# Relativistic quantum mechanics

Special theory of relativity predicts negative energy as well $E^2 =p^2 + m^2$ which when merged with quantum mechanics predicts antiparticle (Dirac equation). But what does it mean that a free particle can have negative energy? I mean to say can I experimentally differentiate between a particle (say electron) with positive energy and one with negative energy? And also the general solution of Dirac equation is a linear combination of both positive energy (spin up and down) and negative energy (spin up and down) states, so what does it mean that if i measure the energy of an electron very large number of times, about half the time I will get positive and other half negative?

• I can't immediately see the connection between spin up/ down and positive or negative energy states, I have to say. But I will read more about it – user108787 Nov 12 '16 at 18:07