Hawking Radiation

>>8408768
Empty space isn't really empty. Random pairs of particles pop into existence and then annihilate each other. When a pair of these particles comes into existence right at the border of a black holes event horizon the particle within the black hole can't escape it's gravity. The other particle is able to escape and the black hole thus loses energy.

>>8408768
A virtual particle is a spontaneous generation of energy from the vacuum.
They don't exist long and usually occur in pairs.
Near the event horizon, the pair exists longer than normal, and there's a chance that half of the pair can escape the horizon.

Since its a virtual particle, it is theorized that it can escape the black hole even though it has mass.

>>8408771
>>8408773
But then how does this cause the Black Hole to lose mass/energy? Are the particles formed from energy inside the event horizon? And shouldn't everything inside the event horizon be in the singularity?

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>>8408780
This is the part I don't get either. Can anyone here explain? Don't hesitate to give a comicated explaination.

>>8408771
>>8408773
Virtual particles have been tested? or remain theoretical?

Wouldn't a virtual particle formed just outside the event horizon just get sucked back in due to gravity?

Wouldn't this result in long-term change in the black hole?

>>8408771
Why would the virtual particle falling in decrease the black hole's mass? Shouldn't it add to it instead? If it somehow has "negative energy", why doesn't that happen to the escaping particle?

>>8408768
The ultra-basic explanation:
It would violate uncertainty if we knew that a vacuum was really totally empty, so there must be shit popping in and out of existence--a particle and an antiparticle

As others have said, if one of them crosses the event horizon and the other one doesn't, the free one could escape. Since it can't annihilate with its buddy, it's no longer "virtual."

Because the area around the black hole is pretty much a closed system, it would be bad for conservation of energy if a particle left and there was the same amount of energy around and in the black hole as there was before.

So the black hole does the universe a solid and loses mass equal to the energy of the particle that escaped. It probably changes momentum too, especially if the black hole has angular momentum.

>>8408773
So a pair of particles exist, then usually immediately kill each other

somehow these happen near the surface of the black hole and instead of killing each other they split, one gets captured and the other doesn't and it somehow escapes the black hole's wicked gravity.

How does the black hole lose mass if it swallowed one (or one half) of a particle?

how does the other particle escape a black hole's wicked gravity?

>>8409034
>how does the other particle escape a black hole's wicked gravity?
Im not sure about the rest of your questions but this is the (relatively) easy part. All it has to do is go really fast, which isnt much of problem

>>8408804
They can't be observed, but they fit the current models extremely well. >>8409034
Since it's a virtual particle, it isn't really effected by forces until it becomes real.

The particles come from the vacuum. When a pair is generated, it takes that much energy from the vacuum leaving a "hole". The vacuum around a black hole is considered part of the hole, so when the vacuum looses energy, the black hole does.

>>8409063
I thought a vacuum was literally nothing

So this vacuum somehow has and retains energy within itself and itself is apart of the black hole?

>>8409053

If light can't escape how does this particle?

How does it go the speed of light and escape but other particle and waves cannot?

One of the pair will be anti matter. The antimatter partner is slightly more likely to fall into the black hole, where it annihilates with a normal matter particle, shrinking the black hole. This makes little sense to me too.

>>8409032
So basically it makes no logical sense outside of "If this didn't happen the universe would explode"?

>>8408780
>>8408792

I am no expert. But I believe that essentially they are particle and anti-particle (hence why under normal conditions they're able to annihilate). If an anti-particle enters the black hole, the black hole has lost mass.

virtual particle appears at the edge, one side in one out -> half drops into black hole and other escapes.

The doomed particle would balance the positive energy of the outgoing particle by carrying negative energy inwards — something allowed by quantum rules.

>>8409075
>If light can't escape how does this particle?
Light can escape from outside the event horizon

>>8409063
Well ... virtual particles remain theoretical, that while this can not be real ...

>>8409084
I got quantum mechanics, thermodynamics, and I think some information theory from his explanation...

>>8408804
Correct me if I'm wrong but aren't virtual particles required for gamma rays to generate electron/positron pairs? Or any pair production scenario in general? Since pair production happens regularly in particle accelerators and cosmic ray events, wouldn't this prove somewhat that virtual particles exist? Also I think the Casimir effect is also explained by virtual particles.

Since this thread is already about virtual particles and hawking radiation, would it be possible to create something like a zero point energy thing with an artificial event horizon? As I understand it, Hawking radiation relies on virtual particles near the event horizon. One particle falls in with negative energy/mass somehow and one escapes with positive energy/mass. If we could make an artificial event horizon, we could trap particles with negative energy and then harvest the positive energy particles as free energy. Since the particles emitted would consist of 50% matter and 50% antimatter, this would be easily harvested as usable energy since they would annihilate and produce gamma rays that we can use as heat to power generators. We could store the negative energy particles for possibly novel uses such as making a warp drive (Alcubierre drive) which needs particles of negative energy anyways, or as a weapon. A negative energy bomb would be pretty awesome, I think that's what happened to eva unit 04.

