Destruction of virtual particles and virtual particle pairs

[Maximise24]

I'm trying to understand the process that destroys particles very shortly after they "appear". I have read that they are usually annihilated by a virtual antiparticle, much in the same way as can happen to real particles. However, is this always the case? And if so, is it an intrinsic property of these particles to appear in pairs and why exactly is this?

In other words: could a virtual (anti)particle be created on its "own", without a partner, for example because of the Heisenberg time-energy uncertainty relation, simply because it exists too briefly for it to have any real energy? Apparently, a virtual pair can be split up (Hawking radiation), but can they also be created that way?

 

[Bill_K]

Creation and absorption of any particle, virtual or not, must obey the conservation laws. A photon can be created alone, but an electron cannot because it is a negatively charged particle, and a positively charged particle (positron) must be created at the same time.

because of the Heisenberg time-energy uncertainty relation, simply because it exists too briefly for it to have any real energy?

Energy must always be conserved too. Not just on the average, or over a long time, it must be exactly conserved whenever a particle is created or absorbed. If the new particle carries away energy, one of the other particles must lose the same amount to make up for it.

 

[phinds]

FYI, there is an analogy regarding Hawking Radiation that says it is caused by virtual particle pairs popping into existence just outside the event horizon of a black hole, wherein one of the pair falls in and the other heads off into space, and the one that falls in always reduces the mass of the BH, thus evaporating it via Hawking Radiation.

BUT ... Hawking himself has said that this is JUST a way of talking about it in English and that actual particle-pair production is NOT the true reason for Hawking Radiation.

 

[Bill_K]

FYI, there is an analogy regarding Hawking Radiation that says it is caused by virtual particle pairs popping into existence just outside the event horizon of a black hole, wherein one of the pair falls in and the other heads off into space, and the one that falls in always reduces the mass of the BH, thus evaporating it via Hawking Radiation.

BUT ... Hawking himself has said that this is JUST a way of talking about it in English and that actual particle-pair production is NOT the true reason for Hawking Radiation.

It's easy to think the picture is that of an itty bitty particle being created "just outside" the horizon of a great big black hole. In fact, Hawking radiation is a global effect (so you can't say where it happens) and it only happens when the size of the particle is comparable to the size of the hole. Furthermore it's not just energy that disappears into the hole. If the emitted particle is electrically charged, the electric charge of the hole must change so as to compensate, just as if an antiparticle had fallen in.

 

[phinds]

... it only happens when the size of the particle is comparable to the size of the hole.

This would seem to clearly imply that only really tiny BHs experience Hawking Radiation. Doesn't seem to make any sense.

 

[Bill_K]

This would seem to clearly imply that only really tiny BHs experience Hawking Radiation. Doesn't seem to make any sense.

That's correct. As the hole gets smaller, the process goes faster. For astronomical size holes the rate is quite negligible!

 

[phinds]

That's correct. As the hole gets smaller, the process goes faster. For astronomical size holes the rate is quite negligible!

So you're telling me there are particles the size of supermassive black holes? Is this some kind of joke?

 

[Bill_K]

So you're telling me there are particles the size of supermassive black holes? Is this some kind of joke?

No no, the effect is appreciable only for SMALL black holes. And yes, large (i.e. long de Broglie wavelength, very low energy) particles.

 

[mfb]

A photon can be created alone

With a 4-vector of (0,0,0,0)? How is that a "photon"? How is that anything?

In fact, Hawking radiation is a global effect (so you can't say where it happens) and it only happens when the size of the particle is comparable to the size of the hole.

To clarify: The "size" of a photon is given by its wavelength in that description, and the size of massive particles by their de-Broglie wavelength.

 

[Bill_K]

A photon can be created alone

With a 4-vector of (0,0,0,0)? How is that a "photon"? How is that anything?
.

The OP asked whether virtual particles have to be created in pairs. I answered that a photon can be created alone, by which I meant without creating a second particle. For example an electron can emit and reabsorb a virtual photon.

 

[mfb]

Okay, connected to other particles, a single photon can appear. But then you also get interactions like $W^- \to e^- \bar{\nu_e}$, where an electron appears without a positron.

 

[Maximise24]

Okay, connected to other particles, a single photon can appear. But then you also get interactions like $W^- \to e^- \bar{\nu_e}$, where an electron appears without a positron.

So, if I understand correctly, virtual particles can appear "on their own" (provided they do not break any conservation laws) in connection to other real particles, but not, say, in a vacuum, where there will always be a virtual antiparticle created with it?

 

[mfb]

Yes. The connection to real particles is necessary for energy/momentum conservation.