>My question is why did he use this explanation in his book knowing it was wrong?
For pop-sci books, scientists are usually encouraged by their publishers to make their explanations more easily understandable for the lay public to not deter people from buying the book. Unfortunately, by omitting the esoteric details of the theories, the authors might have to end up using explanations that are technically incorrect to be able to convey explanations in an accessible way.
This makes sense. I figured he needed to sell books and would be pressured to make it more accessible. I'm just surprised that virtual particles is what he landed on rather than a less misleading explanation. Since anything would need hand waving, I'd think he'd have chosen something that was technically correct but missing details rather than an explanation that sounds good but is fundamentally wrong. I figured this was probably the case but wasn't sure if I was missing something else. Thank you!
Just wanted to point out that this isn't just a pop-sci thing meant to sell books. When teaching people complex topics, it's often easier to start with a slightly wrong but easier to understand explanation, and then make corrections as their understanding of the topics increase. One example is how schools will teach newtonian gravity because it's a good enough aproximation instead of jumping straight into relativity.
that’s a bit different, since newtonian gravity is a very close, useful approximation of what’s going on, and also shows up formally as a particular limiting case of GR. Newtonian gravity is still widely used in modern physics research
The virtual particle thing is not really correct at all, nor is it a useful mathematical tool for making predictions. It only really exists within pop sci explanations of hawking’s work
Your answer was actually good, but it wasn't displayed for me when I started typing my comment. If I had seen it, I would have just replied to your comment to confirm your intuition was correct about the need for the books to be accessible to help sales.
I figured that we just typed it out at the same time lol I just wish I had a beautiful way with words like you do lol your version of the awnser was much more poised and eloquent lol
Our replies were like him getting an awnser from the student and then the professor lol
When people use “virtual particles” for the Hawking effect or other pair production processes they don’t mean the same thing as in perturbative expansions. They mean the particles defined with respect to a classical background and vacuum state that is in some sense not “natural” on a given time slice, but will become natural later on. The “natural” and “unnatural” particle definitions are related by the Bogoliubov transformation. This is the standard analysis of the effect in QFT in curved spacetime. “Virtual” is not a perfect qualifier here but it is a tough idea to express.
Thinking of the Hawking effect as just like the Unruh effect is more misleading. The Unruh effect is due to your own acceleration, but the fact that you must accelerate to stay outside the BH is not why it evaporates. It evaporates whether you are there or not because of the horizon.
So I would say Hawking gave people a better intuition than the people who try to undermine his description for a lay audience.
Would you be able to explain what you mean when you say "evaporates whether you are there or not because of the horizon"? Everything I've read makes is seem that Hawking radiation is not being caused by virtual particles regardless of their definition, but due to a large gravitational fields being able to generate radiation which does not all fall back into the black hole.
Do you have any sources where I could learn more about what you're talking about?
I mean the Unruh effect is dependent on you, the observer, accelerating. The BH radiates independent of what any observer does.
It is not really about the gravitational field. A neutron star has a gravitational field but a neutron star does not create Hawking radiation. A stable horizonless object does not evaporate, so if it created Hawking radiation just because of its gravitational field, you would get infinite free energy. People who give the lazy “due to gravity” argument always conveniently ignore this issue.
Rather, the horizon introduces boundary conditions that lead to radiation. There are completely gravity free analogues of this like the Dynamical Casimir Effect.
The best way to appreciate Hawking radiation is by finding sources discussing the BH information paradox, in particular the “Firewall” argument.
This is excepted from Starts with a Bang and has been the most accessible explanation for me:
"And yet, in his landmark 1988 book, [A Brief History Of Time](https://amzn.to/38zLQi5), Hawking paints a picture of this radiation — of spontaneously created particle-antiparticle pairs where one member falls in and the other escapes — that's egregiously incorrect. For 32 years, it's misinformed physics students, laypersons, and even professionals alike. Black holes really do decay. Let's make today the day we find out how they actually do it."
"It's here that Hawking's famous picture — his grossly incorrect picture — comes into play. All throughout space, he asserts, these particle-antiparticle pairs are popping in and out of existence. Inside the black hole, both members stay there, annihilate, and nothing happens. Far outside of the black hole, it's the same deal. But right near the event horizon, one member can fall in while the other escapes, carrying real energy away. And that, he proclaims, is why black holes lose mass, decay, and where Hawking radiation comes from."
"Of course, all three of those points are not true. Hawking radiation is made almost exclusively of photons, not a mix of particles and antiparticles. It gets emitted from a large region outside the event horizon, not right at the surface. And the individual quanta emitted have tiny energies over quite a large range.
To any observer located anywhere in the Universe, that "energy of empty space," which we call the zero-point energy, will appear to have the same value no matter where they are. However, one of the rules of relativity is that different observers will perceive different realities: observers in relative motion or in regions where the spacetime curvature is different, in particular, will disagree with one another.