>>8409415
t. Madman who wants a black hole near earth

>>8409089

No, particles and anti-particles have the same mass.

So does the infalling particle HAVE to be the antimatter one for the black hole to lose mass?

>>8409448
There might be a way to create something that does the same thing to virtual particles as a black hole event horizon but without an actual black hole. Thats why I said artificial event horizon, not black hole. A small black hole would be useless since it would decay too quickly anyways.

>>8409458
Statistically equal amounts of antimatter and matter fall in from virtual particles except that those have negative energy according to hawking. I tried to find out why online but only found some mumbo jumbo saying that inside a black hole the negative energy particle would actually be observed as having positive energy. Apparently shit is so fucked inside a black hole that time and space get swapped or some shit.

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>>8408768
"Empty" space is a field of constantly self-annihilating particles.

At the edge of a black hole's event horizon, sometimes one of these particles falls into the black hole before annihilation can occur.

The surviving particle is emitted as Hawking radiation.

The particle that falls in, instead, annihilates a particle within the black hole, thus it loses mass.

The smaller the black hole's event horizon, the more quickly this happens, thus small black holes evaporate fairly quickly, while large ones can takes magnitudes of trillions of years.

There is a possible flaw in this theory, in that it may violate the law of conservation of information.
https://en.wikipedia.org/wiki/Black_hole_information_paradox#Hawking_radiation

https://www.youtube.com/watch?v=aPgLvRNKpI0

...But, it's probably a thing, as otherwise CERN has killed us all - or more importantly, all those much more powerful cosmic ray collisions that happen above us would have done so long ago.

>>8409308
Effects of virtual particles are measurable.
https://en.wikipedia.org/wiki/Lamb_shift#Experimental_work

>>8409519
>The particle that falls in, instead, annihilates a particle within the black hole
[citation needed]

>>8408792
>>>8408780
>This is the part I don't get either. Can anyone here explain?

Okay.

Energy CANNOT be created from nothing. Period, full stop.

Vacuum pairs always annihilate each other, preserving this fact.

The event horizon breaks this mechanism. The black is is thus 'doing work' to the universe by breaking those pairs.

The surviving particles radiate outward, giving the hole a temperature.

By doing work, the black hole expends energy.

Energy is mass.

Black hole loses mass.

Simple enuf?

>>8409546
The only issue there is that you've not described the process through which the black hole expends energy.

It's not enough to say, "Energy CANNOT be created from nothing. Period, full stop." thus the black hole magically loses mass to avoid violating this rule. These rules don't enforce themselves, they derive from mechanical principles of cause and effect. (Though, I won't get into the conundrum of the existence of the universe itself that does rather suggest the rule can be violated.)

>>8408804
>Virtual particles have been tested? or remain theoretical?
Look up The Casimir Effect

>>8409580
the one thing that the BH has in common with the rest of the universe, is its gravity field.

the virtual pair borrows its energy from that

when the other one escapes and becomes real, half of that borrowed energy isn't returned

a lesser gravity field = a smaller BH

(source: my ass)

>>8409075
Because Vacuum in physic is different from the common, ideal, vacuum, which is called "Free Space", and doesn't exist outside theory.

View all educational boards Academic Results online
http://www.result.pk/

>>8409613
uh oh, a virtual article just became real

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>>8408792
Virtual particles are not normal particles, their energy momentum does not have to be on shell, meaning it does not have to satisfy the relationship E^2 = p^2 + m^2, E >= 0.

if a normal particle or antiparticle fell into a black hole then it would add energy E = mc^2 (assuming we let the momentum be 0), but its different for virtual particles. Its energy and momentum depends on the process that created them, in this case 2 particles are made with some energy (E) and (-E) , since the sum must be 0 due to conservation of energy.

One particle falls into the black hole forcing the other one to become a normal particle, this particle MUST have positive energy thus the other particle collapses the the state with negative energy, this negative energy is then added to the black hole, thus the black hole loses energy, thus mass.

>IMPORTANT
Note that virtual particles are just a way to easily think about quantum processes, they are actually just terms in a Taylor expansion that look like particles, but not realy, which is why they can have any energy or momentum they want (Some virtual particles dont even have to satisfy the Spin Statistics theorems that say bosons have to have integer spin and fermions half integer).

