Years ago, I thought Ethan Siegel was a decent science writer. His texts seemed to be full of data that sort of overlapped with some basic knowledge about many physics questions. However, in the recent year or two, I stopped following him after I saw a vast excess of totally wrong, unreasonable, and sometimes toxic "punch lines" in his articles such as the claims that:
- WIMP is dead (premature)
- only childish pictures are known about the electron (BS)
- consensus is the core of science which is defined as mindless obedience to a scientifically illiterate, psychologically ill Scandinavian teenager (!!!)
- it's shocking we still can't precisely count planets with ETs (not shocking at all, even the extraterrestrial life is basically ill-defined, and heavily uncertain, too)
- the so-called minorities' situation should never be fairly compared to ours, their supremacy cannot be questioned (he really wrote that almost precisely!)
The only problem with Siegel's tirade is that this picture of the radiation emitted by black holes is totally right, of course. The Hawking radiation is a variation of the Unruh radiation in the context of a black hole (curved) spacetime. In the operator formalism, both Unruh and Hawking radiation may be described as special examples of "particle production". The vacuum state \(\ket 0\) is generally defined as the lowest energy eigenstate of some Hamiltonian \(H\).
In the context of acceleration or black holes, the funny thing is that this operator isn't really unique. \(H\) is a generator of the evolution along some time coordinate \(t\) but as you should know, there is no "unique and universal" time coordinate in the theory of relativity. In special relativity, the ambiguity is only "up to the choice of an inertial reference frame". In general relativity, any (mostly) nonlinear transformation of coordinates may produce an equally allowed time coordinate \(t'=t'(t,x,y,z)\).
So if we want to identify the ground state \(\ket 0\), we need to know which time \(t\) and/or the corresponding Hamiltonian \(H\) we mean. That time may be some natural time used by an observer. But what matters a lot in this context isn't a black life. What matters a lot is whether the observer is accelerating and how much. Mutually accelerating observers will pick different Hamiltonians and those will also have different ground states \(\ket 0\). One observer's ground state will be a squeezed-and-coherent non-vacuum state from the viewpoint of another, and vice versa.
It means that in the context of general relativity (with curved spacetimes and ambiguous choices of time coordinates), the number of particles in a state depends on the acceleration of the observer (because it's true even for the ground state). If you want to find out the transformations, it's useful to realize that quantum fields are written as "sums of creation and annihilation operators" for particles and antiparticles, respectively. A particular field operator may have positive-energy creation operators for particles; and negative-energy annihilation operators for antiparticles. However, I used the word "energy" so we need to define \(H\) which depends on the choice of \(t\) and therefore the acceleration of the observer.
In the language of creation and annihilation operators, the key idea is that we want all creation operators to "add positive energy". Annihilation operators add a negative energy. That's how we separate them. But to separate them, we need to define an energy operator by a formula for \(H\) and it depends on the acceleration. In general, one accelerating observer will interpret some combination of creation and annihilation operators as his creation operators. The two observers will differ by their separation of the modes to positive- and negative-energy modes because they use a different formula for \(H\), the energy operator. In special relativity, the future and past cones for the energy-momentum remain the same as sets; in general relativity, they are mixed.
So you may transform the column of creation and annihilation operators of one observer by a matrix to get another segregation to creation and annihilation operators; that linear transformation is called the Bogoliubov transformation. The Unruh radiation (seen by an accelerating observer in the flat spacetime) is just a few extra words on top of the Bogoliubov transformation. The Hawking radiation – which was ironically found before the Unruh radiation – requires an extra layer of complexity due to the curved spacetime. The fun about the black hole spacetime is that it allows the observers to interpolate between a frame that "looks nonaccelerating", an observer slowly falling to a black hole, and one that looks like accelerating relatively to the initial one, a freeling falling observer. Inside the black hole (on the inner side of the event horizon), there is no time-like Killing vector field that could define \(H\) over there. Due to this interpolation, different Unruh-like frames are natural for the initial and final state and the particle production that was just a "subjective effect" in the Unruh case becomes the damn real Hawking radiation in the black hole context.
In the Feynman path integral approach, antiparticles look just like particles moving backward in time (thanks, Max). The Hawking particle must come from somewhere, it can't be created out of nothing, especially if it carries conserved charges etc. So there must be a corresponding antiparticle which is just a continuation of the same world line. But because this other particle isn't emitted, it's clear that its world line must continue beneath the event horizon (it must belong to the black hole interior), whatever the exact trajectories are.
I don't understand what leads people like Siegel – who obviously don't understand topics such as the Hawking radiation at the technical level – to write these totally wrong, arrogant, and insulting things about physics and physicists. Does Siegel really believe that he understands the Hawking radiation better than Hawking did? Sorry, you don't, Mr Siegel. You are a stupid monkey in comparison. And you are a super stupid monkey relatively to the best Hawking radiation experts of 2020 whose understanding is much deeper than Hawking's (but only Hawking really discovered it as the first man).
The tone of this article seems odd to me. I think the picture in which one member of a virtual pair falls into a black hole is instructive, and captures the spirit of Hawking's computation of the temperature of an evaporating black hole. https://t.co/S8nUi87nsb— John Preskill (@preskill) July 9, 2020
Now, trained high-energy physicist and quantum computing leader John Preskill knows very well that Ethan Siegel is full of šit. After all, it seems fair to me to include Preskill among the experts who actually understand Hawking radiation better than Hawking did. How does Preskill express the fact that Siegel is full of šit? "The tone of this article seems odd to me." Holy cow. The tone is annoyingly arrogant (not just odd) but it's really the content, not the tone, that matters here, unlike the black lives. And the content is completely wrong. Lies and pseudoscience have been spreading cataclysmically in recent years (the fake news media have increasingly favored pseudoscience over science) and if "the tone seems odd to me" (Preskill's tweet that got 70 likes including me) is the only response that the likes of Preskill do against an avalanche of lies in the would-be science media (Siegel's totally wrong article has over 75k views by now), then it's clear that the likes of Preskill have given up any defense of their field against ignorant mobs.