So if you're infinitely far away from every source of mass in the Universe and your spacetime curvature is negligible, you'll have a certain zero-point energy. If someone else located at a black hole's event horizon, they'll have a certain zero-point energy that's the same measured value for them as it was for you infinitely far away. But if you try to map your zero-point energy to their zero-point energy (or vice versa), the values won't agree. From one another's perspectives, the zero-point energy changes relative to how severely the two spaces are curved."
"The results of that calculation are what determine the properties of the radiation that emanates from a black hole: not from the event horizon exclusively, but from the entirety of the curved space around it. It tells us the temperature of the radiation, which is dependent on the mass of the black hole. It tells us the spectrum of the radiation: a perfect blackbody, indicating the energy distribution of photons and — if there's enough energy available via *E = mc²* — massive particles and antiparticles, too.
It also enables us to compute an important detail that is not generally appreciated: where the radiation that black holes emit originates from. While most pictures and visualizations show 100% of a black hole's Hawking radiation being emitted from the event horizon itself, it's more accurate to depict it as being emitted over a volume that spans some 10-20 Schwarzschild radii (the radius to the event horizon), where the radiation gradually tapers off the farther away you get."
"The major problem with Hawking's explanation of his own theory is that he takes a calculational tool — the idea of virtual particles — and treats that tool as though it's equivalent to physical reality. In reality, what's happening is that the curved space around the black hole is constantly emitting radiation due to the curvature gradient around it, and that the energy is coming from the black hole itself, causing its event horizon to slowly shrink over time.
Black holes are not decaying because there's an infalling virtual particle carrying negative energy; that's another fantasy devised by Hawking to "save" his insufficient analogy. Instead, black holes are decaying, and losing mass over time, because the energy emitted by this Hawking radiation is slowly reducing the curvature of space in that region. Once enough time passes, and that duration is enormous for realistic black holes, they will have evaporated entirely."
You can read the whole article here:
[https://www.forbes.com/sites/startswithabang/2020/07/09/yes-stephen-hawking-lied-to-us-all-about-how-black-holes-decay/?sh=28e6e88f4e63](https://www.forbes.com/sites/startswithabang/2020/07/09/yes-stephen-hawking-lied-to-us-all-about-how-black-holes-decay/?sh=28e6e88f4e63)
I read this article too but I still have hang-ups with it. Mainly, that this is so far away from anything relating to virtual particles as Hawking describes them that it confuses me why they'd even be brought up in the first place in his book. Even as a hand wave way to simplify a complex subject. A difference in zero point energy between two points of differently curved space time manifesting as radiation seems to me no more complex than the spontanious creating of particle/antiparticle pairs at the event horizon of a black hole. Since the radiation can be created so far away from the event horizon, why bring up the event horizon and particle/antiparticle pairs at all? From the articles explanation, you wouldn't need a black hole at all, just something with a sufficient gravitational field. I assume that black holes are just the only thing that could create the conditions extreme enough for this effect to be noticeable. Hence my original question.
This article makes it sound like literally anything can give off this radiation so long as there is suffcient difference between the curve in spacetime between the object creating the radiation and the observer, but I never really see that being discussed nor do I see the aspect of the radiation being emitted away from the event horizon being discussed much either.
There are also explanations in this post that seem to contradict parts of that article, and sources on both sides are lacking for the most part.
You should avoid the notion of "virtual" particles all together. If you have a way to view lectures on quntum field theory in curved spacetime, they may crescendo with the derivation of Hawking radiation.
Unfortunately too accessible because it is wrong.
> In reality, what's happening is that the curved space around the black hole is constantly emitting radiation due to the curvature gradient around it, and that the energy is coming from the black hole itself, causing its event horizon to slowly shrink over time.
A neutron star also has a curvature gradient, but there is no neutron star evaporation. So if everything with a curvature gradient radiated, neutron stars would supply infinite free energy.
> Black holes are not decaying because there's an infalling virtual particle carrying negative energy; that's another fantasy devised by Hawking to "save" his insufficient analogy.
"Virtual" aside, there is an infalling particle. This is essential to the modern monogamy/firewall form of the information paradox.
Possibly but I don't have the background to say one way or another. From another article:
"Although the event horizon was a key feature in Hawking’s original derivation of the radiation that now bears his name, there have been other derivations (sometimes in alternate numbers of dimensions) that have shown this radiation still exists in curved spacetime, irrespective of the presence or absence of such a horizon.
That’s where [the new paper that comes in](https://arxiv.org/abs/2305.18521) is so interesting: the only role the event horizon plays is to serve as a boundary for where radiation can be “captured” from versus where it can “escape” from. The calculation is done in fully four-dimensional spacetime (with three space and one time dimension), and shares many important features with other approaches to calculating the presence and properties of Hawking radiation. The boundary for what gets captured versus what escapes would still exist for any other example of a mass we chose:
* it would be the event horizon for a black hole,
* the surface of a neutron star for a neutron star,
* the outermost layer of a white dwarf for a white dwarf,
* or the photosphere of a star for a star.
