Hawking Radiation

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As far as I understand the theory, Black Holes "radiate", by having a pair of virtual particles (negative + positive) at the edge of the Event Horizon.

When the Negative particle enters the boundary of "no-return", because it is negative it will destroy the matter inside the black hole, and the radiation is really just the positive particle which managed to escape the black hole.

Now, I don't know if I understood this correctly - please correct me if I'm wrong in the above assumption BUT:
In case I'm right, there's a thing I don't get:

Virtual particles are created all the time in the "quantum foam". Which means a positive particle could just as well enter the black hole, equally as much as the negative particles. Which... according to statistics is 50 % either way.

In other words, how are negative particles supposed to become the majority of virtual particles entering the black hole (which is needed for the "radiation" to occur)? If a positive particle enters the black hole, the black hole will get larger. If it's 50-50 - it makes no difference, in which case Black Holes don't evaporate/get smaller.

Again, I'm not entirely sure I got this assumption right in the first place. I which case, I'll have to blame popular media for their stupid explanation. Because this above explanation makes no sense - at all!

I was listening to this earlier in the year and remember that they said some interesting things on the issue of black holes storing a copy of whatever passed through on the event horizon while also sending the matter in, and Susskind did hit on some difficult paradoxes that they were trying to figure out. Not sure if they got into the charge of the particles but it was still a deeper conversation than I'd heard in most other places (got into 'D-Branes' a bit as well).

It's 50-50 weather regular matter or antimater enters the black hole - but both matter and antimatter have positive mass/energy.

The virtual particle pairs are created "borrowing" energy from the vacuum (the most realistic model of the phenomenon that's not made of pretty advanced Math ) and normally, they "return" the energy to the vacuum by annihilating, quickly enough to fit inside Heisenberg uncertainly principle.

The "debt" is carried by the pair as a whole, even if they are spacially separated (that's called quantum entanglement).
In presence of strong potentials - like next to whatever is happening inside a black hole - the "borrowed" energy can be then taken from whatever is creating this potential and the particle can be "normally" emited.

So, when one particle falls inside the black hole, the virtual energy of the pair becomes real energy taken from inside the black hole. The pair, in a way, "tunnels" energy out of the black hole. It can be viewed as "a particle with negative energy" falls inside the black hole but it means the particle that falls into the black hole carries energetic debt of the whole pair.

Quantum mechanics can be pretty counter-intuitive.

So, to put it in some order:
1. Pairs of particle-antiparticle are appearing and disappearing all the time as normal fluctuations of the vacuum;
2. A pair exists on "borrowed" energy that it has to return to stay within the uncertainty principle;
3. Normally, the pair returns its debt by annihilating (disappearing);
4. As long as the particles exist, they can and they do interact with their environment;
5. If the pair can take energy for their debt from their environment, they can become "regular" particles and fly away;
6. If it all happens at the horizon of events, one particle falls into the black hole and the other flies away, using energy sucked from the black hole.

I would have to read up on what exactly the theory of "Hawking Radiation" is.

My understanding of Matter / Anti-Matter is that both Matter and Antimatter have mass - the same kind of mass - the same reaction to gravity and acceleration. When (for example) a proton and an antiproton collide they obey the law of conservation of mass/energy - that is they don't so much disappear as they convert to high energy gamma photons - which is to say - radiation. "Negative particles" usually means particles with a negative static electric charge - at least that is how I have heard the term used. An electron is a quantum particle with a small mass and a negative one charge. A proton is comprised of three quantum particles with a total of plus one charge (I think it is two plus 2/3 charge particles and one minus 1/3 charge particle - I would have to double check on the Wikipedia under Nucleons) and it has a larger mass. The neutron is also made of three quantum particles with a total of zero charge and a mass very similar but slightly larger than the proton. Because of this there used to be a theory that a nutron was a proton and an electron somehow bound together, but I think that is no longer considered true or even an option.

I know there are ideas in quantum theory that include the possibility of negative (less than zero) energy so I suppose it would follow that there might be particles with negative mass - but this is out of my current knowledge. A FTL (faster than llight) particle would need a vector mass (with "i" in it) so that the square of the mass is negative - if the known equations are to hold. A negative mass would not do it. No FTL particles are known and some think they will never be found, others allow for the possibility.

Some quantum particles have other additional properties besides mass and static electric charge, like spin. I took relativity in college, but all my knowledge of quantum is self taught from reading on the internet (and the odd magazine article).

This is all off-the-top-of-my-head - I could do more research and try to get back to you on your central question - but it seems you have already answered it yourself. I may have gotten some of my facts wrong.

I think you are correct in that quantum uncertainty does allow for quantum particles to just pop up now and then in a vacuum. Heisenberg uncertainty has to do with the inability to know something about a particle without somehow affecting it so you cannot know the position and velocity of a particle at the same time - to get one you have to change the other. I think this is another kind of uncertainty than quantum tunneling uncertainty - which I think is the principal behind the electron tunneling microscope.

My knowledge is not certain enough for me to speak authoritatively on this (this is a third kind of uncertainty )

If there is a particular article you are reading I would be happy to look at it and give my personal take on what it is saying in "non-expert" speak.

