Meaning of Negative Energy

I feel that negative energy only comes up when it is compared to a reference point (e.g. gravitational potential at infinity is 0 thus negative everywhere else), but from Einstein's energy-mass equivalence equation $E^2=\left(mc^2\right)^2 + \left(pc\right)^2$ it is clear that negative energy is a valid solution to the equation. So what does it signify? It doesn't have anything to do with a reference point.

• Valid solutions are not always physical solutions. – probably_someone Mar 1 '18 at 23:53
• – BRT Mar 2 '18 at 3:57