# String mass and relativity

1. Sep 3, 2004

### Mike2

I have two questions about how the mass of the string might change due to relativistic effects. As I understand it, the mass of fermions is determined by the amplitude and frequency of vibrations of strings. The greater the frequency, the greater the mass. Also in special relativity, time slows down as you approach the speed of light. So frequencies slow near c. Clock run slower. Also in general relativity, again, time slows down near heavy objects, or in other words, frequencies get faster as you move away from heavy objects.

If this is so, then question one is: Wouldn't the vibration frequency of strings slow down as a string approaches the speed of light. And wouldn't this mean that mass (string frequency) approach zero near c? And question two: Wouldn't the frequency of strings (and thus the mass of objects) tend to increase as it moves out of a gravitational well? This latter question might be the explanation for effects attributed to dark matter and dark energy. But I will save that discussion for after my premises are confirmed.

I've looked in Zwiebach's new book and in Hatfield's introduction to QFT of points and string. Neither book seems to address this question, though I may not have looked carefully enough. Yet this does seem to be a fundamental question that should be asked. So I do appreciate any insight you might have in this area. Thanks.

Mike

2. Sep 7, 2004

### Mike2

Some have suggested that the mass of a string, like the energy of particles in a well, will depend not on the frequency but on the mode of vibration - on the eigenvalue derived from the diff eqs involved. If that is the case, then eigenvalues, or mode number, or number of nodes would not change with a Lorentz transformation. So the question is whether the mass of a superstring depend on frequency or mode number.