# Special relativity and particle creation

Does special relativity predict the possibility of particle creation? Is it due to the relativistic energy-momentum dispersion $$E^{2}=m^{2}c^{4}+p^{2}c^{2}$$ which shows that mass is simply a form of energy, and as such other forms of energy can be converted into mass energy, or equivalently, mass energy can be converted into other forms of energy, implying the possibilities of matter creation and annihilation respectively?

Given this, would it be correct to say that Newtonian mechanics cannot account for matter creation/annihilation since there is a clear distinction between mass and energy in this theory, and hence there is no way to describe such a conversion that would be required to create/annihilate matter?

• Well the prediction of antimatter is linked directly to the discovery of the Dirac equation which was an attempt to find a relativistic version of the Schrodinger equation (by taking the `square root' of the Klein Gordon equation), so in that way antimatter is a prediction of relativistic quantum mechanics. – gautampk May 16 '17 at 21:55
• @gautampk But, before taking quantum mechanics into consideration, if one treats particles classically is special relativity enough to predict (or correctly describe) particle creation? In several introductory notes that I've read on SR the author discusses relativistic kinematics and dynamics and the notion of *threshold energies * for particle creation without even mentioning quantum mechanics. – Feyn_example May 16 '17 at 22:00
• It is my understanding that you can't have any notion of 'where particles come from' without quantum mechanics. Of course, you can posit that there exist particles and then do kinematic calculations, which is what you do in classical mechanics, but there's no concept of the dynamics of the particles -- where they come from, why they have the properties they do etc. Threshold energies and particle creation are definitely quantum mechanical concepts. That doesn't mean there weren't older non-quantum attempts at explanation, but they aren't really of use anymore. – gautampk May 16 '17 at 22:12
• @gautampk Fair enough. Is it not possible to draw any conclusions on the subject from the relativistic energy-dispersion relation? I mean, doesn't it imply that mass is not necessarily conserved - it can be converted into other forms of energy (what is conserved is the total energy). This is clearly different from Newtonian mechanics where mass is always conserved (it can neither be created or destroyed in this sense). – Feyn_example May 16 '17 at 22:26
• Relativistic dispersion relation isn't really a statement about energy conservation so much as it is a statement about frame invariance. $E^2 - p^2 = m^2$ (natural units so $c=1$), is really saying that $m$ is the magnitude of the energy-momentum four vector. As a magnitude it is a scalar, and therefore must be invariant under a change of basis. Conservation is a property of a specific theory (or its Lagrangian), but the dispersion relation is a statement about the entire framework of relativity. Of course, if a theory is Poincare invariant then both $E$ and $p$ are conserved so $m$ is also. – gautampk May 16 '17 at 22:53

• Also, is it correct to say that whilst the individual masses of particles in a given system may not be conserved, the invariant mass of the total system $m_{total}^{2}=E^{2}_{total}-p^{2}_{total$ is conserved? (For example, if one considers the interaction $e^{+}e^{-}\rightarrow\gamma\gamma$, then the individual masses of the electron and positron are not conserved, however the total invariant mass of the system is, $m^{2}_{before}=E^{2}_{before}-p^{2}_{before}=E^{2}_{after}-p^{2}_{after}=m^{2}_{after}$) – Feyn_example May 17 '17 at 19:36