When we say
>'a virtual pair is created and one of them falls into the black hole'
we actually mean that the vacuum field interacts in a complex way with the black hole and one of the terms when we Taylor expand this interaction look like a particle falling into the black hole with negative energy.

>>8409075
In quantum field theory, adding energy to "empty" space excites it, resulting in what we see as particles and forces.

However, the vacuum itself contains latent energy. Virtual particles arise spontaneously from this energy, lowering the vacuum by that amount. In this sense, you can create something from nothing. Keep in mind it's not nothing, though.

There's also a chance that the vacuum will move from its current energy state to a lower one, causing the release in the difference in energy at every point in space. This would be a disaster as it would literally cause the laws of physics to change

>>8409638
lolwut
>negative energy
>falling into the black hole forces the other particle to be not the anti-particle

i dont even...

>>8409638
>One particle falls into the black hole forcing the other one to become a normal particle, this particle MUST have positive energy thus the other particle collapses the the state with negative energy
Could you explain this part a bit more? Generally I would assume that the hole either gains or loses energy depending on which particle falls into it and which leaves. This would however mean that on average the hole gains and loses the same amount of energy and that hawking radiation doesnt exist/ consists of equal amounts of energy and anti energy. I understand that that is not what we observe but I dont get why only antiparticles fall into the horizon/ why the particles that do fall always end up being the antiparticle after the wavefuncion collapses.

Long story short, black holes evaporate into heat.

Over a VERY long time.

>>8408780
conservation of energy
the gravitational force of the black hole is what causes hawking radiation to exist, so, logically, it should also be the source of the energy
In particular, the gravitational force of the black hole is caused by the black hole's mass, and E = mc^2, so the mass of the black hole may be considered energy under certain circumstances
This energy is the source of the energy for hawking radiation.

>>8409643
>negative energy
yes, virtual particles can have negative energy.

>falling into the black hole forces the other particle to be not the anti-particle
by normal particle I meant not virtual. a normal particle can be a normal antiparticle. should have called it nonvirtual instead of normal.

>>8409644
see
>>8409649
I should have been more clear. the particle that falls in is virtual particle or antiparticle, no matter which one falls in the one escaping will be the non-virtual partile (which I called 'normal' above) which has positive mass and the one falling in will have negative. while still virtual the particles will be in a superposition of positive and negative energy (most likely). When a virtual particle promotes to a non-virtual particle (which happens when it cannot join with its pair again) it must have positive energy, thus the wave function collapses to the state where the virtual particle now in the black hole has negative energy.

>>8409638
>2 particles are made with some energy (E) and (-E) , since the sum must be 0 due to conservation of energy.

sum doesn't have be zero if the time is short enough

[math] \displaystyle
\Delta E \cdot \Delta t \geq \frac{h}{4 \pi}
[/math]

>>8409652
>When a virtual particle promotes to a non-virtual particle (which happens when it cannot join with its pair again) it must have positive energy
Still not completely understanding it. Why is only the particle outside "promoted" to being a real particle but not the one inside the hole, since both are prevented from rejoining and annihilating each other?

>>8409519
So the particle that falls into the black hole annihilates a particle that was already inside the black hole? Does that mean that the black hole is no longer neutral inside (the particle that falls in destroys an anti-particle inside). Would this set off a chain reaction of particles inside the black hole annihilating each other?

>>8409652
>called 'normal' above
just use 'real' like the rest of the world

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>>8409659
because the one inside the black hole is never observed, its created and then is absorbed by the black hole. You can think of the black hole as a big particle interacting with the vacuum, the virtual particle falling into it is internal to the Feynman diagram so it remains virtual. pic shows a typical process. Anything that begins and ends inside the diagram is vertual, only particles going out of it (black hole and here 2 other particles) are real.

>>8409663
thats the word im looking for.

Virtual particles are theoretical,

Are not these virtual particles gravitons?

The mutual virtual particle annihilation is a concept that describes the process of a particle that exists below the plank threshold, but it does not guarantee that there is a particle there.

What guarantees that something is there is the energy potential in the space, that can be come from a electric field or the gravity field.

So, if Hawking radiation is detected, should not be the evidence of the graviton?

>>8409725
>Are not these virtual particles gravitons?
no

off-course assuming gravitons exist there will be an effect on all quantum processes due to virtual gravitons, but its not needed for the derivation of hawking radiation, and because gravity is so week, the virtual gravitons are not expected to have a big effect on any process.

>>8409519
>The particle that falls in, instead, annihilates a particle within the black hole, thus it loses mass.
Even if that is the case, energy is still conserved and mass and energy are indistinguishable from each other as in E=mc^2 since the formed photon can't escape the black hole.

