QFT newbie-creation of particle and anti-particle

[rsaad]

Hi,
I read the following in an online source:
In relativistic settings, momentum and energy are equal so the uncertainty principle, for a particle of mass m which is trapped in a box of size L, becomes delta E>= $\hbar$c/L. If uncertainty exceeds delta E=2mc^2, we get pairs of particles and anti-particles from the vacuum.

What I do not understand is these pairs created out of nothing? Has this got to do with field folding up and making these new pairs around the particle in the box?

 

[mfb]

In relativistic settings, momentum and energy are equal

They are not. Do you mean E=pc for ultrarelativistic particles?

If uncertainty exceeds delta E=2mc^2, we get pairs of particles and anti-particles from the vacuum.

Why should we? The "old" particle cannot just release its energy (what is its state afterwards?), and the new particles could be confined to the potential well, too - so they need even more energy.

 

[Bill_K]

In relativistic settings, momentum and energy are equal so the uncertainty principle, for a particle of mass m which is trapped in a box of size L, becomes delta E>= $\hbar$c/L. If uncertainty exceeds delta E=2mc^2, we get pairs of particles and anti-particles from the vacuum.

Never mind the uncertainty principle, it's the zero point energy that's involved here. If you confine a particle to a box of side L, the particle in its ground state has kinetic energy. As you decrease L, this kinetic energy increases. The critical point comes when the kinetic energy approaches the particle's rest mass mc², and at this point there will be sufficient energy for additional particles of the same type to be created. The value of L at this point is called the Compton wavelength, equal to ħ/mc.

Note there is no need to wonder where this energy came from - it's already present in the particle's motion. And the particle got that energy from whatever squeezed it into the box.