[quanghieuci (OP)]

hi
I am looking for some historical background on the origins of string theory. In particular the linking of scattering amplitudes to the Euler beta function which led on to the work of Leonard Susskind.

and the second question

I have been thinking about this for a while now. With quarks and electrons there has to be an amount of kinetic energy that can be defined. The velocity component cannot reach the speed of light since these particles have rest mass. An object composed of atoms that is accelerated near to the speed of light must be adding to the individual kinetic energies of all its constituent particles. Therefore there has to be an effect on the velocity of those particles to prevent them from reaching light speed. Any thoughts?

thx all!

[evan_au]

You could start here: https://en.wikipedia.org/wiki/History_of_string_theory#1968.E2.80.931974:_dual_resonance_model
The links and references should give you more information.

there has to be an effect on the velocity of those particles to prevent them from reaching light speed.

The first comment is that an electron is not really a little particle whizzing around the nucleus at nearly the speed of light.

This simplified model of an atom could make you think that an atom traveling near the speed of light would have electrons traveling at twice the speed of light.

An electron is better viewed as a little fuzzball surrounding the nucleus, which represents the probability of finding the electron at some particular location.

But even if the Sun+Planets model of the atom were correct, Einstein's addition of velocities formula ensures that the electrons don't go faster than the speed of light.

And from the viewpoint of someone traveling along with the atom, it would look perfectly normal.

[jeffreyH]

Start here.
https://en.m.wikipedia.org/wiki/Gabriele_Veneziano

[jeffreyH]

The beta function and its relationship to the gamma function can be found on wikipedia. Near the end of the article you can find out how to calculate the beta function in excel.
https://en.m.wikipedia.org/wiki/Beta_function

[jeffreyH]

For anyone wanting a no nonsense examination this is the best place.
https://brilliant.org/wiki/beta-function/