>>8408768
Its Stephen Hawking's way of still feeling relevant in the scientific community
>Fuck i forgot to put my name on something, uhh uhhhhh HAWKING RADIATION

>>8409715
>because the one inside the black hole is never observed,
Will someone inside the event horizon see the in-falling particle as a virtual particle or will they see the roles reversed? From the perspective of an in-falling observer, energy conservation no longer holds or he can detect negative energy.

Black Hole War by Leonard Susskind is a pretty good book to read on the topic

>>8409916
It's a good question. There's no consensus on this.

>>8409454
But then if the anti particle hits a particle in the black hole, then it loses mass

>>8410750
Energy is the same as mass.

>>8408771
This can only be a claim made by someone who has no clue why "virtual pairs" of particles come into existence in the first place.

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>>8408768
Blackholes don't exist so something that is also made up based on something that doesn't exist also won't exist.

HOWEVER! I'm sure you can get a grant to explain all the "holes" in blackholes. Or, I suppose you could fuck off and do something else with your brain power and grant money that will actually help humanity.

Hawking radiation is a laughable concept that fails already when you consider that half of the "escaping" particles have opposite polarity that can annihilate the other "escaping" half just as well.

>>8410823
They aren't entangled or any such, so they've no method to seek out and annihilate each other.

I am a bit confused as to why the black hole doesn't absorb roughly as many positive particles as negative ones though, thus negating the evaporation effect, if not the Hawking radiation.

>>8409638
>One particle falls into the black hole forcing the other one to become a normal particle, this particle MUST have positive energy thus the other particle collapses the the state with negative energy,
This is quickly turning into a five year old asking why the sky is blue... But, yes, why MUST it?

>>8410821
>Blackholes don't exist
>>>/x/

>>8409580
>The only issue there is that you've not described the process through which the black hole expends energy.

Yes I have.

Mass is energy. They are the same thing.

Particles escaping the black are have mass, ergo, they are also energy.

Mass/energy.

Is this not clear?

>>8411067
The particles aren't escaping the black hole, that's part of the problem.

Half of a new set of particles that would normally MAD, is being absorbed by the black hole. One particle, that in this position and energy level would had escaped anyways, is spinning off the accretion disc, and the other is being absorbed.

The black hole isn't doing any more "work" than it normally does. It doesn't normally lose mass by absorbing energy, nor does it lose mass when something fails to enter its event horizon.

Now, if you said something along the lines of the negative energy particle is, by nature of it being negative, removing mass from the black hole upon absorption, that'd be another thing.

Though no one's explained the mechanics behind that either, nor why the black hole doesn't absorb a roughly even number of positive and negative particles, negating the evaporation.

>>8410839
>This is quickly turning into a five year old asking why the sky is blue... But, yes, why MUST it?
Because if there were negative energy states then a particle could continue to loose energy as it emits these particles with negative energy, it would result in no stable particles, and in fact any particle with positive energy would almost instantly emit a bunch of particles and loose all its energy. Another way to look at it is that the lowest possible energy is the vacuum, but if there exists a negative energy particle then there is no lowest energy since you can always lower it by adding another particle . For more detail you can look up the history of the Dirac equation and antimatter, naively antimater looks like matter with negative energy, but since it leads to all kinds of problems it was eventually realized that its antimatter with positive energy.

>>8408997
No, by definition it wouldn't, the event horizon is where it gets sucked in

>>8409017
It is a shitty analogy, don't look too far into it.

>>8411129
Is already been mentioned but I'll say it again.

The vacuum around a black hole is considered part of the black hole.

When a virtual particle becomes real, the vacuum loses energy. Therefore, the hole loses energy

>>8411582
That's... Not what you said... Though I also think that's not quite right either, as from that perspective, all of space is part of the black hole.

Technically, even the event horizon isn't part of the black hole - it's just a side effect of the singularity and the mass orbiting inside said, the former being the only object that could truly be defined as such.

The event horizon is not symmetrical. From the inside of the Black hole, you can't cross it but stuff comes in, from the outside you can cross it but nothing comes out. This somehow translate into the energy being positive outside and negative inside, but that's not trivial at all.

If you really want to know how the energy is calculated, it's via a certain "norm" of the field elements which is actually not a norm but a pseudo-norm : it's not derived from a normal inner product, but from a "Krein product", which respects the signature of space-time. Basically it's a norm that can be negative. It doesn't invalidate the stability of the vacuum, though, its just because your coordinates can't be adapted to both inside and outside the black hole. You'd need to invert the energy scale, but in order to do that you also have to invert the direction of propagation of your particles : it faithfully describes what happens inside the black hole, but not outside.

