I may have poorly titled this post, since the lecture I'm talking about isn't just about tachyons, really. What I'm referring to is what Leonard Susskind says between the 50-60 minute mark: http://www.youtube.com/watch?v=gCyImLu0HSI&feature=youtu.be&t=46m30s In the video, Susskind concludes that there are the only two polarization states of the first excited state of the open string, so then this string must be massless, like a photon. For this to happen, the ground state must have a negative mass squared. Why must [tex]m_0^2 +1 =0[/tex] and how do we know that the a's and the b's represent the only two polarization states? I understand that if there are only two polarization states, then the particle must be massless to preserve Lorentz invariance, but the rest is confusing to me. Can someone clear this up for me? I have no formal exposure to QM (and I apologize for this); regardless, I will try to decipher any technical answer given. Thanks so much.