Monday, September 8, 2008

String Theory and the Size of Fundamental Particles

A reader of String Theory Demystified recently emailed me a question on the size of fundamental particles. I thought I would state the question here because it may be a point of confusion for other readers:

I'm in Chapter 2 of String Theory and enjoying it very much thus far. But I have a fundamental misunderstanding. Fundamental particles are supposed to be strings according to the text. But strings are of Planck scale length [10**(-35) m], which is twenty orders of magnitude smaller than fundamental particles. So how can strings & particles be one in the same? Does that mean it takes on the order of 10**(20) strings to make a particle?

The answer to this question is no. A fundamental particle, like an electron-is a string. Moreover its a single string. In the standard model, the fundamental particles which include electrons and quarks are point particles-they have zero extension in space. Think of a string as having a tiny bit of extension along one direction.

The scale he is referring to is a composite system. Let's take for example, the Bohr model of the atom. So, the size of an atom is often quoted as about 0.3 nm (nanometers). But what this value quotes is not the size of any fundamental particle, but is rather an average estimate for the radius of the electron orbit about the nucleus.

Now a proton or neutron is not a fundamental particle. Its a bound state of three quarks. The size of a proton or neutron is the boundary within which the quarks are trapped so to speak. It is this size which is compared to the Planck length to give the 20 orders of magnitude.


steve said...

I asked the original question cited above, and now I have another for Dr. McMahon. On pp.9-10 of String Theory Demystified you note that replacing a point particle with a 1-D string helps avoid infinities in the calculations. And you appeal to the uncertainty relation involving position & momentum. Could one use a similar line of argument to say that time should be restricted to a finite minimum size as well ("time strings") by appeal to the energy-time uncertainty relation? Whys should only the spatial components have string-like characteristics, and not the time dimension? Thanks in advance.

GNH said...

I don't think that is necessary for the basic ideas of the theory, extension in space gets rid of the gravitational infinities. That being said, people have explored modified uncertainty relations involving time, including a proposal that delta_x * delta_t >= ls^2 where ls is the fundamental length scale. But I don't know if this introduces any concept of a "time string" as you describe it. I will post a link to a paper that discusses this, but note that is very advanced.