What is Hawking Radiation

[INRM]

Nobody?

 

[Schneibster]

Why? What conservation law would be broken if a single photon appeared as a virtual particle?

Angular momentum.

 

[RecoveringYuppy]

OK, but that raises a few more questions for me.

So a photon carries angular momentum. I understand then that the creation of a real photon out of nothing would violate a conservation law. But does that mean the creation of single virtual photon is precluded? Or does it mean that the angular momentum has to be "borrowed" from another nearby particle? Virtual particles are invoked to explain how forces are carried, correct? Is there anything comparable to this scenario or is this scenario precluded by something I'm unaware of: two particles exchange a single virtual photon resulting in an exchange of angluar momentum. I'll see if I can do some research to make my question more clear.

Another point raised in this thread I'm having trouble with:

Someone made the statement that all conservation laws can be broken for a short period of time but also said that vps had to be created in particle/anti-particle pairs. The requirement that virtual particles be created in pairs would seem to be demanded in order to satisfy a conservation law. If conservation laws can be broken for a short time where does the demand for vps to come in pairs come from?

 

[RecoveringYuppy]

Wikipedia is my friend.

http://en.wikipedia.org/wiki/Virtual_particle

The description of beta decay near the bottom of the article begins with:

The restriction to particle-antiparticle pairs is actually only necessary if the particles in question carry a conserved quantity, such as electric charge, which is not present in the initial or final state.

So beta decay is close enough to my scenario to address my confusions. The virtual particle (a W) isn't created as a pair, the W acts to carry the conserved quantity (charge in this example).

Any opinions on whether that article is accurate?

 

[Schneibster]

OK, but that raises a few more questions for me.

So a photon carries angular momentum. I understand then that the creation of a real photon out of nothing would violate a conservation law. But does that mean the creation of single virtual photon is precluded? Or does it mean that the angular momentum has to be "borrowed" from another nearby particle? Virtual particles are invoked to explain how forces are carried, correct? Is there anything comparable to this scenario or is this scenario precluded by something I'm unaware of: two particles exchange a single virtual photon resulting in an exchange of angluar momentum. I'll see if I can do some research to make my question more clear.

There are "hard" and "soft" conservation laws. The conservation of fermion number, for example, is a hard conservation law; you will never see a situation, even in a virtual interaction, in which the number of fermions in the universe changes; there is no quantity to which fermion number is conjugate under uncertainty.

Spin angular momentum is another one of these "hard" conservation laws. The difference between the "hard" conservation laws and the "soft" conservation laws that are vulnerable to non-conservation in situations where the non-conservation is indetectible due to uncertainty is that the "hard" conservation laws are not conjugate under Noether's theorem to symmetries. Only the "soft" conservation laws are. Interestingly, angular momentum falls into both classes.

The particular type of angular momentum I was speaking of is spin angular momentum. This is a conserved quantity that you will never see not to be conserved, even in a virtual interaction. But continuous angular momentum, that is, angular momentum measured in multiple planes of rotation, is subject to uncertainty, and is not conserved in a virtual interaction. Of course, angular momentum is conserved if you can measure it; but it can be violated if you can't due to uncertainty.

The difference between the symmetries that are conjugate under Noether's Theorem with conservation laws and those that are not, is that the conjugate symmetries are continuous. Discrete symmetries are not covered by Noether's Theorem. But discrete conservation laws are also not uncertain.

I believe that there is a deep relation between the Uncertainty Principle and Noether's Theorem. This is shown in the DCQE, the Aspect experiment, and Afshar's experiment.

Another point raised in this thread I'm having trouble with:

Someone made the statement that all conservation laws can be broken for a short period of time

No, they can't. Discrete conservation laws like conservation of fermion number and conservation of spin angular momentum aren't broken ever. They're not uncertain.

but also said that vps had to be created in particle/anti-particle pairs.

Keep two things in mind:
1. Only the discrete symmetries are not uncertain, and thus are never violated.
2. The photon is its own antiparticle.

The requirement that virtual particles be created in pairs would seem to be demanded in order to satisfy a conservation law. If conservation laws can be broken for a short time where does the demand for vps to come in pairs come from?

I think I've explained this satisfactorily. I admit to having had a bottle of La Fin du Monde and another of Ruination IPA. So hopefully no one comes along and makes a fool of me. If they do, it was worthwhile.

 

[RecoveringYuppy]

Yep, I think you explained that very well. The reference to Noether's theorem looks like it will be particularly useful. Thank you.

See if you can find Dogfish head IPA. Comes in three varieties, 60, 90 and 120 minute infusions of hops. I like the 60 best.