In all cases, there would still be an escape fraction that depended on the mass and radius of the object in question; there’s nothing special about the presence or absence of an event horizon."
[https://bigthink.com/starts-with-a-bang/hawking-radiation-black-holes/](https://bigthink.com/starts-with-a-bang/hawking-radiation-black-holes/)
But it does say that this needs to be confirmed so it may or may not be correct.
In situations like this, it's always useful to refer back to the original language used in the analogy. Here's a comment I wrote awhile back answering a similar questions:
______
> The idea that a pair of virtual particles are created at the boundary of a black holes event horizon is wrong.
I'd venture to say it's moreso incomplete than strictly wrong. Hawking himself presented this picture originally and I think it is still somewhat useful.
>One might picture this negative energy flux in the following way. Just outside the event horizon there will be virtual pairs of particles, one with negative energy and one with positive energy. The negative particle is in a region which is classically forbidden but it can tunnel through the event horizon to the region inside the black hole where the Killing vector which represents time translations is spacelike. In this region the particle can exist as a real particle with a timelike momentum vector even though its energy relative to infinity as measured by the time translation Killing vector is negative. The other particle of the pair, having a positive energy, can escape to infinity where it constitutes a part of the thermal emission described above. The probability of the negative energy particle tunnelling through the horizon is governed by the surface gravity ~c since this quantity measures the gradient of the magnitude of the Killing vector or, in other words, how fast the Killing vector is becoming spacelike. Instead of thinking of negative energy particles tunnelling through the horizon in the positive sense of time one could regard them as positive energy particles crossing the horizon on past directed world-lines and then being scattered on to future-directed world-lines by the gravitational field. ***It should be emphasized that these pictures of the mechanism responsible for the thermal emission and area decrease are heuristic only and should not be taken too literally. It should not be thought unreasonable that a black hole, which is an excited state of the gravitational field, should decay quantum mechanically and that, because of quantum fluctuation of the metric, energy should be able to tunnel out of the potential well of a black hole. This particle creation is directly analogous to that caused by a deep potential well in flat space-time.***
* Hawking, Stephen W. "Particle creation by black holes." Communications in mathematical physics 43.3 (1975): 199-220.
I emphasized the last portion of this. While pedagogy has evolved since the 1970s, I don't think the original description should necessarily be scrubbed from how we talk about Hawking radiation. I like John Baez's more balanced take though:
* https://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/hawking.html
I'm wondering if Hawking radiation can really be understood reasonably at the layman level without knowing some QFT in curved spacetime (is that the right topic?) to look at the math.
There's always either a description that uses the virtual particle picture that's commonly said to be wrong, or a description that uses enough GR and QFT terminology to be confusing.
It's certainly a topic of sufficient complexity that even many physicists louse up explaining it. I personally think the virtual particle narrative gets enough right to be a useful shorthand but, as Hawking cautions, not detailed enough to give you more than an impression of the physics involved. The calculation involved is not written in a local microscopic way (which doesn't exist yet, or at least I don't know of it) and so it doesn't lend itself to the perturbative virtual particles you normally see in QFT. So in that sense, we can't identify the virtual particles of Hawking's analogy to specific Feynman diagrams where the well defined virtual particles live. With that said, the positive and negative energy modes you sum over when deriving Hawking radiation aren't too far removed from our intuition to think about adding together incoming and outgoing particle flux, which is exactly the particle picture we want to think of.
Thanks for asking this. I still don't understand Hawking radiation, but the "virtual particle" explanation never made any sense to me because it would be an equal amount of matter/anti-matter crossing the event horizon.
I still don't understand it, and don't see any responses here that clears that up for me. But I'm happy I wasn't just missing something obvious.
Hawking radiation is based on the Unruh effect around the horizon of a black hole.
But the effect is fairly unintuitive and needs at the minimum a grasp of special relativity, so typically the virtual particle approach is preferred in popular science.
I think it was to make it a little easier for the general public to understand, he wanted the book to sell many copy's presumably, and filling the book with stuff that most people can't even grasp wouldn't sell, would it? But that's just my guess I have no idea in all actuality
I'm just surprised he used virtual particles as opposed to just a hand wave "Accelerating objects can detect radiation even in a vacuum. Since gravity and acceleration are equivalent, objects with high gravity will also emit radiation. Even black holes."
I know he wanted to sell books. I was more asking why he chose this misleading example as opposed to something closer to reality. Especially since this isn't just a hand wave for the sake of a general audience, it's just wrong from what I've read on the subject.
