The photon as a mediator particle

[espen180]

I would like to ask some questions about the photon as a mediator particle of the electromagnetic force.

As far as I know, in order to dertermine the complete state of a photon, we need to know the values of two entities, which are the position and momentum 4-vectors $$x^{\mu}$$ and $$p^{\mu}$$. These are related through the HUP:
$$\Delta x^{\mu}\Delta p^{\mu}\geq \frac{\hbar}{2}$$ (no summation)
Also, photons always follow geodesic curves in space-time.

However, despite the fact that no geodesics exit from beyond the event horizon of a black hole, charged black holes exert a Lorentz force on other charged bodies. It appears like photons, when mediating the Lorentz force, are exempt from the rules of GR. I see two possibilities:

1. I have misunderstood something fundamental about charged black holes.
2. I don't know enough particle physics to make intelligent guesses about mediator particles.

If anyone could explain the issue to me, I would appreciate it.

 

[Prathyush]

i googled and found the following
https://www.physicsforums.com/showthread.php?t=65583
summarizing virtual particles do not obey several properties that normal particles obey, they can travel faster than light, need not be on the mass shell and hence blind to the event horizon.
also this is purely speculation and only a correct theory of QGR can tell us the answer

 

[bcrowell]

Interesting question.

One thing to point out is that what's really forbidden by GR is for *information* to escape from inside the event horizon; if it did, then there would be a local Minkowski frame in which the information was going faster than c, and that leads to a violation of causality.

But the virtual photons coming from a charged black hole don't carry any information. By the no-hair theorem, you can't use them to gain any information about the distribution of charges inside the event horizon, or about the motion of the charges.

 

[espen180]

As a "relativist", I have a little problem with speeds and transfers exceeding c. Putting that aside, I would like to raise a point mentioned in the thread Prathyush linked to.

If the photons do not carry no "information" at all, how can they "inform" the outside world about the existence of and amount of charge inside the black hole?

 

[bcrowell]

As a "relativist", I have a little problem with speeds and transfers exceeding c. Putting that aside, I would like to raise a point mentioned in the thread Prathyush linked to. If the photons do not carry no "information" at all, how can they "inform" the outside world about the existence of and amount of charge inside the black hole?

To carry information, a wave has to be modulated. You can't carry information with just a DC signal (or with an unmodulated sine wave). This is why, for example, you can have phase velocities greater than c.

This is exactly the same issue as the question of how the black hole can inform the outside world of the existence and amount of mass inside the black hole. This is information that was already present, and determinable by outside observers, before the black hole collapsed.

 

[Prathyush]

A very interesting point, was unaware till now.

To carry information, a wave has to be modulated. You can't carry information with just a DC signal (or with an unmodulated sine wave). This is why, for example, you can have phase velocities greater than c.

This is information that was already present, and determinable by outside observers, before the black hole collapsed.

What do u mean by this? Even a long time after the black hole collapse we can determine the mass of the black hole

 

[bcrowell]

This is information that was already present, and determinable by outside observers, before the black hole collapsed.

What do u mean by this? Even a long time after the black hole collapse we can determine the mass of the black hole

Causality is violated if, for instance, I get information about which shirt I'm going to wear tomorrow. If I find out that I'm going to wear the red shirt tomorrow, I can create a paradox by intentionally wearing the blue shirt instead. This type of causality violation occurs in relativity whenever you have a particle with a spacelike world-line. This includes particles like tachyons that move faster than c, and it includes particles escaping through the event horizon of a black hole.

Causality is not violated if I find out that 2+2=4, or that the mass of the sun has a certain value. These facts were true before I was born, and will still be true after I'm dead. Knowing the mass of a black hole is the same way. It doesn't create the possibility of any violation of causality. By conservation of mass-energy, the mass stays the same. It was the same before the black hole collapsed, and it will keep on being the same in the future.