.

In the string theory the different modes of vibration give us different particles, right?

So, one type of vibrational mode will allow a string to function as a quark and another will create a photon. (You may be cringing by this point - sorry)

My point is that for a violin string by plucking it or bowing it we introduce a third point of interaction (not just the two attached ends anymore) and also the tone is mostly produced by the vibration of the entire instrument which is a very complex set of frequencies.

Also to produce different notes (disregarding overtones) on a violin one has to shorten or lengthen the string (changing it's length by pressing fingers down).

The question is then how complex are the vibrations of string-theory and do the strings have different lengths/thicknesses?

On a violin string there are twelve basic pure notes but there would be infinitely many microtones based on shortening or lengthening the string.

On the violin each string is the same length but different thickness giving four fundamental notes.

Therefore to get back to Sean Carroll's analogy - I realise that "Strings" are the most fundamental and basic building blocks of everything else but do they depend upon vibrating differently or thickness and length too?

Could a fundamental string be as long as a violin string provided it's other dimensions remain very tiny?

Answer 1

The strings in string theory are very different to guitar strings. They are not clamped at the ends like a guitar string. Instead they have free ends or they are formed into a loop. Also they have a fixed string tension that isn't dependent on their length.

Classically if you have a free string with a constant tension that tension would immediately make it contract to a point. However for a quantum string the Heisenberg uncertainty principle prevents it collapsing to a point just as it prevents a hydrogen atom collapsing to a point. So the quantum strings exist in a state where the tension in the string and the uncertainty principle balance out.

Because the strings are not clamped at the ends like guitar strings this means they have more vibrational modes available than guitar strings do. However they also vibrate in a nine dimensional space unlike guitar strings, which vibrate in three dimensional space. This also increases the number of vibrational modes available.

Finally, the length of a string can be arbitrarily long but it takes energy to increase the string length. It would take so much energy to increase the length to macroscopic dimensions that this is never going to happen, though I have seen suggestions that cosmic inflation could have stretched strings to macroscopic lengths during the first moments of the universe's existence.

You need to be a little cautious about claiming everything is really made up from strings. If we write down the states of a quantum string we find they naturally fall into groups that correspond to the states we get in quantum field theory, and quantum field theory is a tried and tested part of physics. Whether this means everything is actually made from little bits of string, or whether this is just a convenient mathematical model is debatable.