The whole thing is way clearer if you think it terms of field, and not particles. If you have some knowledge of Special Relativity and/or Field Theory, look up the Unruh effect. It's a simpler computation of the same thing.

>>8408804
Casimir effect

>>8411582

Also, that's... just plain wrong.

>>8408804
Neither. Virtual particles are just a calculation apparatus. Their actual existence is unverifiable by definition : if you see it, then it's not virtual. Their being not observed enables us to consider particles which don't really respect local causality is all. That's useful for quantum effects.

>>8411595
https://en.wikipedia.org/wiki/Lamb_shift#Experimental_work

>>8411588
>>8411601
You guys have no idea what you are talking about. These dont prove virtual particles are somehow 'real', it proves the interactions in QFT is correct. as already said virtual particles are just a visual representation of the terms of a Taylor expansion of the interaction.

>>8411601
I don't really get what you're trying to say with that admittedly related link.
The Lamb Shift exists. It's a quantum effect, in the sense that it is only there because of the Q in QFT. So there's a loop (and ergo virtual particles) in the Feynman diagrams that we use in the computation... Is it meant as an example of what I said?

>>8411613
Their effect is measurable,
something that can be said of quarks too.
If quarks exist, so do virtual particles (which of course aren't really particles but waves, history gave us a shitty name)

https://profmattstrassler.com/articles-and-posts/particle-physics-basics/virtual-particles-what-are-they/

>>8411642
The fact that their effect is measurable doesn't prove their existence. The problem in your reasoning and in the simplification of your source is that virtual particles don't just translate real, local (on-shell), perturbations in the field, but also maybe-real-maybe-not, non-local quantum probabilistic fluctuations. If you postulate that all eventualities of the quantum world exist, copenhagen-style, then sure, virtual particles exist as a superposed state. If you don't, then not necessarily.
Another way to see that is that you can do an asymptotic expansion of a non-quantum field theory. You also get virtual particles, but they don't need to be non-local because you won't have any loops. In that case, okay, they "exist" in the sense that if you resum all of their contributions, you should get your field perturbation. But as soon as your theory is Quantum, you get loops in your diagrams, particles need to be off-shell sometimes and wht they represent is a kind of "mean" perturbation over different field eventualities, you can't be sure which one actually exists.

>>8411642
"quarks exist" and "virtual particles exist" are two vastly different postulates.
"quarks exist" means "there are quark fields", which is an actual axiom of the Standard Model.
"virtual particles exist" means, in the context of your source, "the inner lines of feynman diagrams are the translation of actual perturbations on the field, that really do happen in real life even though we're never actually looking at them but only at their by-products", which is an interpretation of Quantum Field Theory's calculations.

>>8408768
just try to understand the jumble of math you retarded nigger faggot

>>8408768

The explanation is actually way sturdier when you use fields instead of particles, but it's a bit harder to grasp.

-- Particles are oscillations of fields. the frequency of a radiation is its energy

-- Now, there is a doppler effect around a black hole : frequencies get higher and higher as you approach the event horizon. In particular, that means that if there is a light source falling into the event horizn, and you're watching from outside, then the frequency of the light gets more and more displaced to the lower end of the spectrum (infrared) until it is on the event horizon, at which point the frequency reaches 0 and you can't see it anymore. This means that the only way light is going to come to you from the event horizon is if the frequency of the source is infinite, which is impossible, right?

-- Not right. Actually, your fields are quantum, which means that they have random fluctuations, which get bigger and bigger as you're looking at smaller scales. So the random fluctuations at infinite frequencies can actually come to you from the event horizon. They have a certain energy (actually they look like a black-body radiation, so you can even define that energy as a temperature).

-- Energy doesn't just come out of nothingness, so the Black Hole has to be losing mass.

There you go, no notion of negative energy.

>>8410839
>I am a bit confused as to why the black hole doesn't absorb roughly as many positive particles as negative ones though, thus negating the evaporation effect, if not the Hawking radiation.
long story short, all of this is just an analogy of some bullshit quantum mechanics.
The virtual particle is an entangled system and its interaction with the black hole causing it to split guarantees the particle sucked in is negative energy

>>8408768
It's there in the picture...can you not understand that?

>>8411811
This sounds right even though Ive never heard it before. At least I dont know enough about fields to question it in any way.
Do you have a source for it? Especially interested in why the doppler effect is happening at the event horizon and how the black hole exactly is losing energy without the use of antiparticles. Thanks!

>>8412746

Well, I don't have a synthetic source for it but it's basically saying the same thing with fields instead of particles, and looking at only one side of the horizon to simplify the whole thing.

