# Hawking radiation: why only one way?

I'm trying to understand how Hawking radiation works but, as usual, most explanations are oversimplified so they don't appear to make sense.

If I understood correctly, pairs of particles and antiparticles pop into existence everywhere in the universe all the time, and usually annihilate each other shortly afterwards. But close to a black hole, it is possible for the antiparticle to be swallowed up by the black hole (reducing the mass of the hole) while the normal particle gets away, and this basically has the same effect as if the black hole were radiating.

But why doesn't this happen the other way around, then? The black hole might just as well swallow up the normal particle while the antiparticle gets away. The black hole would be "emitting" both normal and antiparticles, and keeping the same amount of mass, receiving both particles and antiparticles all the time.

I probably misunderstood the whole thing, so I would appreciate it if someone could enlighten me...

OK, got it. It's not about matter and antimatter, but about positive and negative energy. If the positive energy particle fell in, it would leave behind a negative energy particle which is not allowed to exist. In the other direction, the negative energy particle becomes a positive energy particle inside the warped space-time of the black hole (even though it still has negative energy as seen from outside), so it is allowed to exist while its partner flies away.

I don't quite get why the positive energy particle somehow knows it's not allowed to fall into the hole and leave its negative energy partner behind, but I guess I'll have to read up on quantum mechanics for that.

diazona
Homework Helper
I don't quite get why the positive energy particle somehow knows it's not allowed to fall into the hole and leave its negative energy partner behind, but I guess I'll have to read up on quantum mechanics for that.
Yeah, probably... when it seems like a particle "knows" that it's not allowed to do something, the usual quantum mechanical explanation is that the wavefunction interferes destructively with itself and cancels out. Though I'm not sure if that applies in this specific case (I don't know the mathematical details of Hawking radiation).

sylas
Yeah, probably... when it seems like a particle "knows" that it's not allowed to do something, the usual quantum mechanical explanation is that the wavefunction interferes destructively with itself and cancels out. Though I'm not sure if that applies in this specific case (I don't know the mathematical details of Hawking radiation).

It isn't that any particle "knows" one thing or another.

As an aside, Professor Carlip is one of those treasures of academia: a working research physicist who also has the ability and enthusiasm to explain these kinds of things for a amateur readers.

Anyhow, here is an extract from his explanation:

Now, finally, here's a way to understand Hawking radiation. Picture a virtual pair created outside a black hole event horizon. One of the particles will have a positive energy E, the other a negative energy -E, with energy defined in terms of a time coordinate outside the horizon. As long as both particles stay outside the horizon, they have to recombine in a time less than h/E. Suppose, though, that in this time the negative-energy particle crosses the horizon. The criterion for it to continue to exist as a real particle is now that it must have positive energy relative to the timelike coordinate inside the horizon, i.e., that it must be moving radially inward. This can occur regardless of its energy relative to an external time coordinate.

So the black hole can absorb the negative-energy particle from a vacuum fluctuation without violating the uncertainty principle, leaving its positive-energy partner free to escape to infinity. The effect on the energy of the black hole, as seen from the outside (that is, relative to an external timelike coordinate) is that it decreases by an amount equal to the energy carried off to infinity by the positive-energy particle. Total energy is conserved, because it always was, thoughout the process -- the net energy of the particle-antiparticle pair was zero.

Note that this doesn't work in the other direction -- you can't have the positive-energy particle cross the horizon and leaves the negative- energy particle stranded outside, since a negative-energy particle can't continue to exist outside the horizon for a time longer than h/E. So the black hole can lose energy to vacuum fluctuations, but it can't gain energy.

So in other words, you have a continuous random mix of fluctuations going on all the time. Sometimes it just so happens that by an accident of circumstance, the "negative energy" particle in a virtual pair can cross the horizon, which results in a state in which the requirement for cancelation is removed, and the particles can continue to exist as real particles. One is a normal real particle outside the horizon, either matter or anti-matter but with positive energy as all real particles must have. The other has been taken up into the black hole, giving it a negative increment in energy.

At least, that's my understanding of Steve Carlip's account.

Cheers -- sylas

Al68
I'm trying to understand how Hawking radiation works but, as usual, most explanations are oversimplified so they don't appear to make sense.

If I understood correctly, pairs of particles and antiparticles pop into existence everywhere in the universe all the time, and usually annihilate each other shortly afterwards. But close to a black hole, it is possible for the antiparticle to be swallowed up by the black hole (reducing the mass of the hole) while the normal particle gets away, and this basically has the same effect as if the black hole were radiating.

But why doesn't this happen the other way around, then? The black hole might just as well swallow up the normal particle while the antiparticle gets away. The black hole would be "emitting" both normal and antiparticles, and keeping the same amount of mass, receiving both particles and antiparticles all the time.