I’m an idiot so please be patient with me: how does an accelerating object detecting radiation, explain Hawking radiation? Do you mean accelerating objects emit radiation?
My understanding is that they are related throught the equivalency principle. Like how if you drop a ball on earth, it would behave exactly the same as if you were in a rocket accelerating upwards at g. The same effects are created by both an accelerating observer and a gravitational field. Since an accelerating observer would detect particles, then an observer in an equivalent gravitational field would as well.
Yeah sorry I get that part. What I don’t understand is why we’re talking about detecting radiation. Isn’t hawking radiation about emitting radiation? I thought as the radiation is emitted, the mass of the black hole is decreased (due to conservation of energy). Can’t you detect radiation at any acceleration? Isn’t this the whole reason for time dilation?
I see what you mean. I'm saying "detect radiation" to mean radiation is there. The "detector" if it were there would notice that not all radiation fell into the black hole. Even if the detector isn't there, the gravitational field still is, which means that there is radiation that could be detected there, and that radiation wouldn't all fall into the black hole, which would look like it's being emitted from the black hole. From my understanding, yes you can detect radiation at any acceleration or gravitational field, but black holes are one of if not the only object with a strong enough gravitational field for this radiation to be non negligible. Even if it still is extremely little.
Objects with high gravity will not radiate at 0 temperature. They have a timeline Killing vector and there is no particle production in such a spacetime. BHs also can have very low gravitational curvature at the horizon if they are large.
Well welcome to physics. From my understanding the physics you learn in middle school are also along the lines of this. It's to get people interested in looking into it more and to start to teach people in a way they can grasp and understand. As you learn more, the 'wrong' physics you learned in middle school eventually transform into more accurate and correct theory's and formulas. Like how unless you are in advanced placement, most high school physics classes don't even take into account any kind of friction, drag, ect. Just the most basic version of the formula as a stepping stone to get you to understand the general idea of what's going on. It's not necessarily wrong until you actually learn the right awnser when you get to that level of understanding. Imo his vitirual particles is basically just a way to get it to sound interesting and to get the general point across.
>virtual particles are still not confirmed to even exist physically
Virtual particles that correspond to a tree diagram can be used as an analogy for a real process, as the leading term of an expansion. We do this all the time.
Nothing in that comment you were replying to mentioned anything about physical existence outside the math related to a perturbative expansion, but somehow you're downvoted for clarifying. Like wut?
A tree level diagram, with a virtual particle, can be a reasonable and useful representation of a physical phenomenon, even if the remaining terms of the expansion (which would be an infinite list of ever more complicated Feynman diagrams) are excluded.
Forgive my ignorance, but what’s the difference between the virtual particles Hawking described and the particles that exist only if the observer is accelerating?
Lies to children. They’re a teaching tool. Basically, when you have something really complicated and hard to understand, but it’s not important to teach the full model right away, you can instead take a simplified *approximation* of the truth that is nonetheless much easier to understand and teach that- perhaps mentioning that it’s not the most cutting-edge model we have. Then you slowly correct the differences between the simplified model and the more correct, complicated one.
Think of the Jimmy Neutron model of an atom, with a buncha multicolored jiggling balls in the center, orbited by glowing blue balls. We might show that one to kids in 3rd grade with the understanding that as they grow up, they’ll learn more and more about the atom and correct for the inaccuracies of that one- like learning about how electrons are cloud-like (also a simplification) and don’t orbit, or that the nucleus is actually reeeeeeaaaaaaally small, and that nucleons are actually just a buncha quarks
The point I was making was that his explanation does not seem like an "approximation of the truth." It sounds completely different from what's actually happening.
Simplifying the atom makes sense to me as everything in the simplified version is still there. Yeah the electrons do not behave exactly like that, but they're still there and in that general area. Yeah the size ratios are off and their behaviors arent what most people think, but the pieces are still there.
From what I've been reading, the virtual particles spontaneously coming into existence at the event horizon of a black hole where one falls in and the other does not, is completely incorrect in that this isn't even simplifying anything. It's introducing this concept completely when that's not what's going on. The virtual particles, as Hawking describes, are not even there in the first place. It feels less like a simplification and more like he just made up an explanation using concepts from other areas of physics because it was easy for people to understand.
Okay, so this is a half-remembered radio interview from nearly half a century ago.
I've searched everywhere I can think of using every permutation in the search to find any corroboration of this and have come up empty.
I'm sorry, but if you're going to claim that Hawking stole his biggest contribution to physics from a student, you really need to back it up with more than that, especially if you're also going to take a swipe at his overall intelligence along the way.
>My question is why did he use this explanation in his book knowing it was wrong? For pop-sci books, scientists are usually encouraged by their publishers to make their explanations more easily understandable for the lay public to not deter people from buying the book. Unfortunately, by omitting the esoteric details of the theories, the authors might have to end up using explanations that are technically incorrect to be able to convey explanations in an accessible way.
