Black holes and conservation of charge

[mrspeedybob]

Suppose you take a quantity of matter and separate the protons from the electrons, Now drop the electrons into a black hole. My understanding is that photons are the force carriers for the electromagnetic field. Since no photons can escape the black hole there should be no electrostatic attraction between the black hole and the left over protons. It is as if the black hole absorbed a negative charge but remained neutral. This seems to violate the law of conservation of charge. Any thoughts?

 

[Dale]

Since no photons can escape the black hole there should be no electrostatic attraction between the black hole and the left over protons.

Virtual photons can. They are weird, and they are the particles which mediate a static field.

 

[Cleonis]

Suppose you take a quantity of matter and separate the protons from the electrons, Now drop the electrons into a black hole. My understanding is that photons are the force carriers for the electromagnetic field. Since no photons can escape the black hole there should be no electrostatic attraction between the black hole and the left over protons. It is as if the black hole absorbed a negative charge but remained neutral. This seems to violate the law of conservation of charge. Any thoughts?

A black hole with a charge surplus will act as an electrically charged object, affecting charged particles surrounding it. That is, the event horizon does not act as a cutoff for the electrostatic field.

About black holes
All the mass that has fallen into a black hole contributes to the outside gravitational field of the black hole. One may ask the counterpart of the question you asked about the electromagnetic field. Why is the event horizon not acting as a cutoff for gravitational interaction? If it was billions of years ago that matter fell into the black hole, how come the gravitational field of that matter is still there?

Well, one can think of the outside gravitational field as the field of the matter just as it crossed the event horizon. Whatever happens inside the event horizon does not reach outside, so the gravitational interaction is not with what is inside the event horizon. For eternity the gravitational interaction is with the matter just as it crossed the event horizon.
The fact that the infalling of matter was billions of years ago is not necessarily a problem; the closer to the event horizon the stronger the gravitational time dilation.


About fields
The standard view is that electromagnetic interaction is, like the other interactions, mediated by a field.
The word 'field' has been in use for so long that it's tempting to think we actually know what a field is, but really all we know is the properties of the interaction.

Perhaps the following comparison has some merit:
- In a double slit experiment the probability distribution of where a photon will hit the screen is a continuum. But an actual event of a photon being detected (by the screen) occurs at a precise point.
- The field that surrounds a charged object is a continuum. However, a quantummechanical description of two charged particles interacting with each other has the changes of momentum as quantisized events.


There is another sense in which the quantization of the electromagnetic field manifests itself. This is when electromagnetic energy is confined to a small space. It is possible to construct socalled 'quantum dots'. In the case of quantum dots there is a relatively large energy gap between allowed energy levels.

It's not that the field itself always exists as a cloud of "quanta of field". Rather it's interaction that is quantum in nature.


In all it's definitely not correct to think of the mediator of electromagnetic interaction as "propagating photons". As pointed out by Dalespam, the mediator of electromagnetic interaction is sometimes referred to as 'virtual photons'. There's a reason for that word 'virtual'.