Strings can represent?

[William Sharkey]

1. I know that string theory has many variants and is more or less invented, but I am just looking for a starting point, so it's okay if you can answer in generalities.
2. I have read that the way that a "string" vibrates determines what subatomic particle it is.
3. For example, one vibration mode might make the string act like a proton.
4. Is it possible to change the amplitude of the vibration of the string? Are vibrational amplitudes set, stepped or continuous?
5. Is string theory usually constructed so that a single string maps to a single subatomic particle? What is stopping a string from representing multiple particles, like 5 protons and and three electrons ? To take this further, could a single string represent trillions of particles, or perhaps the entire universe?
6. If there are two loops of string, but one is set spinning, does the spinning one stretch? If it stretches, is there a test/measurement that can be done to determine the direction of spinning?
7. Is there a limit to how much vibration or energy a string can have?
8. If the mater is made of vibrating strings, do events only occur when string collisions occur? Would string theory predict that the speed of flow of information depends on the rate of string collisions?
9. If a collision occurs at one point on a string, is that information transmitted instantaneously to all points on the string, or does it have to take time travel/propagate around the loop?

Edited October 9, 2010 by William Sharkey

[ajb]

I hope this goes towards an answer of some of your questions...

 

In essence the vibrational modes of a string correspond to a point-like particle. A little more correctly, one can set up a centre-of-mass momenta for a string. This corresponds to the degrees of freedom of a point-like particle. The oscillations of the string correspond to an infinite number of internal degrees of freedom. Specifying different choices here corresponds to different particles.

 

So, from the quantised string we have a Hilbert space and an infinite collection of creation and annihilation operators that act on the ground state of a string. This state is the vacuum state. Note that these operators do not create or destroy strings, they act on the state space of a single string "generating" all the particles.

[William Sharkey]

 

In essence the vibrational modes of a string correspond to a point-like particle.

 

 

 

1. Are string modes the frequencies of harmonics that the string vibrates at, like Fundamental, 2*Fundamental, 3*Fundamental etc...?
2. So strings can be defined by their frequency spectra + phase spectra + overall string positions in space?

 

So, from the quantised string we have a Hilbert space

 

1. Wouldn't it be rare that a string's spectra would only contain energy at a single frequency/mode at a time? 
2. What mechanism or constraint leads to quantization of string energy?
3. When a string is plucked on a musical instrument, I know that at the beginning, the string contains a wide band of spectral energy, but as time moves forward, the wide-band energy is corralled and settles at the harmonics of the string. Does such a phenomenon occur when strings collide, or does energy always reside in "modes"?
4. Is "quantization" an active process which throws away information in a continuous environment, or is "quantization" an informational constraint of the environment that is never really interferes with data?

[ajb]

The method of quantisation of a single string is more or less standard methods of first quantisation. (I don't like this name, but it is standard terminology). You can do this canonically or via path integrals.

 

There are plenty of good introductory books to string theory. By introductory I mean that the reader should be up to speed on modern physics like quantum mechanics and special relativity.

 

I suggest having a look at

 

BUSSTEPP Lectures on String Theory, R. Szabo, 2002, arXiv:hep-th/0207142v1.

 

As for a proper book I suggest

 

A First Course in String Theory, Barton Zwiebach , Cambridge University Press (10 Jun 2004).

 

The pair of books by Joseph Polchinski, Sting theory vol I and vol II also come highly recommended.