Interesting and relevant - basically the way I read this is that "virtual particles" are not particles at all but are wave behavior. However so are "real particles". This is consistent with the anecdotes in Feynman's books about the development of Feynman diagrams.

Virtual particle
https://en.wikipedia.org/wiki/Virtual_particle

"In physics, a virtual particle is a transient quantum fluctuation that exhibits some of the characteristics of an ordinary particle, while having its existence limited by the uncertainty principle. The concept of virtual particles arises in perturbation theory of quantum field theory where interactions between ordinary particles are described in terms of exchanges of virtual particles. A process involving virtual particles can be described by a schematic representation known as a Feynman diagram, in which virtual particles are represented by internal lines.[1][2]

Virtual particles do not necessarily carry the same mass as the corresponding real particle, although they always conserve energy and momentum. The closer its characteristics come to those of ordinary particles, the longer the virtual particle exists. They are important in the physics of many processes, including particle scattering and Casimir forces. In quantum field theory, forces—such as the electromagnetic repulsion or attraction between two charges—can be thought of as due to the exchange of virtual photons between the charges. Virtual photons are the exchange particle for the electromagnetic interaction.

The term is somewhat loose and vaguely defined, in that it refers to the view that the world is made up of "real particles". It is not. "Real particles" are better understood to be excitations of the underlying quantum fields. Virtual particles are also excitations of the underlying fields, but are "temporary" in the sense that they appear in calculations of interactions, but never as asymptotic states or indices to the scattering matrix. The accuracy and use of virtual particles in calculations is firmly established, but as they cannot be detected in experiments, deciding how to precisely describe them is a topic of debate.[3] Since it is possible to perform quantum field theory calculations completely absent virtual particles being referenced in the math used, as seen in Lattice Field Theory, then it is believed virtual particles are simply a mathematical tool. "

So, magz, you are probably much better prepared to look at the real math than I am.

I read a few articles on Hawking Radiation and I read it this way:

What do we mean by negative energy? Negative Energy in this context is energy related to gravity.
If you take a golf ball and lift it above the surface of the earth it gains potential energy.
If conservation of energy is not in place you could explain this by saying "the potential energy was created" but it couldn't have been - because of conservation of energy. So instead you say "the golf ball gains potential energy while the earth gains negative potential energy and all is right with the universe because the cancel out and the net change is zero".

So . . . if mass can be converted to energy and energy to mass the net mass/energy is also conserved.
So . . . The mass of the black hole is gaining negative (potential) energy when the black body radiation is leaving the vicinity of black hole then the black body radiation has positive (potential) energy.
If you measure the mass of the black hole as the total of mass (converted to energy) plus energy (which doesn't need to be converted) then, mathematically, the number goes down as the black hole gains negative energy.

And . . . since the mass is just quantum field wave behavior anyway . . . the mass of the black hole goes down as a result.

Which is to say - there is no mass or energy really there is just waves - and waves are weird.

Any billiard ball analogy is only useful if the math comes out the same. But it is really still just the waves.

So wave-particle duality is resolved - it was really just all waves all along.

OR

The Math is only as good as its ability to mimic the sum total of physics experiments - the experimental observations are the real thing - the math is just a model. Or as Einstein put it: "Mathematics to the extent that it applies to reality is not precise and to the extent that it is precise does not apply to reality" The Pythagoreans were wrong and the Universe was right.
The map it not the territory.

P.S. Hawking's Theory is accepted but not proved. But that is how things usually go with quantum.

physicsforums.com - Forums - Physics - Quantum Physics - Hawking radiation and entanglement


Completely unrelated:

Last edited by Fenn on 08 Sep 2021, 2:21 pm, edited 1 time in total.

I'm burned out and it's not my time to be active but I promise to respond... it's really fascinating world.
The uncertainty principle is all the same. It can be explained on any wave, including sound. You need several wave periods to have determined frequency - so a sound needs to last some time to have well-defined frequency. A pop sound, well-defined in a very short time, on the other hand, has undefined frequency = mix of lots of frequencies. The sound needs to be "spread" in either time, or frequency, or both.
The same with quantum wave-particles. Their properties are "spread" and if one is well-determined, the other becomes a mix of all possibilities.

A useful model of antimatter as "negative particles" is Dirac sea.

The difference between real and virtual particles is - real particles can be directly caught in a detector. Virtual particles can't. As one professor said, "when you break the energy conservation law, you need to be fast. No experiment must catch you."
But virtual particles can sometimes gain enough energy from their environment to become real. In an example of a pair next to a black hole, the pair "sucks" energy from the black hole - then one particle falls on the black hole while the other particle flies away, resulting in the black hole losing energy.
Mathematically it looks the same as if a particle with negative energy fell on the black hole.

Well, goodnight.

You are very close to the answer, but you need to add an anti-electron neutrino into the mix. When a “free” neutron decays (one down quark converts to an up quark, with the other two quarks not effected), the result is the formation of two particles: a proton (containing the three quarks) and a W- boson. The W- boson only lasts about 3.0x10^-15 seconds before it decays into an electron and an anti-electron neutrino.