If you want, you can look up the Unruh effect. It's a simple case of Hawking radiation, with a simple metric (Rindler) and a simple expansion of the vacuum. I've only seen it done using the formalism of fields, but I think if you look it up you can find a followable, step-by-step computation, if you have at least some notion of what a field is and are ready to accept how to quantize them.

The doppler effect around the horizon, that's just black hole physics 101. Actually even Einstein Gravity 101. It's called Gravitational Redshift and I think you can find it pretty much anywhere.

Now, truth be told, if you look at what happens on both sides of the horizon, you will find negative energy modes of oscillation on one of them, but that's actually because of what happens to your metric as you cross the horizon (there's a sign change between a time coordinate and a space coordinate, and your energy formula has to account for that).

Btw, I think they're not really "anti-particles"... especially because the computation is generally done with a hermitian scalar field (the simplest kind, which is it's own anti-particle, like a photon). It's the same particle, just with negative energy relatively to your referential frame.

I actually think an observer on the inside of the black hole, and using proper coordinates, would see it as positive energy (let's hope so, otherwise his vacuum state is unstable and that's a whole new shitstorm)... But who cares about him? You're outside, and in your coordinates, he's getting negative energy and you're getting positive energy. Cause energy is frame and coordinate dependent in General Relativity anyway.

>>8412746
If or when you're somewhat confortable with Special Relativity and Second Quantization, try this one:

https://arxiv.org/abs/0710.4345

Particularly section 2 (the accelerated detector).

If you're feeling particularly adventurous, there's even this :

https://arxiv.org/abs/gr-qc/0308048

>>8413637
>>8413649
>If or when you're somewhat confortable with Special Relativity and Second Quantization
See you in two years then... I tried to watch some lectures on the Unruh effect but didnt get very far. Im afraid just knowing about le Quantum Mechanics popsci without the actual maths or physics to back it up will result in nothing meaningful.

When is a good poin to go for a QM lecture? Is it smart to do nuclear physics and solid state physics beforehand or is that not important for it? Also what maths should I know? Calc 2 and Vector Analysis enough?
Special Relativity will have to wait until my masters anyways Im afraid...

Black holes do not lose mass from particle-antiparticle annihilation, they lose mass because the particles were virtual, and one of them remains real. It does not matter if the escaping particle is a particle, antiparticle, or photon. In each case, the blackhole loses energy. How is this possible? Particles and antiparticles both have positive mass, just opposite electric charge. So when the vacuum spontaneously emits a particle and anti particle, although charge is conserved, mass is not conserved.

This mass can exist because of the Heisenberg uncertainty principle >>8409658. If the uncertainty or change in time is small, then the uncertainty or change in energy will be large. Basically we are saying that if two virtual particles have a total energy [math] \Delta E [/math] then they can exist for a time [math] \Delta t [/math] without any violation to physical laws like conservation of Energy. In order to make sense of the uncertainty principle, we claim that virtual particles "borrow" this [math] \Delta E [/math] from something around it, and then after [math] \Delta t [/math] they "return" the energy. This energy can be borrowed from anything.

Now, we know blackholes are just points of infinite density within the event horizon. These are regions of space-time that are infinitely curved (as long as you're within the event horizon). Outside of the event horizon, spacetime is significantly curved. It's not infinite, but it's still extreme. As described by Einstein, spacetime curvature is caused by mass or energy. The blackhole doesn't really have mass or photons, it's just a point. Instead the energy manifests itself as pure spacetime curvature. So when other anons in this thread said that the virtual particles stole energy from the vacuum, what I think they meant is that they stole the energy from the spacetime, causing it to be less curved, and thus reducing the blackholes energy.

>>8413662
>is it smart to do nuclear physics and solid state physics beforehand or is that not important for it?

Well QM is basically all about mathematical formalism, and shifting your mindset from "explaining the whole phenomenon" to "calculating probabilites for outcomes given certain initial conditions". So you can try your hand at Nukes and S.S. before, but it won't help you much. There is some semi-classical/semi-quantum stuff in both, but that usually doesn't really help, because it requires you to know both classical mechanics, QM, and how to navigate from one to the other.

>When is a good point to go for a QM lecture? Also what maths should I know?

Well anytime you want is good, but the one thing you really need to know about is linear algebra. You need to be able to manipulate Complex (as in not real) vectors in finite and eventually infinite dimensions, with the usual scalar products (so complex prehilbertian spaces at least). Also, you need to know a bit about matrices and operators, especially why we like to diagonalize them, what a hermitian operator is, and the spectral theorem (at least in its finite dimensional formulation). Also Fourier Transforms.

Second Quantization is vaguely understandable as soon as you feel comfortable with the QM formalism (it's just how to do the same thing for fields instead of punctual objects).