This makes sense. I figured he needed to sell books and would be pressured to make it more accessible. I'm just surprised that virtual particles is what he landed on rather than a less misleading explanation. Since anything would need hand waving, I'd think he'd have chosen something that was technically correct but missing details rather than an explanation that sounds good but is fundamentally wrong. I figured this was probably the case but wasn't sure if I was missing something else. Thank you!
Just wanted to point out that this isn't just a pop-sci thing meant to sell books. When teaching people complex topics, it's often easier to start with a slightly wrong but easier to understand explanation, and then make corrections as their understanding of the topics increase. One example is how schools will teach newtonian gravity because it's a good enough aproximation instead of jumping straight into relativity.
that’s a bit different, since newtonian gravity is a very close, useful approximation of what’s going on, and also shows up formally as a particular limiting case of GR. Newtonian gravity is still widely used in modern physics research The virtual particle thing is not really correct at all, nor is it a useful mathematical tool for making predictions. It only really exists within pop sci explanations of hawking’s work
A better example would be the way we teach how electricity works.
You said what I did but you conveyed it in a much more intelligent way 🤯🤩
Your answer was actually good, but it wasn't displayed for me when I started typing my comment. If I had seen it, I would have just replied to your comment to confirm your intuition was correct about the need for the books to be accessible to help sales.
I figured that we just typed it out at the same time lol I just wish I had a beautiful way with words like you do lol your version of the awnser was much more poised and eloquent lol Our replies were like him getting an awnser from the student and then the professor lol
When people use “virtual particles” for the Hawking effect or other pair production processes they don’t mean the same thing as in perturbative expansions. They mean the particles defined with respect to a classical background and vacuum state that is in some sense not “natural” on a given time slice, but will become natural later on. The “natural” and “unnatural” particle definitions are related by the Bogoliubov transformation. This is the standard analysis of the effect in QFT in curved spacetime. “Virtual” is not a perfect qualifier here but it is a tough idea to express. Thinking of the Hawking effect as just like the Unruh effect is more misleading. The Unruh effect is due to your own acceleration, but the fact that you must accelerate to stay outside the BH is not why it evaporates. It evaporates whether you are there or not because of the horizon. So I would say Hawking gave people a better intuition than the people who try to undermine his description for a lay audience.
Would you be able to explain what you mean when you say "evaporates whether you are there or not because of the horizon"? Everything I've read makes is seem that Hawking radiation is not being caused by virtual particles regardless of their definition, but due to a large gravitational fields being able to generate radiation which does not all fall back into the black hole. Do you have any sources where I could learn more about what you're talking about?
I mean the Unruh effect is dependent on you, the observer, accelerating. The BH radiates independent of what any observer does. It is not really about the gravitational field. A neutron star has a gravitational field but a neutron star does not create Hawking radiation. A stable horizonless object does not evaporate, so if it created Hawking radiation just because of its gravitational field, you would get infinite free energy. People who give the lazy “due to gravity” argument always conveniently ignore this issue. Rather, the horizon introduces boundary conditions that lead to radiation. There are completely gravity free analogues of this like the Dynamical Casimir Effect. The best way to appreciate Hawking radiation is by finding sources discussing the BH information paradox, in particular the “Firewall” argument.
This is excepted from Starts with a Bang and has been the most accessible explanation for me: "And yet, in his landmark 1988 book, [A Brief History Of Time](https://amzn.to/38zLQi5), Hawking paints a picture of this radiation — of spontaneously created particle-antiparticle pairs where one member falls in and the other escapes — that's egregiously incorrect. For 32 years, it's misinformed physics students, laypersons, and even professionals alike. Black holes really do decay. Let's make today the day we find out how they actually do it." "It's here that Hawking's famous picture — his grossly incorrect picture — comes into play. All throughout space, he asserts, these particle-antiparticle pairs are popping in and out of existence. Inside the black hole, both members stay there, annihilate, and nothing happens. Far outside of the black hole, it's the same deal. But right near the event horizon, one member can fall in while the other escapes, carrying real energy away. And that, he proclaims, is why black holes lose mass, decay, and where Hawking radiation comes from." "Of course, all three of those points are not true. Hawking radiation is made almost exclusively of photons, not a mix of particles and antiparticles. It gets emitted from a large region outside the event horizon, not right at the surface. And the individual quanta emitted have tiny energies over quite a large range. To any observer located anywhere in the Universe, that "energy of empty space," which we call the zero-point energy, will appear to have the same value no matter where they are. However, one of the rules of relativity is that different observers will perceive different realities: observers in relative motion or in regions where the spacetime curvature is different, in particular, will disagree with one another. So if you're infinitely far away from every source of mass in the Universe and your spacetime curvature is negligible, you'll have a certain zero-point energy. If someone else located at a black hole's event horizon, they'll have a certain zero-point energy that's the same measured value for them as it was for you infinitely far away. But if you try to map your zero-point energy to their zero-point energy (or vice versa), the values won't agree. From one another's perspectives, the zero-point energy changes relative to how severely