(Neutrinos and anti-neutrinos do not actively interact with either matter nor anti-matter, so they are often overlooked. They literally pass through everything until they find their opposite particle.)

When an electron neutrino and an anti-neutrino annihilate, the resulting electromagnetic energy released is equivalent to two photons in the blue range of the visible spectrum. That amount is very hard to see in regular sunlight, so it must be measured in completely dark areas, like under a polar ice cap or in a very deep well. Electrons/positrons contain enough energy to be converted under annihilation events into high field x-rays (511 KeV), while protons/anti-protons and neutrons/anti-neutrons would be gammas if converted that way.

On further reading I take back what I said about quantum uncertainty allowing for quantum tunneling being different from the Heisenberg's uncertainty principle. Magz told me I was wrong and upon further reading I now agree with her.
Velocity is change of position over time, and so it quantum tunneling.

I think the idea of negative energy is interesting. I still think my statement about negative potential energy as a way to describe gravity is correct based on what I have read. Frankly the term "potential energy" has always troubled me when it comes to other statements and physics equations having to do with energy and gravity. It never felt symmetric.

I seem to recall that Einstein knew about quantum entanglement and it troubled him. I don't think he completely understood it. I suppose an arm chair physicist like me should be too upset if it is something I don't understand too.

I will just point to the wikipedia articles on this stuff. If wikipedia is wrong - you can edit it.

wikipedia - Virtual particle

"A virtual particle does not precisely obey the energy–momentum relation m2c4 = E2 − p2c2. Its kinetic energy may not have the usual relationship to velocity. It can be negative.[5]:110 This is expressed by the phrase off mass shell.[4]:119 The probability amplitude for a virtual particle to exist tends to be canceled out by destructive interference over longer distances and times. As a consequence, a real photon is massless and thus has only two polarization states, whereas a virtual one, being effectively massive, has three polarization states. "

wikipedia - Negative energy - Gravitational potential energy

The positive gravitational attraction between two massive objects is accompanied by a negative amount of gravitational potential in the field which attracts them. As the distance between them approaches infinity, the gravitational attraction approaches zero from the positive side of the real number line and the gravitational potential approaches zero from the negative side. Therefore, as two massive objects move towards each other, the motion accelerates under gravity causing an increase in the (positive) kinetic energy of the system and an increase of the same amount in the (negative) gravitational potential energy of the object. This is because the law of conservation of energy requires that the net energy of the system will not change. The gravitational potential energy is a kind of binding energy. [2]

A universe in which positive energy dominates will eventually collapse in a "Big Crunch", while an "open" universe in which negative energy dominates will either expand indefinitely or eventually disintegrate in a "big rip". In the zero-energy universe model ("flat" or "Euclidean"), the total amount of energy in the universe is exactly zero: its amount of positive energy in the form of matter is exactly cancelled out by its negative energy in the form of gravity.[3] (It is unclear which, if any, of these models accurately describes the real universe.)

Also:

wikipedia - Casimir effect

wikipedia - Quantum fluctuation

What bugged Einstein about quantum entanglement is presented as EPR paradox.
It led to Bell inequalities that can be tested experimentally.

The experiment results agree with quantum mechanics, as counter-intuitive as it is.

There's no fundamental reason for the energy of the whole Universe to be conserved - conservation of energy is bound by Noether's theorem to invariability of physical systems against time translations (starting them at different points of time).
But the whole evolving Universe is not invariable against time translations because the time is a part of the system itself. So, in very large timescales, energy doesn't have to be conserved.

True Story:
I was walking through the Wedge (a wedge shaped enclosed common area with seating between two dorms) on my way to lunch my sophomore year in college. Harold McKeirnan was sitting on one of the benches scribbling madly in intense concentration. "Hey, h" I said. He always went by "h". Never capital, always lowercase. My friend h was the best physics student in school. "I am calculating the exact probability that Don Ross will disappear from his seat there in the Wedge and reappear in the middle of the quad," he said as he continued with his intense calculation, without looking up he said "first I need the precise wave form representation of the Wedge," h continued in deep thought. "Oh," I said as I continued to the cafeteria. Interesting school.

Good luck with precise wave form representation of something of the size of the Wedge!
Precise wave form representation of a big molecule is a challenge enough, isn't it, QuantumChemist?

Sometimes when h wrote his name he would write h bar instead.

Yes, that can be a real pain the more complicated the system gets. I would hate to have to do that for a protein molecule with so many atoms to deal with. Decades ago as an undergrad, my class covered relatively small molecule waveform representations (and ways to further resolve them) in Physical Chemistry 2. I remember that it was not fun to do.

Side note: I tend to think energy representations as vector spirals rather than as waves. Spirals look like waves when viewed from the side, but have an added dimensionality. That subtitle difference helps me understand the formation process of substructures of particles from electromagnetic “waves” during E => mc^2 conversions. The => (arrow) means the process is going towards the right side of the equation.

Yes - that is what makes the story funny. Kind of an in joke.

A bit like this:

https://gizmodo.com/the-fake-chemical-c ... un-5887014

It is, however, a true story. You had to know h.