I probably misunderstood the whole thing, so I would appreciate it if someone could enlighten me...
It does happen the other way around half the time, but both particle and anti particles have positive mass (and positive energy).

The anti- prefix refers to charge and spin, not mass. All anti-matter has positive mass.

okay - someone please elucidate a bit more for me.
1. a negative energy particle is somehow "allowed" to exist inside the EH of a BH, but not allowed to exist outside of it? sounds like voodoo to me...
2. both the matter particle and the antimatter particle have positive mass - where does this mass go? if you add positive mass to the BH, how does its mass decrease? how can antimatter have positive mass and negative energy at the same time?
3. i STILL do not understand why only a negative energy particle can fall into a BH - what do you mean a negative energy particle is not allowed to exist - antimatter can exist in the real world for longer the the planck time, doesnt it? (ie, " since a negative-energy particle can't continue to exist outside the horizon for a time longer than h/E...")

jnorman:

I agree, it doesnt make any sense. My reasoning would be:
"What pulls particles into a black hole: gravitation.
What controls the pull/push of gravitation: mass.
Positive mass certainly seem to attract positive mass, one would recon that negative mass would attract negative mass. Also, negative mass would push positive mass away. The logical thing would be positve-mass particles would be swallowed by the black hole 100% and negative particles would be pushed away 100%.."

But, I suspect these physics are used only to "visualize" what happens. But I dont know.

Staff Emeritus
2021 Award
Positive mass certainly seem to attract positive mass, one would recon that negative mass would attract negative mass. Also, negative mass would push positive mass away. The logical thing would be positve-mass particles would be swallowed by the black hole 100% and negative particles would be pushed away 100%.."

A) there is no negative mass.

B) antiparticles fall down, not up.

C) popularizations are, by necessity, oversimplifications. Understanding the popularization is not the same as understanding the thing itself.

A) there is no negative mass.

B) antiparticles fall down, not up.

C) popularizations are, by necessity, oversimplifications. Understanding the popularization is not the same as understanding the thing itself.

a) Then people should stop reffering to it as negative mass :)..

b) Why does antiparticles fall down and not up? If one have a theoretical basis for saying it is so, well fine.. I would like to understand it a little better. Though, if this is just a mathematical quirk, It is not physics.

c) I agree that popularizations are oversimplification. The question one should ask oneself, does the popularization contribute to a greater understanding of the real physics, or the principles in play? In this case I would say no. Instead of greater understanding one paves the way for countless misinterpretations.

b) Why does antiparticles fall down and not up? If one have a theoretical basis for saying it is so, well fine.. I would like to understand it a little better. Though, if this is just a mathematical quirk, It is not physics.
If you would spin antimatter in a centrifuge, would you expect it to move to the center of the centrifuge? No, it would be pushed to the outside, just like everything else. Of course centrifugal force is not a "real" force but a pseudo-force, but the point of General Relativity is that gravity, too, is a pseudo-force. Space-time is curved, and particles just follow the closest path to a straight line.

If GR seems too complicated, you can even find the same answer using just Newtonian gravity. Even considering negative mass, you'll still find that antiparticles fall down. With the mass of a particle negative, the force would change sign, but in "F=ma" the mass would change the sign a second time so the resulting accelleration is the same as for a normal particle.

No matter which way you calculate, you'll always find the mass of the particle is divided away, and any negative sign is divided away with it.

In yet other words, if a mass of 10 kg falls as quickly as a mass of 1 kg or 100 kg, why would a mass of -1 kg suddenly behave differently? A particle's mass simply does not matter when determining which way it will go.

With the mass of a particle negative, the force would change sign, but in "F=ma" the mass would change the sign a second time so the resulting accelleration is the same as for a normal particle.

Are you sure about this? I'm more familiar with the concept that the Force would change sign because you insert the negative in for negative mass.

F=ma Force is positive, particle accelerates in the direction of force applied.

F=-ma Force is negative, particle accelerates opposite the force.

The force is not already negative when you insert negative mass.

Also, some theories have been proposed to counter this very thing. The 'Lucas Generalization' suggests that the mass should have an absolute value function around it. The fact that these have been proposed indicates to me that what I was saying up there was correct.

Also, negative mass is a form of exotic matter. Wiki it. It shows how negative mass would accelerate in the opposite direction of the applied force.

Also, negative mass is a form of exotic matter. Wiki it. It shows how negative mass would accelerate in the opposite direction of the applied force.
Suppose a negative mass particle is in the vicinity of the earth. The force of gravity on a normal particle would point towards the earth, but the force of gravity on a negative mass particle points away from the earth. The normal particle will accellerate in the same direction as the force of gravity, so it moves towards the earth. The negative mass particle will accelerate in the opposite direction of the force, so... it, too, moves towards the earth.