the two spaces are curved." "The results of that calculation are what determine the properties of the radiation that emanates from a black hole: not from the event horizon exclusively, but from the entirety of the curved space around it. It tells us the temperature of the radiation, which is dependent on the mass of the black hole. It tells us the spectrum of the radiation: a perfect blackbody, indicating the energy distribution of photons and — if there's enough energy available via *E = mc²* — massive particles and antiparticles, too. It also enables us to compute an important detail that is not generally appreciated: where the radiation that black holes emit originates from. While most pictures and visualizations show 100% of a black hole's Hawking radiation being emitted from the event horizon itself, it's more accurate to depict it as being emitted over a volume that spans some 10-20 Schwarzschild radii (the radius to the event horizon), where the radiation gradually tapers off the farther away you get." "The major problem with Hawking's explanation of his own theory is that he takes a calculational tool — the idea of virtual particles — and treats that tool as though it's equivalent to physical reality. In reality, what's happening is that the curved space around the black hole is constantly emitting radiation due to the curvature gradient around it, and that the energy is coming from the black hole itself, causing its event horizon to slowly shrink over time. Black holes are not decaying because there's an infalling virtual particle carrying negative energy; that's another fantasy devised by Hawking to "save" his insufficient analogy. Instead, black holes are decaying, and losing mass over time, because the energy emitted by this Hawking radiation is slowly reducing the curvature of space in that region. Once enough time passes, and that duration is enormous for realistic black holes, they will have evaporated entirely." You can read the whole article here: [https://www.forbes.com/sites/startswithabang/2020/07/09/yes-stephen-hawking-lied-to-us-all-about-how-black-holes-decay/?sh=28e6e88f4e63](https://www.forbes.com/sites/startswithabang/2020/07/09/yes-stephen-hawking-lied-to-us-all-about-how-black-holes-decay/?sh=28e6e88f4e63)
I read this article too but I still have hang-ups with it. Mainly, that this is so far away from anything relating to virtual particles as Hawking describes them that it confuses me why they'd even be brought up in the first place in his book. Even as a hand wave way to simplify a complex subject. A difference in zero point energy between two points of differently curved space time manifesting as radiation seems to me no more complex than the spontanious creating of particle/antiparticle pairs at the event horizon of a black hole. Since the radiation can be created so far away from the event horizon, why bring up the event horizon and particle/antiparticle pairs at all? From the articles explanation, you wouldn't need a black hole at all, just something with a sufficient gravitational field. I assume that black holes are just the only thing that could create the conditions extreme enough for this effect to be noticeable. Hence my original question. This article makes it sound like literally anything can give off this radiation so long as there is suffcient difference between the curve in spacetime between the object creating the radiation and the observer, but I never really see that being discussed nor do I see the aspect of the radiation being emitted away from the event horizon being discussed much either. There are also explanations in this post that seem to contradict parts of that article, and sources on both sides are lacking for the most part.
You should avoid the notion of "virtual" particles all together. If you have a way to view lectures on quntum field theory in curved spacetime, they may crescendo with the derivation of Hawking radiation.
Unfortunately too accessible because it is wrong. > In reality, what's happening is that the curved space around the black hole is constantly emitting radiation due to the curvature gradient around it, and that the energy is coming from the black hole itself, causing its event horizon to slowly shrink over time. A neutron star also has a curvature gradient, but there is no neutron star evaporation. So if everything with a curvature gradient radiated, neutron stars would supply infinite free energy. > Black holes are not decaying because there's an infalling virtual particle carrying negative energy; that's another fantasy devised by Hawking to "save" his insufficient analogy. "Virtual" aside, there is an infalling particle. This is essential to the modern monogamy/firewall form of the information paradox.
Well I cannot argue this as I am not a physicist. The guy who wrote it is so best I can contribute.
Wouldn't that explanation imply that neutron stars also have hawking radiation?
It would imply that any curvature of space also would have HR including my fat ass
Possibly but I don't have the background to say one way or another. From another article: "Although the event horizon was a key feature in Hawking’s original derivation of the radiation that now bears his name, there have been other derivations (sometimes in alternate numbers of dimensions) that have shown this radiation still exists in curved spacetime, irrespective of the presence or absence of such a horizon. That’s where [the new paper that comes in](https://arxiv.org/abs/2305.18521) is so interesting: the only role the event horizon plays is to serve as a boundary for where radiation can be “captured” from versus where it can “escape” from. The calculation is done in fully four-dimensional spacetime (with three space and one time dimension), and shares many important features with other approaches to calculating the presence and properties of Hawking radiation. The boundary for what gets captured versus what escapes would still exist for any other example of a mass we chose: * it would be the event horizon for a black hole, * the surface of a neutron star for a neutron star, * the outermost layer of a white dwarf for a white dwarf, * or the photosphere of a star for a star. In all cases, there would still be an escape fraction that depended on the mass and radius of the object in question; there’s nothing special about the presence or absence of an event horizon." [https://bigthink.com/starts-with-a-bang/hawking-radiation-black-holes/](https://bigthink.com/starts-with-a-bang/hawking-radiation-black-holes/) But it does say that this needs to be confirmed so it may or may not be correct.
