What determines the velocity of a bosonic string in string theory?

[Alamino]

I've started to study superstring now and I have a little doubt. If you consider the open string with free ends, Polchinski's book says that the ends move with the speed of light. But if the ends move this fast, as the length of the string is fixed the rest of it must have the same velocity. If it depends only on the boundary conditions, massive states of the string will have the same velocity... It should not be this way, what am I doing wrong?

 

[selfAdjoint]

What they did was to imagine the string SPINNING, so the middle was moving slower than the ends. But I think the real answer was to remove the freedom from the ends by having them fixed with Dirichlet boundary conditions to what were at first called "walls" and are now called D-branes. This was I believe the origin of the brane idea in string physics.

 

[R0man]

The velocity of a bosonic string is a fundamental concept in string theory and can be a bit confusing at first. It is important to understand that the velocity of the string is not the same as the velocity of the endpoints. The endpoints of the string are fixed and move at the speed of light due to the boundary conditions, but the rest of the string can have a different velocity.

This concept can be better understood by considering the different modes of vibration of the string. The open string with free ends has both left-moving and right-moving modes, which can have different velocities. The speed of light is the maximum velocity that any particle can travel, so the endpoint of the string must move at this speed. However, the rest of the string can have a lower velocity, depending on the specific mode of vibration.

Additionally, the velocity of a string is not a fixed value. It can change depending on the energy and momentum of the string, as well as the background spacetime it is moving through. So while the endpoints of the string may always move at the speed of light, the rest of the string can have a variable velocity depending on the circumstances.

In summary, the velocity of a bosonic string is not solely determined by the boundary conditions, but rather by the specific mode of vibration and the energy and momentum of the string. The endpoints may move at the speed of light, but the rest of the string can have a different velocity. I hope this helps clarify any confusion you may have had. Keep studying and exploring the fascinating world of superstrings!