>Special Relativity will have to wait until my masters anyways Im afraid...
Well that's kind of surprising, cause it's probably the easiest to grasp. You just need to have an understanding of Euclidian geometry and prepare to just shit on it for a while, 'cause you're going to twist it into Lorentzian geometry. You also need to be okay with adding a number on top of your usual 3d-vectors.

Once you've defined 4-speed and 4-acceleration, you can do Rindler coordinates ; then you're goind to 2nd-quantize your way into Unruh. It's gonna hurt a bit when you realize that the notion of "vacuum" is actually relative.

>>8413662
Erratum : before doing the transition QM->2nd Quantization, you'll probably need a modicum of variational mechanics (Lagrangian and Hamiltonian mechanics... That would be a good parallel study to QM formalism anyway if you don't already know it)

>>8413679
Well that'd be a good, simple way to look at it, but energy surplus or minus in the Heisenberg principle is NOT borrowed from anywhere ; Heisenberg actually breaks the energy conservation theorem (which is true as a mean over time, and not over a very short time, quantum style). You could say that a fluctuation somehow becomes premanent because of gravity, and gravitational energy somehow lowers for the sake of energy conservation, but that's kind of a non-explanation, seeing as you're basically saying "some unknown quantum-gravity-type interaction takes place and shit comes out of the black hole"

Also, while it's true that anti-particles have positive inertial mass it's not experimentally verified whether their gravitational mass has the same sign. Equivalence principle is an experimental fact only for normal matter, the standard model doesn't say anything about it, and we don't have a definite theory of quantum gravity. In the case of Hawking, though, it's true that their mass doesn't have to be negative in order for the Hawking radiation to happen. Only their energy. Which it is, relative to the exterior observator.

>>8408768
Theres a lot of retarded explanations and half right explanations ITT. Let me try to clear this up. The empty vacuum of space has energy, its not exactly empty. All over the universe at all times subatomic particles and anti-particles spontaneously form in pairs. Under normal circumstances these pairs immediately collide and annihilate eachother, which gives us zero point energy or vacuum energy, and is responsible for the Cassimir effect (google it). When a black hole forms there is some point outside the event horizon where gravity is strong enough to separate these virtual pairs, yet weak enough to allow some to escape. This causes anti-particles to fall into the black hole and annihilate a little bit of mass inside the black hole, while the anti-particle's particle pair floats off into space as Hawking radiation. Net energy is not created or destroyed, because an equal amount of mass is destroyed inside the black hole as is let off as hawking radiation. Nothing has to escape the even horizon because the particles are separated outside the event horizon. The vast majority of these particle pairs fall into the black hole, but for some only one of the two particles is captured. As to why there are more anti-particles falling into the black hole than standard particles, i am not sure.

>>8413679
One question, wiseanon.

If the vacuum or space doesn't have any substantial energy field on it (being gravitational or electrical), the "existence" of virtual particles is less likely?

>>8413817
>Heisenberg actually breaks the energy conservation theorem
Which is why I said "in order to make sense of the uncertainty principle". I don't know where or how the uncertainty principle was derived, so I don't know how fundamental it is, but my intuition tells me Energy conservation is more fundamental. Heisenberg doesn't "break energy conservation" as much as it's only a strange exception to energy conservation for short time scales.

>anti-particles have positive inertial mass it's not experimentally verified whether their gravitational mass has the same sign
Wouldn't we be able to observe positrons "falling up" from gravity if this were the case? I don't work at LEP but I don't think it's justifiable to say it's not experimentally verified when experiments that would need to take this effect into account don't.

>>8413836
>As to why there are more anti-particles falling into the black hole than standard particles, i am not sure.
Maybe you should reread the thread. A lot of those half right explanations have the same problem.

>>8413841
I think the existence of virtual particles only depends on the uncertainty in energy, not the total energy. Remember, when talking about energy we could take any reference point to be our origin, and the total energy around a blackhole could therefore be positive, negative, or zero.

>>8413860
>Wouldn't we be able to observe positrons "falling up" from gravity if this were the case?

Actually no. Not at LEP, not at LHC, not anywhere. We don't see the effects of gravity on individual particles, because gravity is so weak and they're so light. It's one of the big problems of quantum gravity. Most theories of quantum gravity do have positive gravitational mass though, because making gravity work without the equivalence principle is kind of a hassle, but the best experiment we have is this
http://alpha.web.cern.ch/
So we know that the ratio of grav. mass and inert. mass is somewhere between -65 and +110.
So... yeah. It seems unlikely but it's possible as yet.

>>8413896
thanks

>>8413860
>Heisenberg doesn't "break energy conservation" as much as it's only a strange exception to energy conservation for short time scales.

