If one had a high enough electric field could one pull electrons and positrons into existence out of the vacuum?(adsbygoogle = window.adsbygoogle || []).push({});

The field needs to be high enough to accelerate the virtual particles away from each other strongly enough so they don't get a chance to recombine.

If a particle has acceleration g then there is a horizon distance r behind it given by:

r = c^2 / g..........(1)

such that no light signal starting at a distance of r or greater could ever reach the accelerating particle. Thus no virtual partner particle at a distance r or greater could recombine with the accelerating particle. This gives us an uncertainty in the particle position that we can convert into a momentum and then into an energy using the uncertainty principle.

If we have the uncertainty principle:

Momentum * distance = Planck constant

using E = p c

E / c * r = h

E = h c / r

Substituting for r in the above equation using (1)

E = h g / c

as E = M c^2

then we have

M = h g / c^3

Thus if we provide an acceleration g using an electric field we can produce a pair of particles of mass M.

For electrons/positrons being accelerated by a field F we have:

m_e = (h / c^3) * (e F / m_e)

F = m_e^2 c^3 / h e

F = field = 10^17 Volts / metre

It seems to me that the rest mass energy of the particle pair doesn't come out of the applied electric field but rather from out of the vacuum itself. The applied field just provides the acceleration to separate the virtual particles. The extra energy supplied to the particles during their acceleration could in principle be recovered in the process of bringing them back to rest.

Is this right?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Could a high electric field pull particles out of the vacuum?

**Physics Forums | Science Articles, Homework Help, Discussion**