I Why do quantum physicists claim that particles can tunnel out of a quantum well?

[shaiyefet]

Hi everyone,Every time I read an article about black hole evaporation through Hawking radiation, it seems to me that the writer didn't bother to connect all the dots so it will be clear for dummies like me.In many articles, I find 2 contradictory statements:1. Black hole emits a radiation (i.e photons !) with a spectrum identical to black body radiation at a temperature which is inversely proportional to the black hole mass.2. This radiation is created from a pair of particles that appears at the event horizon, one with negative energy that falls in and the other with positive energy that escapes. Hence the total energy (hence mass, E=mc^2) of the black hole is reduces.I can't find the logic in here:1. If the black hole emits particles, where do the photons of the black body radiation comes from?2. Why is the negative energy particle always falls in? The positive energy particle should fall in sometimes with equal probability, so the whole evaporation process should cancel out.3. What is a negative energy particle anyway?? From E=mc^2 it should have negative mass? How is that possible??4. If we consider the option that both particles has positive mass, than it doesn't matter which one falls in, but then the black hole acquires mass, not losing it.
Can anyone solve this for me, please?Thanks,

 

[phinds]

The whole "particle pair" description of Hawking Radiation is a hueristic and is NOT to be taken as what actually happens (although it almost always is, incorrectly, in pop-sci presentations). Hawking said that the particle pair heuristic was the only thing he could come up with to describe in English what really can only be described in the math.

Again, it is NOT what actually happens so all your questions are based on incorrect descriptions you have read about Hawking Radiation.

 

[DrStupid]

If the black hole emits particles, where do the photons of the black body radiation comes from?

Annihilation of matter and antimatter particles.

Why is the negative energy particle always falls in?

It has negative energy because it is already in and there is no way out.

What is a negative energy particle anyway?? From E=mc^2 it should have negative mass? How is that possible??

The potential energy is negative.

For the general limits of the particle explanation see phinds' post.

 

[Chronos]

Hawking radiation is a combination of particles and photons. Particles carry off a disproportionate share of energy. Low mass black holes can create more massive particles as they can support a higher Hawking temperature. For a more detailed discussion of the process, see; https://arxiv.org/abs/1601.04040,Hawking Radiation of Mass Generating Particles From Dyonic Reissner Nordström Black Hole.

 

[shaiyefet]

I think I've found a different approach for a simple explanation:We know that the entropy of a system is a measure for the number of possible microscopic configurations for a given macroscopic parameters of the system.

Since we don’t know what is going on inside the event horizon, then the black hole (for an outside observer) is basically a ball with mass M and radius R.

One can calculate (don’t ask me how) the entropy for this ball, and it depends only on the macroscopic parameter M.

Once can now calculate the temperature of the black hole from the derivative of the entropy.

Now that we know the temperature of this ball, one would expect it, like any other body, to radiate a black body radiation according to its temperature.

One can explain that this radiation actually comes from quantum fluctuations of the electromagnetic field around the zero mean value. These fluctuations happen near the event horizon.

The negative energy fluctuations gets sucked in the black hole (reducing its energy hence the mass) but the positive energy fluctuations escape as black body radiation.

The only thing I'm missing is an intuitive explanation why the negative fluctuations are sucked in.Thanks,

 

[phinds]

Now that we know the temperature of this ball, one would expect it, like any other body, to radiate a black body radiation according to its temperature.

No, we would not expect this. If nothing can escape from inside the EH, including EM radiation, why would you "expect" radiation? Black holes are not LIKE other black bodies.

Prior to Hawking, it was assumed that BH's did NOT radiate, not that they did radiate.

 

[stefan r]

Plutonium radiates alpha particles. A plutonium atom does this on average 48000 years (half life 24k). Are you comfortable with that?

The quantum physicists claim that "the alpha particle tunnels out of the quantum well". Should we picture particles with pick axes digging out of a well? Physicists also say that the particles are lost (uncertain about either position and momentum) and periodically find themselves outside of the well. Stepping outside the well is something like jumping a fence, if the outside is a lower energy (like a cliff beyond a safety fence) the particle suddenly has a lot of energy. It is worthwhile being very skeptical of the description. Quantum mechanics is entirely based on mathematics. The English language that is used to describe the conclusions drawn by quantum mechanics is mostly fiction, however, the conclusions can be tested by experiment.

The Hawking radiation is inverse proportional to the black hole's mass. The radius of the event horizon is proportional to the mass. Larger mass means the event horizon is further away from most of the mass. That lowers the frequency/probability that any particle will "find itself" near the event horizon.

Lean a fence against a brick wall and then jump over it. You should hit the wall and land back inside the fence. When you measure yourself you find that you are still inside the same fence and on the same floor. There is no mass change. If Hawking is correct then virtual matter/antimatter pairs are popping up everywhere. It is only at the event horizon of a black hole that some matter/antimatter pairs separate. Maybe imagine a tidal force pulling apart the virtual pair. Small black holes have a lot of tidal force and can pull apart things that are otherwise tightly bound.