Maybe Siegel thinks that he "understands" the Hawking radiation and by this understanding, he means that he has memorized some definition or one-sentence explanation of what is going on, and it sounds different. But a true understanding of physics (or anything that is comparably intelligent) is not about memorization. Equally importantly, physics allows many "very differently sounding" descriptions to be correct simultaneously. So in various formalisms and pictures, Heisenberg, Schrödinger, Dirac, Feynman pictures (with a curved classical background or black hole microstates described in a stringy or non-stringy way, using the AdS/CFT, Matrix theory, or something else etc.), the same physical process may be described in ways that surely sound totally different when translated to plain English, a general point (that is decisive in all of physics whose correct language is math, not English: everyone who has doubts about this rudimentary proposition is 100% incompetent in physics) that Siegel probably doesn't understand at all. Hawking's "split virtual pair" sounds different than another explanation that Siegel has decided to consider "correct", because of his arbitrary mood swings, and that's probably why he screams that every other sentence is a lie. It is not a lie. It's Siegel's article that is a giant lie. Your approach to knowledge isn't enough to answer advanced physics questions, Mr Siegel.
If you thought that Siegel understands the Hawking radiation at least in one picture and at least approximately, I can easily prove you wrong by an even more stunning mistake:
This leads us to a phenomenal conclusion: that all collapsed objects that curve spacetime should emit Hawking radiation. It may be a tiny, imperceptible amount of Hawking radiation, swamped by thermal ...Wow. He really has no clue. This is what the most retarded kids in the kindergarten think about the Hawking radiation when they hear about it for the first time. Every object that has some mass, like the Earth or a neutron star, emits a qualitatively similar radiation as a black hole does. No need to apologize, stupid person, but it doesn't. There is precisely zero Hawking radiation coming from a neutron star or from a planet. The Hawking radiation only comes from black holes i.e. from objects that have event horizons. No event horizon means no Hawking radiation. Nada. Strictly zero. It is the event horizon where all the magic happens (indeed, the magic may be described as the separation of a particle pair, as Siegel wants to deny) and neutron stars and planets don't have any event horizons. So for a static neutron star, for example, even one that is rather close to collapsing into a black hole, there is only one natural Hamiltonian \(H\) which is basically relevant for every region in the spacetime. Relatively to this \(H\), we may define the ground state \(\ket 0\). Any observer may sensibly use the Fock space built upon this vacuum, it never becomes singular or "time-space reversed" because there is no event horizon, and that's why there can't be any particle production or Hawking radiation!
To say that neutron stars "also" emit the Hawking radiation is the theoretical physicist's counterpart of the biologist's saying that women also produce millions of sperms. It just proves the speaker's absolute ignorance about the whole subdiscipline. Again, look how John Preskill responded to this shockingly stupid assertion by Siegel:
And I'm puzzled by the assertion "that all collapsed objects that curve spacetime should emit Hawking radiation." An essential feature of Hawking's computation is that an observer who falls past the event horizon of a black hole encounters nothing but vacuum fluctuations.— John Preskill (@preskill) July 9, 2020
Weak tea blah blah blah. And he got 17 "likes" including mine. Sorry, Prof Preskill, you won't defend the field from aggressive and arrogant brain-dead mobs that get 75k views for each of these totally wrong diatribes if you use these invisible tools to criticize the wrong statements.
Incidentally, Preskill's particular debunking of Siegel's assertion is misleading, too. It's really right because Preskill more or less wrote the correct sentence that "for the Hawking calculation to work, the spacetime including the interior of the gravitating object must be empty". This sentence is surely correct, Hawking calculated something about a black hole which was empty inside, so the calculation clearly wasn't directly applicable to a neutron star or a planet. But Preskill's explanation leads you to wrong ideas about the reasons why the black holes emit the radiation and other objects don't. Surely the presence of the baryonic matter (in a neutron star) or the iron (in the Earth) isn't the reason why these objects don't emit the radiation. If you add something to the object (baryons, iron), you would expect a more complex pattern of radiation, not a less complex one (you would expect some radiation to be added, not subtracted). Instead, it's the absence of the event horizon in the neutron stars and planets that is the reason why they don't emit the Hawking radiation. It's the event horizon that is literally acting as the black body emitting the thermal radiation whose temperature (as defined from infinity) may be calculated from the "local gravitational acceleration" at the event horizon. For static spacetimes with matter, no event horizon means no source of the Hawking-like thermal radiation.
P.S.: Holy cow, Siegel wrote another article about the Hawking radiation a week ago where he completely denied that it existed. Nothing can get from the black hole, he argued, so only the accretion disks outside the event horizon may be seen. But that's exactly what Hawking proved slightly wrong. Things may still get away from the event horizon and a totally real Hawking radiation is coming from it. A micron-sized black hole emits visible light, as any micron-sized light bulb. Siegel demonstrably misunderstands that the Hawking radiation really exists, he believes that it doesn't. It's like a physics counterpart of the biology belief that sperms don't exist.