All of this is just guessing on my part. I might be wrong, but it seems logical. Maybe you found a different formula for gravity where the masses have absolute value signs on them, but then a negative mass will attract positive masses again, which seems less likely than the other way around.

Anyway, imagine for a moment that negative mass particles exist and move away from positive masses. So if you would somehow create a negative mass ping pong ball here on earth, it would immediately start "falling" upwards, away from the earth. However, you would also have to consider the gravity of the sun. The ping pong ball would need to fall away from the sun, too, so if you release the ball at noon, it may actually be pushed towards the earth more than it's pushed away from it. Unless you consider the gravity from our galaxy, too. Now it will be moving in yet another direction. Where do you stop? All this flies in the face of General Relativity which says that observers should only need to worry about those fields of gravity they're not freefalling in. In a lab on earth, only the earth's gravity should matter. Otherwise it's going to be really, really difficult to determine where things are going to go.

nrqed
Homework Helper
Gold Member
okay - someone please elucidate a bit more for me.
1. a negative energy particle is somehow "allowed" to exist inside the EH of a BH, but not allowed to exist outside of it? sounds like voodoo to me...
I agree that it does not make much sense seen that way.

But I think that the key point is that we must not think of the situation as "a negative energy state inside a black hole", i.e. two separate entities. Instead, we should think of it as "a black hole with a decreased energy". In other words, quantum fluctuations occur near the even horizon which "borrow" energy from the black hole to create a particle (necessarily of positive energy) outside the black hole, which can sometimes escape to infinity. This way, we never talk about negative energy states (which are unphysical) . What happens is only that quantum fluctuations allow the stealing" of energy from the black hole to create particles just outside the event horizon.

Also, negative mass is a form of exotic matter. Wiki it. It shows how negative mass would accelerate in the opposite direction of the applied force.
Another strange thing I just thought of... If a normal particle hits a wall, the force from the wall will push it back. A negative mass particle will instead tend to accelerate through the wall?! They would be unstoppable! (unless you push them from behind)

Another strange thing I just thought of... If a normal particle hits a wall, the force from the wall will push it back. A negative mass particle will instead tend to accelerate through the wall?! They would be unstoppable! (unless you push them from behind)

This is correct.

Suppose a negative mass particle is in the vicinity of the earth. The force of gravity on a normal particle would point towards the earth, but the force of gravity on a negative mass particle points away from the earth. The normal particle will accellerate in the same direction as the force of gravity, so it moves towards the earth. The negative mass particle will accelerate in the opposite direction of the force, so... it, too, moves towards the earth.

All of this is just guessing on my part. I might be wrong, but it seems logical. Maybe you found a different formula for gravity where the masses have absolute value signs on them, but then a negative mass will attract positive masses again, which seems less likely than the other way around.

Anyway, imagine for a moment that negative mass particles exist and move away from positive masses. So if you would somehow create a negative mass ping pong ball here on earth, it would immediately start "falling" upwards, away from the earth. However, you would also have to consider the gravity of the sun. The ping pong ball would need to fall away from the sun, too, so if you release the ball at noon, it may actually be pushed towards the earth more than it's pushed away from it. Unless you consider the gravity from our galaxy, too. Now it will be moving in yet another direction. Where do you stop? All this flies in the face of General Relativity which says that observers should only need to worry about those fields of gravity they're not freefalling in. In a lab on earth, only the earth's gravity should matter. Otherwise it's going to be really, really difficult to determine where things are going to go.

I think that you think that I thought that negative masss particles are repelled by ositive masses. Using Relativity, the positive mass particles tend to curve spacetime as to make the negative mas particles fall towards them. Newton's idea of Gravity doesn't always work. I agree with the concencus, that negative is attracted to positive, but positive is attracted to negative.

I agree that it does not make much sense seen that way.

But I think that the key point is that we must not think of the situation as "a negative energy state inside a black hole", i.e. two separate entities. Instead, we should think of it as "a black hole with a decreased energy". In other words, quantum fluctuations occur near the even horizon which "borrow" energy from the black hole to create a particle (necessarily of positive energy) outside the black hole, which can sometimes escape to infinity. This way, we never talk about negative energy states (which are unphysical) . What happens is only that quantum fluctuations allow the stealing" of energy from the black hole to create particles just outside the event horizon.

I agree as well that the OP brings up a good point. Although, when you think in terms of your last paragraph, the 'stealing energy concept,' it seems to give no real explanation as to why it happened. It just shows what happened. So, why does this happen is very difficult for me to understand as well.

jtbell
Mentor
Speculative posts related to negative mass have been deleted.

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Speculative posts related to negative mass have been deleted.

How are "speculative" posts defined?
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Is there somewhere on this forum open to "specualtion?"

George Jones
Staff Emeritus
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How are "speculative" posts defined?
Are not all advancements in physics related to speculation?
Is there somewhere on this forum open to "specualtion?"

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