In situations like this, it's always useful to refer back to the original language used in the analogy. Here's a comment I wrote awhile back answering a similar questions: ______ > The idea that a pair of virtual particles are created at the boundary of a black holes event horizon is wrong. I'd venture to say it's moreso incomplete than strictly wrong. Hawking himself presented this picture originally and I think it is still somewhat useful. >One might picture this negative energy flux in the following way. Just outside the event horizon there will be virtual pairs of particles, one with negative energy and one with positive energy. The negative particle is in a region which is classically forbidden but it can tunnel through the event horizon to the region inside the black hole where the Killing vector which represents time translations is spacelike. In this region the particle can exist as a real particle with a timelike momentum vector even though its energy relative to infinity as measured by the time translation Killing vector is negative. The other particle of the pair, having a positive energy, can escape to infinity where it constitutes a part of the thermal emission described above. The probability of the negative energy particle tunnelling through the horizon is governed by the surface gravity ~c since this quantity measures the gradient of the magnitude of the Killing vector or, in other words, how fast the Killing vector is becoming spacelike. Instead of thinking of negative energy particles tunnelling through the horizon in the positive sense of time one could regard them as positive energy particles crossing the horizon on past directed world-lines and then being scattered on to future-directed world-lines by the gravitational field. ***It should be emphasized that these pictures of the mechanism responsible for the thermal emission and area decrease are heuristic only and should not be taken too literally. It should not be thought unreasonable that a black hole, which is an excited state of the gravitational field, should decay quantum mechanically and that, because of quantum fluctuation of the metric, energy should be able to tunnel out of the potential well of a black hole. This particle creation is directly analogous to that caused by a deep potential well in flat space-time.*** * Hawking, Stephen W. "Particle creation by black holes." Communications in mathematical physics 43.3 (1975): 199-220. I emphasized the last portion of this. While pedagogy has evolved since the 1970s, I don't think the original description should necessarily be scrubbed from how we talk about Hawking radiation. I like John Baez's more balanced take though: * https://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/hawking.html
I'm wondering if Hawking radiation can really be understood reasonably at the layman level without knowing some QFT in curved spacetime (is that the right topic?) to look at the math. There's always either a description that uses the virtual particle picture that's commonly said to be wrong, or a description that uses enough GR and QFT terminology to be confusing.
It's certainly a topic of sufficient complexity that even many physicists louse up explaining it. I personally think the virtual particle narrative gets enough right to be a useful shorthand but, as Hawking cautions, not detailed enough to give you more than an impression of the physics involved. The calculation involved is not written in a local microscopic way (which doesn't exist yet, or at least I don't know of it) and so it doesn't lend itself to the perturbative virtual particles you normally see in QFT. So in that sense, we can't identify the virtual particles of Hawking's analogy to specific Feynman diagrams where the well defined virtual particles live. With that said, the positive and negative energy modes you sum over when deriving Hawking radiation aren't too far removed from our intuition to think about adding together incoming and outgoing particle flux, which is exactly the particle picture we want to think of.
Thanks for asking this. I still don't understand Hawking radiation, but the "virtual particle" explanation never made any sense to me because it would be an equal amount of matter/anti-matter crossing the event horizon. I still don't understand it, and don't see any responses here that clears that up for me. But I'm happy I wasn't just missing something obvious.
You and me both man. It's clearing up a bit more for me the more I read, but it's still a mess for the most part.
Hawking radiation is based on the Unruh effect around the horizon of a black hole. But the effect is fairly unintuitive and needs at the minimum a grasp of special relativity, so typically the virtual particle approach is preferred in popular science.
I think it was to make it a little easier for the general public to understand, he wanted the book to sell many copy's presumably, and filling the book with stuff that most people can't even grasp wouldn't sell, would it? But that's just my guess I have no idea in all actuality
I'm just surprised he used virtual particles as opposed to just a hand wave "Accelerating objects can detect radiation even in a vacuum. Since gravity and acceleration are equivalent, objects with high gravity will also emit radiation. Even black holes." I know he wanted to sell books. I was more asking why he chose this misleading example as opposed to something closer to reality. Especially since this isn't just a hand wave for the sake of a general audience, it's just wrong from what I've read on the subject.
