The information paradox was first mooted by Stephen Hawking in 1976. See Brian Koberlein’s black holes tell no tales or do they? for a tidy introduction to the subject. Then see Hawking’s paper on the breakdown of predictability in gravitational collapse. You can find a copy online courtesy of Sci-Hub. Hawking said information is lost down a black hole and the quantum emission is completely random and uncorrelated, and that “this means there is no S matrix for the process of black-hole formation and evaporation”. The S-matrix is the scattering matrix which is to do with unitarity and reversibility and conservation laws. For example you can perform pair production to create a proton and an antiproton, and you can annihilate a proton and an antiproton. Either way you start or finish with zero net charge. However you could start with two identical black holes and throw a succession of protons into one, and a succession of antiprotons into the other. In both cases the Hawking radiation is said to be the same, and charge is not conserved.


Image courtesy of phys org

Hence Hawking said “there must be nonconservation of information in black-hole formation and evaporation just as there must be a nonconservation of baryon number”. As to why this should be particularly contentious I’m not sure. In hot metal typesetting the used slugs were melted down for re-use. In proton-antiproton annihilation to gamma photons you lose all information about quarks and gluons. We surely wouldn’t expect much in the way of information in the very early universe, and we have baryon asymmetry which looks like proof of nonconservation of baryon number.

A slow start

It didn’t seem to be particularly contentious in 1976. When you look at Hawking’s publications the earliest mention of information is 1996. In Matt Strassler’s information paradox article you can read about what Hawking showed in 1974-1975, and the next date mentioned is 1992. When you use Google scholar to look at citations for Hawking’s paper, there were none in 1976. There’s 1,728 as I write, but there were only sixteen in 1977, and it looks like the only paper that continues the theme was by Hawking himself. There were eight citations in 1978, then six in 1979, and none of them concern information loss. There were fourteen citations in 1980 when only one paper concerned information loss. That was is black-hole evaporation predictable? by Don Page. His paper is somewhat critical, saying black holes may be no more unpredictable than other phenomena. There were seven citations in 1981 including Hawking’s interacting quantum fields around a black hole, and eight in 1982, including Hawking’s paper on the unpredictability of quantum gravity. The latter feels like clickbait for quantum physicists, particularly since Hawking talked of “virtual black holes which appear and disappear again”. The only paper that responds is again by Don Page: is quantum gravity deterministic and/or time symmetric? Again it’s somewhat critical. It ends up saying this: “the most conservative possibility still remains open [2], that H0 and H2 are trivial and that full quantum gravity gives an S matrix which is both deterministic and time symmetric”. I note that Hawking’s 1983 paper thermodynamics of black holes in anti-de Sitter space was co-authored with Don Page.

The black hole war begins

1983 looks fairly quiet, with only four citations plus four mentions in proceedings. However the search for violations of quantum mechanics by John Ellis, John Hagelin, Dimitiri Nanopoulos, and Mark Srednicki refers to Hawking’s 1982 paper on the unpredictability of quantum gravity with 649 citations, not to Hawking’s 1976 paper on the breakdown of predictability in gravitational collapse. 1983 was also when Leonard Susskind and Gerard ‘t Hooft got involved. Susskind is the author of the black hole war, a 480-page book published in 2008. Woit speaks well of it. See the Washington Post for an excerpt: “Stephen claimed that ‘information is lost in black hole evaporation’ and, worse, he seemed to prove it. If that was true, Gerard and I realized, the foundations of our subject were destroyed”. Susskind talks about Wile E Coyote running off a cliff, calls Hawking half a cosmologist, and goes on to say this: “Stephen's lecture was the last that day. For about an hour afterward, Gerard stood glaring at the diagram on Werner's blackboard. Everyone else had left. I can still see the intense frown on Gerard's face and the amused smile on Stephen's. Almost nothing was said. It was an electric moment. On the blackboard was a Penrose diagram, a type of diagram representing a black hole. The horizon (the edge of the black hole) was drawn as a dashed line, and the singularity at the center of the black hole was an ominous-looking jagged line. Lines pointing inward through the horizon represented bits of information falling past the horizon into the singularity. There were no lines coming back out. According to Stephen, those bits were irretrievably lost. To make matters worse, Stephen had proved that black holes eventually evaporate and disappear, leaving no trace of what has fallen in”. To make matters even worse, Susskind said Hawking “postulated that the vacuum - empty space - was full of ‘virtual’ black holes that flashed into and out of existence so rapidly that we didn't notice them. The effect of these virtual black holes, he claimed, was to erase information, even if there was no ‘real’ black hole in the vicinity”. Did you know that black holes were popping in and out of existence inside your head erasing information? Me neither...
Last edited:
This is just a sample of some of the writing I've been doing recently. For some strange reason I can't post in the Physics and Maths section. If anybody is interested in any particular topic I may have something on it.
For some strange reason I can't post in the Physics and Maths section.
Refer to your personal messages from May 2017 for the reason. You were excluded from posting to the Science sections of sciforums for 6 months.

As it happens, your exclusion period ended 1 week ago. However, this particular process is not automated, and you did not remind me to lift your exclusion. I have now done so.

If you are excluded again, having previously been excluded for 8 months, it will be for a much longer period (years at least, and perhaps permanent).
I'm a little confused on the purpose of your post...

Who is the information aimed at in particular?