I guess it's pointless to argue that but the two things are one and the same. If there is an exception at some scale for a universal law, then we say that universal law "breaks down" at that scale. Just like Newtonian physics "break down" at relativstic speeds, and at quantum scales.

>>8413836

Technically they don't mean "anti-particle" but something to the tune of "particles with negative energy relatively to the outside observer". Actually the calculations of Hawking Radiation mostly uses fields that don't have anti-particles, such as the photon.
So it's more like "the gravitational field separates vacuum into some positive energy/negative energy pair of particles, and always absorbs the negative energy for two reasons (other than do the math and it'll work) :

1) The horizon is not symmetrical. outside, you can cross it, but nothing can cross it from inside. Which means there isn't actually a reason why positive energy and negative energy should be emitted equally in both directions (and when you do the computation, you always find a sign difference which, ultimately, is caused by the fact that the geometry of space-time is Lorentzian, and the horizon brutally switches two signs in its metric).

2)a) negative energy wouldn't make sense for where the observer is actually standing : if it existed then his vacuum state would be unstable and all of his physics would break down.

2)b) It's not a problem for inside the horizon, though, because his choice of space-time coordinates isn't adapted to the inside of the horizon. In order to adapt the coordinates to an observer inside of the horizon, we would have to invert the energy scales.

So in conclusion, he sees energy flowing out of the horizon, with negative energy flowing in which, by a coordinate change, is the same as positive energy flowing out for an inside observer. Everybody's happy and the Black Hole can spray its entropy everywhere in peace."

>>8411642
The effects described by virtual particles obviously exist.

Virtual particles, however, don't necessarily "exist"- they're *calculation tools*, ways of mathematically representing stuff that we don't know how to calculate.

This article from Prof. Matt Strassler's (very good!) blog is a pretty good way to understand them from a layman POV:
https://profmattstrassler.com/articles-and-posts/particle-physics-basics/virtual-particles-what-are-they/

A quick tl;dr of that article - in QFT, particles are waves in quantum fields. However, not all disturbances in quantum fields are actually particles - think of things like evanescent waves in optics, or static electrical fields. Our mathematical apparatus for calculating stuff in QFT doesn't have a general way to describe these, so we *represent* them by treating them as a combination of "virtual" particles with values for mass/energy/momentum that would be illegal for a proper waves. If you add up an infinite series of these virtual-particle interactions, you get the equivalent of the full interaction.

If you're a little more technical, virtual particles are for quantum fields what the Green's functions are for (among other things) classical electromagnetism.)

This does get into questions about in what sense *anything* in our model is actually real and not just a calculation tool, but virtual particles specifically are generally viewed as an artifact of the perturbative methods (Make a guess by solving a related problem that's simple enough to be exactly solvable, and then tweak that quess by adding an infinite series of "small" contributions from increasingly complex approximations) we're forced to use to solve quantum field theory problem. The individual terms of an infinite series approximation aren't "real" - what's real is the actual number they approximate.

>>8408768
I found the simplest, but least precise (while still remaining kinda true) explanation. It's kind of a bore in a non-magical kind of way, though.
From a Quantum Mechanics standpoint (and more precisely, a Quantum Field Theory standpoint), the fundamental constant usually called "c" is only the speed of light in the sense of the "mean" speed of light. The speed of photons actually fluctuates randomly, following the laws Quantum Mechanics (embodied by the Feynman propagator). So particles shouldn't get out, but actually some do. Very slowly at first, but faster and faster as the black hole shrinks. Since this only hinges on pure randomness, the spectrum of the ensuing radiation is a black-body spectrum etc. It's basically a tunnel effect for the fundamental limit of c.
Isn't it kind of boring that way?

>>8413983
Anybody has a source on this? Precisely the variation in c and the tunnelling through the event horizon. What is the potential of the event horizon for a particle to tunnel through?

>>8413983
Bullshit, any perturbations in a field FTL cancel out when you sum the propagators.

>>8414050
That claim doesn't look trivial in the context of a curved space-time with a horizon present. Can you prove it?

>>8410819
You are exactly correct

>>8408997
>Wouldn't a virtual particle formed just outside the event horizon just get sucked back in due to gravity?

>Wouldn't this result in long-term change in the black hole?

I think that the point is that for any given particle/mass/vector, there exists a very fine line (distance from the singularities center) where above that line, the particle escapes from the black holes gravity.

And below that point, the particle falls into the black hole.

And that a virtual particle pair, statistically, could come into being ON that line, and one half would escape, and the other half would not...

Generating a stream of these virtual particles from any sufficiently massive object (Escape velocity > c).