$$\require{cancel}$$
We have seen in section 3.3 that no continuous process of acceleration can boost a material object to $$c$$. That is, the subluminal (slower than light) nature of a electron or a person is a fundamental feature of its identity and can never be changed. Einstein can never get on his motorcycle and drive at $$c$$ as he imagined when he was a young man, so we material beings can never see the world from a frame of reference that travels at $$c$$.
Our universe does, however, contain ingredients such as light rays, gluons, and gravitational waves that travel at $$c$$, so we might wonder whether these things could be put together to form observers who do move at $$c$$. But this is not possible according to special relativity, because if we let $$v$$ approach infinity, extrapolation of figure 3.3.1  shows that the Lorentz transformation would compress all of spacetime onto the light cone, reducing its number of dimensions by $$1$$. Distinct points would be merged, which would make it impossible to use this frame to describe the same phenomena that a subluminal observer could describe. That is, the transformation would not be one-to-one, and this is unacceptable physically.