E = mc EE 2 ?

[JHAQ]

I know electrons have wave-particle duality but they also have mass , even if very small . When one generates electricity , is one actually doing the reverse of E = mc EE 2 & generating mass ?

[pulkit]

No !

When one generates electricity all that is done is give electrons energy and a net "drift velocity" in a direction opposite to current.

[Severian]

People here seem to have too rigid an idea of mass. The photon, for example, is continually shifting between a normal photon and an electro-poritron pair: [math]\gamma \to e^+e^- \to \gamma \to e^+e^- \to \gamma \to e^+e^- \to \gamma[/math] etc. So in a way, we are changing energy into mass (and back) all the time.

 

In fact normally this sort of shifting would give a quantum correction to the particle mass. For example, the Higgs boson does [math]H \to t \bar t \to H \to t \bar t \to H \to t \bar t \to H \to t \bar t \to H[/math] etc. When we measure the Higgs boson mass (in the future!) this would cause a shift in the effective Hiiggs mass since one cannot in principle distinguish the Higgs boson from a highly virtual top--anti-top pair.

 

In the case of the photon though, when one calculates the quantum correction to the mass, one finds that it is zero, keeping the photon massles. At first sight this is surprising, but on deeper examination one realises that the photon is kept massless by a symmetry: the local U(1) symmetry of electromagnetism. Since the original system is symmetric under U(1), the quantum corrections must be too and the photon remains massless.

 

In fact, pretty much any massless particle must have an associated symmetry since otherwise quantum corrections would give them a finite mass. The gluon for example is massless because of the SU(3) color symmetry of QCD.

[[Tycho?]]

Hmm, I didn't know that photons continually switched like that, I thought only high energy gamma rays did that. Wait a sec. When this happens to gamma rays, 2 photons are emitted when the pair collides. How does this happen with lower frequency photons?

[swansont]

'']Hmm, I didn't know that photons continually switched like that, I thought only high energy gamma rays did that. Wait a sec. When this happens to gamma rays, 2 photons are emitted when the pair collides. How does this happen with lower frequency photons?

 

It can, and does, happen at any energy as long as dE dT < hbar/2

 

You don't get two gammas because you weren't following conservation of energy to begin with.

[Severian]

Yes, the electron and positron are virtual - they are not om mass-shell, so [math] E_e^2-p_e^2c^2 \neq m_e^2 c^4[/math]. As Swantson says (sort of), they are allowed to be off-shell only for a short time (inversely proportional to how off shell they are).

 

Try the math if you like: you will see that you cannot have [math]\gamma \to e^+e^-[/math] while keeping [math]E_{\gamma}=p_{\gamma} c[/math] and [math]E_e^2-p_e^2c^2 = m_e^2 c^4[/math]

 

For your HE gamma rays, you have [math] \gamma \gamma \to e^+e^-[/math]. The extra photon lets you keep all the (external) particles on shell.