# I don't understand Hawking Radiation

This is my understanding of Hawking Radiation:

Fluctuations in the quantum foam cause particle/antiparticle pairs to be generated all the time.

Normally, these pairs annihilate immediately and no one is ever the wiser.

In the vicinity of a black hole, one of the pair can be captured by the black hole while the other radiates away.

Somehow, this causes the black hole to lose mass.

It sounds like mass is gained to me. What am I missing here?

Thanks,
Rob

You’ll probably get a better explanation from a practicing physicist, but when virtual particle-antiparticle pairs are produced, they are entangled. That means their properties hare “shared” and you can’t tell what they are until you measure them at which point the properties lock in for both of the pair. (You may have read about quantum entanglement and “teleportation”.)

After one of the pair of virtual particles interacts with the black hole, the measurement occurs. The one that survives has a given amount of energy/mass, so the other one must have negative energy/mass as it is conserved. This reduces the positive mass of the black hole.

You don’t actually need a black hole for this. It can happen in an accelerated frame of reference (and by General Relativity a gravitational field is equivalent to an accelerated frame. The Unruh effect is that an accelerated observer will see black body radiation when an inertial observer does not.

Why can’t things go the other way? That is, why can’t the particle absorbed by the hole be the one with the positive mass and the one that gets away have negative mass? Also, I wasn’t aware that anti particles had negative mass.

Rob

Anti-particles don’t have negative mass. No matter which particle goes into the black hole, the one that doesn’t go into the black hole has mass and energy.

But the equations have to balance. So, if the one coming out of the vicinity of the black hole has mass, but the pair as a whole has no no net energy, then the one that went into the black hole must have had negative energy.

Because nothing real has negative mass. That’s what it means for the particle pairs to be “virtual”; they can only exist for a tiny amount of time before ceasing to exist. It doesn’t matter if the matter or antimatter particle falls into the hole; if one of them is lost behind the event horizon of the black hole, it can’t annihilate the other particle and return to non-existence. The particle that escapes must then become real, which requires real energy that must come from somewhere.

Actually, the whole ‘virtual particle-antiparticle pairs’-explanation should be viewed with some skepticism. One problem is that the particles in question would have wavelengths of the order of the black hole horizon, hence, one can’t really say that they pop out of the vacuum ‘near’ the horizon. In fact, I’m not sure there is any good description of the whole process in terms of dynamics near the horizon (though if there is, I’d appreciate a pointer).

Unfortunately, I’m not sure that there really is an easy-to-understand explanation for the effect. Basically, one part of it is that the notion of what is a vacuum state is not invariant between different observers in different states of motion; what you call a vacuum might not be one for me. One way of thinking about this is by realizing that observers in different states of motion have different notions of time, and in quantum mechanics, time is related to energy (in a similar way to how position is related to momentum). But then, such observers will necessarily have a different notion of what the state with least energy, i.e. the vacuum, is.

So, in general, an accelerated observer sees a non-vacuum state where an inertial observer sees a vacuum; this is the so-called Unruh effect. Hawking radiation essentially follows from this by noting that an observer on the horizon must necessarily be accelerated in order to be stationary. Hence, such an observer sees a thermal bath of particles where an inertial observer sees only vacuum.

This has the disadvantage of being somewhat less intuitive, and quite hard to explain without getting into the details of Bogoliubov transformations and positive/negative frequency decompositions of the quantum fields, but the advantage is that you need no spooky negative energy particles in order to decrease the mass of the black hole—it’s simply decreased because it radiates, and hence, looses energy.

The energy of the negative energy particles is the energy calculated by an observer at infinity who is acting as a bookkeeper. Negative energy particles cannot escape to the observer at infinity without enough energy being added to them for their total energy to be positive (as calculated by the bookkeeping observer).

So the observer at infinity can directly observe the Hawking radiation which arrives to him, which as HMHW says is a quantum effect due to how they view the vacuum state of quantum fields near the event horizon, but can also infer a flux of negative energy particles into the black hole.

Right; you shouldn’t think of the mass of the particles, but rather think of their total energy. Under familiar circumstances like we’re used to, the energy of an object is dominated by its mass, but near a black hole, the gravitational potential energy and kinetic energy are also relevant. Any particle whose non-mass energy is positive will escape, and any particle whose non-mass energy will fall in.

It’s worth noting here that the Hawking radiation case is a very rare one: Most of the time, both particles have negative non-mass energy, and so both are consumed. It’s only occasionally that one has enough non-mass energy to escape at all, and so Hawking radiation is a very slow process.

What follows is my bull@#\$% talky explanation I made for myself, undoubtedly sub-par for those who know how to do math, BUT…

I understand that Hawking radiation is inversely proportional to the mass of the black hole. Tidal force at the event horizon is also inversely proportional to black hole size.

Sooooo… I always imagine that the tidal force is actually ripping apart those tiny virtual particle pairs, which is why we sometimes see one of them, and why we see more for the smaller holes.
Is this crazy talk? I’m not seeing how this analogy works with Unruh effect.