Energy?

  In a chapter of a book, the author gives this relation for a
  system with mass m = 0:

E^2/c^2 = p^"3-vector" * p^"3-vector"

  . Then he writes, "This implies that either there is no particle
  at all, E = 0, or we have a particle, E <> 0, and therefore
  p^'3-vector' <> 0.".

  So, his intention is to kind of prove that a particle without mass
  must have momentum.

  But I wonder: Does "E = 0" really mean, "there is no particle."?

  300 years ago, folks would have said, "m = 0" means that there is
  no particle! Today, we know that there are particles with no mass.

  Can we be confident that "E = 0" means "no particle", or could there
  be a particle with "E = 0"?

  Here's the Unicode:

E²/c² = p⃗ · p⃗

  and

|This implies that either there is no particle at all, E = 0, or we
|have a particle, E ≠ 0, and therefore p⃗ ≠ 0.