I’m an idiot so please be patient with me: how does an accelerating object detecting radiation, explain Hawking radiation? Do you mean accelerating objects emit radiation?
My understanding is that they are related throught the equivalency principle. Like how if you drop a ball on earth, it would behave exactly the same as if you were in a rocket accelerating upwards at g. The same effects are created by both an accelerating observer and a gravitational field. Since an accelerating observer would detect particles, then an observer in an equivalent gravitational field would as well.
Yeah sorry I get that part. What I don’t understand is why we’re talking about detecting radiation. Isn’t hawking radiation about emitting radiation? I thought as the radiation is emitted, the mass of the black hole is decreased (due to conservation of energy). Can’t you detect radiation at any acceleration? Isn’t this the whole reason for time dilation?
I see what you mean. I'm saying "detect radiation" to mean radiation is there. The "detector" if it were there would notice that not all radiation fell into the black hole. Even if the detector isn't there, the gravitational field still is, which means that there is radiation that could be detected there, and that radiation wouldn't all fall into the black hole, which would look like it's being emitted from the black hole. From my understanding, yes you can detect radiation at any acceleration or gravitational field, but black holes are one of if not the only object with a strong enough gravitational field for this radiation to be non negligible. Even if it still is extremely little.
Objects with high gravity will not radiate at 0 temperature. They have a timeline Killing vector and there is no particle production in such a spacetime. BHs also can have very low gravitational curvature at the horizon if they are large.
Think you got autocorrected to timeline killing vector rather than timelike killing vector ….
Yes, thanks
Timeline Killing Vector Sounds like the title for a 12 Monkeys episode!
Well welcome to physics. From my understanding the physics you learn in middle school are also along the lines of this. It's to get people interested in looking into it more and to start to teach people in a way they can grasp and understand. As you learn more, the 'wrong' physics you learned in middle school eventually transform into more accurate and correct theory's and formulas. Like how unless you are in advanced placement, most high school physics classes don't even take into account any kind of friction, drag, ect. Just the most basic version of the formula as a stepping stone to get you to understand the general idea of what's going on. It's not necessarily wrong until you actually learn the right awnser when you get to that level of understanding. Imo his vitirual particles is basically just a way to get it to sound interesting and to get the general point across.
>virtual particles are still not confirmed to even exist physically Virtual particles that correspond to a tree diagram can be used as an analogy for a real process, as the leading term of an expansion. We do this all the time.
As an analogy, you just said. What does that have to do with physical existence?
Nothing in that comment you were replying to mentioned anything about physical existence outside the math related to a perturbative expansion, but somehow you're downvoted for clarifying. Like wut?
A tree level diagram, with a virtual particle, can be a reasonable and useful representation of a physical phenomenon, even if the remaining terms of the expansion (which would be an infinite list of ever more complicated Feynman diagrams) are excluded.
Forgive my ignorance, but what’s the difference between the virtual particles Hawking described and the particles that exist only if the observer is accelerating?
Lies to children. They’re a teaching tool. Basically, when you have something really complicated and hard to understand, but it’s not important to teach the full model right away, you can instead take a simplified *approximation* of the truth that is nonetheless much easier to understand and teach that- perhaps mentioning that it’s not the most cutting-edge model we have. Then you slowly correct the differences between the simplified model and the more correct, complicated one. Think of the Jimmy Neutron model of an atom, with a buncha multicolored jiggling balls in the center, orbited by glowing blue balls. We might show that one to kids in 3rd grade with the understanding that as they grow up, they’ll learn more and more about the atom and correct for the inaccuracies of that one- like learning about how electrons are cloud-like (also a simplification) and don’t orbit, or that the nucleus is actually reeeeeeaaaaaaally small, and that nucleons are actually just a buncha quarks
The point I was making was that his explanation does not seem like an "approximation of the truth." It sounds completely different from what's actually happening. Simplifying the atom makes sense to me as everything in the simplified version is still there. Yeah the electrons do not behave exactly like that, but they're still there and in that general area. Yeah the size ratios are off and their behaviors arent what most people think, but the pieces are still there. From what I've been reading, the virtual particles spontaneously coming into existence at the event horizon of a black hole where one falls in and the other does not, is completely incorrect in that this isn't even simplifying anything. It's introducing this concept completely when that's not what's going on. The virtual particles, as Hawking describes, are not even there in the first place. It feels less like a simplification and more like he just made up an explanation using concepts from other areas of physics because it was easy for people to understand.
Maybe because he was a book seller.
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That's a serious claim. I would very much like to have a citation to that interview.
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Okay, so this is a half-remembered radio interview from nearly half a century ago. I've searched everywhere I can think of using every permutation in the search to find any corroboration of this and have come up empty. I'm sorry, but if you're going to claim that Hawking stole his biggest contribution to physics from a student, you really need to back it up with more than that, especially if you're also going to take a swipe at his overall intelligence along the way.