I have been mulling over the idea of the oft-quoted 'prohibition' on particles travelling 'faster than light'. While this is often mentioned in the media and even in physics books, it rarely explains exactly what is meant by that, or precisely what laws of nature form the basis of the 'prohibition'. The media usually say that it is prohibited by 'relativity', but that is vague and not at all helpful. An example of a type of 'prohibition' is SR's rule for velocity composition: s = (u+c)/(1+uv/c2), where u is the velocity of observer A relative to observer B, v is the velocity of an object X relative to observer A and s is X's velocity relative to observer B. In this case, provided u,v<c we will also have s<c. After a fair bit of reflection I have reached a tentative idea that perhaps what 'relativity' says is that no particle can have a spacelike four velocity (ie g(v,v)>0). I like that characterisation of the 'prohibition' because it is coordinate-independent and seems to be consistent with what I understand about physics. It also avoids conflict with observations such as the superluminal recession of distant galaxies. But I have no idea whether that 'law', which I just made up and have never seen written down, is really what GR (or SR) says. So my questions are: 1. When we say nothing can travel faster than light, are we really saying that no particle can have a space-like four-velocity? If not that, then what is the best characterisation of this 'law'. 2. How does this rule follow from the postulates of GR? 3. What about the additional rule that no massive particle can have a light-like four-velocity? (g(v,v)=0). Does that also follow from the postulates of GR? How?