[ This post is a translation of an article from Sabina Hossenfelder ]"A Brief History of Time" Stephen Hawking was one of the first popular science books I read, and I hated it. I hated because I did not understand. The frustration of this book was one of the main reasons why I became a physicist — well, at least I know who to blame for that.
Note Per .: I added links and some illustrations, and also removed a part of the text that had no special relevance to the case (the place is noted in the text).
The original post cannot boast of an ideal narrative structure, which I did not change. But the problem is very important and relevant, and for her discussion and explanation of Sabina, you can forgive the inaccuracies of style.
Post can be considered an extended commentary on the recent publication of the translation of Ethan.
I stopped hating this book - admittedly, at the request of Hawking, the general public’s interest in fundamental questions of physics (connected with black holes) was kindled. But from time to time I still want to hit the damn book. Not because I do not understand her, but because she has convinced so many people that
they understand her.
In this book, Hawking painted a graceful picture of black hole evaporation, which is now used everywhere. In his view, black holes evaporate, because the pairs of virtual particles arising near the horizon are broken by tidal forces. One of the particles is beyond the horizon of events, and falls into a black hole, and the second flies away to the outside. As a result, a black hole constantly radiates particles on the event horizon. It is simple, it is intuitive, and it is completely wrong.
Such an explanation is a simple illustration, no more. In reality - you will not be surprised - the situation is more complicated.
Pairs of particles - as far as it makes sense to talk about particles in quantum physics - are not localized in space. They are “smeared” over a region of space comparable to the radius of a black hole (
approx. Lane is akin to how an electron moves not around a specific orbit around the nucleus of an atom, being at some point of it, but “smeared” around a nucleus. ). Pairs of particles do not appear as points, but as clouds, blurred everywhere around a black hole, and they are separated only at distances comparable to the radius of a black hole. The picture Hawking drew for non-specialists is not supported by any math. There is an element of truth in it, but one should not take it too seriously - this can be the source of many delusions.
The fact that Hawking’s explanation is not accurate is not new - from the beginning of the 70s it was known that Hawking radiation does not arise on the very horizon. Already in the
textbook of Birrell and Davis (1984) it is clearly written that if we assume the occurrence of radiation on the horizon and consider the process of radiation in the opposite direction in time: track particles approaching the event horizon from afar and increasing the frequency ("
blue displacement "), this will not give a correct description of the area near the event horizon. The correct approach will be different: particles from the Hawking pair at birth are “smeared” and mixed with each other, so that we can speak of them as “particles” only in a local sense (
meaning the local coordinate system from the point of view of GRT). . ). Moreover, one must honestly consider observable quantities, such as the moment-moment tensor.
The assumption of the occurrence of pairs at some distance from the event horizon was necessary to solve the riddle that puzzled physicists in the 70s and 80s. The radiation temperature of a black hole is very small when viewed from afar. But in order for this radiation to escape from the attraction of the black hole in general, it must initially have enormous energy near the horizon. And then an observer falling into a black hole would turn into ash, passing through the area with such energy. This in turn violates the
principle of equivalence , according to which an observer falling into a black hole should not notice anything unusual when crossing the horizon.
To solve this problem, it is necessary to take into account that radiation cannot be considered as coming from the horizon itself. If you honestly calculate
the energy-momentum tensor near the horizon, it turns out that it is sufficiently small, and remains so at the intersection of the horizon. In fact, it is how small that a falling observer will be able to notice the difference with a flat space only at distances comparable to the radius of the black hole (which is also the size of the curvature of space-time). Then everything converges, and no violation of the equivalence principle arises.
[I know it all sounds like a
firewall problem I
discussed earlier, but this is a slightly different effect.
(comment. The firewall problem arises if we consider the entanglement between a radiated particle and a fallen into a black hole. In order to satisfy the principles of quantum mechanics, these correlations must be destroyed. When the correlations break down, enormous energy is released, which creates a "fiery wall" on the horizon.) This raises various problems when calculating near the horizon. The idea of a firewall can be criticized on the grounds that in the
original article about a firewall, the energy-momentum tensor was not calculated. Unlike
others, I don't think the problem is this.]
The real, supported by calculations, the reason for the emission of particles by black holes is that for different observers the concept of a particle is different.
We are used to the fact that the particle is either with us or not. However, this is true only as long as we move uniformly relative to each other. If the observer (we) is accelerated, the very definition of a particle for it changes. What appears to be an empty vacuum for an observer with uniform motion turns out to be filled with particles during acceleration.
This effect is named after
Bill Unrue , who proposed it almost simultaneously with the black hole radiation hypothesis by Hawking. The effect itself is too small for our usual accelerations, and we never notice it.
The Unruh effect is closely related to the effect of the Hawking black holes evaporation. When black holes appear, matter collapsing into a black hole creates a dynamic spacetime that accelerates between observers in the past and the future. As a result, the space-time around the collapsing matter, which did not contain particles before the appearance of a black hole, turns out to be filled with thermal radiation in the later stages of collapse. That is, Hawking radiation is the same vacuum that originally surrounded the collapsing substance (
just as in the Unruh effect, the vacuum is filled with radiation as the observer accelerates ).
This is the source of radiation from black holes: the definition of a particle itself depends on the observer. Not as simple as the Hawking picture, but much more accurate.
The picture with particle-antiparticle pairs on the horizon, proposed by Hawking, has become so incredibly popular that now even some physicists believe that this is exactly what is happening (
Approx. Per. Before Sabina, I myself thought so shame ). The fact that the blue shift of the radiation, when considering its propagation back in time from infinity to the horizon, gives so much energy on the horizon, has been lost in the literature. Unfortunately, misunderstanding of the connection between the flow of Hawking particles far from BH and near the event horizon leads to the incorrect conclusion that this flow is much stronger than it actually is. For example, this
led Mersini-Houghton to errors in deriving evidence that black holes do not exist at all.
(
Note. The article is shortened for readability, the original post discusses the book “Spooky action at a distance” and calculations , where the exact distance at which Hawking radiation occurs — several BH radii — is calculated and the source of the effect is discussed in detail )
If Hawking's book taught me one thing, it's that sticky visual metaphors can be a curse as much as a boon.
